| 1 |
742 |
jeremybenn |
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
|
| 2 |
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
|
| 3 |
|
|
<html xmlns="http://www.w3.org/1999/xhtml"><head><title>Testing</title><meta name="generator" content="DocBook XSL-NS Stylesheets V1.76.1"/><meta name="keywords" content=" 	ISO C++ , 	policy , 	container , 	data , 	structure , 	associated , 	tree , 	trie , 	hash , 	metaprogramming "/><meta name="keywords" content=" ISO C++ , library "/><meta name="keywords" content=" ISO C++ , runtime , library "/><link rel="home" href="../index.html" title="The GNU C++ Library"/><link rel="up" href="policy_data_structures.html" title="Chapter 22. Policy-Based Data Structures"/><link rel="prev" href="policy_data_structures_design.html" title="Design"/><link rel="next" href="policy_data_structures_biblio.html" title="Acknowledgments"/></head><body><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Testing</th></tr><tr><td align="left"><a accesskey="p" href="policy_data_structures_design.html">Prev</a> </td><th width="60%" align="center">Chapter 22. Policy-Based Data Structures</th><td align="right"> <a accesskey="n" href="policy_data_structures_biblio.html">Next</a></td></tr></table><hr/></div><div class="section" title="Testing"><div class="titlepage"><div><div><h2 class="title"><a id="pbds.test"/>Testing</h2></div></div></div><div class="section" title="Regression"><div class="titlepage"><div><div><h3 class="title"><a id="pbds.test.regression"/>Regression</h3></div></div></div><p>The library contains a single comprehensive regression test.
|
| 4 |
|
|
For a given container type in this library, the test creates
|
| 5 |
|
|
an object of the container type and an object of the
|
| 6 |
|
|
corresponding standard type (e.g., <code class="classname">std::set</code>). It
|
| 7 |
|
|
then performs a random sequence of methods with random
|
| 8 |
|
|
arguments (e.g., inserts, erases, and so forth) on both
|
| 9 |
|
|
objects. At each operation, the test checks the return value of
|
| 10 |
|
|
the method, and optionally both compares this library's
|
| 11 |
|
|
object with the standard's object as well as performing other
|
| 12 |
|
|
consistency checks on this library's object (e.g.,
|
| 13 |
|
|
order preservation, when applicable, or node invariants, when
|
| 14 |
|
|
applicable).</p><p>Additionally, the test integrally checks exception safety
|
| 15 |
|
|
and resource leaks. This is done as follows. A special
|
| 16 |
|
|
allocator type, written for the purpose of the test, both
|
| 17 |
|
|
randomly throws an exceptions when allocations are performed,
|
| 18 |
|
|
and tracks allocations and de-allocations. The exceptions thrown
|
| 19 |
|
|
at allocations simulate memory-allocation failures; the
|
| 20 |
|
|
tracking mechanism checks for memory-related bugs (e.g.,
|
| 21 |
|
|
resource leaks and multiple de-allocations). Both
|
| 22 |
|
|
this library's containers and the containers' value-types are
|
| 23 |
|
|
configured to use this allocator.</p><p>For granularity, the test is split into the
|
| 24 |
|
|
several sources, each checking only some containers.</p><p>For more details, consult the files in
|
| 25 |
|
|
<code class="filename">testsuite/ext/pb_ds/regression</code>.</p></div><div class="section" title="Performance"><div class="titlepage"><div><div><h3 class="title"><a id="pbds.test.performance"/>Performance</h3></div></div></div><div class="section" title="Hash-Based"><div class="titlepage"><div><div><h4 class="title"><a id="performance.hash"/>Hash-Based</h4></div></div></div><p/><div class="section" title="Text find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.text_find"/>
|
| 26 |
|
|
Text <code class="function">find</code>
|
| 27 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.text_find.info"/>
|
| 28 |
|
|
Description
|
| 29 |
|
|
</h6></div></div></div><p>
|
| 30 |
|
|
This test inserts a number of values with keys from an
|
| 31 |
|
|
arbitrary text (<a class="xref" href="policy_data_structures.html#biblio.wickland96thirty" title="Thirty Years Among the Dead">[biblio.wickland96thirty]</a>) into a container,
|
| 32 |
|
|
then performs a series of finds using
|
| 33 |
|
|
<code class="function">find</code> . It measures the average
|
| 34 |
|
|
time for <code class="function">find</code> as a function of
|
| 35 |
|
|
the number of values inserted.</p><p>
|
| 36 |
|
|
It uses the test file:
|
| 37 |
|
|
<code class="filename">
|
| 38 |
|
|
performance/ext/pb_ds/text_find_timing_test.cc
|
| 39 |
|
|
</code>
|
| 40 |
|
|
</p><p>
|
| 41 |
|
|
And uses the data file:
|
| 42 |
|
|
<code class="filename">
|
| 43 |
|
|
filethirty_years_among_the_dead_preproc.txt
|
| 44 |
|
|
</code>
|
| 45 |
|
|
</p><p>The test checks the effect of different range-hashing
|
| 46 |
|
|
functions, trigger policies, and cache-hashing policies.
|
| 47 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.text_find.results"/>
|
| 48 |
|
|
Results
|
| 49 |
|
|
</h6></div></div></div><p>The graphic below show the results for the native
|
| 50 |
|
|
and collision-chaining hash types the the function
|
| 51 |
|
|
applied being a text find timing test using
|
| 52 |
|
|
<code class="function">find</code>.
|
| 53 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_hash_text_find.png" style="text-align: middle"/></div></div><p>
|
| 54 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 55 |
|
|
instantiated with the types in the following table.
|
| 56 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 57 |
|
|
n_hash_map_ncah
|
| 58 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 59 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 60 |
|
|
</td><td style="text-align: left">
|
| 61 |
|
|
<code class="classname">cache_hash_code</code>
|
| 62 |
|
|
</td><td style="text-align: left">
|
| 63 |
|
|
<code class="constant">false</code>
|
| 64 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 65 |
|
|
cc_hash_mod_prime_1div1_nsth_map
|
| 66 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 67 |
|
|
<code class="classname">cc_hash_table</code>
|
| 68 |
|
|
</td><td style="text-align: left">
|
| 69 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 70 |
|
|
</td><td style="text-align: left">
|
| 71 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 72 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 73 |
|
|
<code class="classname">Resize_Policy</code>
|
| 74 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 75 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 76 |
|
|
</td><td style="text-align: left">
|
| 77 |
|
|
<code class="classname">Size_Policy</code>
|
| 78 |
|
|
</td><td style="text-align: left">
|
| 79 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 80 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 81 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 82 |
|
|
</td><td style="text-align: left">
|
| 83 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 84 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 85 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 86 |
|
|
cc_hash_mask_exp_1div2_sth_map
|
| 87 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 88 |
|
|
<code class="classname">
|
| 89 |
|
|
cc_hash_table
|
| 90 |
|
|
</code>
|
| 91 |
|
|
</td><td style="text-align: left">
|
| 92 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 93 |
|
|
</td><td style="text-align: left">
|
| 94 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 95 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 96 |
|
|
<code class="classname">Resize_Policy</code>
|
| 97 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 98 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 99 |
|
|
</td><td style="text-align: left">
|
| 100 |
|
|
<code class="classname">Size_Policy</code>
|
| 101 |
|
|
</td><td style="text-align: left">
|
| 102 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 103 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 104 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 105 |
|
|
</td><td style="text-align: left">
|
| 106 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 107 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 108 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 109 |
|
|
cc_hash_mask_exp_1div1_nsth_map
|
| 110 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 111 |
|
|
<code class="classname">cc_hash_table</code>
|
| 112 |
|
|
</td><td style="text-align: left">
|
| 113 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 114 |
|
|
</td><td style="text-align: left">
|
| 115 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 116 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 117 |
|
|
<code class="classname">Resize_Policy</code>
|
| 118 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 119 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 120 |
|
|
</td><td style="text-align: left">
|
| 121 |
|
|
<code class="classname">Size_Policy</code>
|
| 122 |
|
|
</td><td style="text-align: left">
|
| 123 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 124 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 125 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 126 |
|
|
</td><td style="text-align: left">
|
| 127 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 128 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 129 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 130 |
|
|
cc_hash_mask_exp_1div2_nsth_map
|
| 131 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 132 |
|
|
<code class="classname">cc_hash_table</code>
|
| 133 |
|
|
</td><td style="text-align: left">
|
| 134 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 135 |
|
|
</td><td style="text-align: left">
|
| 136 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 137 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 138 |
|
|
<code class="classname">Resize_Policy</code>
|
| 139 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 140 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 141 |
|
|
</td><td style="text-align: left">
|
| 142 |
|
|
<code class="classname">Size_Policy</code>
|
| 143 |
|
|
</td><td style="text-align: left">
|
| 144 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 145 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 146 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 147 |
|
|
</td><td style="text-align: left">
|
| 148 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 149 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 150 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.text_find.observations"/>
|
| 151 |
|
|
Observations
|
| 152 |
|
|
</h6></div></div></div><p>In this setting, the range-hashing scheme affects performance
|
| 153 |
|
|
more than other policies. As the results show, containers using
|
| 154 |
|
|
mod-based range-hashing (including the native hash-based container,
|
| 155 |
|
|
which is currently hard-wired to this scheme) have lower performance
|
| 156 |
|
|
than those using mask-based range-hashing. A modulo-based
|
| 157 |
|
|
range-hashing scheme's main benefit is that it takes into account
|
| 158 |
|
|
all hash-value bits. Standard string hash-functions are designed to
|
| 159 |
|
|
create hash values that are nearly-uniform as is (<a class="xref" href="policy_data_structures.html#biblio.knuth98sorting" title="The Art of Computer Programming - Sorting and Searching">[biblio.knuth98sorting]</a>).</p><p>Trigger policies, i.e. the load-checks constants, affect
|
| 160 |
|
|
performance to a lesser extent.</p><p>Perhaps surprisingly, storing the hash value alongside each
|
| 161 |
|
|
entry affects performance only marginally, at least in this
|
| 162 |
|
|
library's implementation. (Unfortunately, it was not possible to run
|
| 163 |
|
|
the tests with <code class="classname">std::tr1::unordered_map</code> 's
|
| 164 |
|
|
<code class="classname">cache_hash_code = true</code> , as it appeared to
|
| 165 |
|
|
malfuntion.)</p></div></div><div class="section" title="Integer find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.int_find"/>
|
| 166 |
|
|
Integer <code class="function">find</code>
|
| 167 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_find.info"/>
|
| 168 |
|
|
Description
|
| 169 |
|
|
</h6></div></div></div><p>This test inserts a number of values with uniform
|
| 170 |
|
|
integer keys into a container, then performs a series of finds
|
| 171 |
|
|
using <code class="function">find</code>. It measures the average time
|
| 172 |
|
|
for <code class="function">find</code> as a function of the number of values
|
| 173 |
|
|
inserted.</p><p>
|
| 174 |
|
|
It uses the test file:
|
| 175 |
|
|
<code class="filename">
|
| 176 |
|
|
performance/ext/pb_ds/random_int_find_timing.cc
|
| 177 |
|
|
</code>
|
| 178 |
|
|
</p><p>The test checks the effect of different underlying
|
| 179 |
|
|
hash-tables,
|
| 180 |
|
|
range-hashing functions, and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_find.results"/>
|
| 181 |
|
|
Results
|
| 182 |
|
|
</h6></div></div></div><p>
|
| 183 |
|
|
There are two sets of results for this type, one for
|
| 184 |
|
|
collision-chaining hashes, and one for general-probe hashes.
|
| 185 |
|
|
</p><p>The first graphic below shows the results for the native and
|
| 186 |
|
|
collision-chaining hash types. The function applied being a random
|
| 187 |
|
|
integer timing test using <code class="function">find</code>.
|
| 188 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_cc_hash_int_find.png" style="text-align: middle"/></div></div><p>
|
| 189 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 190 |
|
|
instantiated with the types in the following table.
|
| 191 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 192 |
|
|
n_hash_map_ncah
|
| 193 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 194 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 195 |
|
|
</td><td style="text-align: left">
|
| 196 |
|
|
<code class="classname">cache_hash_code</code>
|
| 197 |
|
|
</td><td style="text-align: left">
|
| 198 |
|
|
<code class="constant">false</code>
|
| 199 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 200 |
|
|
cc_hash_mod_prime_1div1_nsth_map
|
| 201 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 202 |
|
|
<code class="classname">cc_hash_table</code>
|
| 203 |
|
|
</td><td style="text-align: left">
|
| 204 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 205 |
|
|
</td><td style="text-align: left">
|
| 206 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 207 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 208 |
|
|
<code class="classname">Resize_Policy</code>
|
| 209 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 210 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 211 |
|
|
</td><td style="text-align: left">
|
| 212 |
|
|
<code class="classname">Size_Policy</code>
|
| 213 |
|
|
</td><td style="text-align: left">
|
| 214 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 215 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 216 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 217 |
|
|
</td><td style="text-align: left">
|
| 218 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 219 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 220 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 221 |
|
|
cc_hash_mod_prime_1div2_nsth_map
|
| 222 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 223 |
|
|
<code class="classname">
|
| 224 |
|
|
cc_hash_table
|
| 225 |
|
|
</code>
|
| 226 |
|
|
</td><td style="text-align: left">
|
| 227 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 228 |
|
|
</td><td style="text-align: left">
|
| 229 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 230 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 231 |
|
|
<code class="classname">Resize_Policy</code>
|
| 232 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 233 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 234 |
|
|
</td><td style="text-align: left">
|
| 235 |
|
|
<code class="classname">Size_Policy</code>
|
| 236 |
|
|
</td><td style="text-align: left">
|
| 237 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 238 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 239 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 240 |
|
|
</td><td style="text-align: left">
|
| 241 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 242 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 243 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 244 |
|
|
cc_hash_mask_exp_1div1_nsth_map
|
| 245 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 246 |
|
|
<code class="classname">cc_hash_table</code>
|
| 247 |
|
|
</td><td style="text-align: left">
|
| 248 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 249 |
|
|
</td><td style="text-align: left">
|
| 250 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 251 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 252 |
|
|
<code class="classname">Resize_Policy</code>
|
| 253 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 254 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 255 |
|
|
</td><td style="text-align: left">
|
| 256 |
|
|
<code class="classname">Size_Policy</code>
|
| 257 |
|
|
</td><td style="text-align: left">
|
| 258 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 259 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 260 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 261 |
|
|
</td><td style="text-align: left">
|
| 262 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 263 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 264 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 265 |
|
|
cc_hash_mask_exp_1div2_nsth_map
|
| 266 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 267 |
|
|
<code class="classname">cc_hash_table</code>
|
| 268 |
|
|
</td><td style="text-align: left">
|
| 269 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 270 |
|
|
</td><td style="text-align: left">
|
| 271 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 272 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 273 |
|
|
<code class="classname">Resize_Policy</code>
|
| 274 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 275 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 276 |
|
|
</td><td style="text-align: left">
|
| 277 |
|
|
<code class="classname">Size_Policy</code>
|
| 278 |
|
|
</td><td style="text-align: left">
|
| 279 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 280 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 281 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 282 |
|
|
</td><td style="text-align: left">
|
| 283 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 284 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 285 |
|
|
</td></tr></tbody></table></div><p>
|
| 286 |
|
|
</p><p>
|
| 287 |
|
|
</p><p>And the second graphic shows the results for the native and
|
| 288 |
|
|
general-probe hash types. The function applied being a random
|
| 289 |
|
|
integer timing test using <code class="function">find</code>.
|
| 290 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_gp_hash_int_find.png" style="text-align: middle"/></div></div><p>
|
| 291 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 292 |
|
|
instantiated with the types in the following table.
|
| 293 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 294 |
|
|
n_hash_map_ncah
|
| 295 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 296 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 297 |
|
|
</td><td style="text-align: left">
|
| 298 |
|
|
<code class="classname">cache_hash_code</code>
|
| 299 |
|
|
</td><td style="text-align: left">
|
| 300 |
|
|
<code class="constant">false</code>
|
| 301 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 302 |
|
|
gp_hash_mod_quadp_prime_1div2_nsth_map
|
| 303 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 304 |
|
|
<code class="classname">gp_hash_table</code>
|
| 305 |
|
|
</td><td style="text-align: left">
|
| 306 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 307 |
|
|
</td><td style="text-align: left">
|
| 308 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 309 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 310 |
|
|
<code class="classname">Probe_Fn</code>
|
| 311 |
|
|
</td><td style="text-align: left">
|
| 312 |
|
|
<code class="classname">quadratic_probe_fn</code>
|
| 313 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 314 |
|
|
<code class="classname">Resize_Policy</code>
|
| 315 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 316 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 317 |
|
|
</td><td style="text-align: left">
|
| 318 |
|
|
<code class="classname">Size_Policy</code>
|
| 319 |
|
|
</td><td style="text-align: left">
|
| 320 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 321 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 322 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 323 |
|
|
</td><td style="text-align: left">
|
| 324 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 325 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 326 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 327 |
|
|
gp_hash_mask_linp_exp_1div2_nsth_map
|
| 328 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 329 |
|
|
<code class="classname">
|
| 330 |
|
|
gp_hash_table
|
| 331 |
|
|
</code>
|
| 332 |
|
|
</td><td style="text-align: left">
|
| 333 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 334 |
|
|
</td><td style="text-align: left">
|
| 335 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 336 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 337 |
|
|
<code class="classname">Probe_Fn</code>
|
| 338 |
|
|
</td><td style="text-align: left">
|
| 339 |
|
|
<code class="classname">linear_probe_fn</code>
|
| 340 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 341 |
|
|
<code class="classname">Resize_Policy</code>
|
| 342 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 343 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 344 |
|
|
</td><td style="text-align: left">
|
| 345 |
|
|
<code class="classname">Size_Policy</code>
|
| 346 |
|
|
</td><td style="text-align: left">
|
| 347 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 348 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 349 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 350 |
|
|
</td><td style="text-align: left">
|
| 351 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 352 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 353 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_find.observations"/>
|
| 354 |
|
|
Observations
|
| 355 |
|
|
</h6></div></div></div><p>In this setting, the choice of underlying hash-table affects
|
| 356 |
|
|
performance most, then the range-hashing scheme and, only finally,
|
| 357 |
|
|
other policies.</p><p>When comparing probing and chaining containers, it is
|
| 358 |
|
|
apparent that the probing containers are less efficient than the
|
| 359 |
|
|
collision-chaining containers (
|
| 360 |
|
|
<code class="classname">std::tr1::unordered_map</code> uses
|
| 361 |
|
|
collision-chaining) in this case.</p><p>Hash-Based Integer Subscript Insert Timing Test shows
|
| 362 |
|
|
a different case, where the situation is reversed;
|
| 363 |
|
|
</p><p>Within each type of hash-table, the range-hashing scheme
|
| 364 |
|
|
affects performance more than other policies; Hash-Based Text
|
| 365 |
|
|
<code class="function">find</code> Find Timing Test also shows this. In the
|
| 366 |
|
|
above graphics should be noted that
|
| 367 |
|
|
<code class="classname">std::tr1::unordered_map</code> are hard-wired
|
| 368 |
|
|
currently to mod-based schemes.
|
| 369 |
|
|
</p></div></div><div class="section" title="Integer Subscript find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.int_subscript_find"/>
|
| 370 |
|
|
Integer Subscript <code class="function">find</code>
|
| 371 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_find.info"/>
|
| 372 |
|
|
Description
|
| 373 |
|
|
</h6></div></div></div><p>This test inserts a number of values with uniform
|
| 374 |
|
|
integer keys into a container, then performs a series of finds
|
| 375 |
|
|
using <code class="function">operator[]</code>. It measures the average time
|
| 376 |
|
|
for <code class="function">operator[]</code> as a function of the number of
|
| 377 |
|
|
values inserted.</p><p>
|
| 378 |
|
|
It uses the test file:
|
| 379 |
|
|
<code class="filename">
|
| 380 |
|
|
performance/ext/pb_ds/random_int_subscript_find_timing.cc
|
| 381 |
|
|
</code>
|
| 382 |
|
|
</p><p>The test checks the effect of different underlying
|
| 383 |
|
|
hash-tables, range-hashing functions, and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_find.results"/>
|
| 384 |
|
|
Results
|
| 385 |
|
|
</h6></div></div></div><p>
|
| 386 |
|
|
There are two sets of results for this type, one for
|
| 387 |
|
|
collision-chaining hashes, and one for general-probe hashes.
|
| 388 |
|
|
</p><p>The first graphic below shows the results for the native
|
| 389 |
|
|
and collision-chaining hash types, using as the function
|
| 390 |
|
|
applied an integer subscript timing test with
|
| 391 |
|
|
<code class="function">find</code>.
|
| 392 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_cc_hash_int_subscript_find.png" style="text-align: middle"/></div></div><p>
|
| 393 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 394 |
|
|
instantiated with the types in the following table.
|
| 395 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 396 |
|
|
n_hash_map_ncah
|
| 397 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 398 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 399 |
|
|
</td><td style="text-align: left">
|
| 400 |
|
|
<code class="classname">cache_hash_code</code>
|
| 401 |
|
|
</td><td style="text-align: left">
|
| 402 |
|
|
<code class="constant">false</code>
|
| 403 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 404 |
|
|
cc_hash_mod_prime_1div1_nsth_map
|
| 405 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 406 |
|
|
<code class="classname">cc_hash_table</code>
|
| 407 |
|
|
</td><td style="text-align: left">
|
| 408 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 409 |
|
|
</td><td style="text-align: left">
|
| 410 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 411 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 412 |
|
|
<code class="classname">Resize_Policy</code>
|
| 413 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 414 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 415 |
|
|
</td><td style="text-align: left">
|
| 416 |
|
|
<code class="classname">Size_Policy</code>
|
| 417 |
|
|
</td><td style="text-align: left">
|
| 418 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 419 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 420 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 421 |
|
|
</td><td style="text-align: left">
|
| 422 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 423 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 424 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 425 |
|
|
cc_hash_mod_prime_1div2_nsth_map
|
| 426 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 427 |
|
|
<code class="classname">cc_hash_table</code>
|
| 428 |
|
|
</td><td style="text-align: left">
|
| 429 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 430 |
|
|
</td><td style="text-align: left">
|
| 431 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 432 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 433 |
|
|
<code class="classname">Resize_Policy</code>
|
| 434 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 435 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 436 |
|
|
</td><td style="text-align: left">
|
| 437 |
|
|
<code class="classname">Size_Policy</code>
|
| 438 |
|
|
</td><td style="text-align: left">
|
| 439 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 440 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 441 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 442 |
|
|
</td><td style="text-align: left">
|
| 443 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 444 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 445 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 446 |
|
|
cc_hash_mask_exp_1div1_nsth_map
|
| 447 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 448 |
|
|
<code class="classname">cc_hash_table</code>
|
| 449 |
|
|
</td><td style="text-align: left">
|
| 450 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 451 |
|
|
</td><td style="text-align: left">
|
| 452 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 453 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 454 |
|
|
<code class="classname">Resize_Policy</code>
|
| 455 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 456 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 457 |
|
|
</td><td style="text-align: left">
|
| 458 |
|
|
<code class="classname">Size_Policy</code>
|
| 459 |
|
|
</td><td style="text-align: left">
|
| 460 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 461 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 462 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 463 |
|
|
</td><td style="text-align: left">
|
| 464 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 465 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 466 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 467 |
|
|
cc_hash_mask_exp_1div2_nsth_map
|
| 468 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 469 |
|
|
<code class="classname">cc_hash_table</code>
|
| 470 |
|
|
</td><td style="text-align: left">
|
| 471 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 472 |
|
|
</td><td style="text-align: left">
|
| 473 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 474 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 475 |
|
|
<code class="classname">Resize_Policy</code>
|
| 476 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 477 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 478 |
|
|
</td><td style="text-align: left">
|
| 479 |
|
|
<code class="classname">Size_Policy</code>
|
| 480 |
|
|
</td><td style="text-align: left">
|
| 481 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 482 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 483 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 484 |
|
|
</td><td style="text-align: left">
|
| 485 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 486 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 487 |
|
|
</td></tr></tbody></table></div><p>
|
| 488 |
|
|
</p><p>
|
| 489 |
|
|
</p><p>And the second graphic shows the results for the native and
|
| 490 |
|
|
general-probe hash types. The function applied being a random
|
| 491 |
|
|
integer timing test using <code class="function">find</code>.
|
| 492 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_gp_hash_int_subscript_find.png" style="text-align: middle"/></div></div><p>
|
| 493 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 494 |
|
|
instantiated with the types in the following table.
|
| 495 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 496 |
|
|
n_hash_map_ncah
|
| 497 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 498 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 499 |
|
|
</td><td style="text-align: left">
|
| 500 |
|
|
<code class="classname">cache_hash_code</code>
|
| 501 |
|
|
</td><td style="text-align: left">
|
| 502 |
|
|
<code class="constant">false</code>
|
| 503 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 504 |
|
|
gp_hash_mod_quadp_prime_1div2_nsth_map
|
| 505 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 506 |
|
|
<code class="classname">gp_hash_table</code>
|
| 507 |
|
|
</td><td style="text-align: left">
|
| 508 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 509 |
|
|
</td><td style="text-align: left">
|
| 510 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 511 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 512 |
|
|
<code class="classname">Probe_Fn</code>
|
| 513 |
|
|
</td><td style="text-align: left">
|
| 514 |
|
|
<code class="classname">quadratic_probe_fn</code>
|
| 515 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 516 |
|
|
<code class="classname">Resize_Policy</code>
|
| 517 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 518 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 519 |
|
|
</td><td style="text-align: left">
|
| 520 |
|
|
<code class="classname">Size_Policy</code>
|
| 521 |
|
|
</td><td style="text-align: left">
|
| 522 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 523 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 524 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 525 |
|
|
</td><td style="text-align: left">
|
| 526 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 527 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 528 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 529 |
|
|
gp_hash_mask_linp_exp_1div2_nsth_map
|
| 530 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 531 |
|
|
<code class="classname">
|
| 532 |
|
|
gp_hash_table
|
| 533 |
|
|
</code>
|
| 534 |
|
|
</td><td style="text-align: left">
|
| 535 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 536 |
|
|
</td><td style="text-align: left">
|
| 537 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 538 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 539 |
|
|
<code class="classname">Probe_Fn</code>
|
| 540 |
|
|
</td><td style="text-align: left">
|
| 541 |
|
|
<code class="classname">linear_probe_fn</code>
|
| 542 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 543 |
|
|
<code class="classname">Resize_Policy</code>
|
| 544 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 545 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 546 |
|
|
</td><td style="text-align: left">
|
| 547 |
|
|
<code class="classname">Size_Policy</code>
|
| 548 |
|
|
</td><td style="text-align: left">
|
| 549 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 550 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 551 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 552 |
|
|
</td><td style="text-align: left">
|
| 553 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 554 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 555 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_find.observations"/>
|
| 556 |
|
|
Observations
|
| 557 |
|
|
</h6></div></div></div><p>This test shows similar results to Hash-Based
|
| 558 |
|
|
Integer <code class="classname">find</code> Find Timing test.</p></div></div><div class="section" title="Integer Subscript insert"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.int_subscript_insert"/>
|
| 559 |
|
|
Integer Subscript <code class="function">insert</code>
|
| 560 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_insert.info"/>
|
| 561 |
|
|
Description
|
| 562 |
|
|
</h6></div></div></div><p>This test inserts a number of values with uniform i.i.d.
|
| 563 |
|
|
integer keys into a container, using
|
| 564 |
|
|
<code class="function">operator[]</code>. It measures the average time for
|
| 565 |
|
|
<code class="function">operator[]</code> as a function of the number of
|
| 566 |
|
|
values inserted.</p><p>
|
| 567 |
|
|
It uses the test file:
|
| 568 |
|
|
<code class="filename">
|
| 569 |
|
|
performance/ext/pb_ds/random_int_subscript_insert_timing.cc
|
| 570 |
|
|
</code>
|
| 571 |
|
|
</p><p>The test checks the effect of different underlying
|
| 572 |
|
|
hash-tables.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_insert.results"/>
|
| 573 |
|
|
Results
|
| 574 |
|
|
</h6></div></div></div><p>
|
| 575 |
|
|
There are two sets of results for this type, one for
|
| 576 |
|
|
collision-chaining hashes, and one for general-probe hashes.
|
| 577 |
|
|
</p><p>The first graphic below shows the results for the native
|
| 578 |
|
|
and collision-chaining hash types, using as the function
|
| 579 |
|
|
applied an integer subscript timing test with
|
| 580 |
|
|
<code class="function">insert</code>.
|
| 581 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_cc_hash_int_subscript_insert.png" style="text-align: middle"/></div></div><p>
|
| 582 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 583 |
|
|
instantiated with the types in the following table.
|
| 584 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 585 |
|
|
n_hash_map_ncah
|
| 586 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 587 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 588 |
|
|
</td><td style="text-align: left">
|
| 589 |
|
|
<code class="classname">cache_hash_code</code>
|
| 590 |
|
|
</td><td style="text-align: left">
|
| 591 |
|
|
<code class="constant">false</code>
|
| 592 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 593 |
|
|
cc_hash_mod_prime_1div1_nsth_map
|
| 594 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 595 |
|
|
<code class="classname">cc_hash_table</code>
|
| 596 |
|
|
</td><td style="text-align: left">
|
| 597 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 598 |
|
|
</td><td style="text-align: left">
|
| 599 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 600 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 601 |
|
|
<code class="classname">Resize_Policy</code>
|
| 602 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 603 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 604 |
|
|
</td><td style="text-align: left">
|
| 605 |
|
|
<code class="classname">Size_Policy</code>
|
| 606 |
|
|
</td><td style="text-align: left">
|
| 607 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 608 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 609 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 610 |
|
|
</td><td style="text-align: left">
|
| 611 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 612 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 613 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 614 |
|
|
cc_hash_mod_prime_1div2_nsth_map
|
| 615 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 616 |
|
|
<code class="classname">cc_hash_table</code>
|
| 617 |
|
|
</td><td style="text-align: left">
|
| 618 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 619 |
|
|
</td><td style="text-align: left">
|
| 620 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 621 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 622 |
|
|
<code class="classname">Resize_Policy</code>
|
| 623 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 624 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 625 |
|
|
</td><td style="text-align: left">
|
| 626 |
|
|
<code class="classname">Size_Policy</code>
|
| 627 |
|
|
</td><td style="text-align: left">
|
| 628 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 629 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 630 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 631 |
|
|
</td><td style="text-align: left">
|
| 632 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 633 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 634 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 635 |
|
|
cc_hash_mask_exp_1div1_nsth_map
|
| 636 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 637 |
|
|
<code class="classname">cc_hash_table</code>
|
| 638 |
|
|
</td><td style="text-align: left">
|
| 639 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 640 |
|
|
</td><td style="text-align: left">
|
| 641 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 642 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 643 |
|
|
<code class="classname">Resize_Policy</code>
|
| 644 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 645 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 646 |
|
|
</td><td style="text-align: left">
|
| 647 |
|
|
<code class="classname">Size_Policy</code>
|
| 648 |
|
|
</td><td style="text-align: left">
|
| 649 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 650 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 651 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 652 |
|
|
</td><td style="text-align: left">
|
| 653 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 654 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 655 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 656 |
|
|
cc_hash_mask_exp_1div2_nsth_map
|
| 657 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 658 |
|
|
<code class="classname">cc_hash_table</code>
|
| 659 |
|
|
</td><td style="text-align: left">
|
| 660 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 661 |
|
|
</td><td style="text-align: left">
|
| 662 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 663 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 664 |
|
|
<code class="classname">Resize_Policy</code>
|
| 665 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 666 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 667 |
|
|
</td><td style="text-align: left">
|
| 668 |
|
|
<code class="classname">Size_Policy</code>
|
| 669 |
|
|
</td><td style="text-align: left">
|
| 670 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 671 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 672 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 673 |
|
|
</td><td style="text-align: left">
|
| 674 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 675 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 676 |
|
|
</td></tr></tbody></table></div><p>
|
| 677 |
|
|
</p><p>
|
| 678 |
|
|
</p><p>And the second graphic shows the results for the native and
|
| 679 |
|
|
general-probe hash types. The function applied being a random
|
| 680 |
|
|
integer timing test using <code class="function">find</code>.
|
| 681 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_gp_hash_int_subscript_insert.png" style="text-align: middle"/></div></div><p>
|
| 682 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 683 |
|
|
instantiated with the types in the following table.
|
| 684 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 685 |
|
|
n_hash_map_ncah
|
| 686 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 687 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 688 |
|
|
</td><td style="text-align: left">
|
| 689 |
|
|
<code class="classname">cache_hash_code</code>
|
| 690 |
|
|
</td><td style="text-align: left">
|
| 691 |
|
|
<code class="constant">false</code>
|
| 692 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 693 |
|
|
gp_hash_mod_quadp_prime_1div2_nsth_map
|
| 694 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 695 |
|
|
<code class="classname">gp_hash_table</code>
|
| 696 |
|
|
</td><td style="text-align: left">
|
| 697 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 698 |
|
|
</td><td style="text-align: left">
|
| 699 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 700 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 701 |
|
|
<code class="classname">Probe_Fn</code>
|
| 702 |
|
|
</td><td style="text-align: left">
|
| 703 |
|
|
<code class="classname">quadratic_probe_fn</code>
|
| 704 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 705 |
|
|
<code class="classname">Resize_Policy</code>
|
| 706 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 707 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 708 |
|
|
</td><td style="text-align: left">
|
| 709 |
|
|
<code class="classname">Size_Policy</code>
|
| 710 |
|
|
</td><td style="text-align: left">
|
| 711 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 712 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 713 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 714 |
|
|
</td><td style="text-align: left">
|
| 715 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 716 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 717 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 718 |
|
|
gp_hash_mask_linp_exp_1div2_nsth_map
|
| 719 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 720 |
|
|
<code class="classname">
|
| 721 |
|
|
gp_hash_table
|
| 722 |
|
|
</code>
|
| 723 |
|
|
</td><td style="text-align: left">
|
| 724 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 725 |
|
|
</td><td style="text-align: left">
|
| 726 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 727 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 728 |
|
|
<code class="classname">Probe_Fn</code>
|
| 729 |
|
|
</td><td style="text-align: left">
|
| 730 |
|
|
<code class="classname">linear_probe_fn</code>
|
| 731 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 732 |
|
|
<code class="classname">Resize_Policy</code>
|
| 733 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 734 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 735 |
|
|
</td><td style="text-align: left">
|
| 736 |
|
|
<code class="classname">Size_Policy</code>
|
| 737 |
|
|
</td><td style="text-align: left">
|
| 738 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 739 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 740 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 741 |
|
|
</td><td style="text-align: left">
|
| 742 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 743 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 744 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_insert.observations"/>
|
| 745 |
|
|
Observations
|
| 746 |
|
|
</h6></div></div></div><p>In this setting, as in Hash-Based Text
|
| 747 |
|
|
<code class="function">find</code> Find Timing test and Hash-Based
|
| 748 |
|
|
Integer <code class="function">find</code> Find Timing test , the choice
|
| 749 |
|
|
of underlying hash-table underlying hash-table affects performance
|
| 750 |
|
|
most, then the range-hashing scheme, and
|
| 751 |
|
|
finally any other policies.</p><p>There are some differences, however:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>In this setting, probing tables function sometimes more
|
| 752 |
|
|
efficiently than collision-chaining tables.
|
| 753 |
|
|
This is explained shortly.</p></li><li class="listitem"><p>The performance graphs have a "saw-tooth" shape. The
|
| 754 |
|
|
average insert time rises and falls. As values are inserted
|
| 755 |
|
|
into the container, the load factor grows larger. Eventually,
|
| 756 |
|
|
a resize occurs. The reallocations and rehashing are
|
| 757 |
|
|
relatively expensive. After this, the load factor is smaller
|
| 758 |
|
|
than before.</p></li></ol></div><p>Collision-chaining containers use indirection for greater
|
| 759 |
|
|
flexibility; probing containers store values contiguously, in
|
| 760 |
|
|
an array (see Figure Motivation::Different
|
| 761 |
|
|
underlying data structures A and B, respectively). It
|
| 762 |
|
|
follows that for simple data types, probing containers access
|
| 763 |
|
|
their allocator less frequently than collision-chaining
|
| 764 |
|
|
containers, (although they still have less efficient probing
|
| 765 |
|
|
sequences). This explains why some probing containers fare
|
| 766 |
|
|
better than collision-chaining containers in this case.</p><p>
|
| 767 |
|
|
Within each type of hash-table, the range-hashing scheme affects
|
| 768 |
|
|
performance more than other policies. This is similar to the
|
| 769 |
|
|
situation in Hash-Based Text
|
| 770 |
|
|
<code class="function">find</code> Find Timing Test and Hash-Based
|
| 771 |
|
|
Integer <code class="function">find</code> Find Timing Test.
|
| 772 |
|
|
Unsurprisingly, however, containers with lower α<sub>max</sub> perform worse in this case,
|
| 773 |
|
|
since more re-hashes are performed.</p></div></div><div class="section" title="Integer find with Skewed-Distribution"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.zlob_int_find"/>
|
| 774 |
|
|
Integer <code class="function">find</code> with Skewed-Distribution
|
| 775 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.zlob_int_find.info"/>
|
| 776 |
|
|
Description
|
| 777 |
|
|
</h6></div></div></div><p>This test inserts a number of values with a markedly
|
| 778 |
|
|
non-uniform integer keys into a container, then performs
|
| 779 |
|
|
a series of finds using <code class="function">find</code>. It measures the average
|
| 780 |
|
|
time for <code class="function">find</code> as a function of the number of values in
|
| 781 |
|
|
the containers. The keys are generated as follows. First, a
|
| 782 |
|
|
uniform integer is created. Then it is then shifted left 8 bits.</p><p>
|
| 783 |
|
|
It uses the test file:
|
| 784 |
|
|
<code class="filename">
|
| 785 |
|
|
performance/ext/pb_ds/hash_zlob_random_int_find_timing.cc
|
| 786 |
|
|
</code>
|
| 787 |
|
|
</p><p>The test checks the effect of different range-hashing
|
| 788 |
|
|
functions and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.zlob_int_find.results"/>
|
| 789 |
|
|
Results
|
| 790 |
|
|
</h6></div></div></div><p>The graphic below show the results for the native, collision-chaining, and general-probing hash types.
|
| 791 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_hash_zlob_int_find.png" style="text-align: middle"/></div></div><p>
|
| 792 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 793 |
|
|
instantiated with the types in the following table.
|
| 794 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 795 |
|
|
n_hash_map_ncah
|
| 796 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 797 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 798 |
|
|
</td><td style="text-align: left">
|
| 799 |
|
|
<code class="classname">cache_hash_code</code>
|
| 800 |
|
|
</td><td style="text-align: left">
|
| 801 |
|
|
<code class="constant">false</code>
|
| 802 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 803 |
|
|
cc_hash_mod_prime_1div1_nsth_map
|
| 804 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 805 |
|
|
<code class="classname">cc_hash_table</code>
|
| 806 |
|
|
</td><td style="text-align: left">
|
| 807 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 808 |
|
|
</td><td style="text-align: left">
|
| 809 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 810 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 811 |
|
|
<code class="classname">Resize_Policy</code>
|
| 812 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 813 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 814 |
|
|
</td><td style="text-align: left">
|
| 815 |
|
|
<code class="classname">Size_Policy</code>
|
| 816 |
|
|
</td><td style="text-align: left">
|
| 817 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 818 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 819 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 820 |
|
|
</td><td style="text-align: left">
|
| 821 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 822 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 823 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 824 |
|
|
cc_hash_mask_exp_1div1_nsth_map
|
| 825 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 826 |
|
|
<code class="classname">
|
| 827 |
|
|
cc_hash_table
|
| 828 |
|
|
</code>
|
| 829 |
|
|
</td><td style="text-align: left">
|
| 830 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 831 |
|
|
</td><td style="text-align: left">
|
| 832 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 833 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 834 |
|
|
<code class="classname">Resize_Policy</code>
|
| 835 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 836 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 837 |
|
|
</td><td style="text-align: left">
|
| 838 |
|
|
<code class="classname">Size_Policy</code>
|
| 839 |
|
|
</td><td style="text-align: left">
|
| 840 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 841 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 842 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 843 |
|
|
</td><td style="text-align: left">
|
| 844 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 845 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 846 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 847 |
|
|
gp_hash_mod_quadp_prime_1div2_nsth_map
|
| 848 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 849 |
|
|
<code class="classname">gp_hash_table</code>
|
| 850 |
|
|
</td><td style="text-align: left">
|
| 851 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 852 |
|
|
</td><td style="text-align: left">
|
| 853 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 854 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 855 |
|
|
<code class="classname">Probe_Fn</code>
|
| 856 |
|
|
</td><td style="text-align: left">
|
| 857 |
|
|
<code class="classname">quadratic_probe_fn</code>
|
| 858 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 859 |
|
|
<code class="classname">Resize_Policy</code>
|
| 860 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 861 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 862 |
|
|
</td><td style="text-align: left">
|
| 863 |
|
|
<code class="classname">Size_Policy</code>
|
| 864 |
|
|
</td><td style="text-align: left">
|
| 865 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 866 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 867 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 868 |
|
|
</td><td style="text-align: left">
|
| 869 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 870 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 871 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.zlob_int_find.observations"/>
|
| 872 |
|
|
Observations
|
| 873 |
|
|
</h6></div></div></div><p>In this setting, the distribution of keys is so skewed that
|
| 874 |
|
|
the underlying hash-table type affects performance marginally.
|
| 875 |
|
|
(This is in contrast with Hash-Based Text
|
| 876 |
|
|
<code class="function">find</code> Find Timing Test, Hash-Based
|
| 877 |
|
|
Integer <code class="function">find</code> Find Timing Test, Hash-Based
|
| 878 |
|
|
Integer Subscript Find Timing Test and Hash-Based
|
| 879 |
|
|
Integer Subscript Insert Timing Test.)</p><p>The range-hashing scheme affects performance dramatically. A
|
| 880 |
|
|
mask-based range-hashing scheme effectively maps all values
|
| 881 |
|
|
into the same bucket. Access degenerates into a search within
|
| 882 |
|
|
an unordered linked-list. In the graphic above, it should be noted that
|
| 883 |
|
|
<code class="classname">std::tr1::unordered_map</code> is hard-wired currently to mod-based and mask-based schemes,
|
| 884 |
|
|
respectively.</p><p>When observing the settings of this test, it is apparent
|
| 885 |
|
|
that the keys' distribution is far from natural. One might ask
|
| 886 |
|
|
if the test is not contrived to show that, in some cases,
|
| 887 |
|
|
mod-based range hashing does better than mask-based range
|
| 888 |
|
|
hashing. This is, in fact just the case. A
|
| 889 |
|
|
more natural case in which mod-based range hashing is better was not encountered.
|
| 890 |
|
|
Thus the inescapable conclusion: real-life key distributions are handled better
|
| 891 |
|
|
with an appropriate hash function and a mask-based
|
| 892 |
|
|
range-hashing function. (<code class="filename">pb_ds/example/hash_shift_mask.cc</code>
|
| 893 |
|
|
shows an example of handling this a-priori known skewed
|
| 894 |
|
|
distribution with a mask-based range-hashing function). If hash
|
| 895 |
|
|
performance is bad, a χ<sup>2</sup> test can be used
|
| 896 |
|
|
to check how to transform it into a more uniform
|
| 897 |
|
|
distribution.</p><p>For this reason, this library's default range-hashing
|
| 898 |
|
|
function is mask-based.</p></div></div><div class="section" title="Erase Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.erase_mem"/>
|
| 899 |
|
|
Erase Memory Use
|
| 900 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.erase_mem.info"/>
|
| 901 |
|
|
Description
|
| 902 |
|
|
</h6></div></div></div><p>This test inserts a number of uniform integer keys
|
| 903 |
|
|
into a container, then erases all keys except one. It measures
|
| 904 |
|
|
the final size of the container.</p><p>
|
| 905 |
|
|
It uses the test file:
|
| 906 |
|
|
<code class="filename">
|
| 907 |
|
|
performance/ext/pb_ds/hash_random_int_erase_mem_usage.cc
|
| 908 |
|
|
</code>
|
| 909 |
|
|
</p><p>The test checks how containers adjust internally as their
|
| 910 |
|
|
logical size decreases.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.erase_mem.results"/>
|
| 911 |
|
|
Results
|
| 912 |
|
|
</h6></div></div></div><p>The graphic below show the results for the native, collision-chaining, and general-probing hash types.
|
| 913 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_hash_int_erase_mem.png" style="text-align: middle"/></div></div><p>
|
| 914 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 915 |
|
|
instantiated with the types in the following table.
|
| 916 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 917 |
|
|
n_hash_map_ncah
|
| 918 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 919 |
|
|
<code class="classname">std::tr1::unordered_map</code>
|
| 920 |
|
|
</td><td style="text-align: left">
|
| 921 |
|
|
<code class="classname">cache_hash_code</code>
|
| 922 |
|
|
</td><td style="text-align: left">
|
| 923 |
|
|
<code class="constant">false</code>
|
| 924 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 925 |
|
|
cc_hash_mod_prime_1div1_nsth_map
|
| 926 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 927 |
|
|
<code class="classname">cc_hash_table</code>
|
| 928 |
|
|
</td><td style="text-align: left">
|
| 929 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 930 |
|
|
</td><td style="text-align: left">
|
| 931 |
|
|
<code class="classname">direct_mod_range_hashing</code>
|
| 932 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 933 |
|
|
<code class="classname">Resize_Policy</code>
|
| 934 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 935 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 936 |
|
|
</td><td style="text-align: left">
|
| 937 |
|
|
<code class="classname">Size_Policy</code>
|
| 938 |
|
|
</td><td style="text-align: left">
|
| 939 |
|
|
<code class="classname">hash_prime_size_policy</code>
|
| 940 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 941 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 942 |
|
|
</td><td style="text-align: left">
|
| 943 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 944 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
|
| 945 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 946 |
|
|
cc_hash_mask_exp_1div2_nsth_map
|
| 947 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 948 |
|
|
<code class="classname">
|
| 949 |
|
|
cc_hash_table
|
| 950 |
|
|
</code>
|
| 951 |
|
|
</td><td style="text-align: left">
|
| 952 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 953 |
|
|
</td><td style="text-align: left">
|
| 954 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 955 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 956 |
|
|
<code class="classname">Resize_Policy</code>
|
| 957 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 958 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 959 |
|
|
</td><td style="text-align: left">
|
| 960 |
|
|
<code class="classname">Size_Policy</code>
|
| 961 |
|
|
</td><td style="text-align: left">
|
| 962 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 963 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 964 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 965 |
|
|
</td><td style="text-align: left">
|
| 966 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 967 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 968 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
|
| 969 |
|
|
gp_hash_mask_linp_exp_1div2_nsth_set
|
| 970 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 971 |
|
|
<code class="classname">gp_hash_table</code>
|
| 972 |
|
|
</td><td style="text-align: left">
|
| 973 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 974 |
|
|
</td><td style="text-align: left">
|
| 975 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 976 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 977 |
|
|
<code class="classname">Probe_Fn</code>
|
| 978 |
|
|
</td><td style="text-align: left">
|
| 979 |
|
|
<code class="classname">linear_probe_fn</code>
|
| 980 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 981 |
|
|
<code class="classname">Resize_Policy</code>
|
| 982 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 983 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 984 |
|
|
</td><td style="text-align: left">
|
| 985 |
|
|
<code class="classname">Size_Policy</code>
|
| 986 |
|
|
</td><td style="text-align: left">
|
| 987 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 988 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 989 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 990 |
|
|
</td><td style="text-align: left">
|
| 991 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 992 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 993 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.erase_mem.observations"/>
|
| 994 |
|
|
Observations
|
| 995 |
|
|
</h6></div></div></div><p>The standard's hash-based containers act very differently than trees in
|
| 996 |
|
|
this respect. When erasing numerous keys from an standard
|
| 997 |
|
|
associative-container, the resulting memory user varies greatly
|
| 998 |
|
|
depending on whether the container is tree-based or hash-based.
|
| 999 |
|
|
This is a fundamental consequence of the standard's interface for
|
| 1000 |
|
|
associative containers, and it is not due to a specific
|
| 1001 |
|
|
implementation.</p></div></div></div><div class="section" title="Branch-Based"><div class="titlepage"><div><div><h4 class="title"><a id="performance.branch"/>Branch-Based</h4></div></div></div><p/><div class="section" title="Text insert"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.text_insert"/>
|
| 1002 |
|
|
Text <code class="function">insert</code>
|
| 1003 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_insert.info"/>
|
| 1004 |
|
|
Description
|
| 1005 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an arbitrary
|
| 1006 |
|
|
text ([ wickland96thirty ]) into a container
|
| 1007 |
|
|
using <code class="function">insert</code> . It measures the average time
|
| 1008 |
|
|
for <code class="function">insert</code> as a function of the number of
|
| 1009 |
|
|
values inserted.</p><p>The test checks the effect of different underlying
|
| 1010 |
|
|
data structures.</p><p>
|
| 1011 |
|
|
It uses the test file:
|
| 1012 |
|
|
<code class="filename">
|
| 1013 |
|
|
performance/ext/pb_ds/tree_text_insert_timing.cc
|
| 1014 |
|
|
</code>
|
| 1015 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_insert.results"/>
|
| 1016 |
|
|
Results
|
| 1017 |
|
|
</h6></div></div></div><p>The three graphics below show the results for the native
|
| 1018 |
|
|
tree and this library's node-based trees, the native tree and
|
| 1019 |
|
|
this library's vector-based trees, and the native tree
|
| 1020 |
|
|
and this library's PATRICIA-trie, respectively.
|
| 1021 |
|
|
</p><p>The graphic immediately below shows the results for the
|
| 1022 |
|
|
native tree type and several node-based tree types.
|
| 1023 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_insert_node.png" style="text-align: middle"/></div><p>
|
| 1024 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1025 |
|
|
instantiated with the types in the following table.
|
| 1026 |
|
|
</p></div><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1027 |
|
|
n_map
|
| 1028 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1029 |
|
|
<code class="classname">std::map</code>
|
| 1030 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1031 |
|
|
splay_tree_map
|
| 1032 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1033 |
|
|
<code class="classname">tree</code>
|
| 1034 |
|
|
</td><td style="text-align: left">
|
| 1035 |
|
|
<code class="classname">Tag</code>
|
| 1036 |
|
|
</td><td style="text-align: left">
|
| 1037 |
|
|
<code class="classname">splay_tree_tag</code>
|
| 1038 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1039 |
|
|
<code class="classname">Node_update</code>
|
| 1040 |
|
|
</td><td style="text-align: left">
|
| 1041 |
|
|
<code class="classname">null_node_update</code>
|
| 1042 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1043 |
|
|
rb_tree_map
|
| 1044 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1045 |
|
|
<code class="classname">tree</code>
|
| 1046 |
|
|
</td><td style="text-align: left">
|
| 1047 |
|
|
<code class="classname">Tag</code>
|
| 1048 |
|
|
</td><td style="text-align: left">
|
| 1049 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1050 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1051 |
|
|
<code class="classname">Node_update</code>
|
| 1052 |
|
|
</td><td style="text-align: left">
|
| 1053 |
|
|
<code class="classname">null_node_update</code>
|
| 1054 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the
|
| 1055 |
|
|
native tree type and a vector-based tree type.
|
| 1056 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_insert_vector.png" style="text-align: middle"/></div></div><p>
|
| 1057 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1058 |
|
|
instantiated with the types in the following table.
|
| 1059 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1060 |
|
|
n_map
|
| 1061 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1062 |
|
|
<code class="classname">std::map</code>
|
| 1063 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1064 |
|
|
ov_tree_map
|
| 1065 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1066 |
|
|
<code class="classname">tree</code>
|
| 1067 |
|
|
</td><td style="text-align: left">
|
| 1068 |
|
|
<code class="classname">Tag</code>
|
| 1069 |
|
|
</td><td style="text-align: left">
|
| 1070 |
|
|
<code class="classname">ov_tree_tag</code>
|
| 1071 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1072 |
|
|
<code class="classname">Node_update</code>
|
| 1073 |
|
|
</td><td style="text-align: left">
|
| 1074 |
|
|
<code class="classname">null_node_update</code>
|
| 1075 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the
|
| 1076 |
|
|
native tree type and a PATRICIA trie type.
|
| 1077 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_insert_trie.png" style="text-align: middle"/></div></div><p>
|
| 1078 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1079 |
|
|
instantiated with the types in the following table.
|
| 1080 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1081 |
|
|
n_map
|
| 1082 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1083 |
|
|
<code class="classname">std::map</code>
|
| 1084 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1085 |
|
|
pat_trie_map
|
| 1086 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1087 |
|
|
<code class="classname">tree</code>
|
| 1088 |
|
|
</td><td style="text-align: left">
|
| 1089 |
|
|
<code class="classname">Tag</code>
|
| 1090 |
|
|
</td><td style="text-align: left">
|
| 1091 |
|
|
<code class="classname">pat_trie_tag</code>
|
| 1092 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1093 |
|
|
<code class="classname">Node_update</code>
|
| 1094 |
|
|
</td><td style="text-align: left">
|
| 1095 |
|
|
<code class="classname">null_node_update</code>
|
| 1096 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_insert.observations"/>
|
| 1097 |
|
|
Observations
|
| 1098 |
|
|
</h6></div></div></div><p>Observing the first graphic implies that for this setting, a splay tree
|
| 1099 |
|
|
(<code class="classname">tree</code> with <code class="classname">Tag
|
| 1100 |
|
|
</code> = <code class="classname">splay_tree_tag</code>) does not do
|
| 1101 |
|
|
well. See also the Branch-Based
|
| 1102 |
|
|
Text <code class="function">find</code> Find Timing Test. The two
|
| 1103 |
|
|
red-black trees perform better.</p><p>Observing the second graphic, an ordered-vector tree
|
| 1104 |
|
|
(<code class="classname">tree</code> with <code class="classname">Tag
|
| 1105 |
|
|
</code> = <code class="classname">ov_tree_tag</code>) performs
|
| 1106 |
|
|
abysmally. Inserting into this type of tree has linear complexity
|
| 1107 |
|
|
[ austern00noset].</p><p>Observing the third and last graphic, A PATRICIA trie
|
| 1108 |
|
|
(<code class="classname">trie</code> with <code class="classname">Tag
|
| 1109 |
|
|
</code> = <code class="classname">pat_trie_tag</code>) has abysmal
|
| 1110 |
|
|
performance, as well. This is not that surprising, since a
|
| 1111 |
|
|
large-fan-out PATRICIA trie works like a hash table with
|
| 1112 |
|
|
collisions resolved by a sub-trie. Each time a collision is
|
| 1113 |
|
|
encountered, a new "hash-table" is built A large fan-out PATRICIA
|
| 1114 |
|
|
trie, however, doe does well in look-ups (see Branch-Based
|
| 1115 |
|
|
Text <code class="function">find</code> Find Timing Test). It may be
|
| 1116 |
|
|
beneficial in semi-static settings.</p></div></div><div class="section" title="Text find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.text_find"/>
|
| 1117 |
|
|
Text <code class="function">find</code>
|
| 1118 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_find.info"/>
|
| 1119 |
|
|
Description
|
| 1120 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 1121 |
|
|
arbitrary text ([wickland96thirty]) into
|
| 1122 |
|
|
a container, then performs a series of finds using
|
| 1123 |
|
|
<code class="function">find</code>. It measures the average time
|
| 1124 |
|
|
for <code class="function">find</code> as a function of the number of
|
| 1125 |
|
|
values inserted.</p><p>
|
| 1126 |
|
|
It uses the test file:
|
| 1127 |
|
|
<code class="filename">
|
| 1128 |
|
|
performance/ext/pb_ds/text_find_timing.cc
|
| 1129 |
|
|
</code>
|
| 1130 |
|
|
</p><p>The test checks the effect of different underlying
|
| 1131 |
|
|
data structures.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_find.results"/>
|
| 1132 |
|
|
Results
|
| 1133 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 1134 |
|
|
native tree type and several other tree types.
|
| 1135 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_find.png" style="text-align: middle"/></div></div><p>
|
| 1136 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1137 |
|
|
instantiated with the types in the following table.
|
| 1138 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1139 |
|
|
n_map
|
| 1140 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1141 |
|
|
<code class="classname">std::map</code>
|
| 1142 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1143 |
|
|
splay_tree_map
|
| 1144 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1145 |
|
|
<code class="classname">tree</code>
|
| 1146 |
|
|
</td><td style="text-align: left">
|
| 1147 |
|
|
<code class="classname">Tag</code>
|
| 1148 |
|
|
</td><td style="text-align: left">
|
| 1149 |
|
|
<code class="classname">splay_tree_tag</code>
|
| 1150 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1151 |
|
|
<code class="classname">Node_Update</code>
|
| 1152 |
|
|
</td><td style="text-align: left">
|
| 1153 |
|
|
<code class="classname">null_node_update</code>
|
| 1154 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1155 |
|
|
rb_tree_map
|
| 1156 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1157 |
|
|
<code class="classname">tree</code>
|
| 1158 |
|
|
</td><td style="text-align: left">
|
| 1159 |
|
|
<code class="classname">Tag</code>
|
| 1160 |
|
|
</td><td style="text-align: left">
|
| 1161 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1162 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1163 |
|
|
<code class="classname">Node_Update</code>
|
| 1164 |
|
|
</td><td style="text-align: left">
|
| 1165 |
|
|
<code class="classname">null_node_update</code>
|
| 1166 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1167 |
|
|
ov_tree_map
|
| 1168 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1169 |
|
|
<code class="classname">tree</code>
|
| 1170 |
|
|
</td><td style="text-align: left">
|
| 1171 |
|
|
<code class="classname">Tag</code>
|
| 1172 |
|
|
</td><td style="text-align: left">
|
| 1173 |
|
|
<code class="classname">ov_tree_tag</code>
|
| 1174 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1175 |
|
|
<code class="classname">Node_Update</code>
|
| 1176 |
|
|
</td><td style="text-align: left">
|
| 1177 |
|
|
<code class="classname">null_node_update</code>
|
| 1178 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1179 |
|
|
pat_trie_map
|
| 1180 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1181 |
|
|
<code class="classname">tree</code>
|
| 1182 |
|
|
</td><td style="text-align: left">
|
| 1183 |
|
|
<code class="classname">Tag</code>
|
| 1184 |
|
|
</td><td style="text-align: left">
|
| 1185 |
|
|
<code class="classname">pat_trie_tag</code>
|
| 1186 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1187 |
|
|
<code class="classname">Node_Update</code>
|
| 1188 |
|
|
</td><td style="text-align: left">
|
| 1189 |
|
|
<code class="classname">null_node_update</code>
|
| 1190 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_find.observations"/>
|
| 1191 |
|
|
Observations
|
| 1192 |
|
|
</h6></div></div></div><p>For this setting, a splay tree (<code class="classname">tree</code>
|
| 1193 |
|
|
with <code class="classname">Tag
|
| 1194 |
|
|
</code> = <code class="classname">splay_tree_tag</code>) does not do
|
| 1195 |
|
|
well. This is possibly due to two reasons:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>A splay tree is not guaranteed to be balanced [motwani95random]. If a
|
| 1196 |
|
|
splay tree contains n nodes, its average root-leaf
|
| 1197 |
|
|
path can be m >> log(n).</p></li><li class="listitem"><p>Assume a specific root-leaf search path has length
|
| 1198 |
|
|
m, and the search-target node has distance m'
|
| 1199 |
|
|
from the root. A red-black tree will require m + 1
|
| 1200 |
|
|
comparisons to find the required node; a splay tree will
|
| 1201 |
|
|
require 2 m' comparisons. A splay tree, consequently,
|
| 1202 |
|
|
can perform many more comparisons than a red-black tree.</p></li></ol></div><p>An ordered-vector tree (<code class="classname">tree</code>
|
| 1203 |
|
|
with <code class="classname">Tag</code> = <code class="classname">ov_tree_tag</code>), a red-black
|
| 1204 |
|
|
tree (<code class="classname">tree</code>
|
| 1205 |
|
|
with <code class="classname">Tag</code> = <code class="classname">rb_tree_tag</code>), and the
|
| 1206 |
|
|
native red-black tree all share approximately the same
|
| 1207 |
|
|
performance.</p><p>An ordered-vector tree is slightly slower than red-black
|
| 1208 |
|
|
trees, since it requires, in order to find a key, more math
|
| 1209 |
|
|
operations than they do. Conversely, an ordered-vector tree
|
| 1210 |
|
|
requires far lower space than the others. ([austern00noset], however,
|
| 1211 |
|
|
seems to have an implementation that is also faster than a
|
| 1212 |
|
|
red-black tree).</p><p>A PATRICIA trie (<code class="classname">trie</code>
|
| 1213 |
|
|
with <code class="classname">Tag</code> = <code class="classname">pat_trie_tag</code>) has good
|
| 1214 |
|
|
look-up performance, due to its large fan-out in this case. In
|
| 1215 |
|
|
this setting, a PATRICIA trie has look-up performance comparable
|
| 1216 |
|
|
to a hash table (see Hash-Based Text
|
| 1217 |
|
|
<code class="classname">find</code> Timing Test), but it is order
|
| 1218 |
|
|
preserving. This is not that surprising, since a large-fan-out
|
| 1219 |
|
|
PATRICIA trie works like a hash table with collisions resolved
|
| 1220 |
|
|
by a sub-trie. A large-fan-out PATRICIA trie does not do well on
|
| 1221 |
|
|
modifications (see Tree-Based and Trie-Based
|
| 1222 |
|
|
Text Insert Timing Test). Therefore, it is possibly beneficial in
|
| 1223 |
|
|
semi-static settings.</p></div></div><div class="section" title="Text find with Locality-of-Reference"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.text_lor_find"/>
|
| 1224 |
|
|
Text <code class="function">find</code> with Locality-of-Reference
|
| 1225 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_lor_find.info"/>
|
| 1226 |
|
|
Description
|
| 1227 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 1228 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 1229 |
|
|
a container, then performs a series of finds using
|
| 1230 |
|
|
<code class="function">find</code>. It is different than Tree-Based and
|
| 1231 |
|
|
Trie-Based Text <code class="function">find</code> Find Timing Test in the
|
| 1232 |
|
|
sequence of finds it performs: this test performs multiple
|
| 1233 |
|
|
<code class="function">find</code>s on the same key before moving on to the next
|
| 1234 |
|
|
key. It measures the average time for <code class="function">find</code> as a
|
| 1235 |
|
|
function of the number of values inserted.</p><p>
|
| 1236 |
|
|
It uses the test file:
|
| 1237 |
|
|
<code class="filename">
|
| 1238 |
|
|
performance/ext/pb_ds/tree_text_lor_find_timing.cc
|
| 1239 |
|
|
</code>
|
| 1240 |
|
|
</p><p>The test checks the effect of different underlying
|
| 1241 |
|
|
data structures in a locality-of-reference setting.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_lor_find.results"/>
|
| 1242 |
|
|
Results
|
| 1243 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 1244 |
|
|
native tree type and several other tree types.
|
| 1245 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_lor_find.png" style="text-align: middle"/></div></div><p>
|
| 1246 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1247 |
|
|
instantiated with the types in the following table.
|
| 1248 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1249 |
|
|
n_map
|
| 1250 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1251 |
|
|
<code class="classname">std::map</code>
|
| 1252 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1253 |
|
|
splay_tree_map
|
| 1254 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1255 |
|
|
<code class="classname">tree</code>
|
| 1256 |
|
|
</td><td style="text-align: left">
|
| 1257 |
|
|
<code class="classname">Tag</code>
|
| 1258 |
|
|
</td><td style="text-align: left">
|
| 1259 |
|
|
<code class="classname">splay_tree_tag</code>
|
| 1260 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1261 |
|
|
<code class="classname">Node_Update</code>
|
| 1262 |
|
|
</td><td style="text-align: left">
|
| 1263 |
|
|
<code class="classname">null_node_update</code>
|
| 1264 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1265 |
|
|
rb_tree_map
|
| 1266 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1267 |
|
|
<code class="classname">tree</code>
|
| 1268 |
|
|
</td><td style="text-align: left">
|
| 1269 |
|
|
<code class="classname">Tag</code>
|
| 1270 |
|
|
</td><td style="text-align: left">
|
| 1271 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1272 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1273 |
|
|
<code class="classname">Node_Update</code>
|
| 1274 |
|
|
</td><td style="text-align: left">
|
| 1275 |
|
|
<code class="classname">null_node_update</code>
|
| 1276 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1277 |
|
|
ov_tree_map
|
| 1278 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1279 |
|
|
<code class="classname">tree</code>
|
| 1280 |
|
|
</td><td style="text-align: left">
|
| 1281 |
|
|
<code class="classname">Tag</code>
|
| 1282 |
|
|
</td><td style="text-align: left">
|
| 1283 |
|
|
<code class="classname">ov_tree_tag</code>
|
| 1284 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1285 |
|
|
<code class="classname">Node_Update</code>
|
| 1286 |
|
|
</td><td style="text-align: left">
|
| 1287 |
|
|
<code class="classname">null_node_update</code>
|
| 1288 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1289 |
|
|
pat_trie_map
|
| 1290 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1291 |
|
|
<code class="classname">tree</code>
|
| 1292 |
|
|
</td><td style="text-align: left">
|
| 1293 |
|
|
<code class="classname">Tag</code>
|
| 1294 |
|
|
</td><td style="text-align: left">
|
| 1295 |
|
|
<code class="classname">pat_trie_tag</code>
|
| 1296 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1297 |
|
|
<code class="classname">Node_Update</code>
|
| 1298 |
|
|
</td><td style="text-align: left">
|
| 1299 |
|
|
<code class="classname">null_node_update</code>
|
| 1300 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_lor_find.observations"/>
|
| 1301 |
|
|
Observations
|
| 1302 |
|
|
</h6></div></div></div><p>For this setting, an ordered-vector tree
|
| 1303 |
|
|
(<code class="classname">tree</code> with <code class="classname">Tag</code>
|
| 1304 |
|
|
= <code class="classname">ov_tree_tag</code>), a red-black tree
|
| 1305 |
|
|
(<code class="classname">tree</code> with <code class="classname">Tag</code>
|
| 1306 |
|
|
= <code class="classname">rb_tree_tag</code>), and the native red-black
|
| 1307 |
|
|
tree all share approximately the same performance.</p><p>A splay tree (<code class="classname">tree</code>
|
| 1308 |
|
|
with <code class="classname">Tag</code> = <code class="classname">splay_tree_tag</code>) does
|
| 1309 |
|
|
much better, since each (successful) find "bubbles" the
|
| 1310 |
|
|
corresponding node to the root of the tree.</p></div></div><div class="section" title="split and join"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.split_join"/>
|
| 1311 |
|
|
<code class="function">split</code> and <code class="function">join</code>
|
| 1312 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.split_join.info"/>
|
| 1313 |
|
|
Description
|
| 1314 |
|
|
</h6></div></div></div><p>This test a container, inserts into a number of values, splits
|
| 1315 |
|
|
the container at the median, and joins the two containers. (If the
|
| 1316 |
|
|
containers are one of this library's trees,
|
| 1317 |
|
|
it splits and joins with the <code class="function">split</code> and
|
| 1318 |
|
|
<code class="function">join</code> method; otherwise, it uses the <code class="function">erase</code> and
|
| 1319 |
|
|
<code class="function">insert</code> methods.) It measures the time for splitting
|
| 1320 |
|
|
and joining the containers as a function of the number of
|
| 1321 |
|
|
values inserted.</p><p>
|
| 1322 |
|
|
It uses the test file:
|
| 1323 |
|
|
<code class="filename">
|
| 1324 |
|
|
performance/ext/pb_ds/tree_split_join_timing.cc
|
| 1325 |
|
|
</code>
|
| 1326 |
|
|
</p><p>The test checks the performance difference of <code class="function">join</code>
|
| 1327 |
|
|
as opposed to a sequence of <code class="function">insert</code> operations; by
|
| 1328 |
|
|
implication, this test checks the most efficient way to erase a
|
| 1329 |
|
|
sub-sequence from a tree-like-based container, since this can
|
| 1330 |
|
|
always be performed by a small sequence of splits and joins.
|
| 1331 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.split_join.results"/>
|
| 1332 |
|
|
Results
|
| 1333 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 1334 |
|
|
native tree type and several other tree types.
|
| 1335 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_split_join.png" style="text-align: middle"/></div></div><p>
|
| 1336 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1337 |
|
|
instantiated with the types in the following table.
|
| 1338 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1339 |
|
|
n_set
|
| 1340 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1341 |
|
|
<code class="classname">std::set</code>
|
| 1342 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1343 |
|
|
splay_tree_set
|
| 1344 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1345 |
|
|
<code class="classname">tree</code>
|
| 1346 |
|
|
</td><td style="text-align: left">
|
| 1347 |
|
|
<code class="classname">Tag</code>
|
| 1348 |
|
|
</td><td style="text-align: left">
|
| 1349 |
|
|
<code class="classname">splay_tree_tag</code>
|
| 1350 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1351 |
|
|
<code class="classname">Node_Update</code>
|
| 1352 |
|
|
</td><td style="text-align: left">
|
| 1353 |
|
|
<code class="classname">null_node_update</code>
|
| 1354 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1355 |
|
|
rb_tree_set
|
| 1356 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1357 |
|
|
<code class="classname">tree</code>
|
| 1358 |
|
|
</td><td style="text-align: left">
|
| 1359 |
|
|
<code class="classname">Tag</code>
|
| 1360 |
|
|
</td><td style="text-align: left">
|
| 1361 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1362 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1363 |
|
|
<code class="classname">Node_Update</code>
|
| 1364 |
|
|
</td><td style="text-align: left">
|
| 1365 |
|
|
<code class="classname">null_node_update</code>
|
| 1366 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1367 |
|
|
ov_tree_set
|
| 1368 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1369 |
|
|
<code class="classname">tree</code>
|
| 1370 |
|
|
</td><td style="text-align: left">
|
| 1371 |
|
|
<code class="classname">Tag</code>
|
| 1372 |
|
|
</td><td style="text-align: left">
|
| 1373 |
|
|
<code class="classname">ov_tree_tag</code>
|
| 1374 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1375 |
|
|
<code class="classname">Node_Update</code>
|
| 1376 |
|
|
</td><td style="text-align: left">
|
| 1377 |
|
|
<code class="classname">null_node_update</code>
|
| 1378 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1379 |
|
|
pat_trie_map
|
| 1380 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1381 |
|
|
<code class="classname">tree</code>
|
| 1382 |
|
|
</td><td style="text-align: left">
|
| 1383 |
|
|
<code class="classname">Tag</code>
|
| 1384 |
|
|
</td><td style="text-align: left">
|
| 1385 |
|
|
<code class="classname">pat_trie_tag</code>
|
| 1386 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1387 |
|
|
<code class="classname">Node_Update</code>
|
| 1388 |
|
|
</td><td style="text-align: left">
|
| 1389 |
|
|
<code class="classname">null_node_update</code>
|
| 1390 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.split_join.observations"/>
|
| 1391 |
|
|
Observations
|
| 1392 |
|
|
</h6></div></div></div><p>In this test, the native red-black trees must be split and
|
| 1393 |
|
|
joined externally, through a sequence of <code class="function">erase</code> and
|
| 1394 |
|
|
<code class="function">insert</code> operations. This is clearly
|
| 1395 |
|
|
super-linear, and it is not that surprising that the cost is
|
| 1396 |
|
|
high.</p><p>This library's tree-based containers use in this test the
|
| 1397 |
|
|
<code class="function">split</code> and <code class="function">join</code> methods,
|
| 1398 |
|
|
which have lower complexity: the <code class="function">join</code> method
|
| 1399 |
|
|
of a splay tree (<code class="classname">tree</code>
|
| 1400 |
|
|
with <code class="classname">Tag </code>
|
| 1401 |
|
|
= <code class="classname">splay_tree_tag</code>) is quadratic in the
|
| 1402 |
|
|
length of the longest root-leaf path, and linear in the total
|
| 1403 |
|
|
number of elements; the <code class="function">join</code> method of a
|
| 1404 |
|
|
red-black tree (<code class="classname">tree</code>
|
| 1405 |
|
|
with <code class="classname">Tag </code>
|
| 1406 |
|
|
= <code class="classname">rb_tree_tag</code>) or an ordered-vector tree
|
| 1407 |
|
|
(<code class="classname">tree</code> with <code class="classname">Tag </code>
|
| 1408 |
|
|
= <code class="classname">ov_tree_tag</code>) is linear in the number of
|
| 1409 |
|
|
elements.</p><p>Asides from orders of growth, this library's trees access their
|
| 1410 |
|
|
allocator very little in these operations, and some of them do not
|
| 1411 |
|
|
access it at all. This leads to lower constants in their
|
| 1412 |
|
|
complexity, and, for some containers, to exception-free splits and
|
| 1413 |
|
|
joins (which can be determined
|
| 1414 |
|
|
via <code class="classname">container_traits</code>).</p><p>It is important to note that <code class="function">split</code> and
|
| 1415 |
|
|
<code class="function">join</code> are not esoteric methods - they are the most
|
| 1416 |
|
|
efficient means of erasing a contiguous range of values from a
|
| 1417 |
|
|
tree based container.</p></div></div><div class="section" title="Order-Statistics"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.order_statistics"/>
|
| 1418 |
|
|
Order-Statistics
|
| 1419 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.order_statistics.info"/>
|
| 1420 |
|
|
Description
|
| 1421 |
|
|
</h6></div></div></div><p>This test creates a container, inserts random integers into the
|
| 1422 |
|
|
the container, and then checks the order-statistics of the
|
| 1423 |
|
|
container's values. (If the container is one of this
|
| 1424 |
|
|
library's trees, it does this with
|
| 1425 |
|
|
the <code class="function">order_of_key</code> method of
|
| 1426 |
|
|
<code class="classname">tree_order_statistics_node_update</code>
|
| 1427 |
|
|
; otherwise, it uses the <code class="function">find</code> method and
|
| 1428 |
|
|
<code class="function">std::distance</code>.) It measures the average
|
| 1429 |
|
|
time for such queries as a function of the number of values
|
| 1430 |
|
|
inserted.</p><p>
|
| 1431 |
|
|
It uses the test file:
|
| 1432 |
|
|
<code class="filename">
|
| 1433 |
|
|
performance/ext/pb_ds/tree_order_statistics_timing.cc
|
| 1434 |
|
|
</code>
|
| 1435 |
|
|
</p><p>The test checks the performance difference of policies based
|
| 1436 |
|
|
on node-invariant as opposed to a external functions.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.order_statistics.results"/>
|
| 1437 |
|
|
Results
|
| 1438 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 1439 |
|
|
native tree type and several other tree types.
|
| 1440 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_order_statistics.png" style="text-align: middle"/></div></div><p>
|
| 1441 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1442 |
|
|
instantiated with the types in the following table.
|
| 1443 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1444 |
|
|
n_set
|
| 1445 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1446 |
|
|
<code class="classname">std::set</code>
|
| 1447 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1448 |
|
|
splay_tree_ost_set
|
| 1449 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1450 |
|
|
<code class="classname">tree</code>
|
| 1451 |
|
|
</td><td style="text-align: left">
|
| 1452 |
|
|
<code class="classname">Tag</code>
|
| 1453 |
|
|
</td><td style="text-align: left">
|
| 1454 |
|
|
<code class="classname">splay_tree_tag</code>
|
| 1455 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1456 |
|
|
<code class="classname">Node_Update</code>
|
| 1457 |
|
|
</td><td style="text-align: left">
|
| 1458 |
|
|
<code class="classname">tree_order_statistics_node_update</code>
|
| 1459 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 1460 |
|
|
rb_tree_ost_set
|
| 1461 |
|
|
</td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1462 |
|
|
<code class="classname">tree</code>
|
| 1463 |
|
|
</td><td style="text-align: left">
|
| 1464 |
|
|
<code class="classname">Tag</code>
|
| 1465 |
|
|
</td><td style="text-align: left">
|
| 1466 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1467 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1468 |
|
|
<code class="classname">Node_Update</code>
|
| 1469 |
|
|
</td><td style="text-align: left">
|
| 1470 |
|
|
<code class="classname">tree_order_statistics_node_update</code>
|
| 1471 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.order_statistics.observations"/>
|
| 1472 |
|
|
Observations
|
| 1473 |
|
|
</h6></div></div></div><p>In this test, the native red-black tree can support
|
| 1474 |
|
|
order-statistics queries only externally, by performing a
|
| 1475 |
|
|
<code class="classname">find</code> (alternatively, <code class="classname">lower_bound</code> or
|
| 1476 |
|
|
<code class="classname">upper_bound</code> ) and then using <code class="classname">std::distance</code> .
|
| 1477 |
|
|
This is clearly linear, and it is not that surprising that the
|
| 1478 |
|
|
cost is high.</p><p>This library's tree-based containers use in this test the
|
| 1479 |
|
|
<code class="classname">order_of_key</code> method of <code class="classname">tree_order_statistics_node_update</code>.
|
| 1480 |
|
|
This method has only linear complexity in the length of the
|
| 1481 |
|
|
root-node path. Unfortunately, the average path of a splay tree
|
| 1482 |
|
|
(<code class="classname">tree</code>
|
| 1483 |
|
|
with <code class="classname">Tag =</code> <code class="classname">splay_tree_tag</code> ) can
|
| 1484 |
|
|
be higher than logarithmic; the longest path of a red-black
|
| 1485 |
|
|
tree (<code class="classname">tree</code>
|
| 1486 |
|
|
with <code class="classname">Tag =</code> <code class="classname">rb_tree_tag</code> ) is
|
| 1487 |
|
|
logarithmic in the number of elements. Consequently, the splay
|
| 1488 |
|
|
tree has worse performance than the red-black tree.</p></div></div></div><div class="section" title="Multimap"><div class="titlepage"><div><div><h4 class="title"><a id="performance.multimap"/>Multimap</h4></div></div></div><p/><div class="section" title="Text find with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_find_small"/>
|
| 1489 |
|
|
Text <code class="function">find</code> with Small Secondary-to-Primary Key Ratios
|
| 1490 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_small.info"/>
|
| 1491 |
|
|
Description
|
| 1492 |
|
|
</h6></div></div></div><p>This test inserts a number of pairs into a container. The
|
| 1493 |
|
|
first item of each pair is a string from an arbitrary text
|
| 1494 |
|
|
[wickland96thirty], and
|
| 1495 |
|
|
the second is a uniform i.i.d.integer. The container is a
|
| 1496 |
|
|
"multimap" - it considers the first member of each pair as a
|
| 1497 |
|
|
primary key, and the second member of each pair as a secondary
|
| 1498 |
|
|
key (see Motivation::Associative
|
| 1499 |
|
|
Containers::Alternative to Multiple Equivalent Keys). There
|
| 1500 |
|
|
are 400 distinct primary keys, and the ratio of secondary keys
|
| 1501 |
|
|
to primary keys ranges from 1 to 5.</p><p>The test measures the average find-time as a function of the
|
| 1502 |
|
|
number of values inserted. For this library's containers, it
|
| 1503 |
|
|
finds the secondary key from a container obtained from finding
|
| 1504 |
|
|
a primary key. For the native multimaps, it searches a range
|
| 1505 |
|
|
obtained using <code class="classname">std::equal_range</code> on a primary key.</p><p>
|
| 1506 |
|
|
It uses the test file:
|
| 1507 |
|
|
<code class="filename">
|
| 1508 |
|
|
performance/ext/pb_ds/multimap_text_find_timing_small.cc
|
| 1509 |
|
|
</code>
|
| 1510 |
|
|
</p><p>The test checks the find-time scalability of different
|
| 1511 |
|
|
"multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_small.results"/>
|
| 1512 |
|
|
Results
|
| 1513 |
|
|
</h6></div></div></div><p>The graphic below show the results for "multimaps" which
|
| 1514 |
|
|
use a tree-based container for primary keys.
|
| 1515 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_small_s2p_tree.png" style="text-align: middle"/></div></div><p>
|
| 1516 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1517 |
|
|
instantiated with the types in the following table.
|
| 1518 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1519 |
|
|
n_mmap
|
| 1520 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1521 |
|
|
<code class="classname">std::multimap</code>
|
| 1522 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1523 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 1524 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1525 |
|
|
<code class="classname">tree</code>
|
| 1526 |
|
|
</td><td style="text-align: left">
|
| 1527 |
|
|
<code class="classname">Tag</code>
|
| 1528 |
|
|
</td><td style="text-align: left">
|
| 1529 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1530 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1531 |
|
|
<code class="classname">Node_Update</code>
|
| 1532 |
|
|
</td><td style="text-align: left">
|
| 1533 |
|
|
<code class="classname">null_node_update</code>
|
| 1534 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1535 |
|
|
<code class="classname">Mapped</code>
|
| 1536 |
|
|
</td><td style="text-align: left">
|
| 1537 |
|
|
<code class="classname">list_update</code>
|
| 1538 |
|
|
</td><td style="text-align: left">
|
| 1539 |
|
|
<code class="classname">Update_Policy</code>
|
| 1540 |
|
|
</td><td style="text-align: left">
|
| 1541 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 1542 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1543 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 1544 |
|
|
</td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
|
| 1545 |
|
|
<code class="classname">tree</code>
|
| 1546 |
|
|
</td><td style="text-align: left">
|
| 1547 |
|
|
<code class="classname">Tag</code>
|
| 1548 |
|
|
</td><td style="text-align: left">
|
| 1549 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1550 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1551 |
|
|
<code class="classname">Node_Update</code>
|
| 1552 |
|
|
</td><td style="text-align: left">
|
| 1553 |
|
|
<code class="classname">null_node_update</code>
|
| 1554 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1555 |
|
|
<code class="classname">Mapped</code>
|
| 1556 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 1557 |
|
|
<code class="classname">cc_hash_table</code>
|
| 1558 |
|
|
</td><td style="text-align: left">
|
| 1559 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1560 |
|
|
</td><td style="text-align: left">
|
| 1561 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1562 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1563 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1564 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1565 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1566 |
|
|
</td><td style="text-align: left">
|
| 1567 |
|
|
<code class="classname">Size_Policy</code>
|
| 1568 |
|
|
</td><td style="text-align: left">
|
| 1569 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1570 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 1571 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1572 |
|
|
</td><td style="text-align: left">
|
| 1573 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1574 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1575 |
|
|
</td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
|
| 1576 |
|
|
use a hash-based container for primary keys.
|
| 1577 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_small_s2p_hash.png" style="text-align: middle"/></div></div><p>
|
| 1578 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1579 |
|
|
instantiated with the types in the following table.
|
| 1580 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1581 |
|
|
n_hash_mmap
|
| 1582 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1583 |
|
|
<code class="classname">std::tr1::unordered_multimap</code>
|
| 1584 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1585 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 1586 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 1587 |
|
|
<code class="classname">
|
| 1588 |
|
|
cc_hash_table
|
| 1589 |
|
|
</code>
|
| 1590 |
|
|
</td><td style="text-align: left">
|
| 1591 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1592 |
|
|
</td><td style="text-align: left">
|
| 1593 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1594 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1595 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1596 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1597 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1598 |
|
|
</td><td style="text-align: left">
|
| 1599 |
|
|
<code class="classname">Size_Policy</code>
|
| 1600 |
|
|
</td><td style="text-align: left">
|
| 1601 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1602 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 1603 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1604 |
|
|
</td><td style="text-align: left">
|
| 1605 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1606 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1607 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1608 |
|
|
<code class="classname">Mapped</code>
|
| 1609 |
|
|
</td><td style="text-align: left">
|
| 1610 |
|
|
<code class="classname">list_update</code>
|
| 1611 |
|
|
</td><td style="text-align: left">
|
| 1612 |
|
|
<code class="classname">Update_Policy</code>
|
| 1613 |
|
|
</td><td style="text-align: left">
|
| 1614 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 1615 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1616 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 1617 |
|
|
</td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
|
| 1618 |
|
|
<code class="classname">
|
| 1619 |
|
|
cc_hash_table
|
| 1620 |
|
|
</code>
|
| 1621 |
|
|
</td><td style="text-align: left">
|
| 1622 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1623 |
|
|
</td><td style="text-align: left">
|
| 1624 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1625 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1626 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1627 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1628 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1629 |
|
|
</td><td style="text-align: left">
|
| 1630 |
|
|
<code class="classname">Size_Policy</code>
|
| 1631 |
|
|
</td><td style="text-align: left">
|
| 1632 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1633 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 1634 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1635 |
|
|
</td><td style="text-align: left">
|
| 1636 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1637 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1638 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1639 |
|
|
<code class="classname">Mapped</code>
|
| 1640 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 1641 |
|
|
<code class="classname">cc_hash_table</code>
|
| 1642 |
|
|
</td><td style="text-align: left">
|
| 1643 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1644 |
|
|
</td><td style="text-align: left">
|
| 1645 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1646 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1647 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1648 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1649 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1650 |
|
|
</td><td style="text-align: left">
|
| 1651 |
|
|
<code class="classname">Size_Policy</code>
|
| 1652 |
|
|
</td><td style="text-align: left">
|
| 1653 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1654 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 1655 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1656 |
|
|
</td><td style="text-align: left">
|
| 1657 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1658 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1659 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_small.observations"/>
|
| 1660 |
|
|
Observations
|
| 1661 |
|
|
</h6></div></div></div><p>See Observations::Mapping-Semantics
|
| 1662 |
|
|
Considerations.</p></div></div><div class="section" title="Text find with Large Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_find_large"/>
|
| 1663 |
|
|
Text <code class="function">find</code> with Large Secondary-to-Primary Key Ratios
|
| 1664 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_large.info"/>
|
| 1665 |
|
|
Description
|
| 1666 |
|
|
</h6></div></div></div><p>This test inserts a number of pairs into a container. The
|
| 1667 |
|
|
first item of each pair is a string from an arbitrary text
|
| 1668 |
|
|
[wickland96thirty], and
|
| 1669 |
|
|
the second is a uniform integer. The container is a
|
| 1670 |
|
|
"multimap" - it considers the first member of each pair as a
|
| 1671 |
|
|
primary key, and the second member of each pair as a secondary
|
| 1672 |
|
|
key. There
|
| 1673 |
|
|
are 400 distinct primary keys, and the ratio of secondary keys
|
| 1674 |
|
|
to primary keys ranges from 1 to 5.</p><p>The test measures the average find-time as a function of the
|
| 1675 |
|
|
number of values inserted. For this library's containers, it
|
| 1676 |
|
|
finds the secondary key from a container obtained from finding
|
| 1677 |
|
|
a primary key. For the native multimaps, it searches a range
|
| 1678 |
|
|
obtained using <code class="classname">std::equal_range</code> on a primary key.</p><p>
|
| 1679 |
|
|
It uses the test file:
|
| 1680 |
|
|
<code class="filename">
|
| 1681 |
|
|
performance/ext/pb_ds/multimap_text_find_timing_large.cc
|
| 1682 |
|
|
</code>
|
| 1683 |
|
|
</p><p>The test checks the find-time scalability of different
|
| 1684 |
|
|
"multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_large.results"/>
|
| 1685 |
|
|
Results
|
| 1686 |
|
|
</h6></div></div></div><p>The graphic below show the results for "multimaps" which
|
| 1687 |
|
|
use a tree-based container for primary keys.
|
| 1688 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_tree.png" style="text-align: middle"/></div></div><p>
|
| 1689 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1690 |
|
|
instantiated with the types in the following table.
|
| 1691 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1692 |
|
|
n_mmap
|
| 1693 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1694 |
|
|
<code class="classname">std::multimap</code>
|
| 1695 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1696 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 1697 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1698 |
|
|
<code class="classname">tree</code>
|
| 1699 |
|
|
</td><td style="text-align: left">
|
| 1700 |
|
|
<code class="classname">Tag</code>
|
| 1701 |
|
|
</td><td style="text-align: left">
|
| 1702 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1703 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1704 |
|
|
<code class="classname">Node_Update</code>
|
| 1705 |
|
|
</td><td style="text-align: left">
|
| 1706 |
|
|
<code class="classname">null_node_update</code>
|
| 1707 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1708 |
|
|
<code class="classname">Mapped</code>
|
| 1709 |
|
|
</td><td style="text-align: left">
|
| 1710 |
|
|
<code class="classname">list_update</code>
|
| 1711 |
|
|
</td><td style="text-align: left">
|
| 1712 |
|
|
<code class="classname">Update_Policy</code>
|
| 1713 |
|
|
</td><td style="text-align: left">
|
| 1714 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 1715 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1716 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 1717 |
|
|
</td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
|
| 1718 |
|
|
<code class="classname">tree</code>
|
| 1719 |
|
|
</td><td style="text-align: left">
|
| 1720 |
|
|
<code class="classname">Tag</code>
|
| 1721 |
|
|
</td><td style="text-align: left">
|
| 1722 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1723 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1724 |
|
|
<code class="classname">Node_Update</code>
|
| 1725 |
|
|
</td><td style="text-align: left">
|
| 1726 |
|
|
<code class="classname">null_node_update</code>
|
| 1727 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1728 |
|
|
<code class="classname">Mapped</code>
|
| 1729 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 1730 |
|
|
<code class="classname">cc_hash_table</code>
|
| 1731 |
|
|
</td><td style="text-align: left">
|
| 1732 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1733 |
|
|
</td><td style="text-align: left">
|
| 1734 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1735 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1736 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1737 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1738 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1739 |
|
|
</td><td style="text-align: left">
|
| 1740 |
|
|
<code class="classname">Size_Policy</code>
|
| 1741 |
|
|
</td><td style="text-align: left">
|
| 1742 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1743 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 1744 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1745 |
|
|
</td><td style="text-align: left">
|
| 1746 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1747 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1748 |
|
|
</td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
|
| 1749 |
|
|
use a hash-based container for primary keys.
|
| 1750 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
|
| 1751 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1752 |
|
|
instantiated with the types in the following table.
|
| 1753 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1754 |
|
|
n_hash_mmap
|
| 1755 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1756 |
|
|
<code class="classname">std::tr1::unordered_multimap</code>
|
| 1757 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1758 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 1759 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 1760 |
|
|
<code class="classname">
|
| 1761 |
|
|
cc_hash_table
|
| 1762 |
|
|
</code>
|
| 1763 |
|
|
</td><td style="text-align: left">
|
| 1764 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1765 |
|
|
</td><td style="text-align: left">
|
| 1766 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1767 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1768 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1769 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1770 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1771 |
|
|
</td><td style="text-align: left">
|
| 1772 |
|
|
<code class="classname">Size_Policy</code>
|
| 1773 |
|
|
</td><td style="text-align: left">
|
| 1774 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1775 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 1776 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1777 |
|
|
</td><td style="text-align: left">
|
| 1778 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1779 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1780 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1781 |
|
|
<code class="classname">Mapped</code>
|
| 1782 |
|
|
</td><td style="text-align: left">
|
| 1783 |
|
|
<code class="classname">list_update</code>
|
| 1784 |
|
|
</td><td style="text-align: left">
|
| 1785 |
|
|
<code class="classname">Update_Policy</code>
|
| 1786 |
|
|
</td><td style="text-align: left">
|
| 1787 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 1788 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1789 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 1790 |
|
|
</td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
|
| 1791 |
|
|
<code class="classname">
|
| 1792 |
|
|
cc_hash_table
|
| 1793 |
|
|
</code>
|
| 1794 |
|
|
</td><td style="text-align: left">
|
| 1795 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1796 |
|
|
</td><td style="text-align: left">
|
| 1797 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1798 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1799 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1800 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1801 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1802 |
|
|
</td><td style="text-align: left">
|
| 1803 |
|
|
<code class="classname">Size_Policy</code>
|
| 1804 |
|
|
</td><td style="text-align: left">
|
| 1805 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1806 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 1807 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1808 |
|
|
</td><td style="text-align: left">
|
| 1809 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1810 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1811 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1812 |
|
|
<code class="classname">Mapped</code>
|
| 1813 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 1814 |
|
|
<code class="classname">cc_hash_table</code>
|
| 1815 |
|
|
</td><td style="text-align: left">
|
| 1816 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1817 |
|
|
</td><td style="text-align: left">
|
| 1818 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1819 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1820 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1821 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1822 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1823 |
|
|
</td><td style="text-align: left">
|
| 1824 |
|
|
<code class="classname">Size_Policy</code>
|
| 1825 |
|
|
</td><td style="text-align: left">
|
| 1826 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1827 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 1828 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1829 |
|
|
</td><td style="text-align: left">
|
| 1830 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1831 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1832 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_large.observations"/>
|
| 1833 |
|
|
Observations
|
| 1834 |
|
|
</h6></div></div></div><p>See Observations::Mapping-Semantics
|
| 1835 |
|
|
Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_small"/>
|
| 1836 |
|
|
Text <code class="function">insert</code> with Small
|
| 1837 |
|
|
Secondary-to-Primary Key Ratios
|
| 1838 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_small.info"/>
|
| 1839 |
|
|
Description
|
| 1840 |
|
|
</h6></div></div></div><p>This test inserts a number of pairs into a container. The
|
| 1841 |
|
|
first item of each pair is a string from an arbitrary text
|
| 1842 |
|
|
[wickland96thirty], and
|
| 1843 |
|
|
the second is a uniform integer. The container is a
|
| 1844 |
|
|
"multimap" - it considers the first member of each pair as a
|
| 1845 |
|
|
primary key, and the second member of each pair as a secondary
|
| 1846 |
|
|
key. There
|
| 1847 |
|
|
are 400 distinct primary keys, and the ratio of secondary keys
|
| 1848 |
|
|
to primary keys ranges from 1 to 5.</p><p>The test measures the average insert-time as a function of
|
| 1849 |
|
|
the number of values inserted. For this library's containers,
|
| 1850 |
|
|
it inserts a primary key into the primary associative
|
| 1851 |
|
|
container, then a secondary key into the secondary associative
|
| 1852 |
|
|
container. For the native multimaps, it obtains a range using
|
| 1853 |
|
|
<code class="classname">std::equal_range</code>, and inserts a value only if it was
|
| 1854 |
|
|
not contained already.</p><p>
|
| 1855 |
|
|
It uses the test file:
|
| 1856 |
|
|
<code class="filename">
|
| 1857 |
|
|
performance/ext/pb_ds/multimap_text_insert_timing_small.cc
|
| 1858 |
|
|
</code>
|
| 1859 |
|
|
</p><p>The test checks the insert-time scalability of different
|
| 1860 |
|
|
"multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_small.results"/>
|
| 1861 |
|
|
Results
|
| 1862 |
|
|
</h6></div></div></div><p>The graphic below show the results for "multimaps" which
|
| 1863 |
|
|
use a tree-based container for primary keys.
|
| 1864 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_small_s2p_tree.png" style="text-align: middle"/></div></div><p>
|
| 1865 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1866 |
|
|
instantiated with the types in the following table.
|
| 1867 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1868 |
|
|
n_mmap
|
| 1869 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1870 |
|
|
<code class="classname">std::multimap</code>
|
| 1871 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1872 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 1873 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1874 |
|
|
<code class="classname">tree</code>
|
| 1875 |
|
|
</td><td style="text-align: left">
|
| 1876 |
|
|
<code class="classname">Tag</code>
|
| 1877 |
|
|
</td><td style="text-align: left">
|
| 1878 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1879 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1880 |
|
|
<code class="classname">Node_Update</code>
|
| 1881 |
|
|
</td><td style="text-align: left">
|
| 1882 |
|
|
<code class="classname">null_node_update</code>
|
| 1883 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1884 |
|
|
<code class="classname">Mapped</code>
|
| 1885 |
|
|
</td><td style="text-align: left">
|
| 1886 |
|
|
<code class="classname">list_update</code>
|
| 1887 |
|
|
</td><td style="text-align: left">
|
| 1888 |
|
|
<code class="classname">Update_Policy</code>
|
| 1889 |
|
|
</td><td style="text-align: left">
|
| 1890 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 1891 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1892 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 1893 |
|
|
</td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
|
| 1894 |
|
|
<code class="classname">tree</code>
|
| 1895 |
|
|
</td><td style="text-align: left">
|
| 1896 |
|
|
<code class="classname">Tag</code>
|
| 1897 |
|
|
</td><td style="text-align: left">
|
| 1898 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 1899 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1900 |
|
|
<code class="classname">Node_Update</code>
|
| 1901 |
|
|
</td><td style="text-align: left">
|
| 1902 |
|
|
<code class="classname">null_node_update</code>
|
| 1903 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1904 |
|
|
<code class="classname">Mapped</code>
|
| 1905 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 1906 |
|
|
<code class="classname">cc_hash_table</code>
|
| 1907 |
|
|
</td><td style="text-align: left">
|
| 1908 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1909 |
|
|
</td><td style="text-align: left">
|
| 1910 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1911 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1912 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1913 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1914 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1915 |
|
|
</td><td style="text-align: left">
|
| 1916 |
|
|
<code class="classname">Size_Policy</code>
|
| 1917 |
|
|
</td><td style="text-align: left">
|
| 1918 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1919 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 1920 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1921 |
|
|
</td><td style="text-align: left">
|
| 1922 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1923 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1924 |
|
|
</td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
|
| 1925 |
|
|
use a hash-based container for primary keys.
|
| 1926 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_small_s2p_hash.png" style="text-align: middle"/></div></div><p>
|
| 1927 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 1928 |
|
|
instantiated with the types in the following table.
|
| 1929 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1930 |
|
|
n_hash_mmap
|
| 1931 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 1932 |
|
|
<code class="classname">std::tr1::unordered_multimap</code>
|
| 1933 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1934 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 1935 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 1936 |
|
|
<code class="classname">
|
| 1937 |
|
|
cc_hash_table
|
| 1938 |
|
|
</code>
|
| 1939 |
|
|
</td><td style="text-align: left">
|
| 1940 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1941 |
|
|
</td><td style="text-align: left">
|
| 1942 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1943 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1944 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1945 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1946 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1947 |
|
|
</td><td style="text-align: left">
|
| 1948 |
|
|
<code class="classname">Size_Policy</code>
|
| 1949 |
|
|
</td><td style="text-align: left">
|
| 1950 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1951 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 1952 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1953 |
|
|
</td><td style="text-align: left">
|
| 1954 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1955 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1956 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 1957 |
|
|
<code class="classname">Mapped</code>
|
| 1958 |
|
|
</td><td style="text-align: left">
|
| 1959 |
|
|
<code class="classname">list_update</code>
|
| 1960 |
|
|
</td><td style="text-align: left">
|
| 1961 |
|
|
<code class="classname">Update_Policy</code>
|
| 1962 |
|
|
</td><td style="text-align: left">
|
| 1963 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 1964 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 1965 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 1966 |
|
|
</td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
|
| 1967 |
|
|
<code class="classname">
|
| 1968 |
|
|
cc_hash_table
|
| 1969 |
|
|
</code>
|
| 1970 |
|
|
</td><td style="text-align: left">
|
| 1971 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1972 |
|
|
</td><td style="text-align: left">
|
| 1973 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1974 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1975 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1976 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1977 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1978 |
|
|
</td><td style="text-align: left">
|
| 1979 |
|
|
<code class="classname">Size_Policy</code>
|
| 1980 |
|
|
</td><td style="text-align: left">
|
| 1981 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 1982 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 1983 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 1984 |
|
|
</td><td style="text-align: left">
|
| 1985 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 1986 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 1987 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 1988 |
|
|
<code class="classname">Mapped</code>
|
| 1989 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 1990 |
|
|
<code class="classname">cc_hash_table</code>
|
| 1991 |
|
|
</td><td style="text-align: left">
|
| 1992 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 1993 |
|
|
</td><td style="text-align: left">
|
| 1994 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 1995 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 1996 |
|
|
<code class="classname">Resize_Policy</code>
|
| 1997 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 1998 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 1999 |
|
|
</td><td style="text-align: left">
|
| 2000 |
|
|
<code class="classname">Size_Policy</code>
|
| 2001 |
|
|
</td><td style="text-align: left">
|
| 2002 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2003 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2004 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2005 |
|
|
</td><td style="text-align: left">
|
| 2006 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2007 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2008 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_small.observations"/>
|
| 2009 |
|
|
Observations
|
| 2010 |
|
|
</h6></div></div></div><p>See Observations::Mapping-Semantics
|
| 2011 |
|
|
Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_large"/>
|
| 2012 |
|
|
Text <code class="function">insert</code> with Small
|
| 2013 |
|
|
Secondary-to-Primary Key Ratios
|
| 2014 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_large.info"/>
|
| 2015 |
|
|
Description
|
| 2016 |
|
|
</h6></div></div></div><p>This test inserts a number of pairs into a container. The
|
| 2017 |
|
|
first item of each pair is a string from an arbitrary text
|
| 2018 |
|
|
[wickland96thirty], and
|
| 2019 |
|
|
the second is a uniform integer. The container is a
|
| 2020 |
|
|
"multimap" - it considers the first member of each pair as a
|
| 2021 |
|
|
primary key, and the second member of each pair as a secondary
|
| 2022 |
|
|
key. There
|
| 2023 |
|
|
are 400 distinct primary keys, and the ratio of secondary keys
|
| 2024 |
|
|
to primary keys ranges from 1 to 5.</p><p>The test measures the average insert-time as a function of
|
| 2025 |
|
|
the number of values inserted. For this library's containers,
|
| 2026 |
|
|
it inserts a primary key into the primary associative
|
| 2027 |
|
|
container, then a secondary key into the secondary associative
|
| 2028 |
|
|
container. For the native multimaps, it obtains a range using
|
| 2029 |
|
|
<code class="classname">std::equal_range</code>, and inserts a value only if it was
|
| 2030 |
|
|
not contained already.</p><p>
|
| 2031 |
|
|
It uses the test file:
|
| 2032 |
|
|
<code class="filename">
|
| 2033 |
|
|
performance/ext/pb_ds/multimap_text_insert_timing_large.cc
|
| 2034 |
|
|
</code>
|
| 2035 |
|
|
</p><p>The test checks the insert-time scalability of different
|
| 2036 |
|
|
"multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_large.results"/>
|
| 2037 |
|
|
Results
|
| 2038 |
|
|
</h6></div></div></div><p>The graphic below show the results for "multimaps" which
|
| 2039 |
|
|
use a tree-based container for primary keys.
|
| 2040 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_large_s2p_tree.png" style="text-align: middle"/></div></div><p>
|
| 2041 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2042 |
|
|
instantiated with the types in the following table.
|
| 2043 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2044 |
|
|
n_mmap
|
| 2045 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2046 |
|
|
<code class="classname">std::multimap</code>
|
| 2047 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2048 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 2049 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2050 |
|
|
<code class="classname">tree</code>
|
| 2051 |
|
|
</td><td style="text-align: left">
|
| 2052 |
|
|
<code class="classname">Tag</code>
|
| 2053 |
|
|
</td><td style="text-align: left">
|
| 2054 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 2055 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2056 |
|
|
<code class="classname">Node_Update</code>
|
| 2057 |
|
|
</td><td style="text-align: left">
|
| 2058 |
|
|
<code class="classname">null_node_update</code>
|
| 2059 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2060 |
|
|
<code class="classname">Mapped</code>
|
| 2061 |
|
|
</td><td style="text-align: left">
|
| 2062 |
|
|
<code class="classname">list_update</code>
|
| 2063 |
|
|
</td><td style="text-align: left">
|
| 2064 |
|
|
<code class="classname">Update_Policy</code>
|
| 2065 |
|
|
</td><td style="text-align: left">
|
| 2066 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 2067 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2068 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 2069 |
|
|
</td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
|
| 2070 |
|
|
<code class="classname">tree</code>
|
| 2071 |
|
|
</td><td style="text-align: left">
|
| 2072 |
|
|
<code class="classname">Tag</code>
|
| 2073 |
|
|
</td><td style="text-align: left">
|
| 2074 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 2075 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2076 |
|
|
<code class="classname">Node_Update</code>
|
| 2077 |
|
|
</td><td style="text-align: left">
|
| 2078 |
|
|
<code class="classname">null_node_update</code>
|
| 2079 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2080 |
|
|
<code class="classname">Mapped</code>
|
| 2081 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 2082 |
|
|
<code class="classname">cc_hash_table</code>
|
| 2083 |
|
|
</td><td style="text-align: left">
|
| 2084 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2085 |
|
|
</td><td style="text-align: left">
|
| 2086 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2087 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2088 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2089 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2090 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2091 |
|
|
</td><td style="text-align: left">
|
| 2092 |
|
|
<code class="classname">Size_Policy</code>
|
| 2093 |
|
|
</td><td style="text-align: left">
|
| 2094 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2095 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2096 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2097 |
|
|
</td><td style="text-align: left">
|
| 2098 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2099 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2100 |
|
|
</td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
|
| 2101 |
|
|
use a hash-based container for primary keys.
|
| 2102 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
|
| 2103 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2104 |
|
|
instantiated with the types in the following table.
|
| 2105 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2106 |
|
|
n_hash_mmap
|
| 2107 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2108 |
|
|
<code class="classname">std::tr1::unordered_multimap</code>
|
| 2109 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2110 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 2111 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 2112 |
|
|
<code class="classname">
|
| 2113 |
|
|
cc_hash_table
|
| 2114 |
|
|
</code>
|
| 2115 |
|
|
</td><td style="text-align: left">
|
| 2116 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2117 |
|
|
</td><td style="text-align: left">
|
| 2118 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2119 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2120 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2121 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2122 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2123 |
|
|
</td><td style="text-align: left">
|
| 2124 |
|
|
<code class="classname">Size_Policy</code>
|
| 2125 |
|
|
</td><td style="text-align: left">
|
| 2126 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2127 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 2128 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2129 |
|
|
</td><td style="text-align: left">
|
| 2130 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2131 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2132 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2133 |
|
|
<code class="classname">Mapped</code>
|
| 2134 |
|
|
</td><td style="text-align: left">
|
| 2135 |
|
|
<code class="classname">list_update</code>
|
| 2136 |
|
|
</td><td style="text-align: left">
|
| 2137 |
|
|
<code class="classname">Update_Policy</code>
|
| 2138 |
|
|
</td><td style="text-align: left">
|
| 2139 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 2140 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2141 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 2142 |
|
|
</td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
|
| 2143 |
|
|
<code class="classname">
|
| 2144 |
|
|
cc_hash_table
|
| 2145 |
|
|
</code>
|
| 2146 |
|
|
</td><td style="text-align: left">
|
| 2147 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2148 |
|
|
</td><td style="text-align: left">
|
| 2149 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2150 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2151 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2152 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2153 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2154 |
|
|
</td><td style="text-align: left">
|
| 2155 |
|
|
<code class="classname">Size_Policy</code>
|
| 2156 |
|
|
</td><td style="text-align: left">
|
| 2157 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2158 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 2159 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2160 |
|
|
</td><td style="text-align: left">
|
| 2161 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2162 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2163 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2164 |
|
|
<code class="classname">Mapped</code>
|
| 2165 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 2166 |
|
|
<code class="classname">cc_hash_table</code>
|
| 2167 |
|
|
</td><td style="text-align: left">
|
| 2168 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2169 |
|
|
</td><td style="text-align: left">
|
| 2170 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2171 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2172 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2173 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2174 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2175 |
|
|
</td><td style="text-align: left">
|
| 2176 |
|
|
<code class="classname">Size_Policy</code>
|
| 2177 |
|
|
</td><td style="text-align: left">
|
| 2178 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2179 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2180 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2181 |
|
|
</td><td style="text-align: left">
|
| 2182 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2183 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2184 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_large.observations"/>
|
| 2185 |
|
|
Observations
|
| 2186 |
|
|
</h6></div></div></div><p>See Observations::Mapping-Semantics
|
| 2187 |
|
|
Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_mem_small"/>
|
| 2188 |
|
|
Text <code class="function">insert</code> with Small
|
| 2189 |
|
|
Secondary-to-Primary Key Ratios Memory Use
|
| 2190 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_small.info"/>
|
| 2191 |
|
|
Description
|
| 2192 |
|
|
</h6></div></div></div><p>This test inserts a number of pairs into a container. The
|
| 2193 |
|
|
first item of each pair is a string from an arbitrary text
|
| 2194 |
|
|
[wickland96thirty], and
|
| 2195 |
|
|
the second is a uniform integer. The container is a
|
| 2196 |
|
|
"multimap" - it considers the first member of each pair as a
|
| 2197 |
|
|
primary key, and the second member of each pair as a secondary
|
| 2198 |
|
|
key. There
|
| 2199 |
|
|
are 100 distinct primary keys, and the ratio of secondary keys
|
| 2200 |
|
|
to primary keys ranges to about 20.</p><p>The test measures the memory use as a function of the number
|
| 2201 |
|
|
of values inserted.</p><p>
|
| 2202 |
|
|
It uses the test file:
|
| 2203 |
|
|
<code class="filename">
|
| 2204 |
|
|
performance/ext/pb_ds/multimap_text_insert_mem_usage_small.cc
|
| 2205 |
|
|
</code>
|
| 2206 |
|
|
</p><p>The test checks the memory scalability of different
|
| 2207 |
|
|
"multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_small.results"/>
|
| 2208 |
|
|
Results
|
| 2209 |
|
|
</h6></div></div></div><p>The graphic below show the results for "multimaps" which
|
| 2210 |
|
|
use a tree-based container for primary keys.
|
| 2211 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_mem_small_s2p_tree.png" style="text-align: middle"/></div></div><p>
|
| 2212 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2213 |
|
|
instantiated with the types in the following table.
|
| 2214 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2215 |
|
|
n_mmap
|
| 2216 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2217 |
|
|
<code class="classname">std::multimap</code>
|
| 2218 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2219 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 2220 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2221 |
|
|
<code class="classname">tree</code>
|
| 2222 |
|
|
</td><td style="text-align: left">
|
| 2223 |
|
|
<code class="classname">Tag</code>
|
| 2224 |
|
|
</td><td style="text-align: left">
|
| 2225 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 2226 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2227 |
|
|
<code class="classname">Node_Update</code>
|
| 2228 |
|
|
</td><td style="text-align: left">
|
| 2229 |
|
|
<code class="classname">null_node_update</code>
|
| 2230 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2231 |
|
|
<code class="classname">Mapped</code>
|
| 2232 |
|
|
</td><td style="text-align: left">
|
| 2233 |
|
|
<code class="classname">list_update</code>
|
| 2234 |
|
|
</td><td style="text-align: left">
|
| 2235 |
|
|
<code class="classname">Update_Policy</code>
|
| 2236 |
|
|
</td><td style="text-align: left">
|
| 2237 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 2238 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2239 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 2240 |
|
|
</td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
|
| 2241 |
|
|
<code class="classname">tree</code>
|
| 2242 |
|
|
</td><td style="text-align: left">
|
| 2243 |
|
|
<code class="classname">Tag</code>
|
| 2244 |
|
|
</td><td style="text-align: left">
|
| 2245 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 2246 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2247 |
|
|
<code class="classname">Node_Update</code>
|
| 2248 |
|
|
</td><td style="text-align: left">
|
| 2249 |
|
|
<code class="classname">null_node_update</code>
|
| 2250 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2251 |
|
|
<code class="classname">Mapped</code>
|
| 2252 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 2253 |
|
|
<code class="classname">cc_hash_table</code>
|
| 2254 |
|
|
</td><td style="text-align: left">
|
| 2255 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2256 |
|
|
</td><td style="text-align: left">
|
| 2257 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2258 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2259 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2260 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2261 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2262 |
|
|
</td><td style="text-align: left">
|
| 2263 |
|
|
<code class="classname">Size_Policy</code>
|
| 2264 |
|
|
</td><td style="text-align: left">
|
| 2265 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2266 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2267 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2268 |
|
|
</td><td style="text-align: left">
|
| 2269 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2270 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2271 |
|
|
</td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
|
| 2272 |
|
|
use a hash-based container for primary keys.
|
| 2273 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
|
| 2274 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2275 |
|
|
instantiated with the types in the following table.
|
| 2276 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2277 |
|
|
n_hash_mmap
|
| 2278 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2279 |
|
|
<code class="classname">std::tr1::unordered_multimap</code>
|
| 2280 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2281 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 2282 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 2283 |
|
|
<code class="classname">
|
| 2284 |
|
|
cc_hash_table
|
| 2285 |
|
|
</code>
|
| 2286 |
|
|
</td><td style="text-align: left">
|
| 2287 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2288 |
|
|
</td><td style="text-align: left">
|
| 2289 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2290 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2291 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2292 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2293 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2294 |
|
|
</td><td style="text-align: left">
|
| 2295 |
|
|
<code class="classname">Size_Policy</code>
|
| 2296 |
|
|
</td><td style="text-align: left">
|
| 2297 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2298 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 2299 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2300 |
|
|
</td><td style="text-align: left">
|
| 2301 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2302 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2303 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2304 |
|
|
<code class="classname">Mapped</code>
|
| 2305 |
|
|
</td><td style="text-align: left">
|
| 2306 |
|
|
<code class="classname">list_update</code>
|
| 2307 |
|
|
</td><td style="text-align: left">
|
| 2308 |
|
|
<code class="classname">Update_Policy</code>
|
| 2309 |
|
|
</td><td style="text-align: left">
|
| 2310 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 2311 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2312 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 2313 |
|
|
</td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
|
| 2314 |
|
|
<code class="classname">
|
| 2315 |
|
|
cc_hash_table
|
| 2316 |
|
|
</code>
|
| 2317 |
|
|
</td><td style="text-align: left">
|
| 2318 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2319 |
|
|
</td><td style="text-align: left">
|
| 2320 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2321 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2322 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2323 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2324 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2325 |
|
|
</td><td style="text-align: left">
|
| 2326 |
|
|
<code class="classname">Size_Policy</code>
|
| 2327 |
|
|
</td><td style="text-align: left">
|
| 2328 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2329 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 2330 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2331 |
|
|
</td><td style="text-align: left">
|
| 2332 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2333 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2334 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2335 |
|
|
<code class="classname">Mapped</code>
|
| 2336 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 2337 |
|
|
<code class="classname">cc_hash_table</code>
|
| 2338 |
|
|
</td><td style="text-align: left">
|
| 2339 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2340 |
|
|
</td><td style="text-align: left">
|
| 2341 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2342 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2343 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2344 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2345 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2346 |
|
|
</td><td style="text-align: left">
|
| 2347 |
|
|
<code class="classname">Size_Policy</code>
|
| 2348 |
|
|
</td><td style="text-align: left">
|
| 2349 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2350 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2351 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2352 |
|
|
</td><td style="text-align: left">
|
| 2353 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2354 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2355 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_small.observations"/>
|
| 2356 |
|
|
Observations
|
| 2357 |
|
|
</h6></div></div></div><p>See Observations::Mapping-Semantics
|
| 2358 |
|
|
Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_mem_large"/>
|
| 2359 |
|
|
Text <code class="function">insert</code> with Small
|
| 2360 |
|
|
Secondary-to-Primary Key Ratios Memory Use
|
| 2361 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_large.info"/>
|
| 2362 |
|
|
Description
|
| 2363 |
|
|
</h6></div></div></div><p>This test inserts a number of pairs into a container. The
|
| 2364 |
|
|
first item of each pair is a string from an arbitrary text
|
| 2365 |
|
|
[wickland96thirty], and
|
| 2366 |
|
|
the second is a uniform integer. The container is a
|
| 2367 |
|
|
"multimap" - it considers the first member of each pair as a
|
| 2368 |
|
|
primary key, and the second member of each pair as a secondary
|
| 2369 |
|
|
key. There
|
| 2370 |
|
|
are 100 distinct primary keys, and the ratio of secondary keys
|
| 2371 |
|
|
to primary keys ranges to about 20.</p><p>The test measures the memory use as a function of the number
|
| 2372 |
|
|
of values inserted.</p><p>
|
| 2373 |
|
|
It uses the test file:
|
| 2374 |
|
|
<code class="filename">
|
| 2375 |
|
|
performance/ext/pb_ds/multimap_text_insert_mem_usage_large.cc
|
| 2376 |
|
|
</code>
|
| 2377 |
|
|
</p><p>The test checks the memory scalability of different
|
| 2378 |
|
|
"multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_large.results"/>
|
| 2379 |
|
|
Results
|
| 2380 |
|
|
</h6></div></div></div><p>The graphic below show the results for "multimaps" which
|
| 2381 |
|
|
use a tree-based container for primary keys.
|
| 2382 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_mem_large_s2p_tree.png" style="text-align: middle"/></div></div><p>
|
| 2383 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2384 |
|
|
instantiated with the types in the following table.
|
| 2385 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2386 |
|
|
n_mmap
|
| 2387 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2388 |
|
|
<code class="classname">std::multimap</code>
|
| 2389 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2390 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 2391 |
|
|
</td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2392 |
|
|
<code class="classname">tree</code>
|
| 2393 |
|
|
</td><td style="text-align: left">
|
| 2394 |
|
|
<code class="classname">Tag</code>
|
| 2395 |
|
|
</td><td style="text-align: left">
|
| 2396 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 2397 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2398 |
|
|
<code class="classname">Node_Update</code>
|
| 2399 |
|
|
</td><td style="text-align: left">
|
| 2400 |
|
|
<code class="classname">null_node_update</code>
|
| 2401 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2402 |
|
|
<code class="classname">Mapped</code>
|
| 2403 |
|
|
</td><td style="text-align: left">
|
| 2404 |
|
|
<code class="classname">list_update</code>
|
| 2405 |
|
|
</td><td style="text-align: left">
|
| 2406 |
|
|
<code class="classname">Update_Policy</code>
|
| 2407 |
|
|
</td><td style="text-align: left">
|
| 2408 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 2409 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2410 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 2411 |
|
|
</td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
|
| 2412 |
|
|
<code class="classname">tree</code>
|
| 2413 |
|
|
</td><td style="text-align: left">
|
| 2414 |
|
|
<code class="classname">Tag</code>
|
| 2415 |
|
|
</td><td style="text-align: left">
|
| 2416 |
|
|
<code class="classname">rb_tree_tag</code>
|
| 2417 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2418 |
|
|
<code class="classname">Node_Update</code>
|
| 2419 |
|
|
</td><td style="text-align: left">
|
| 2420 |
|
|
<code class="classname">null_node_update</code>
|
| 2421 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2422 |
|
|
<code class="classname">Mapped</code>
|
| 2423 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 2424 |
|
|
<code class="classname">cc_hash_table</code>
|
| 2425 |
|
|
</td><td style="text-align: left">
|
| 2426 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2427 |
|
|
</td><td style="text-align: left">
|
| 2428 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2429 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2430 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2431 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2432 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2433 |
|
|
</td><td style="text-align: left">
|
| 2434 |
|
|
<code class="classname">Size_Policy</code>
|
| 2435 |
|
|
</td><td style="text-align: left">
|
| 2436 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2437 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2438 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2439 |
|
|
</td><td style="text-align: left">
|
| 2440 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2441 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2442 |
|
|
</td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
|
| 2443 |
|
|
use a hash-based container for primary keys.
|
| 2444 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
|
| 2445 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2446 |
|
|
instantiated with the types in the following table.
|
| 2447 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2448 |
|
|
n_hash_mmap
|
| 2449 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2450 |
|
|
<code class="classname">std::tr1::unordered_multimap</code>
|
| 2451 |
|
|
</td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2452 |
|
|
rb_tree_mmap_lu_mtf_set
|
| 2453 |
|
|
</td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
|
| 2454 |
|
|
<code class="classname">
|
| 2455 |
|
|
cc_hash_table
|
| 2456 |
|
|
</code>
|
| 2457 |
|
|
</td><td style="text-align: left">
|
| 2458 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2459 |
|
|
</td><td style="text-align: left">
|
| 2460 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2461 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2462 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2463 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2464 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2465 |
|
|
</td><td style="text-align: left">
|
| 2466 |
|
|
<code class="classname">Size_Policy</code>
|
| 2467 |
|
|
</td><td style="text-align: left">
|
| 2468 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2469 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 2470 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2471 |
|
|
</td><td style="text-align: left">
|
| 2472 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2473 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2474 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
|
| 2475 |
|
|
<code class="classname">Mapped</code>
|
| 2476 |
|
|
</td><td style="text-align: left">
|
| 2477 |
|
|
<code class="classname">list_update</code>
|
| 2478 |
|
|
</td><td style="text-align: left">
|
| 2479 |
|
|
<code class="classname">Update_Policy</code>
|
| 2480 |
|
|
</td><td style="text-align: left">
|
| 2481 |
|
|
<code class="classname">lu_move_to_front_policy</code>
|
| 2482 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
|
| 2483 |
|
|
rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
|
| 2484 |
|
|
</td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
|
| 2485 |
|
|
<code class="classname">
|
| 2486 |
|
|
cc_hash_table
|
| 2487 |
|
|
</code>
|
| 2488 |
|
|
</td><td style="text-align: left">
|
| 2489 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2490 |
|
|
</td><td style="text-align: left">
|
| 2491 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2492 |
|
|
</td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2493 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2494 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2495 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2496 |
|
|
</td><td style="text-align: left">
|
| 2497 |
|
|
<code class="classname">Size_Policy</code>
|
| 2498 |
|
|
</td><td style="text-align: left">
|
| 2499 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2500 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
|
| 2501 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2502 |
|
|
</td><td style="text-align: left">
|
| 2503 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2504 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2505 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
|
| 2506 |
|
|
<code class="classname">Mapped</code>
|
| 2507 |
|
|
</td><td rowspan="3" style="text-align: left" valign="top">
|
| 2508 |
|
|
<code class="classname">cc_hash_table</code>
|
| 2509 |
|
|
</td><td style="text-align: left">
|
| 2510 |
|
|
<code class="classname">Comb_Hash_Fn</code>
|
| 2511 |
|
|
</td><td style="text-align: left">
|
| 2512 |
|
|
<code class="classname">direct_mask_range_hashing</code>
|
| 2513 |
|
|
</td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
|
| 2514 |
|
|
<code class="classname">Resize_Policy</code>
|
| 2515 |
|
|
</td><td rowspan="2" style="text-align: left" valign="top">
|
| 2516 |
|
|
<code class="classname">hash_standard_resize_policy</code>
|
| 2517 |
|
|
</td><td style="text-align: left">
|
| 2518 |
|
|
<code class="classname">Size_Policy</code>
|
| 2519 |
|
|
</td><td style="text-align: left">
|
| 2520 |
|
|
<code class="classname">hash_exponential_size_policy</code>
|
| 2521 |
|
|
</td></tr><tr><td style="text-align: left" valign="top">
|
| 2522 |
|
|
<code class="classname">Trigger_Policy</code>
|
| 2523 |
|
|
</td><td style="text-align: left">
|
| 2524 |
|
|
<code class="classname">hash_load_check_resize_trigger</code> with
|
| 2525 |
|
|
α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
|
| 2526 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_large.observations"/>
|
| 2527 |
|
|
Observations
|
| 2528 |
|
|
</h6></div></div></div><p>See Observations::Mapping-Semantics
|
| 2529 |
|
|
Considerations.</p></div></div></div><div class="section" title="Priority Queue"><div class="titlepage"><div><div><h4 class="title"><a id="performance.priority_queue"/>Priority Queue</h4></div></div></div><div class="section" title="Text push"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_push"/>
|
| 2530 |
|
|
Text <code class="function">push</code>
|
| 2531 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push.info"/>
|
| 2532 |
|
|
Description
|
| 2533 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 2534 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 2535 |
|
|
a container using <code class="function">push</code>. It measures the average time
|
| 2536 |
|
|
for <code class="function">push</code> as a function of the number of values
|
| 2537 |
|
|
pushed.</p><p>
|
| 2538 |
|
|
It uses the test file:
|
| 2539 |
|
|
<code class="filename">
|
| 2540 |
|
|
performance/ext/pb_ds/priority_queue_text_push_timing.cc
|
| 2541 |
|
|
</code>
|
| 2542 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 2543 |
|
|
structures.
|
| 2544 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push.results"/>
|
| 2545 |
|
|
Results
|
| 2546 |
|
|
</h6></div></div></div><p>The two graphics below show the results for the native
|
| 2547 |
|
|
priority_queues and this library's priority_queues.
|
| 2548 |
|
|
</p><p>The graphic immediately below shows the results for the
|
| 2549 |
|
|
native priority_queue type instantiated with different underlying
|
| 2550 |
|
|
container types versus several different versions of library's
|
| 2551 |
|
|
priority_queues.
|
| 2552 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_push.png" style="text-align: middle"/></div></div><p>
|
| 2553 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2554 |
|
|
instantiated with the types in the following table.
|
| 2555 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2556 |
|
|
n_pq_vector
|
| 2557 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2558 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2559 |
|
|
</td><td style="text-align: left">
|
| 2560 |
|
|
<code class="classname">Sequence</code>
|
| 2561 |
|
|
</td><td style="text-align: left">
|
| 2562 |
|
|
<code class="classname">std::vector</code>
|
| 2563 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2564 |
|
|
n_pq_deque
|
| 2565 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2566 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2567 |
|
|
</td><td style="text-align: left">
|
| 2568 |
|
|
<code class="classname">Sequence</code>
|
| 2569 |
|
|
</td><td style="text-align: left">
|
| 2570 |
|
|
<code class="classname">std::deque</code>
|
| 2571 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2572 |
|
|
binary_heap
|
| 2573 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2574 |
|
|
<code class="classname">priority_queue</code>
|
| 2575 |
|
|
</td><td style="text-align: left">
|
| 2576 |
|
|
<code class="classname">Tag</code>
|
| 2577 |
|
|
</td><td style="text-align: left">
|
| 2578 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 2579 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2580 |
|
|
binomial_heap
|
| 2581 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2582 |
|
|
<code class="classname">priority_queue</code>
|
| 2583 |
|
|
</td><td style="text-align: left">
|
| 2584 |
|
|
<code class="classname">Tag</code>
|
| 2585 |
|
|
</td><td style="text-align: left">
|
| 2586 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 2587 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2588 |
|
|
rc_binomial_heap
|
| 2589 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2590 |
|
|
<code class="classname">priority_queue</code>
|
| 2591 |
|
|
</td><td style="text-align: left">
|
| 2592 |
|
|
<code class="classname">Tag</code>
|
| 2593 |
|
|
</td><td style="text-align: left">
|
| 2594 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 2595 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2596 |
|
|
thin_heap
|
| 2597 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2598 |
|
|
<code class="classname">priority_queue</code>
|
| 2599 |
|
|
</td><td style="text-align: left">
|
| 2600 |
|
|
<code class="classname">Tag</code>
|
| 2601 |
|
|
</td><td style="text-align: left">
|
| 2602 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 2603 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2604 |
|
|
pairing_heap
|
| 2605 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2606 |
|
|
<code class="classname">priority_queue</code>
|
| 2607 |
|
|
</td><td style="text-align: left">
|
| 2608 |
|
|
<code class="classname">Tag</code>
|
| 2609 |
|
|
</td><td style="text-align: left">
|
| 2610 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 2611 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the binary-heap
|
| 2612 |
|
|
based native priority queues and this library's pairing-heap
|
| 2613 |
|
|
priority_queue data structures.
|
| 2614 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_push.png" style="text-align: middle"/></div></div><p>
|
| 2615 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2616 |
|
|
instantiated with the types in the following table.
|
| 2617 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2618 |
|
|
n_pq_vector
|
| 2619 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2620 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2621 |
|
|
</td><td style="text-align: left">
|
| 2622 |
|
|
<code class="classname">Sequence</code>
|
| 2623 |
|
|
</td><td style="text-align: left">
|
| 2624 |
|
|
<code class="classname">std::vector</code>
|
| 2625 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2626 |
|
|
n_pq_deque
|
| 2627 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2628 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2629 |
|
|
</td><td style="text-align: left">
|
| 2630 |
|
|
<code class="classname">Sequence</code>
|
| 2631 |
|
|
</td><td style="text-align: left">
|
| 2632 |
|
|
<code class="classname">std::deque</code>
|
| 2633 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2634 |
|
|
thin_heap
|
| 2635 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2636 |
|
|
<code class="classname">priority_queue</code>
|
| 2637 |
|
|
</td><td style="text-align: left">
|
| 2638 |
|
|
<code class="classname">Tag</code>
|
| 2639 |
|
|
</td><td style="text-align: left">
|
| 2640 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 2641 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2642 |
|
|
pairing_heap
|
| 2643 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2644 |
|
|
<code class="classname">priority_queue</code>
|
| 2645 |
|
|
</td><td style="text-align: left">
|
| 2646 |
|
|
<code class="classname">Tag</code>
|
| 2647 |
|
|
</td><td style="text-align: left">
|
| 2648 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 2649 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push.observations"/>
|
| 2650 |
|
|
Observations
|
| 2651 |
|
|
</h6></div></div></div><p>Pairing heaps (<code class="classname">priority_queue</code> with
|
| 2652 |
|
|
<code class="classname">Tag</code> = <code class="classname">pairing_heap_tag</code>)
|
| 2653 |
|
|
are the most suited for sequences of <code class="function">push</code> and
|
| 2654 |
|
|
<code class="function">pop</code> operations of non-primitive types (e.g.
|
| 2655 |
|
|
<code class="classname">std::string</code>s). (See Priority Queue
|
| 2656 |
|
|
Text <code class="function">push</code> and <code class="function">pop</code> Timing Test.) They are
|
| 2657 |
|
|
less constrained than binomial heaps, e.g., and since
|
| 2658 |
|
|
they are node-based, they outperform binary heaps. (See
|
| 2659 |
|
|
Priority
|
| 2660 |
|
|
Queue Random Integer <code class="function">push</code> Timing Test for the case
|
| 2661 |
|
|
of primitive types.)</p><p>The standard's priority queues do not seem to perform well in
|
| 2662 |
|
|
this case: the <code class="classname">std::vector</code> implementation needs to
|
| 2663 |
|
|
perform a logarithmic sequence of string operations for each
|
| 2664 |
|
|
operation, and the deque implementation is possibly hampered by
|
| 2665 |
|
|
its need to manipulate a relatively-complex type (deques
|
| 2666 |
|
|
support a O(1) <code class="function">push_front</code>, even though it is
|
| 2667 |
|
|
not used by <code class="classname">std::priority_queue</code>.)</p></div></div><div class="section" title="Text push and pop"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_push_pop"/>
|
| 2668 |
|
|
Text <code class="function">push</code> and <code class="function">pop</code>
|
| 2669 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push_pop.info"/>
|
| 2670 |
|
|
Description
|
| 2671 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 2672 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 2673 |
|
|
a container using <code class="classname">push</code> , then removes them using
|
| 2674 |
|
|
<code class="classname">pop</code> . It measures the average time for <code class="classname">push</code>
|
| 2675 |
|
|
as a function of the number of values.</p><p>
|
| 2676 |
|
|
It uses the test file:
|
| 2677 |
|
|
<code class="filename">
|
| 2678 |
|
|
performance/ext/pb_ds/priority_queue_text_push_pop_timing.cc
|
| 2679 |
|
|
</code>
|
| 2680 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 2681 |
|
|
structures.
|
| 2682 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push_pop.results"/>
|
| 2683 |
|
|
Results
|
| 2684 |
|
|
</h6></div></div></div><p>The two graphics below show the results for the native
|
| 2685 |
|
|
priority_queues and this library's priority_queues.
|
| 2686 |
|
|
</p><p>The graphic immediately below shows the results for the
|
| 2687 |
|
|
native priority_queue type instantiated with different underlying
|
| 2688 |
|
|
container types versus several different versions of library's
|
| 2689 |
|
|
priority_queues.
|
| 2690 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_push_pop.png" style="text-align: middle"/></div></div><p>
|
| 2691 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2692 |
|
|
instantiated with the types in the following table.
|
| 2693 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2694 |
|
|
n_pq_vector
|
| 2695 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2696 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2697 |
|
|
</td><td style="text-align: left">
|
| 2698 |
|
|
<code class="classname">Sequence</code>
|
| 2699 |
|
|
</td><td style="text-align: left">
|
| 2700 |
|
|
<code class="classname">std::vector</code>
|
| 2701 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2702 |
|
|
n_pq_deque
|
| 2703 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2704 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2705 |
|
|
</td><td style="text-align: left">
|
| 2706 |
|
|
<code class="classname">Sequence</code>
|
| 2707 |
|
|
</td><td style="text-align: left">
|
| 2708 |
|
|
<code class="classname">std::deque</code>
|
| 2709 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2710 |
|
|
binary_heap
|
| 2711 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2712 |
|
|
<code class="classname">priority_queue</code>
|
| 2713 |
|
|
</td><td style="text-align: left">
|
| 2714 |
|
|
<code class="classname">Tag</code>
|
| 2715 |
|
|
</td><td style="text-align: left">
|
| 2716 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 2717 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2718 |
|
|
binomial_heap
|
| 2719 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2720 |
|
|
<code class="classname">priority_queue</code>
|
| 2721 |
|
|
</td><td style="text-align: left">
|
| 2722 |
|
|
<code class="classname">Tag</code>
|
| 2723 |
|
|
</td><td style="text-align: left">
|
| 2724 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 2725 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2726 |
|
|
rc_binomial_heap
|
| 2727 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2728 |
|
|
<code class="classname">priority_queue</code>
|
| 2729 |
|
|
</td><td style="text-align: left">
|
| 2730 |
|
|
<code class="classname">Tag</code>
|
| 2731 |
|
|
</td><td style="text-align: left">
|
| 2732 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 2733 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2734 |
|
|
thin_heap
|
| 2735 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2736 |
|
|
<code class="classname">priority_queue</code>
|
| 2737 |
|
|
</td><td style="text-align: left">
|
| 2738 |
|
|
<code class="classname">Tag</code>
|
| 2739 |
|
|
</td><td style="text-align: left">
|
| 2740 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 2741 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2742 |
|
|
pairing_heap
|
| 2743 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2744 |
|
|
<code class="classname">priority_queue</code>
|
| 2745 |
|
|
</td><td style="text-align: left">
|
| 2746 |
|
|
<code class="classname">Tag</code>
|
| 2747 |
|
|
</td><td style="text-align: left">
|
| 2748 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 2749 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the native priority
|
| 2750 |
|
|
queues and this library's pairing-heap priority_queue data
|
| 2751 |
|
|
structures.
|
| 2752 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_push_pop.png" style="text-align: middle"/></div></div><p>
|
| 2753 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2754 |
|
|
instantiated with the types in the following table.
|
| 2755 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2756 |
|
|
n_pq_vector
|
| 2757 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2758 |
|
|
<code class="classname">std::priority_queue</code> adapting <code class="classname">std::vector</code>
|
| 2759 |
|
|
</td><td style="text-align: left">
|
| 2760 |
|
|
<code class="classname">Sequence</code>
|
| 2761 |
|
|
</td><td style="text-align: left">
|
| 2762 |
|
|
<code class="classname">std::vector</code>
|
| 2763 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2764 |
|
|
n_pq_deque
|
| 2765 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2766 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2767 |
|
|
</td><td style="text-align: left">
|
| 2768 |
|
|
<code class="classname">Sequence</code>
|
| 2769 |
|
|
</td><td style="text-align: left">
|
| 2770 |
|
|
<code class="classname">std::deque</code>
|
| 2771 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2772 |
|
|
pairing_heap
|
| 2773 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2774 |
|
|
<code class="classname">priority_queue</code>
|
| 2775 |
|
|
</td><td style="text-align: left">
|
| 2776 |
|
|
<code class="classname">Tag</code>
|
| 2777 |
|
|
</td><td style="text-align: left">
|
| 2778 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 2779 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push_pop.observations"/>
|
| 2780 |
|
|
Observations
|
| 2781 |
|
|
</h6></div></div></div><p>These results are very similar to Priority Queue Text
|
| 2782 |
|
|
<code class="function">push</code> Timing Test. As stated there, pairing heaps
|
| 2783 |
|
|
(<code class="classname">priority_queue</code> with
|
| 2784 |
|
|
<code class="classname">Tag</code>
|
| 2785 |
|
|
= <code class="classname">pairing_heap_tag</code>) are most suited
|
| 2786 |
|
|
for <code class="function">push</code> and <code class="function">pop</code>
|
| 2787 |
|
|
sequences of non-primitive types such as strings. Observing these
|
| 2788 |
|
|
two tests, one can note that a pairing heap outperforms the others
|
| 2789 |
|
|
in terms of <code class="function">push</code> operations, but equals
|
| 2790 |
|
|
binary heaps (<code class="classname">priority_queue</code> with
|
| 2791 |
|
|
<code class="classname">Tag</code>
|
| 2792 |
|
|
= <code class="classname">binary_heap_tag</code>) if the number
|
| 2793 |
|
|
of <code class="function">push</code> and <code class="function">pop</code>
|
| 2794 |
|
|
operations is equal. As the number of <code class="function">pop</code>
|
| 2795 |
|
|
operations is at most equal to the number
|
| 2796 |
|
|
of <code class="function">push</code> operations, pairing heaps are better
|
| 2797 |
|
|
in this case. See Priority Queue Random
|
| 2798 |
|
|
Integer <code class="function">push</code> and <code class="function">pop</code>
|
| 2799 |
|
|
Timing Test for a case which is different.</p></div></div><div class="section" title="Integer push"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.int_push"/>
|
| 2800 |
|
|
Integer <code class="function">push</code>
|
| 2801 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push.info"/>
|
| 2802 |
|
|
Description
|
| 2803 |
|
|
</h6></div></div></div><p>This test inserts a number of values with integer keys
|
| 2804 |
|
|
into a container using <code class="function">push</code>. It
|
| 2805 |
|
|
measures the average time for <code class="function">push</code> as a
|
| 2806 |
|
|
function of the number of values.</p><p>
|
| 2807 |
|
|
It uses the test file:
|
| 2808 |
|
|
<code class="filename">
|
| 2809 |
|
|
performance/ext/pb_ds/priority_queue_random_int_push_timing.cc
|
| 2810 |
|
|
</code>
|
| 2811 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 2812 |
|
|
structures.
|
| 2813 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push.results"/>
|
| 2814 |
|
|
Results
|
| 2815 |
|
|
</h6></div></div></div><p>The two graphics below show the results for the native
|
| 2816 |
|
|
priority_queues and this library's priority_queues.
|
| 2817 |
|
|
</p><p>The graphic immediately below shows the results for the
|
| 2818 |
|
|
native priority_queue type instantiated with different underlying
|
| 2819 |
|
|
container types versus several different versions of library's
|
| 2820 |
|
|
priority_queues.
|
| 2821 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_int_push.png" style="text-align: middle"/></div></div><p>
|
| 2822 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2823 |
|
|
instantiated with the types in the following table.
|
| 2824 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2825 |
|
|
n_pq_vector
|
| 2826 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2827 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2828 |
|
|
</td><td style="text-align: left">
|
| 2829 |
|
|
<code class="classname">Sequence</code>
|
| 2830 |
|
|
</td><td style="text-align: left">
|
| 2831 |
|
|
<code class="classname">std::vector</code>
|
| 2832 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2833 |
|
|
n_pq_deque
|
| 2834 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2835 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2836 |
|
|
</td><td style="text-align: left">
|
| 2837 |
|
|
<code class="classname">Sequence</code>
|
| 2838 |
|
|
</td><td style="text-align: left">
|
| 2839 |
|
|
<code class="classname">std::deque</code>
|
| 2840 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2841 |
|
|
binary_heap
|
| 2842 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2843 |
|
|
<code class="classname">priority_queue</code>
|
| 2844 |
|
|
</td><td style="text-align: left">
|
| 2845 |
|
|
<code class="classname">Tag</code>
|
| 2846 |
|
|
</td><td style="text-align: left">
|
| 2847 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 2848 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2849 |
|
|
binomial_heap
|
| 2850 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2851 |
|
|
<code class="classname">priority_queue</code>
|
| 2852 |
|
|
</td><td style="text-align: left">
|
| 2853 |
|
|
<code class="classname">Tag</code>
|
| 2854 |
|
|
</td><td style="text-align: left">
|
| 2855 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 2856 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2857 |
|
|
rc_binomial_heap
|
| 2858 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2859 |
|
|
<code class="classname">priority_queue</code>
|
| 2860 |
|
|
</td><td style="text-align: left">
|
| 2861 |
|
|
<code class="classname">Tag</code>
|
| 2862 |
|
|
</td><td style="text-align: left">
|
| 2863 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 2864 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2865 |
|
|
thin_heap
|
| 2866 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2867 |
|
|
<code class="classname">priority_queue</code>
|
| 2868 |
|
|
</td><td style="text-align: left">
|
| 2869 |
|
|
<code class="classname">Tag</code>
|
| 2870 |
|
|
</td><td style="text-align: left">
|
| 2871 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 2872 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2873 |
|
|
pairing_heap
|
| 2874 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2875 |
|
|
<code class="classname">priority_queue</code>
|
| 2876 |
|
|
</td><td style="text-align: left">
|
| 2877 |
|
|
<code class="classname">Tag</code>
|
| 2878 |
|
|
</td><td style="text-align: left">
|
| 2879 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 2880 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the binary-heap
|
| 2881 |
|
|
based native priority queues and this library's
|
| 2882 |
|
|
priority_queue data structures.
|
| 2883 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_binary_priority_queue_int_push.png" style="text-align: middle"/></div></div><p>
|
| 2884 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2885 |
|
|
instantiated with the types in the following table.
|
| 2886 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2887 |
|
|
n_pq_vector
|
| 2888 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2889 |
|
|
<code class="classname">std::priority_queue</code> adapting <code class="classname">std::vector</code>
|
| 2890 |
|
|
</td><td style="text-align: left">
|
| 2891 |
|
|
<code class="classname">Sequence</code>
|
| 2892 |
|
|
</td><td style="text-align: left">
|
| 2893 |
|
|
<code class="classname">std::vector</code>
|
| 2894 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2895 |
|
|
n_pq_deque
|
| 2896 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2897 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2898 |
|
|
</td><td style="text-align: left">
|
| 2899 |
|
|
<code class="classname">Sequence</code>
|
| 2900 |
|
|
</td><td style="text-align: left">
|
| 2901 |
|
|
<code class="classname">std::deque</code>
|
| 2902 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2903 |
|
|
binary_heap
|
| 2904 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2905 |
|
|
<code class="classname">priority_queue</code>
|
| 2906 |
|
|
</td><td style="text-align: left">
|
| 2907 |
|
|
<code class="classname">Tag</code>
|
| 2908 |
|
|
</td><td style="text-align: left">
|
| 2909 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 2910 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push.observations"/>
|
| 2911 |
|
|
Observations
|
| 2912 |
|
|
</h6></div></div></div><p>Binary heaps are the most suited for sequences of
|
| 2913 |
|
|
<code class="function">push</code> and <code class="function">pop</code> operations of primitive types
|
| 2914 |
|
|
(e.g. <span class="type">int</span>s). They are less constrained
|
| 2915 |
|
|
than any other type, and since it is very efficient to store
|
| 2916 |
|
|
such types in arrays, they outperform even pairing heaps. (See
|
| 2917 |
|
|
Priority
|
| 2918 |
|
|
Queue Text <code class="function">push</code> Timing Test for the case of
|
| 2919 |
|
|
non-primitive types.)</p></div></div><div class="section" title="Integer push"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.int_push_pop"/>
|
| 2920 |
|
|
Integer <code class="function">push</code>
|
| 2921 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push_pop.info"/>
|
| 2922 |
|
|
Description
|
| 2923 |
|
|
</h6></div></div></div><p>This test inserts a number of values with integer keys
|
| 2924 |
|
|
into a container using <code class="function">push</code> , then removes them
|
| 2925 |
|
|
using <code class="function">pop</code> . It measures the average time for
|
| 2926 |
|
|
<code class="function">push</code> and <code class="function">pop</code> as a function
|
| 2927 |
|
|
of the number of values.</p><p>
|
| 2928 |
|
|
It uses the test file:
|
| 2929 |
|
|
<code class="filename">
|
| 2930 |
|
|
performance/ext/pb_ds/priority_queue_random_int_push_pop_timing.cc
|
| 2931 |
|
|
</code>
|
| 2932 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 2933 |
|
|
structures.
|
| 2934 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push_pop.results"/>
|
| 2935 |
|
|
Results
|
| 2936 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 2937 |
|
|
native priority_queue type instantiated with different underlying
|
| 2938 |
|
|
container types versus several different versions of library's
|
| 2939 |
|
|
priority_queues.
|
| 2940 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_int_push_pop.png" style="text-align: middle"/></div></div><p>
|
| 2941 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 2942 |
|
|
instantiated with the types in the following table.
|
| 2943 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2944 |
|
|
n_pq_vector
|
| 2945 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2946 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2947 |
|
|
</td><td style="text-align: left">
|
| 2948 |
|
|
<code class="classname">Sequence</code>
|
| 2949 |
|
|
</td><td style="text-align: left">
|
| 2950 |
|
|
<code class="classname">std::vector</code>
|
| 2951 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2952 |
|
|
n_pq_deque
|
| 2953 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2954 |
|
|
<code class="classname">std::priority_queue</code>
|
| 2955 |
|
|
</td><td style="text-align: left">
|
| 2956 |
|
|
<code class="classname">Sequence</code>
|
| 2957 |
|
|
</td><td style="text-align: left">
|
| 2958 |
|
|
<code class="classname">std::deque</code>
|
| 2959 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2960 |
|
|
binary_heap
|
| 2961 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2962 |
|
|
<code class="classname">priority_queue</code>
|
| 2963 |
|
|
</td><td style="text-align: left">
|
| 2964 |
|
|
<code class="classname">Tag</code>
|
| 2965 |
|
|
</td><td style="text-align: left">
|
| 2966 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 2967 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2968 |
|
|
binomial_heap
|
| 2969 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2970 |
|
|
<code class="classname">priority_queue</code>
|
| 2971 |
|
|
</td><td style="text-align: left">
|
| 2972 |
|
|
<code class="classname">Tag</code>
|
| 2973 |
|
|
</td><td style="text-align: left">
|
| 2974 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 2975 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2976 |
|
|
rc_binomial_heap
|
| 2977 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2978 |
|
|
<code class="classname">priority_queue</code>
|
| 2979 |
|
|
</td><td style="text-align: left">
|
| 2980 |
|
|
<code class="classname">Tag</code>
|
| 2981 |
|
|
</td><td style="text-align: left">
|
| 2982 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 2983 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2984 |
|
|
thin_heap
|
| 2985 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2986 |
|
|
<code class="classname">priority_queue</code>
|
| 2987 |
|
|
</td><td style="text-align: left">
|
| 2988 |
|
|
<code class="classname">Tag</code>
|
| 2989 |
|
|
</td><td style="text-align: left">
|
| 2990 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 2991 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 2992 |
|
|
pairing_heap
|
| 2993 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 2994 |
|
|
<code class="classname">priority_queue</code>
|
| 2995 |
|
|
</td><td style="text-align: left">
|
| 2996 |
|
|
<code class="classname">Tag</code>
|
| 2997 |
|
|
</td><td style="text-align: left">
|
| 2998 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 2999 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push_pop.observations"/>
|
| 3000 |
|
|
Observations
|
| 3001 |
|
|
</h6></div></div></div><p>Binary heaps are the most suited for sequences of
|
| 3002 |
|
|
<code class="function">push</code> and <code class="function">pop</code> operations of primitive types
|
| 3003 |
|
|
(e.g. <span class="type">int</span>s). This is explained in
|
| 3004 |
|
|
Priority
|
| 3005 |
|
|
Queue Random Int <code class="function">push</code> Timing Test. (See Priority Queue
|
| 3006 |
|
|
Text <code class="function">push</code> Timing Test for the case of primitive
|
| 3007 |
|
|
types.)</p><p>At first glance it seems that the standard's vector-based
|
| 3008 |
|
|
priority queue is approximately on par with this
|
| 3009 |
|
|
library's corresponding priority queue. There are two
|
| 3010 |
|
|
differences however:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>The standard's priority queue does not downsize the underlying
|
| 3011 |
|
|
vector (or deque) as the priority queue becomes smaller
|
| 3012 |
|
|
(see Priority Queue
|
| 3013 |
|
|
Text <code class="function">pop</code> Memory Use Test). It is therefore
|
| 3014 |
|
|
gaining some speed at the expense of space.</p></li><li class="listitem"><p>From Priority Queue Random
|
| 3015 |
|
|
Integer <code class="function">push</code> and <code class="function">pop</code>
|
| 3016 |
|
|
Timing Test, it seems that the standard's priority queue is
|
| 3017 |
|
|
slower in terms of <code class="function">push</code> operations. Since
|
| 3018 |
|
|
the number of
|
| 3019 |
|
|
<code class="function">pop</code> operations is at most that of <code class="function">push</code>
|
| 3020 |
|
|
operations, the test here is the "best" for the standard's
|
| 3021 |
|
|
priority queue.</p></li></ol></div></div></div><div class="section" title="Text pop Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_pop"/>
|
| 3022 |
|
|
Text <code class="function">pop</code> Memory Use
|
| 3023 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_pop.info"/>
|
| 3024 |
|
|
Description
|
| 3025 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 3026 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 3027 |
|
|
a container, then pops them until only one is left in the
|
| 3028 |
|
|
container. It measures the memory use as a function of the
|
| 3029 |
|
|
number of values pushed to the container.</p><p>
|
| 3030 |
|
|
It uses the test file:
|
| 3031 |
|
|
<code class="filename">
|
| 3032 |
|
|
performance/ext/pb_ds/priority_queue_text_pop_mem_usage.cc
|
| 3033 |
|
|
</code>
|
| 3034 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 3035 |
|
|
structures.
|
| 3036 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_pop.results"/>
|
| 3037 |
|
|
Results
|
| 3038 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 3039 |
|
|
native priority_queue type instantiated with different underlying
|
| 3040 |
|
|
container types versus several different versions of library's
|
| 3041 |
|
|
priority_queues.
|
| 3042 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_pop_mem.png" style="text-align: middle"/></div></div><p>
|
| 3043 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 3044 |
|
|
instantiated with the types in the following table.
|
| 3045 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3046 |
|
|
n_pq_vector
|
| 3047 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3048 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3049 |
|
|
</td><td style="text-align: left">
|
| 3050 |
|
|
<code class="classname">Sequence</code>
|
| 3051 |
|
|
</td><td style="text-align: left">
|
| 3052 |
|
|
<code class="classname">std::vector</code>
|
| 3053 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3054 |
|
|
n_pq_deque
|
| 3055 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3056 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3057 |
|
|
</td><td style="text-align: left">
|
| 3058 |
|
|
<code class="classname">Sequence</code>
|
| 3059 |
|
|
</td><td style="text-align: left">
|
| 3060 |
|
|
<code class="classname">std::deque</code>
|
| 3061 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3062 |
|
|
binary_heap
|
| 3063 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3064 |
|
|
<code class="classname">priority_queue</code>
|
| 3065 |
|
|
</td><td style="text-align: left">
|
| 3066 |
|
|
<code class="classname">Tag</code>
|
| 3067 |
|
|
</td><td style="text-align: left">
|
| 3068 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 3069 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3070 |
|
|
binomial_heap
|
| 3071 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3072 |
|
|
<code class="classname">priority_queue</code>
|
| 3073 |
|
|
</td><td style="text-align: left">
|
| 3074 |
|
|
<code class="classname">Tag</code>
|
| 3075 |
|
|
</td><td style="text-align: left">
|
| 3076 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 3077 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3078 |
|
|
rc_binomial_heap
|
| 3079 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3080 |
|
|
<code class="classname">priority_queue</code>
|
| 3081 |
|
|
</td><td style="text-align: left">
|
| 3082 |
|
|
<code class="classname">Tag</code>
|
| 3083 |
|
|
</td><td style="text-align: left">
|
| 3084 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 3085 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3086 |
|
|
thin_heap
|
| 3087 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3088 |
|
|
<code class="classname">priority_queue</code>
|
| 3089 |
|
|
</td><td style="text-align: left">
|
| 3090 |
|
|
<code class="classname">Tag</code>
|
| 3091 |
|
|
</td><td style="text-align: left">
|
| 3092 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 3093 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3094 |
|
|
pairing_heap
|
| 3095 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3096 |
|
|
<code class="classname">priority_queue</code>
|
| 3097 |
|
|
</td><td style="text-align: left">
|
| 3098 |
|
|
<code class="classname">Tag</code>
|
| 3099 |
|
|
</td><td style="text-align: left">
|
| 3100 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 3101 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_pop.observations"/>
|
| 3102 |
|
|
Observations
|
| 3103 |
|
|
</h6></div></div></div><p>The priority queue implementations (excluding the standard's) use
|
| 3104 |
|
|
memory proportionally to the number of values they hold:
|
| 3105 |
|
|
node-based implementations (e.g., a pairing heap) do so
|
| 3106 |
|
|
naturally; this library's binary heap de-allocates memory when
|
| 3107 |
|
|
a certain lower threshold is exceeded.</p><p>Note from Priority Queue Text <code class="function">push</code>
|
| 3108 |
|
|
and <code class="function">pop</code> Timing Test and Priority Queue
|
| 3109 |
|
|
Random Integer <code class="function">push</code>
|
| 3110 |
|
|
and <code class="function">pop</code> Timing Test that this does not
|
| 3111 |
|
|
impede performance compared to the standard's priority
|
| 3112 |
|
|
queues.</p><p>See Hash-Based Erase
|
| 3113 |
|
|
Memory Use Test for a similar phenomenon regarding priority
|
| 3114 |
|
|
queues.</p></div></div><div class="section" title="Text join"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_join"/>
|
| 3115 |
|
|
Text <code class="function">join</code>
|
| 3116 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_join.info"/>
|
| 3117 |
|
|
Description
|
| 3118 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 3119 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 3120 |
|
|
two containers, then merges the containers. It uses
|
| 3121 |
|
|
<code class="function">join</code> for this library's priority queues; for
|
| 3122 |
|
|
the standard's priority queues, it successively pops values from
|
| 3123 |
|
|
one container and pushes them into the other. The test measures
|
| 3124 |
|
|
the average time as a function of the number of values.</p><p>
|
| 3125 |
|
|
It uses the test file:
|
| 3126 |
|
|
<code class="filename">
|
| 3127 |
|
|
performance/ext/pb_ds/priority_queue_text_join_timing.cc
|
| 3128 |
|
|
</code>
|
| 3129 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 3130 |
|
|
structures.
|
| 3131 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_join.results"/>
|
| 3132 |
|
|
Results
|
| 3133 |
|
|
</h6></div></div></div><p>The graphic immediately below shows the results for the
|
| 3134 |
|
|
native priority_queue type instantiated with different underlying
|
| 3135 |
|
|
container types versus several different versions of library's
|
| 3136 |
|
|
priority_queues.
|
| 3137 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_join.png" style="text-align: middle"/></div></div><p>
|
| 3138 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 3139 |
|
|
instantiated with the types in the following table.
|
| 3140 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3141 |
|
|
n_pq_vector
|
| 3142 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3143 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3144 |
|
|
</td><td style="text-align: left">
|
| 3145 |
|
|
<code class="classname">Sequence</code>
|
| 3146 |
|
|
</td><td style="text-align: left">
|
| 3147 |
|
|
<code class="classname">std::vector</code>
|
| 3148 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3149 |
|
|
n_pq_deque
|
| 3150 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3151 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3152 |
|
|
</td><td style="text-align: left">
|
| 3153 |
|
|
<code class="classname">Sequence</code>
|
| 3154 |
|
|
</td><td style="text-align: left">
|
| 3155 |
|
|
<code class="classname">std::deque</code>
|
| 3156 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3157 |
|
|
binary_heap
|
| 3158 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3159 |
|
|
<code class="classname">priority_queue</code>
|
| 3160 |
|
|
</td><td style="text-align: left">
|
| 3161 |
|
|
<code class="classname">Tag</code>
|
| 3162 |
|
|
</td><td style="text-align: left">
|
| 3163 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 3164 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3165 |
|
|
binomial_heap
|
| 3166 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3167 |
|
|
<code class="classname">priority_queue</code>
|
| 3168 |
|
|
</td><td style="text-align: left">
|
| 3169 |
|
|
<code class="classname">Tag</code>
|
| 3170 |
|
|
</td><td style="text-align: left">
|
| 3171 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 3172 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3173 |
|
|
rc_binomial_heap
|
| 3174 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3175 |
|
|
<code class="classname">priority_queue</code>
|
| 3176 |
|
|
</td><td style="text-align: left">
|
| 3177 |
|
|
<code class="classname">Tag</code>
|
| 3178 |
|
|
</td><td style="text-align: left">
|
| 3179 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 3180 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3181 |
|
|
thin_heap
|
| 3182 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3183 |
|
|
<code class="classname">priority_queue</code>
|
| 3184 |
|
|
</td><td style="text-align: left">
|
| 3185 |
|
|
<code class="classname">Tag</code>
|
| 3186 |
|
|
</td><td style="text-align: left">
|
| 3187 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 3188 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3189 |
|
|
pairing_heap
|
| 3190 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3191 |
|
|
<code class="classname">priority_queue</code>
|
| 3192 |
|
|
</td><td style="text-align: left">
|
| 3193 |
|
|
<code class="classname">Tag</code>
|
| 3194 |
|
|
</td><td style="text-align: left">
|
| 3195 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 3196 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_join.observations"/>
|
| 3197 |
|
|
Observations
|
| 3198 |
|
|
</h6></div></div></div><p>In this test the node-based heaps perform <code class="function">join</code> in
|
| 3199 |
|
|
either logarithmic or constant time. The binary heap requires
|
| 3200 |
|
|
linear time, since the well-known heapify algorithm [clrs2001] is linear.</p><p>It would be possible to apply the heapify algorithm to the
|
| 3201 |
|
|
standard containers, if they would support iteration (which they
|
| 3202 |
|
|
don't). Barring iterators, it is still somehow possible to perform
|
| 3203 |
|
|
linear-time merge on a <code class="classname">std::vector</code>-based
|
| 3204 |
|
|
standard priority queue, using <code class="function">top()</code>
|
| 3205 |
|
|
and <code class="function">size()</code> (since they are enough to expose
|
| 3206 |
|
|
the underlying array), but this is impossible for
|
| 3207 |
|
|
a <code class="classname">std::deque</code>-based standard priority queue.
|
| 3208 |
|
|
Without heapify, the cost is super-linear.</p></div></div><div class="section" title="Text modify Up"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_modify_up"/>
|
| 3209 |
|
|
Text <code class="function">modify</code> Up
|
| 3210 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_up.info"/>
|
| 3211 |
|
|
Description
|
| 3212 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 3213 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 3214 |
|
|
into a container then modifies each one "up" (i.e., it
|
| 3215 |
|
|
makes it larger). It uses <code class="function">modify</code> for this library's
|
| 3216 |
|
|
priority queues; for the standard's priority queues, it pops values
|
| 3217 |
|
|
from a container until it reaches the value that should be
|
| 3218 |
|
|
modified, then pushes values back in. It measures the average
|
| 3219 |
|
|
time for <code class="function">modify</code> as a function of the number of
|
| 3220 |
|
|
values.</p><p>
|
| 3221 |
|
|
It uses the test file:
|
| 3222 |
|
|
<code class="filename">
|
| 3223 |
|
|
performance/ext/pb_ds/priority_queue_text_modify_up_timing.cc
|
| 3224 |
|
|
</code>
|
| 3225 |
|
|
</p><p>The test checks the effect of different underlying data
|
| 3226 |
|
|
structures for graph algorithms settings. Note that making an
|
| 3227 |
|
|
arbitrary value larger (in the sense of the priority queue's
|
| 3228 |
|
|
comparison functor) corresponds to decrease-key in standard graph
|
| 3229 |
|
|
algorithms [clrs2001].
|
| 3230 |
|
|
</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_up.results"/>
|
| 3231 |
|
|
Results
|
| 3232 |
|
|
</h6></div></div></div><p>The two graphics below show the results for the native
|
| 3233 |
|
|
priority_queues and this library's priority_queues.
|
| 3234 |
|
|
</p><p>The graphic immediately below shows the results for the
|
| 3235 |
|
|
native priority_queue type instantiated with different underlying
|
| 3236 |
|
|
container types versus several different versions of library's
|
| 3237 |
|
|
priority_queues.
|
| 3238 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_modify_up.png" style="text-align: middle"/></div></div><p>
|
| 3239 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 3240 |
|
|
instantiated with the types in the following table.
|
| 3241 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3242 |
|
|
n_pq_vector
|
| 3243 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3244 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3245 |
|
|
</td><td style="text-align: left">
|
| 3246 |
|
|
<code class="classname">Sequence</code>
|
| 3247 |
|
|
</td><td style="text-align: left">
|
| 3248 |
|
|
<code class="classname">std::vector</code>
|
| 3249 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3250 |
|
|
n_pq_deque
|
| 3251 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3252 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3253 |
|
|
</td><td style="text-align: left">
|
| 3254 |
|
|
<code class="classname">Sequence</code>
|
| 3255 |
|
|
</td><td style="text-align: left">
|
| 3256 |
|
|
<code class="classname">std::deque</code>
|
| 3257 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3258 |
|
|
binary_heap
|
| 3259 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3260 |
|
|
<code class="classname">priority_queue</code>
|
| 3261 |
|
|
</td><td style="text-align: left">
|
| 3262 |
|
|
<code class="classname">Tag</code>
|
| 3263 |
|
|
</td><td style="text-align: left">
|
| 3264 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 3265 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3266 |
|
|
binomial_heap
|
| 3267 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3268 |
|
|
<code class="classname">priority_queue</code>
|
| 3269 |
|
|
</td><td style="text-align: left">
|
| 3270 |
|
|
<code class="classname">Tag</code>
|
| 3271 |
|
|
</td><td style="text-align: left">
|
| 3272 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 3273 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3274 |
|
|
rc_binomial_heap
|
| 3275 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3276 |
|
|
<code class="classname">priority_queue</code>
|
| 3277 |
|
|
</td><td style="text-align: left">
|
| 3278 |
|
|
<code class="classname">Tag</code>
|
| 3279 |
|
|
</td><td style="text-align: left">
|
| 3280 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 3281 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3282 |
|
|
thin_heap
|
| 3283 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3284 |
|
|
<code class="classname">priority_queue</code>
|
| 3285 |
|
|
</td><td style="text-align: left">
|
| 3286 |
|
|
<code class="classname">Tag</code>
|
| 3287 |
|
|
</td><td style="text-align: left">
|
| 3288 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 3289 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3290 |
|
|
pairing_heap
|
| 3291 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3292 |
|
|
<code class="classname">priority_queue</code>
|
| 3293 |
|
|
</td><td style="text-align: left">
|
| 3294 |
|
|
<code class="classname">Tag</code>
|
| 3295 |
|
|
</td><td style="text-align: left">
|
| 3296 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 3297 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the
|
| 3298 |
|
|
native priority queues and this library's pairing and thin heap
|
| 3299 |
|
|
priority_queue data structures.
|
| 3300 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_modify_up_thin.png" style="text-align: middle"/></div></div><p>
|
| 3301 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 3302 |
|
|
instantiated with the types in the following table.
|
| 3303 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3304 |
|
|
thin_heap
|
| 3305 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3306 |
|
|
<code class="classname">priority_queue</code>
|
| 3307 |
|
|
</td><td style="text-align: left">
|
| 3308 |
|
|
<code class="classname">Tag</code>
|
| 3309 |
|
|
</td><td style="text-align: left">
|
| 3310 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 3311 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3312 |
|
|
pairing_heap
|
| 3313 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3314 |
|
|
<code class="classname">priority_queue</code>
|
| 3315 |
|
|
</td><td style="text-align: left">
|
| 3316 |
|
|
<code class="classname">Tag</code>
|
| 3317 |
|
|
</td><td style="text-align: left">
|
| 3318 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 3319 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_up.observations"/>
|
| 3320 |
|
|
Observations
|
| 3321 |
|
|
</h6></div></div></div><p>As noted above, increasing an arbitrary value (in the sense of
|
| 3322 |
|
|
the priority queue's comparison functor) is very common in
|
| 3323 |
|
|
graph-related algorithms. In this case, a thin heap
|
| 3324 |
|
|
(<code class="classname">priority_queue</code> with
|
| 3325 |
|
|
<code class="classname">Tag</code> = <code class="classname">thin_heap_tag</code>)
|
| 3326 |
|
|
outperforms a pairing heap (<code class="classname">priority_queue</code> with
|
| 3327 |
|
|
<code class="classname">Tag</code> = <code class="classname">pairing_heap_tag</code>).
|
| 3328 |
|
|
Conversely, Priority Queue Text
|
| 3329 |
|
|
<code class="function">push</code> Timing Test, Priority Queue
|
| 3330 |
|
|
Text <code class="function">push</code> and <code class="function">pop</code> Timing Test, Priority
|
| 3331 |
|
|
Queue Random Integer <code class="function">push</code> Timing Test, and
|
| 3332 |
|
|
Priority
|
| 3333 |
|
|
Queue Random Integer <code class="function">push</code> and <code class="function">pop</code> Timing
|
| 3334 |
|
|
Test show that the situation is reversed for other
|
| 3335 |
|
|
operations. It is not clear when to prefer one of these two
|
| 3336 |
|
|
different types.</p><p>In this test this library's binary heaps
|
| 3337 |
|
|
effectively perform modify in linear time. As explained in
|
| 3338 |
|
|
Priority Queue Design::Traits, given a valid point-type iterator,
|
| 3339 |
|
|
a binary heap can perform
|
| 3340 |
|
|
<code class="function">modify</code> logarithmically. The problem is that binary
|
| 3341 |
|
|
heaps invalidate their find iterators with each modifying
|
| 3342 |
|
|
operation, and so the only way to obtain a valid point-type
|
| 3343 |
|
|
iterator is to iterate using a range-type iterator until
|
| 3344 |
|
|
finding the appropriate value, then use the range-type iterator
|
| 3345 |
|
|
for the <code class="function">modify</code> operation.</p><p>The explanation for the standard's priority queues' performance
|
| 3346 |
|
|
is similar to that in Priority Queue Text
|
| 3347 |
|
|
<code class="function">join</code> Timing Test.</p></div></div><div class="section" title="Text modify Down"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_modify_down"/>
|
| 3348 |
|
|
Text <code class="function">modify</code> Down
|
| 3349 |
|
|
</h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_down.info"/>
|
| 3350 |
|
|
Description
|
| 3351 |
|
|
</h6></div></div></div><p>This test inserts a number of values with keys from an
|
| 3352 |
|
|
arbitrary text ([ wickland96thirty ]) into
|
| 3353 |
|
|
into a container then modifies each one "down" (i.e., it
|
| 3354 |
|
|
makes it smaller). It uses <code class="function">modify</code> for this library's
|
| 3355 |
|
|
priority queues; for the standard's priority queues, it pops values
|
| 3356 |
|
|
from a container until it reaches the value that should be
|
| 3357 |
|
|
modified, then pushes values back in. It measures the average
|
| 3358 |
|
|
time for <code class="function">modify</code> as a function of the number of
|
| 3359 |
|
|
values.</p><p>
|
| 3360 |
|
|
It uses the test file:
|
| 3361 |
|
|
<code class="filename">
|
| 3362 |
|
|
performance/ext/pb_ds/priority_queue_text_modify_down_timing.cc
|
| 3363 |
|
|
</code>
|
| 3364 |
|
|
</p><p>The main purpose of this test is to contrast Priority Queue
|
| 3365 |
|
|
Text <code class="classname">modify</code> Up Timing Test.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_down.results"/>
|
| 3366 |
|
|
Results
|
| 3367 |
|
|
</h6></div></div></div><p>The two graphics below show the results for the native
|
| 3368 |
|
|
priority_queues and this library's priority_queues.
|
| 3369 |
|
|
</p><p>The graphic immediately below shows the results for the
|
| 3370 |
|
|
native priority_queue type instantiated with different underlying
|
| 3371 |
|
|
container types versus several different versions of library's
|
| 3372 |
|
|
priority_queues.
|
| 3373 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_modify_down.png" style="text-align: middle"/></div></div><p>
|
| 3374 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 3375 |
|
|
instantiated with the types in the following table.
|
| 3376 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3377 |
|
|
n_pq_vector
|
| 3378 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3379 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3380 |
|
|
</td><td style="text-align: left">
|
| 3381 |
|
|
<code class="classname">Sequence</code>
|
| 3382 |
|
|
</td><td style="text-align: left">
|
| 3383 |
|
|
<code class="classname">std::vector</code>
|
| 3384 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3385 |
|
|
n_pq_deque
|
| 3386 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3387 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3388 |
|
|
</td><td style="text-align: left">
|
| 3389 |
|
|
<code class="classname">Sequence</code>
|
| 3390 |
|
|
</td><td style="text-align: left">
|
| 3391 |
|
|
<code class="classname">std::deque</code>
|
| 3392 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3393 |
|
|
binary_heap
|
| 3394 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3395 |
|
|
<code class="classname">priority_queue</code>
|
| 3396 |
|
|
</td><td style="text-align: left">
|
| 3397 |
|
|
<code class="classname">Tag</code>
|
| 3398 |
|
|
</td><td style="text-align: left">
|
| 3399 |
|
|
<code class="classname">binary_heap_tag</code>
|
| 3400 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3401 |
|
|
binomial_heap
|
| 3402 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3403 |
|
|
<code class="classname">priority_queue</code>
|
| 3404 |
|
|
</td><td style="text-align: left">
|
| 3405 |
|
|
<code class="classname">Tag</code>
|
| 3406 |
|
|
</td><td style="text-align: left">
|
| 3407 |
|
|
<code class="classname">binomial_heap_tag</code>
|
| 3408 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3409 |
|
|
rc_binomial_heap
|
| 3410 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3411 |
|
|
<code class="classname">priority_queue</code>
|
| 3412 |
|
|
</td><td style="text-align: left">
|
| 3413 |
|
|
<code class="classname">Tag</code>
|
| 3414 |
|
|
</td><td style="text-align: left">
|
| 3415 |
|
|
<code class="classname">rc_binomial_heap_tag</code>
|
| 3416 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3417 |
|
|
thin_heap
|
| 3418 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3419 |
|
|
<code class="classname">priority_queue</code>
|
| 3420 |
|
|
</td><td style="text-align: left">
|
| 3421 |
|
|
<code class="classname">Tag</code>
|
| 3422 |
|
|
</td><td style="text-align: left">
|
| 3423 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 3424 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3425 |
|
|
pairing_heap
|
| 3426 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3427 |
|
|
<code class="classname">priority_queue</code>
|
| 3428 |
|
|
</td><td style="text-align: left">
|
| 3429 |
|
|
<code class="classname">Tag</code>
|
| 3430 |
|
|
</td><td style="text-align: left">
|
| 3431 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 3432 |
|
|
</td></tr></tbody></table></div><p>The graphic below shows the results for the
|
| 3433 |
|
|
native priority queues and this library's pairing and thin heap
|
| 3434 |
|
|
priority_queue data structures.
|
| 3435 |
|
|
</p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_modify_down_thin.png" style="text-align: middle"/></div></div><p>
|
| 3436 |
|
|
The abbreviated names in the legend of the graphic above are
|
| 3437 |
|
|
instantiated with the types in the following table.
|
| 3438 |
|
|
</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3439 |
|
|
thin_heap
|
| 3440 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3441 |
|
|
<code class="classname">priority_queue</code>
|
| 3442 |
|
|
</td><td style="text-align: left">
|
| 3443 |
|
|
<code class="classname">Tag</code>
|
| 3444 |
|
|
</td><td style="text-align: left">
|
| 3445 |
|
|
<code class="classname">thin_heap_tag</code>
|
| 3446 |
|
|
</td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
|
| 3447 |
|
|
pairing_heap
|
| 3448 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3449 |
|
|
<code class="classname">priority_queue</code>
|
| 3450 |
|
|
</td><td style="text-align: left">
|
| 3451 |
|
|
<code class="classname">Tag</code>
|
| 3452 |
|
|
</td><td style="text-align: left">
|
| 3453 |
|
|
<code class="classname">pairing_heap_tag</code>
|
| 3454 |
|
|
</td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_down.observations"/>
|
| 3455 |
|
|
Observations
|
| 3456 |
|
|
</h6></div></div></div><p>Most points in these results are similar to Priority Queue
|
| 3457 |
|
|
Text <code class="function">modify</code> Up Timing Test.</p><p>It is interesting to note, however, that as opposed to that
|
| 3458 |
|
|
test, a thin heap (<code class="classname">priority_queue</code> with
|
| 3459 |
|
|
<code class="classname">Tag</code> = <code class="classname">thin_heap_tag</code>) is
|
| 3460 |
|
|
outperformed by a pairing heap (<code class="classname">priority_queue</code> with
|
| 3461 |
|
|
<code class="classname">Tag</code> = <code class="classname">pairing_heap_tag</code>).
|
| 3462 |
|
|
In this case, both heaps essentially perform an <code class="function">erase</code>
|
| 3463 |
|
|
operation followed by a <code class="function">push</code> operation. As the other
|
| 3464 |
|
|
tests show, a pairing heap is usually far more efficient than a
|
| 3465 |
|
|
thin heap, so this is not surprising.</p><p>Most algorithms that involve priority queues increase values
|
| 3466 |
|
|
(in the sense of the priority queue's comparison functor), and
|
| 3467 |
|
|
so Priority Queue
|
| 3468 |
|
|
Text <code class="classname">modify</code> Up Timing Test - is more interesting
|
| 3469 |
|
|
than this test.</p></div></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h4 class="title"><a id="pbds.test.performance.observations"/>Observations</h4></div></div></div><div class="section" title="Associative"><div class="titlepage"><div><div><h5 class="title"><a id="observations.associative"/>Associative</h5></div></div></div><div class="section" title="Underlying Data-Structure Families"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.underlying"/>
|
| 3470 |
|
|
Underlying Data-Structure Families
|
| 3471 |
|
|
</h6></div></div></div><p>In general, hash-based containers have better timing performance
|
| 3472 |
|
|
than containers based on different underlying-data structures. The
|
| 3473 |
|
|
main reason to choose a tree-based or trie-based container is if a
|
| 3474 |
|
|
byproduct of the tree-like structure is required: either
|
| 3475 |
|
|
order-preservation, or the ability to utilize node invariants. If
|
| 3476 |
|
|
memory-use is the major factor, an ordered-vector tree gives
|
| 3477 |
|
|
optimal results (albeit with high modificiation costs), and a
|
| 3478 |
|
|
list-based container gives reasonable results.</p></div><div class="section" title="Hash-Based Containers"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.hash"/>
|
| 3479 |
|
|
Hash-Based Containers
|
| 3480 |
|
|
</h6></div></div></div><p>Hash-based containers are typically either collision
|
| 3481 |
|
|
chaining or probing. Collision-chaining
|
| 3482 |
|
|
containers are more flexible internally, and so offer better
|
| 3483 |
|
|
timing performance. Probing containers, if used for simple
|
| 3484 |
|
|
value-types, manage memory more efficiently (they perform far
|
| 3485 |
|
|
fewer allocation-related calls). In general, therefore, a
|
| 3486 |
|
|
collision-chaining table should be used. A probing container,
|
| 3487 |
|
|
conversely, might be used efficiently for operations such as
|
| 3488 |
|
|
eliminating duplicates in a sequence, or counting the number of
|
| 3489 |
|
|
occurrences within a sequence. Probing containers might be more
|
| 3490 |
|
|
useful also in multithreaded applications where each thread
|
| 3491 |
|
|
manipulates a hash-based container: in the standard, allocators have
|
| 3492 |
|
|
class-wise semantics (see [meyers96more] - Item 10); a
|
| 3493 |
|
|
probing container might incur less contention in this case.</p></div><div class="section" title="Hash Policies"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.hash_policies"/>
|
| 3494 |
|
|
Hash Policies
|
| 3495 |
|
|
</h6></div></div></div><p>In hash-based containers, the range-hashing scheme seems to
|
| 3496 |
|
|
affect performance more than other considerations. In most
|
| 3497 |
|
|
settings, a mask-based scheme works well (or can be made to
|
| 3498 |
|
|
work well). If the key-distribution can be estimated a-priori,
|
| 3499 |
|
|
a simple hash function can produce nearly uniform hash-value
|
| 3500 |
|
|
distribution. In many other cases (e.g., text hashing,
|
| 3501 |
|
|
floating-point hashing), the hash function is powerful enough
|
| 3502 |
|
|
to generate hash values with good uniformity properties
|
| 3503 |
|
|
[knuth98sorting];
|
| 3504 |
|
|
a modulo-based scheme, taking into account all bits of the hash
|
| 3505 |
|
|
value, appears to overlap the hash function in its effort.</p><p>The range-hashing scheme determines many of the other
|
| 3506 |
|
|
policies. A mask-based scheme works
|
| 3507 |
|
|
well with an exponential-size policy; for
|
| 3508 |
|
|
probing-based containers, it goes well with a linear-probe
|
| 3509 |
|
|
function.</p><p>An orthogonal consideration is the trigger policy. This
|
| 3510 |
|
|
presents difficult tradeoffs. E.g., different load
|
| 3511 |
|
|
factors in a load-check trigger policy yield a
|
| 3512 |
|
|
space/amortized-cost tradeoff.</p></div><div class="section" title="Branch-Based Containers"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.branch"/>
|
| 3513 |
|
|
Branch-Based Containers
|
| 3514 |
|
|
</h6></div></div></div><p>In general, there are several families of tree-based
|
| 3515 |
|
|
underlying data structures: balanced node-based trees
|
| 3516 |
|
|
(e.g., red-black or AVL trees), high-probability
|
| 3517 |
|
|
balanced node-based trees (e.g., random treaps or
|
| 3518 |
|
|
skip-lists), competitive node-based trees (e.g., splay
|
| 3519 |
|
|
trees), vector-based "trees", and tries. (Additionally, there
|
| 3520 |
|
|
are disk-residing or network-residing trees, such as B-Trees
|
| 3521 |
|
|
and their numerous variants. An interface for this would have
|
| 3522 |
|
|
to deal with the execution model and ACID guarantees; this is
|
| 3523 |
|
|
out of the scope of this library.) Following are some
|
| 3524 |
|
|
observations on their application to different settings.</p><p>Of the balanced node-based trees, this library includes a
|
| 3525 |
|
|
red-black tree, as does standard (in
|
| 3526 |
|
|
practice). This type of tree is the "workhorse" of tree-based
|
| 3527 |
|
|
containers: it offers both reasonable modification and
|
| 3528 |
|
|
reasonable lookup time. Unfortunately, this data structure
|
| 3529 |
|
|
stores a huge amount of metadata. Each node must contain,
|
| 3530 |
|
|
besides a value, three pointers and a boolean. This type might
|
| 3531 |
|
|
be avoided if space is at a premium [austern00noset].</p><p>High-probability balanced node-based trees suffer the
|
| 3532 |
|
|
drawbacks of deterministic balanced trees. Although they are
|
| 3533 |
|
|
fascinating data structures, preliminary tests with them showed
|
| 3534 |
|
|
their performance was worse than red-black trees. The library
|
| 3535 |
|
|
does not contain any such trees, therefore.</p><p>Competitive node-based trees have two drawbacks. They are
|
| 3536 |
|
|
usually somewhat unbalanced, and they perform a large number of
|
| 3537 |
|
|
comparisons. Balanced trees perform one comparison per each
|
| 3538 |
|
|
node they encounter on a search path; a splay tree performs two
|
| 3539 |
|
|
comparisons. If the keys are complex objects, e.g.,
|
| 3540 |
|
|
<code class="classname">std::string</code>, this can increase the running time.
|
| 3541 |
|
|
Conversely, such trees do well when there is much locality of
|
| 3542 |
|
|
reference. It is difficult to determine in which case to prefer
|
| 3543 |
|
|
such trees over balanced trees. This library includes a splay
|
| 3544 |
|
|
tree.</p><p>Ordered-vector trees use very little space
|
| 3545 |
|
|
[austern00noset].
|
| 3546 |
|
|
They do not have any other advantages (at least in this
|
| 3547 |
|
|
implementation).</p><p>Large-fan-out PATRICIA tries have excellent lookup
|
| 3548 |
|
|
performance, but they do so through maintaining, for each node,
|
| 3549 |
|
|
a miniature "hash-table". Their space efficiency is low, and
|
| 3550 |
|
|
their modification performance is bad. These tries might be
|
| 3551 |
|
|
used for semi-static settings, where order preservation is
|
| 3552 |
|
|
important. Alternatively, red-black trees cross-referenced with
|
| 3553 |
|
|
hash tables can be used. [okasaki98mereable]
|
| 3554 |
|
|
discusses small-fan-out PATRICIA tries for integers, but the
|
| 3555 |
|
|
cited results seem to indicate that the amortized cost of
|
| 3556 |
|
|
maintaining such trees is higher than that of balanced trees.
|
| 3557 |
|
|
Moderate-fan-out trees might be useful for sequences where each
|
| 3558 |
|
|
element has a limited number of choices, e.g., DNA
|
| 3559 |
|
|
strings.</p></div><div class="section" title="Mapping-Semantics"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.mapping_semantics"/>
|
| 3560 |
|
|
Mapping-Semantics
|
| 3561 |
|
|
</h6></div></div></div><p>Different mapping semantics were discussed in the introduction and design sections.Here
|
| 3562 |
|
|
the focus will be on the case where a keys can be composed into
|
| 3563 |
|
|
primary keys and secondary keys. (In the case where some keys
|
| 3564 |
|
|
are completely identical, it is trivial that one should use an
|
| 3565 |
|
|
associative container mapping values to size types.) In this
|
| 3566 |
|
|
case there are (at least) five possibilities:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>Use an associative container that allows equivalent-key
|
| 3567 |
|
|
values (such as <code class="classname">std::multimap</code>)</p></li><li class="listitem"><p>Use a unique-key value associative container that maps
|
| 3568 |
|
|
each primary key to some complex associative container of
|
| 3569 |
|
|
secondary keys, say a tree-based or hash-based container.
|
| 3570 |
|
|
</p></li><li class="listitem"><p>Use a unique-key value associative container that maps
|
| 3571 |
|
|
each primary key to some simple associative container of
|
| 3572 |
|
|
secondary keys, say a list-based container.</p></li><li class="listitem"><p>Use a unique-key value associative container that maps
|
| 3573 |
|
|
each primary key to some non-associative container
|
| 3574 |
|
|
(e.g., <code class="classname">std::vector</code>)</p></li><li class="listitem"><p>Use a unique-key value associative container that takes
|
| 3575 |
|
|
into account both primary and secondary keys.</p></li></ol></div><p>Stated simply: there is a simple answer for this. (Excluding
|
| 3576 |
|
|
option 1, which should be avoided in all cases).</p><p>If the expected ratio of secondary keys to primary keys is
|
| 3577 |
|
|
small, then 3 and 4 seem reasonable. Both types of secondary
|
| 3578 |
|
|
containers are relatively lightweight (in terms of memory use
|
| 3579 |
|
|
and construction time), and so creating an entire container
|
| 3580 |
|
|
object for each primary key is not too expensive. Option 4
|
| 3581 |
|
|
might be preferable to option 3 if changing the secondary key
|
| 3582 |
|
|
of some primary key is frequent - one cannot modify an
|
| 3583 |
|
|
associative container's key, and the only possibility,
|
| 3584 |
|
|
therefore, is erasing the secondary key and inserting another
|
| 3585 |
|
|
one instead; a non-associative container, conversely, can
|
| 3586 |
|
|
support in-place modification. The actual cost of erasing a
|
| 3587 |
|
|
secondary key and inserting another one depends also on the
|
| 3588 |
|
|
allocator used for secondary associative-containers (The tests
|
| 3589 |
|
|
above used the standard allocator, but in practice one might
|
| 3590 |
|
|
choose to use, e.g., [boost_pool]). Option 2 is
|
| 3591 |
|
|
definitely an overkill in this case. Option 1 loses out either
|
| 3592 |
|
|
immediately (when there is one secondary key per primary key)
|
| 3593 |
|
|
or almost immediately after that. Option 5 has the same
|
| 3594 |
|
|
drawbacks as option 2, but it has the additional drawback that
|
| 3595 |
|
|
finding all values whose primary key is equivalent to some key,
|
| 3596 |
|
|
might be linear in the total number of values stored (for
|
| 3597 |
|
|
example, if using a hash-based container).</p><p>If the expected ratio of secondary keys to primary keys is
|
| 3598 |
|
|
large, then the answer is more complicated. It depends on the
|
| 3599 |
|
|
distribution of secondary keys to primary keys, the
|
| 3600 |
|
|
distribution of accesses according to primary keys, and the
|
| 3601 |
|
|
types of operations most frequent.</p><p>To be more precise, assume there are m primary keys,
|
| 3602 |
|
|
primary key i is mapped to n<sub>i</sub>
|
| 3603 |
|
|
secondary keys, and each primary key is mapped, on average, to
|
| 3604 |
|
|
n secondary keys (i.e.,
|
| 3605 |
|
|
E(n<sub>i</sub>) = n).</p><p>Suppose one wants to find a specific pair of primary and
|
| 3606 |
|
|
secondary keys. Using 1 with a tree based container
|
| 3607 |
|
|
(<code class="classname">std::multimap</code>), the expected cost is
|
| 3608 |
|
|
E(Θ(log(m) + n<sub>i</sub>)) = Θ(log(m) +
|
| 3609 |
|
|
n); using 1 with a hash-based container
|
| 3610 |
|
|
(<code class="classname">std::tr1::unordered_multimap</code>), the expected cost is
|
| 3611 |
|
|
Θ(n). Using 2 with a primary hash-based container
|
| 3612 |
|
|
and secondary hash-based containers, the expected cost is
|
| 3613 |
|
|
O(1); using 2 with a primary tree-based container and
|
| 3614 |
|
|
secondary tree-based containers, the expected cost is (using
|
| 3615 |
|
|
the Jensen inequality [motwani95random])
|
| 3616 |
|
|
E(O(log(m) + log(n<sub>i</sub>)) = O(log(m)) +
|
| 3617 |
|
|
E(O(log(n<sub>i</sub>)) = O(log(m)) + O(log(n)),
|
| 3618 |
|
|
assuming that primary keys are accessed equiprobably. 3 and 4
|
| 3619 |
|
|
are similar to 1, but with lower constants. Using 5 with a
|
| 3620 |
|
|
hash-based container, the expected cost is O(1); using 5
|
| 3621 |
|
|
with a tree based container, the cost is
|
| 3622 |
|
|
E(Θ(log(mn))) = Θ(log(m) +
|
| 3623 |
|
|
log(n)).</p><p>Suppose one needs the values whose primary key matches some
|
| 3624 |
|
|
given key. Using 1 with a hash-based container, the expected
|
| 3625 |
|
|
cost is Θ(n), but the values will not be ordered
|
| 3626 |
|
|
by secondary keys (which may or may not be required); using 1
|
| 3627 |
|
|
with a tree-based container, the expected cost is
|
| 3628 |
|
|
Θ(log(m) + n), but with high constants; again the
|
| 3629 |
|
|
values will not be ordered by secondary keys. 2, 3, and 4 are
|
| 3630 |
|
|
similar to 1, but typically with lower constants (and,
|
| 3631 |
|
|
additionally, if one uses a tree-based container for secondary
|
| 3632 |
|
|
keys, they will be ordered). Using 5 with a hash-based
|
| 3633 |
|
|
container, the cost is Θ(mn).</p><p>Suppose one wants to assign to a primary key all secondary
|
| 3634 |
|
|
keys assigned to a different primary key. Using 1 with a
|
| 3635 |
|
|
hash-based container, the expected cost is Θ(n),
|
| 3636 |
|
|
but with very high constants; using 1 with a tree-based
|
| 3637 |
|
|
container, the cost is Θ(nlog(mn)). Using 2, 3,
|
| 3638 |
|
|
and 4, the expected cost is Θ(n), but typically
|
| 3639 |
|
|
with far lower costs than 1. 5 is similar to 1.</p></div></div><div class="section" title="Priority_Queue"><div class="titlepage"><div><div><h5 class="title"><a id="observations.priority_queue"/>Priority_Queue</h5></div></div></div><div class="section" title="Complexity"><div class="titlepage"><div><div><h6 class="title"><a id="observations.priority_queue.complexity"/>Complexity</h6></div></div></div><p>The following table shows the complexities of the different
|
| 3640 |
|
|
underlying data structures in terms of orders of growth. It is
|
| 3641 |
|
|
interesting to note that this table implies something about the
|
| 3642 |
|
|
constants of the operations as well (see Amortized <code class="function">push</code>
|
| 3643 |
|
|
and <code class="function">pop</code> operations).</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/></colgroup><thead><tr><th style="text-align: left"> </th><th style="text-align: left"><span class="emphasis"><em><code class="function">push</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">pop</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">modify</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">erase</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">join</code></em></span></th></tr></thead><tbody><tr><td style="text-align: left">
|
| 3644 |
|
|
<code class="classname">std::priority_queue</code>
|
| 3645 |
|
|
</td><td style="text-align: left">
|
| 3646 |
|
|
Θ(n) worst
|
| 3647 |
|
|
Θ(log(n)) amortized
|
| 3648 |
|
|
</td><td style="text-align: left">
|
| 3649 |
|
|
Θ(log(n)) Worst
|
| 3650 |
|
|
</td><td style="text-align: left">
|
| 3651 |
|
|
Θ(n log(n)) Worst
|
| 3652 |
|
|
<sub>[std note 1]</sub>
|
| 3653 |
|
|
</td><td style="text-align: left">
|
| 3654 |
|
|
Θ(n log(n))
|
| 3655 |
|
|
<sub>[std note 2]</sub>
|
| 3656 |
|
|
</td><td style="text-align: left">
|
| 3657 |
|
|
Θ(n log(n))
|
| 3658 |
|
|
<sub>[std note 1]</sub>
|
| 3659 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3660 |
|
|
<code class="classname">priority_queue</code>
|
| 3661 |
|
|
<<code class="classname">Tag</code> =
|
| 3662 |
|
|
<code class="classname">pairing_heap_tag</code>>
|
| 3663 |
|
|
</td><td style="text-align: left">
|
| 3664 |
|
|
O(1)
|
| 3665 |
|
|
</td><td style="text-align: left">
|
| 3666 |
|
|
Θ(n) worst
|
| 3667 |
|
|
Θ(log(n)) amortized
|
| 3668 |
|
|
</td><td style="text-align: left">
|
| 3669 |
|
|
Θ(n) worst
|
| 3670 |
|
|
Θ(log(n)) amortized
|
| 3671 |
|
|
</td><td style="text-align: left">
|
| 3672 |
|
|
Θ(n) worst
|
| 3673 |
|
|
Θ(log(n)) amortized
|
| 3674 |
|
|
</td><td style="text-align: left">
|
| 3675 |
|
|
O(1)
|
| 3676 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3677 |
|
|
<code class="classname">priority_queue</code>
|
| 3678 |
|
|
<<code class="classname">Tag</code> =
|
| 3679 |
|
|
<code class="classname">binary_heap_tag</code>>
|
| 3680 |
|
|
</td><td style="text-align: left">
|
| 3681 |
|
|
Θ(n) worst
|
| 3682 |
|
|
Θ(log(n)) amortized
|
| 3683 |
|
|
</td><td style="text-align: left">
|
| 3684 |
|
|
Θ(n) worst
|
| 3685 |
|
|
Θ(log(n)) amortized
|
| 3686 |
|
|
</td><td style="text-align: left">
|
| 3687 |
|
|
Θ(n)
|
| 3688 |
|
|
</td><td style="text-align: left">
|
| 3689 |
|
|
Θ(n)
|
| 3690 |
|
|
</td><td style="text-align: left">
|
| 3691 |
|
|
Θ(n)
|
| 3692 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3693 |
|
|
<code class="classname">priority_queue</code>
|
| 3694 |
|
|
<<code class="classname">Tag</code> =
|
| 3695 |
|
|
<code class="classname">binomial_heap_tag</code>>
|
| 3696 |
|
|
</td><td style="text-align: left">
|
| 3697 |
|
|
Θ(log(n)) worst
|
| 3698 |
|
|
O(1) amortized
|
| 3699 |
|
|
</td><td style="text-align: left">
|
| 3700 |
|
|
Θ(log(n))
|
| 3701 |
|
|
</td><td style="text-align: left">
|
| 3702 |
|
|
Θ(log(n))
|
| 3703 |
|
|
</td><td style="text-align: left">
|
| 3704 |
|
|
Θ(log(n))
|
| 3705 |
|
|
</td><td style="text-align: left">
|
| 3706 |
|
|
Θ(log(n))
|
| 3707 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3708 |
|
|
<code class="classname">priority_queue</code>
|
| 3709 |
|
|
<<code class="classname">Tag</code> =
|
| 3710 |
|
|
<code class="classname">rc_binomial_heap_tag</code>>
|
| 3711 |
|
|
</td><td style="text-align: left">
|
| 3712 |
|
|
O(1)
|
| 3713 |
|
|
</td><td style="text-align: left">
|
| 3714 |
|
|
Θ(log(n))
|
| 3715 |
|
|
</td><td style="text-align: left">
|
| 3716 |
|
|
Θ(log(n))
|
| 3717 |
|
|
</td><td style="text-align: left">
|
| 3718 |
|
|
Θ(log(n))
|
| 3719 |
|
|
</td><td style="text-align: left">
|
| 3720 |
|
|
Θ(log(n))
|
| 3721 |
|
|
</td></tr><tr><td style="text-align: left">
|
| 3722 |
|
|
<code class="classname">priority_queue</code><<code class="classname">Tag</code> =
|
| 3723 |
|
|
<code class="classname">thin_heap_tag</code>>
|
| 3724 |
|
|
</td><td style="text-align: left">
|
| 3725 |
|
|
O(1)
|
| 3726 |
|
|
</td><td style="text-align: left">
|
| 3727 |
|
|
Θ(n) worst
|
| 3728 |
|
|
Θ(log(n)) amortized
|
| 3729 |
|
|
</td><td style="text-align: left">
|
| 3730 |
|
|
Θ(log(n)) worst
|
| 3731 |
|
|
O(1) amortized,
|
| 3732 |
|
|
or Θ(log(n)) amortized
|
| 3733 |
|
|
<sub>[thin_heap_note]</sub>
|
| 3734 |
|
|
</td><td style="text-align: left">
|
| 3735 |
|
|
Θ(n) worst
|
| 3736 |
|
|
Θ(log(n)) amortized
|
| 3737 |
|
|
</td><td style="text-align: left">
|
| 3738 |
|
|
Θ(n)
|
| 3739 |
|
|
</td></tr></tbody></table></div><p>[std note 1] This
|
| 3740 |
|
|
is not a property of the algorithm, but rather due to the fact
|
| 3741 |
|
|
that the standard's priority queue implementation does not support
|
| 3742 |
|
|
iterators (and consequently the ability to access a specific
|
| 3743 |
|
|
value inside it). If the priority queue is adapting an
|
| 3744 |
|
|
<code class="classname">std::vector</code>, then it is still possible to reduce this
|
| 3745 |
|
|
to Θ(n) by adapting over the standard's adapter and
|
| 3746 |
|
|
using the fact that <code class="function">top</code> returns a reference to the
|
| 3747 |
|
|
first value; if, however, it is adapting an
|
| 3748 |
|
|
<code class="classname">std::deque</code>, then this is impossible.</p><p>[std note 2] As
|
| 3749 |
|
|
with [std note 1], this is not a
|
| 3750 |
|
|
property of the algorithm, but rather the standard's implementation.
|
| 3751 |
|
|
Again, if the priority queue is adapting an
|
| 3752 |
|
|
<code class="classname">std::vector</code> then it is possible to reduce this to
|
| 3753 |
|
|
Θ(n), but with a very high constant (one must call
|
| 3754 |
|
|
<code class="function">std::make_heap</code> which is an expensive linear
|
| 3755 |
|
|
operation); if the priority queue is adapting an
|
| 3756 |
|
|
<code class="classname">std::deque</code>, then this is impossible.</p><p>[thin_heap_note] A thin heap has
|
| 3757 |
|
|
Θ(log(n)) worst case <code class="function">modify</code> time
|
| 3758 |
|
|
always, but the amortized time depends on the nature of the
|
| 3759 |
|
|
operation: I) if the operation increases the key (in the sense
|
| 3760 |
|
|
of the priority queue's comparison functor), then the amortized
|
| 3761 |
|
|
time is O(1), but if II) it decreases it, then the
|
| 3762 |
|
|
amortized time is the same as the worst case time. Note that
|
| 3763 |
|
|
for most algorithms, I) is important and II) is not.</p></div><div class="section" title="Amortized push and pop operations"><div class="titlepage"><div><div><h6 class="title"><a id="observations.priority_queue.amortized_ops"/>
|
| 3764 |
|
|
Amortized <code class="function">push</code>
|
| 3765 |
|
|
and <code class="function">pop</code> operations
|
| 3766 |
|
|
</h6></div></div></div><p>In many cases, a priority queue is needed primarily for
|
| 3767 |
|
|
sequences of <code class="function">push</code> and <code class="function">pop</code> operations. All of
|
| 3768 |
|
|
the underlying data structures have the same amortized
|
| 3769 |
|
|
logarithmic complexity, but they differ in terms of
|
| 3770 |
|
|
constants.</p><p>The table above shows that the different data structures are
|
| 3771 |
|
|
"constrained" in some respects. In general, if a data structure
|
| 3772 |
|
|
has lower worst-case complexity than another, then it will
|
| 3773 |
|
|
perform slower in the amortized sense. Thus, for example a
|
| 3774 |
|
|
redundant-counter binomial heap (<code class="classname">priority_queue</code> with
|
| 3775 |
|
|
<code class="classname">Tag</code> = <code class="classname">rc_binomial_heap_tag</code>)
|
| 3776 |
|
|
has lower worst-case <code class="function">push</code> performance than a binomial
|
| 3777 |
|
|
heap (<code class="classname">priority_queue</code>
|
| 3778 |
|
|
with <code class="classname">Tag</code> = <code class="classname">binomial_heap_tag</code>),
|
| 3779 |
|
|
and so its amortized <code class="function">push</code> performance is slower in
|
| 3780 |
|
|
terms of constants.</p><p>As the table shows, the "least constrained" underlying
|
| 3781 |
|
|
data structures are binary heaps and pairing heaps.
|
| 3782 |
|
|
Consequently, it is not surprising that they perform best in
|
| 3783 |
|
|
terms of amortized constants.</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>Pairing heaps seem to perform best for non-primitive
|
| 3784 |
|
|
types (e.g., <code class="classname">std::string</code>s), as shown by
|
| 3785 |
|
|
Priority
|
| 3786 |
|
|
Queue Text <code class="function">push</code> Timing Test and Priority
|
| 3787 |
|
|
Queue Text <code class="function">push</code> and <code class="function">pop</code> Timing
|
| 3788 |
|
|
Test</p></li><li class="listitem"><p>binary heaps seem to perform best for primitive types
|
| 3789 |
|
|
(e.g., <span class="type">int</span>s), as shown by Priority
|
| 3790 |
|
|
Queue Random Integer <code class="function">push</code> Timing Test and
|
| 3791 |
|
|
Priority
|
| 3792 |
|
|
Queue Random Integer <code class="function">push</code> and <code class="function">pop</code> Timing
|
| 3793 |
|
|
Test.</p></li></ol></div></div><div class="section" title="Graph Algorithms"><div class="titlepage"><div><div><h6 class="title"><a id="observations.priority_queue.graphs"/>
|
| 3794 |
|
|
Graph Algorithms
|
| 3795 |
|
|
</h6></div></div></div><p>In some graph algorithms, a decrease-key operation is
|
| 3796 |
|
|
required [clrs2001];
|
| 3797 |
|
|
this operation is identical to <code class="function">modify</code> if a value is
|
| 3798 |
|
|
increased (in the sense of the priority queue's comparison
|
| 3799 |
|
|
functor). The table above and Priority Queue
|
| 3800 |
|
|
Text <code class="function">modify</code> Up Timing Test show that a thin heap
|
| 3801 |
|
|
(<code class="classname">priority_queue</code> with
|
| 3802 |
|
|
<code class="classname">Tag</code> = <code class="classname">thin_heap_tag</code>)
|
| 3803 |
|
|
outperforms a pairing heap (<code class="classname">priority_queue</code> with
|
| 3804 |
|
|
<code class="classname">Tag</code> = <code class="classname">Tag</code> = <code class="classname">pairing_heap_tag</code>),
|
| 3805 |
|
|
but the rest of the tests show otherwise.</p><p>This makes it difficult to decide which implementation to use in
|
| 3806 |
|
|
this case. Dijkstra's shortest-path algorithm, for example, requires
|
| 3807 |
|
|
Θ(n) <code class="function">push</code> and <code class="function">pop</code> operations
|
| 3808 |
|
|
(in the number of vertices), but O(n<sup>2</sup>)
|
| 3809 |
|
|
<code class="function">modify</code> operations, which can be in practice Θ(n)
|
| 3810 |
|
|
as well. It is difficult to find an a-priori characterization of
|
| 3811 |
|
|
graphs in which the actual number of <code class="function">modify</code>
|
| 3812 |
|
|
operations will dwarf the number of <code class="function">push</code> and
|
| 3813 |
|
|
<code class="function">pop</code> operations.</p></div></div></div></div></div><div class="navfooter"><hr/><table width="100%" summary="Navigation footer"><tr><td align="left"><a accesskey="p" href="policy_data_structures_design.html">Prev</a> </td><td align="center"><a accesskey="u" href="policy_data_structures.html">Up</a></td><td align="right"> <a accesskey="n" href="policy_data_structures_biblio.html">Next</a></td></tr><tr><td align="left" valign="top">Design </td><td align="center"><a accesskey="h" href="../index.html">Home</a></td><td align="right" valign="top"> Acknowledgments</td></tr></table></div></body></html>
|
