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<?xml version="1.0" encoding="utf-8"?>
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<head>
<!-- 2021-08-20 Fri 09:12 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>CLIQUE Benchmark Instances</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="ThanhVu (Vu) Nguyen" />
<link rel="stylesheet" href="https://nguyenthanhvuh.github.io/files/org.css">
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<body>
<div id="content">
<h1 class="title">CLIQUE Benchmark Instances</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org9f13901">1. Utils</a></li>
<li><a href="#org8d37759">2. DIMACS Instances</a></li>
<li><a href="#org97e58ac">3. Additional Instances</a></li>
<li><a href="#orgd963fa3">4. Categories</a></li>
<li><a href="#orge04f43d">5. Other Instances</a></li>
</ul>
</div>
</div>
<hr />
<div id="outline-container-org9f13901" class="outline-2">
<h2 id="org9f13901"><span class="section-number-2">1</span> Utils</h2>
<div class="outline-text-2" id="text-1">
<ul class="org-ul">
<li><a href="https://github.com/unsat/npbench/blob/master/instances/converter">Converter</a>: convert from benchmarks from <code>ascii</code> to <code>binary</code> format and vice versa.</li>
</ul>
</div>
</div>
<div id="outline-container-org8d37759" class="outline-2">
<h2 id="org8d37759"><span class="section-number-2">2</span> DIMACS Instances</h2>
<div class="outline-text-2" id="text-2">
<p>
<a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/">Directory</a>
</p>
<p>
Files from Dimacs <a href="ftp://dimacs.rutgers.edu/pub/challenge/graph/benchmarks/clique/">ftp://dimacs.rutgers.edu/pub/challenge/graph/benchmarks/clique/</a> in binary format (<code>*.clq.b</code>).
</p>
<table id="org2774d32" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right"> </th>
<th scope="col" class="org-left">File</th>
<th scope="col" class="org-right">Max Clique<sup><a id="fnr.1" class="footref" href="#fn.1">1</a></sup></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock200_1.clq.b">brock200_1</a></td>
<td class="org-right">21</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock200_2.clq.b">brock200_2</a></td>
<td class="org-right">12</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock200_3.clq.b">brock200_3</a></td>
<td class="org-right">15</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock200_4.clq.b">brock200_4</a></td>
<td class="org-right">17</td>
</tr>
<tr>
<td class="org-right">5</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock400_1.clq.b">brock400_1</a></td>
<td class="org-right">27</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock400_2.clq.b">brock400_2</a></td>
<td class="org-right">29</td>
</tr>
<tr>
<td class="org-right">7</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock400_3.clq.b">brock400_3</a></td>
<td class="org-right">31</td>
</tr>
<tr>
<td class="org-right">8</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock400_4.clq.b">brock400_4</a></td>
<td class="org-right">33</td>
</tr>
<tr>
<td class="org-right">9</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock800_1.clq.b">brock800_1</a></td>
<td class="org-right">23</td>
</tr>
<tr>
<td class="org-right">10</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock800_2.clq.b">brock800_2</a></td>
<td class="org-right">24</td>
</tr>
<tr>
<td class="org-right">11</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock800_3.clq.b">brock800_3</a></td>
<td class="org-right">25</td>
</tr>
<tr>
<td class="org-right">12</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/brock800_4.clq.b">brock800_4</a></td>
<td class="org-right">26</td>
</tr>
<tr>
<td class="org-right">13</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat200-1.clq.b">c-fat200-1</a></td>
<td class="org-right">12</td>
</tr>
<tr>
<td class="org-right">14</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat200-2.clq.b">c-fat200-2</a></td>
<td class="org-right">24</td>
</tr>
<tr>
<td class="org-right">15</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat200-5.clq.b">c-fat200-5</a></td>
<td class="org-right">58</td>
</tr>
<tr>
<td class="org-right">16</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat500-1.clq.b">c-fat500-1</a></td>
<td class="org-right">14</td>
</tr>
<tr>
<td class="org-right">17</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat500-2.clq.b">c-fat500-2</a></td>
<td class="org-right">26</td>
</tr>
<tr>
<td class="org-right">18</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat500-5.clq.b">c-fat500-5</a></td>
<td class="org-right">64</td>
</tr>
<tr>
<td class="org-right">19</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/c-fat500-10.clq.b">c-fat500-10</a></td>
<td class="org-right">126</td>
</tr>
<tr>
<td class="org-right">20</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/hamming6-2.clq.b">hamming6-2</a></td>
<td class="org-right">32</td>
</tr>
<tr>
<td class="org-right">21</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/hamming6-4.clq.b">hamming6-4</a></td>
<td class="org-right">4</td>
</tr>
<tr>
<td class="org-right">22</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/hamming8-2.clq.b">hamming8-2</a></td>
<td class="org-right">128</td>
</tr>
<tr>
<td class="org-right">23</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/hamming8-4.clq.b">hamming8-4</a></td>
<td class="org-right">16</td>
</tr>
<tr>
<td class="org-right">24</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/hamming10-2.clq.b">hamming10-2</a></td>
<td class="org-right">512</td>
</tr>
<tr>
<td class="org-right">25</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/hamming10-4.clq.b">hamming10-4</a></td>
<td class="org-right">40</td>
</tr>
<tr>
<td class="org-right">26</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/johnson8-2-4.clq.b">johnson8-2-4</a></td>
<td class="org-right">4</td>
</tr>
<tr>
<td class="org-right">27</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/johnson8-4-4.clq.b">johnson8-4-4</a></td>
<td class="org-right">14</td>
</tr>
<tr>
<td class="org-right">28</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/johnson16-2-4.clq.b">johnson16-2-4</a></td>
<td class="org-right">8</td>
</tr>
<tr>
<td class="org-right">29</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/johnson32-2-4.clq.b">johnson32-2-4</a></td>
<td class="org-right">16</td>
</tr>
<tr>
<td class="org-right">30</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/keller4.clq.b">keller4</a></td>
<td class="org-right">11</td>
</tr>
<tr>
<td class="org-right">31</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/keller5.clq.b">keller5</a></td>
<td class="org-right">27</td>
</tr>
<tr>
<td class="org-right">32</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/keller6.clq.b">keller6</a></td>
<td class="org-right">\(\ge\) 59</td>
</tr>
<tr>
<td class="org-right">33</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/MANN_a9.clq.b">MANN_a9</a></td>
<td class="org-right">16</td>
</tr>
<tr>
<td class="org-right">34</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/MANN_a27.clq.b">MANN_a27</a></td>
<td class="org-right">126</td>
</tr>
<tr>
<td class="org-right">35</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/MANN_a44.clq.b">MANN_a45</a></td>
<td class="org-right">345</td>
</tr>
<tr>
<td class="org-right">36</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/MANN_a81.clq.b">MANN_a81</a></td>
<td class="org-right">\(\ge\) 1100</td>
</tr>
<tr>
<td class="org-right">37</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat300-1.clq.b">p_hat300-1</a></td>
<td class="org-right">8</td>
</tr>
<tr>
<td class="org-right">38</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat300-2.clq.b">p_hat300-2</a></td>
<td class="org-right">25</td>
</tr>
<tr>
<td class="org-right">39</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat300-3.clq.b">p_hat300-3</a></td>
<td class="org-right">36</td>
</tr>
<tr>
<td class="org-right">40</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat500-1.clq.b">p_hat500-1</a></td>
<td class="org-right">9</td>
</tr>
<tr>
<td class="org-right">41</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat500-2.clq.b">p_hat500-2</a></td>
<td class="org-right">36</td>
</tr>
<tr>
<td class="org-right">42</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat500-3.clq.b">p_hat500-3</a></td>
<td class="org-right">\(\ge\) 50</td>
</tr>
<tr>
<td class="org-right">43</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat700-1.clq.b">p_hat700-1</a></td>
<td class="org-right">11</td>
</tr>
<tr>
<td class="org-right">44</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat700-2.clq.b">p_hat700-2</a></td>
<td class="org-right">\(\ge\) 44</td>
</tr>
<tr>
<td class="org-right">45</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat700-3.clq.b">p_hat700-3</a></td>
<td class="org-right">\(\ge\) 62</td>
</tr>
<tr>
<td class="org-right">46</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat1000-1.clq.b">p_hat1000-1</a></td>
<td class="org-right">\(\ge\) 10</td>
</tr>
<tr>
<td class="org-right">47</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat1000-2.clq.b">p_hat1000-2</a></td>
<td class="org-right">\(\ge\) 46</td>
</tr>
<tr>
<td class="org-right">48</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat1000-3.clq.b">p_hat1000-3</a></td>
<td class="org-right">\(\ge\) 68</td>
</tr>
<tr>
<td class="org-right">49</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat1500-1.clq.b">p_hat1500-1</a></td>
<td class="org-right">\(\ge\) 12</td>
</tr>
<tr>
<td class="org-right">50</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat1500-2.clq.b">p_hat1500-2</a></td>
<td class="org-right">\(\ge\) 65</td>
</tr>
<tr>
<td class="org-right">51</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/p_hat1500-3.clq.b">p_hat1500-3</a></td>
<td class="org-right">\(\ge\) 94</td>
</tr>
<tr>
<td class="org-right">52</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san200_0.7_1.clq.b">san200_0.7_1</a></td>
<td class="org-right">30</td>
</tr>
<tr>
<td class="org-right">53</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san200_0.7_2.clq.b">san200_0.7_2</a></td>
<td class="org-right">18</td>
</tr>
<tr>
<td class="org-right">54</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san200_0.9_1.clq.b">san200_0.9_1</a></td>
<td class="org-right">70</td>
</tr>
<tr>
<td class="org-right">55</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san200_0.9_2.clq.b">san200_0.9_2</a></td>
<td class="org-right">60</td>
</tr>
<tr>
<td class="org-right">56</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san200_0.9_3.clq.b">san200_0.9_3</a></td>
<td class="org-right">44</td>
</tr>
<tr>
<td class="org-right">57</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san400_0.5_1.clq.b">san400_0.5_1</a></td>
<td class="org-right">13</td>
</tr>
<tr>
<td class="org-right">58</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san400_0.7_1.clq.b">san400_0.7_1</a></td>
<td class="org-right">40</td>
</tr>
<tr>
<td class="org-right">59</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san400_0.7_2.clq.b">san400_0.7_2</a></td>
<td class="org-right">30</td>
</tr>
<tr>
<td class="org-right">60</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san400_0.7_3.clq.b">san400_0.7_3</a></td>
<td class="org-right">22</td>
</tr>
<tr>
<td class="org-right">61</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san400_0.9_1.clq.b">san400_0.9_1</a></td>
<td class="org-right">100</td>
</tr>
<tr>
<td class="org-right">62</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/san1000.clq.b">san1000</a></td>
<td class="org-right">15</td>
</tr>
<tr>
<td class="org-right">63</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/sanr200_0.7.clq.b">sanr200_0.7</a></td>
<td class="org-right">18</td>
</tr>
<tr>
<td class="org-right">64</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/sanr200_0.9.clq.b">sanr200_0.9</a></td>
<td class="org-right">42</td>
</tr>
<tr>
<td class="org-right">65</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/sanr400_0.5.clq.b">sanr400_0.5</a></td>
<td class="org-right">13</td>
</tr>
<tr>
<td class="org-right">66</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/DIMACS_cliques/sanr400_0.7.clq.b">sanr400_0.7</a></td>
<td class="org-right">21</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org97e58ac" class="outline-2">
<h2 id="org97e58ac"><span class="section-number-2">3</span> Additional Instances</h2>
<div class="outline-text-2" id="text-3">
<p>
<a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/">Directory</a>
</p>
<p>
Files from Mike Trick <a href="http://mat.gsia.cmu.edu/COLOR02/clq.html">http://mat.gsia.cmu.edu/COLOR02/clq.html</a>. For the <code>brock</code> graphs below, there is an "off-by-one" error in the comments: if it claims node 26, for example, is in the clique, it is really node 27.
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right"> </th>
<th scope="col" class="org-left">File</th>
<th scope="col" class="org-right">Max Clique<sup><a id="fnr.1.100" class="footref" href="#fn.1">1</a></sup></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/brock200_2.clq">brock200_2</a></td>
<td class="org-right">12</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/brock200_4.clq">brock200_4</a></td>
<td class="org-right">17</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/brock400_2.clq">brock400_2</a></td>
<td class="org-right">29</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/brock400_4.clq">brock400_4</a></td>
<td class="org-right">33</td>
</tr>
<tr>
<td class="org-right">5</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/brock800_2.clq">brock800_2</a></td>
<td class="org-right">24</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/brock800_4.clq">brock800_4</a></td>
<td class="org-right">26</td>
</tr>
<tr>
<td class="org-right">7</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C125.9.clq">C125.9</a></td>
<td class="org-right">\(\ge\) 34</td>
</tr>
<tr>
<td class="org-right">8</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C250.9.clq">C250.9</a></td>
<td class="org-right">\(\ge\) 44</td>
</tr>
<tr>
<td class="org-right">9</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C500.9.clq">C500.9</a></td>
<td class="org-right">\(\ge\) 57</td>
</tr>
<tr>
<td class="org-right">10</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C1000.9.clq">C1000.9</a></td>
<td class="org-right">\(\ge\) 68</td>
</tr>
<tr>
<td class="org-right">11</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C2000.5.clq">C2000.5</a></td>
<td class="org-right">\(\ge\) 16</td>
</tr>
<tr>
<td class="org-right">12</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C2000.9.clq">C2000.9</a></td>
<td class="org-right">\(\ge\) 77</td>
</tr>
<tr>
<td class="org-right">13</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/C4000.5.clq">C4000.5</a></td>
<td class="org-right">\(\ge\) 18</td>
</tr>
<tr>
<td class="org-right">14</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/DSJC500.5.clq">DSJC500.5 </a></td>
<td class="org-right">\(\ge\) 13</td>
</tr>
<tr>
<td class="org-right">15</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/DSJC1000.5.clq">DSJC1000.5</a></td>
<td class="org-right">\(\ge\) 15</td>
</tr>
<tr>
<td class="org-right">16</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/gen200_p0.9_44.clq">gen200_p0.9_44 </a></td>
<td class="org-right">44</td>
</tr>
<tr>
<td class="org-right">17</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/gen200_p0.9_55.clq">gen200_p0.9_55 </a></td>
<td class="org-right">55</td>
</tr>
<tr>
<td class="org-right">18</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/gen400_p0.9_55.clq">gen400_p0.9_55 </a></td>
<td class="org-right">55</td>
</tr>
<tr>
<td class="org-right">19</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/gen400_p0.9_65.clq">gen400_p0.9_65 </a></td>
<td class="org-right">65</td>
</tr>
<tr>
<td class="org-right">20</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/gen400_p0.9_75.clq">gen400_p0.9_75 </a></td>
<td class="org-right">75</td>
</tr>
<tr>
<td class="org-right">21</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/hamming8-4.clq">hamming8-4</a></td>
<td class="org-right">16</td>
</tr>
<tr>
<td class="org-right">22</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/hamming10-4.clq">hamming10-4</a></td>
<td class="org-right">40</td>
</tr>
<tr>
<td class="org-right">23</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/keller4.clq">keller4</a></td>
<td class="org-right">11</td>
</tr>
<tr>
<td class="org-right">24</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/keller5.clq">keller5</a></td>
<td class="org-right">27</td>
</tr>
<tr>
<td class="org-right">25</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/keller6.clq">keller6</a></td>
<td class="org-right">\(\ge\) 59</td>
</tr>
<tr>
<td class="org-right">26</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/MANN_a27.clq%20">MANN_a27</a></td>
<td class="org-right">126</td>
</tr>
<tr>
<td class="org-right">27</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/MANN_a44.clq%20">MANN_a45</a></td>
<td class="org-right">345</td>
</tr>
<tr>
<td class="org-right">28</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/MANN_a81.clq%20">MANN_a81</a></td>
<td class="org-right">\(\ge\) 1100</td>
</tr>
<tr>
<td class="org-right">29</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat300-1.clq">p_hat300-1</a></td>
<td class="org-right">8</td>
</tr>
<tr>
<td class="org-right">30</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat300-2.clq">p_hat300-2</a></td>
<td class="org-right">25</td>
</tr>
<tr>
<td class="org-right">31</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat300-3.clq">p_hat300-3</a></td>
<td class="org-right">36</td>
</tr>
<tr>
<td class="org-right">32</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat700-1.clq">p_hat700-1</a></td>
<td class="org-right">11</td>
</tr>
<tr>
<td class="org-right">33</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat700-2.clq">p_hat700-2</a></td>
<td class="org-right">\(\ge\) 44</td>
</tr>
<tr>
<td class="org-right">34</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat700-3.clq">p_hat700-3</a></td>
<td class="org-right">\(\ge\) 62</td>
</tr>
<tr>
<td class="org-right">35</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat1500-1.clq">p_hat1500-1</a></td>
<td class="org-right">\(\ge\) 12</td>
</tr>
<tr>
<td class="org-right">36</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat1500-2.clq">p_hat1500-2</a></td>
<td class="org-right">\(\ge\) 65</td>
</tr>
<tr>
<td class="org-right">37</td>
<td class="org-left"><a href="https://github.com/unsat/npbench/blob/master/instances/clique/Additional_cliques/p_hat1500-3.clq">p_hat1500-3</a></td>
<td class="org-right">\(\ge\) 94</td>
</tr>
<tr>
<td class="org-right"> </td>
<td class="org-left"> </td>
<td class="org-right"> </td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgd963fa3" class="outline-2">
<h2 id="orgd963fa3"><span class="section-number-2">4</span> Categories</h2>
<div class="outline-text-2" id="text-4">
<p>
Reference: <a href="http://mat.gsia.cmu.edu/contents.clique.ps">http://mat.gsia.cmu.edu/contents.clique.ps</a>,
<a href="https://github.com/unsat/npbench/blob/master/instances/others/cached/contents.clique.ps">(cached)</a>
</p>
<dl class="org-dl">
<dt>CFat</dt><dd>(From Panos Pardalos [email protected])
Problems based on fault diagnosis problems. Original reference is
Berman and Pelc, "Distributed Fault Diagnosis for Multiprocessor Systems,"
Proceedings of the 20th Annual Symposium on Fault-Tolerant Computing,
340-346 (1990).
For more instances, see the generator in graph/contributed/pardalos.</dd>
<dt>Joh</dt><dd>(From Panos Pardalos [email protected])
Problems based on problem in coding theory.
A Johnson graph with parameters n; w; d has a node for every binary vector
of length n with exactly w 1s. Two vertices are adjacent if and only if
their hamming distance is at least d. A clique then represents a feasible
set of vectors for a code.
For more instances, see the generator in graph/contributed/pardalos.</dd>
<dt>Kel</dt><dd>(From Peter Shor [email protected])
Problems based on Keller's conjecture on tilings using hypercubes.
One reference is J.C. Lagarias and P.W. Shor,
"Keller's Cube-Tiling Conjecture is False in High Dimensions,"
Bulletin of the AMS, 27: 279-283 (1992).
For more instances (though they get very large very fast) see either
the generator in graph/contributed/shor or the generator
in graph/contributed/pardalos.</dd>
<dt>Ham</dt><dd>(From Panos Pardalos [email protected])
Another coding theory problem. A Hamming graph with parameters n and d
has a node for each binary vector of length n. Two nodes are adjacent
if and only if the corresponding bit vectors are hamming distance at
least d apart.
For more instances, see the generator in graph/contributed/pardalos.
It has been noted by participants that n- -2 graphs have a maximum
clique of size \(2^{n-1}\).
For a proof of this, see the note in graph/contributed/bourjolly/hamming.tex.</dd>
<dt>San</dt><dd>(From Laura Sanchis [email protected])
Instances based on her "Test Case Construction for Vertex Cover Problem,"
DIMACS Workshop on Computational Support for Discrete Mathematics,
March 1992 along with more recent work that will be part of a technical
report to be published. The generator generates instances with known clique size.</dd>
<dt>SanR</dt><dd>(From Laura Sanchis [email protected])
These are random instances with sizes similar to those in San.</dd>
<dt>Bro</dt><dd>(From Mark Brockington [email protected])
Instances from Mark Brockington and Joe Culberson's generator that
attempts to "hide" cliques in a graph where the expected clique size
is much smaller.
For more instances, see their generator in graph/contributed/brockington.</dd>
<dt>PHat</dt><dd>(From Patrick Soriano and Michel Gendreau [email protected])
Random problems generated with the p hat generator which is a
generalization of the classical uniform random graph generator.
Uses 3 parameters: n, the number of nodes, and a and b, two density
parameters verifying \(0 \le a \le b \le 1\). Generates problem instances
having wider node degree spread and larger clique sizes.
Reference: "Solving the Maximum Clique Problem Using a Tabu Search Approach",
Annals of Operations Research 41, 385-403 (1993).</dd>
<dt>Stein</dt><dd>(From Carlo Mannino [email protected])
Clique formulation of the set covering formulation of the Steiner
Triple Problem. Created using Mannino's code to convert set covering
problems to clique problems.
Notes: <code>MANN</code> graphs belongs to this class.</dd>
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<div id="outline-container-orge04f43d" class="outline-2">
<h2 id="orge04f43d"><span class="section-number-2">5</span> Other Instances</h2>
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<dl class="org-dl">
<dt>BHOSLIB</dt><dd>Benchmarks with Hidden Optimum Solutions for Graph Problems (Maximum Clique, Maximum Independent Set, Minimum Vertex Cover and Vertex Coloring): <a href="http://www.nlsde.buaa.edu.cn/~kexu/benchmarks/graph-benchmarks.htm">http://www.nlsde.buaa.edu.cn/~kexu/benchmarks/graph-benchmarks.htm</a></dd>
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<div id="footnotes">
<h2 class="footnotes">Footnotes: </h2>
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<div class="footdef"><sup><a id="fn.1" class="footnum" href="#fnr.1">1</a></sup> <div class="footpara"><p class="footpara">
Optimal clique size obtained from various resources including <a href="http://www.busygin.dp.ua/dimacs_clique.html">http://www.busygin.dp.ua/dimacs_clique.html</a> and <a href="http://mat.gsia.cmu.edu/contents.clique.ps">http://mat.gsia.cmu.edu/contents.clique.ps</a>
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