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<a href="cliques_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// Maximal clique algorithms, based on the Bron-Kerbosch algorithm.</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// See http://en.wikipedia.org/wiki/Bron-Kerbosch_algorithm</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// and</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// C. Bron and J. Kerbosch, Joep, "Algorithm 457: finding all cliques of an</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// undirected graph", CACM 16 (9): 575-577, 1973.</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// http://dl.acm.org/citation.cfm?id=362367&bnc=1.</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// Keywords: undirected graph, clique, clique cover, Bron, Kerbosch.</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  </div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#ifndef OR_TOOLS_GRAPH_CLIQUES_H_</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#define OR_TOOLS_GRAPH_CLIQUES_H_</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  </div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include <functional></span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <numeric></span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "absl/strings/str_cat.h"</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include "ortools/base/int_type.h"</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "ortools/base/logging.h"</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "ortools/base/strong_vector.h"</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "ortools/util/time_limit.h"</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  </div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// Finds all maximal cliques, even of size 1, in the</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// graph described by the graph callback. graph->Run(i, j) indicates</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// if there is an arc between i and j.</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// This function takes ownership of 'callback' and deletes it after it has run.</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// If 'callback' returns true, then the search for cliques stops.</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a509097448ff5705cf3e64d889362bdec"> 44</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#a509097448ff5705cf3e64d889362bdec">FindCliques</a>(std::function<<span class="keywordtype">bool</span>(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph, <span class="keywordtype">int</span> node_count,</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  std::function<<span class="keywordtype">bool</span>(<span class="keyword">const</span> std::vector<int>&)> callback);</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Covers the maximum number of arcs of the graph with cliques. The graph</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// is described by the graph callback. graph->Run(i, j) indicates if</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// there is an arc between i and j.</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// This function takes ownership of 'callback' and deletes it after it has run.</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// It calls 'callback' upon each clique.</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// It ignores cliques of size 1.</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#afe4b5a6c0e4019314f288e3f4307c114"> 53</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#afe4b5a6c0e4019314f288e3f4307c114">CoverArcsByCliques</a>(std::function<<span class="keywordtype">bool</span>(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph, <span class="keywordtype">int</span> node_count,</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  std::function<<span class="keywordtype">bool</span>(<span class="keyword">const</span> std::vector<int>&)> callback);</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// Possible return values of the callback for reporting cliques. The returned</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// value determines whether the algorithm will continue the search.</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119c"> 58</a></span> <span class="keyword">enum class</span> <a class="code" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119c">CliqueResponse</a> {</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// The algorithm will continue searching for other maximal cliques.</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <a class="code" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119ca2f453cfe638e57e27bb0c9512436111e">CONTINUE</a>,</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// The algorithm will stop the search immediately. The search can be resumed</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// by calling BronKerboschAlgorithm::Run (resp. RunIterations) again.</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <a class="code" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119ca615a46af313786fc4e349f34118be111">STOP</a></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> };</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// The status value returned by BronKerboschAlgorithm::Run and</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// BronKerboschAlgorithm::RunIterations.</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8"> 68</a></span> <span class="keyword">enum class</span> <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> {</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// The algorithm has enumerated all maximal cliques.</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8a8f7afecbc8fbc4cd0f50a57d1172482e">COMPLETED</a>,</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// The search algorithm was interrupted either because it reached the</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// iteration limit or because the clique callback returned</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// CliqueResponse::STOP.</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8a658f2cadfdf09b6046246e9314f7cd43">INTERRUPTED</a></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> };</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Implements the Bron-Kerbosch algorithm for finding maximal cliques.</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// The graph is represented as a callback that gets two nodes as its arguments</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// and it returns true if and only if there is an arc between the two nodes. The</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// cliques are reported back to the user using a second callback.</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// Typical usage:</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// auto graph = [](int node1, int node2) { return true; };</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// auto on_clique = [](const std::vector<int>& clique) {</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// LOG(INFO) << "Clique!";</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// };</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// BronKerboschAlgorithm<int> bron_kerbosch(graph, num_nodes, on_clique);</span></div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// bron_kerbosch.Run();</span></div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// or:</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// BronKerboschAlgorithm bron_kerbosch(graph, num_nodes, clique);</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// bron_kerbosch.RunIterations(kMaxNumIterations);</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// This is a non-recursive implementation of the Bron-Kerbosch algorithm with</span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// pivots as described in the paper by Bron and Kerbosch (1973) (the version 2</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// algorithm in the paper).</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// The basic idea of the algorithm is to incrementally build the cliques using</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// depth-first search. During the search, the algorithm maintains two sets of</span></div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// candidates (nodes that are connected to all nodes in the current clique):</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// - the "not" set - these are candidates that were already visited by the</span></div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// search and all the maximal cliques that contain them as a part of the</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// current clique were already reported.</span></div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// - the actual candidates - these are candidates that were not visited yet, and</span></div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// they can be added to the clique.</span></div>
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|
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// In each iteration, the algorithm does the first of the following actions that</span></div>
|
|
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// applies:</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// A. If there are no actual candidates and there are candidates in the "not"</span></div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// set, or if all actual candidates are connected to the same node in the</span></div>
|
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// "not" set, the current clique can't be extended to a maximal clique that</span></div>
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|
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// was not already reported. Return from the recursive call and move the</span></div>
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|
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// selected candidate to the set "not".</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// B. If there are no candidates at all, it means that the current clique can't</span></div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// be extended and that it is in fact a maximal clique. Report it to the user</span></div>
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|
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// and return from the recursive call. Move the selected candidate to the set</span></div>
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|
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// "not".</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// C. Otherwise, there are actual candidates, extend the current clique with one</span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// of these candidates and process it recursively.</span></div>
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|
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// To avoid unnecessary steps, the algorithm selects a pivot at each level of</span></div>
|
|
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// the recursion to guide the selection of candidates added to the current</span></div>
|
|
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// clique. The pivot can be either in the "not" set and among the actual</span></div>
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|
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">// candidates. The algorithm tries to move the pivot and all actual candidates</span></div>
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|
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// connected to it to the set "not" as quickly as possible. This will fulfill</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// the conditions of step A, and the search algorithm will be able to leave the</span></div>
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|
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// current branch. Selecting a pivot that has the lowest number of disconnected</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// nodes among the candidates can reduce the running time significantly.</span></div>
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|
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment">//</span></div>
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|
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// The worst-case maximal depth of the recursion is equal to the number of nodes</span></div>
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|
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// in the graph, which makes the natural recursive implementation impractical</span></div>
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|
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// for nodes with more than a few thousands of nodes. To avoid the limitation,</span></div>
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|
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment">// this class simulates the recursion by maintaining a stack with the state at</span></div>
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|
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// each level of the recursion. The algorithm then runs in a loop. In each</span></div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// iteration, the algorithm can do one or both of:</span></div>
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|
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// 1. Return to the previous recursion level (step A or B of the algorithm) by</span></div>
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|
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// removing the top state from the stack.</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// 2. Select the next candidate and enter the next recursion level (step C of</span></div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// the algorithm) by adding a new state to the stack.</span></div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// The worst-case time complexity of the algorithm is O(3^(N/3)), and the memory</span></div>
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|
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// complexity is O(N^2), where N is the number of nodes in the graph.</span></div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
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<div class="line"><a name="l00144"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html"> 144</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html">BronKerboschAlgorithm</a> {</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// A callback called by the algorithm to test if there is an arc between a</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// pair of nodes. The callback must return true if and only if there is an</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="comment">// arc. Note that to function properly, the function must be symmetrical</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// (represent an undirected graph).</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#ab7e6d525ff89ae730a1c917f3dccc3f0"> 150</a></span>  <span class="keyword">using</span> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#ab7e6d525ff89ae730a1c917f3dccc3f0">IsArcCallback</a> = std::function<bool(<a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>, <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>)>;</div>
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|
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">// A callback called by the algorithm to report a maximal clique to the user.</span></div>
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|
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// The clique is returned as a list of nodes in the clique, in no particular</span></div>
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|
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// order. The caller must make a copy of the vector if they want to keep the</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// nodes.</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// The return value of the callback controls how the algorithm continues after</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">// this clique. See the description of the values of 'CliqueResponse' for more</span></div>
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|
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// details.</span></div>
|
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<div class="line"><a name="l00159"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#aff90108523eb5a8ec3549adc67355aa1"> 159</a></span>  <span class="keyword">using</span> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#aff90108523eb5a8ec3549adc67355aa1">CliqueCallback</a> =</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  std::function<<a class="code" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119c">CliqueResponse</a>(<span class="keyword">const</span> std::vector<NodeIndex>&)>;</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// Initializes the Bron-Kerbosch algorithm for the given graph and clique</span></div>
|
|
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// callback function.</span></div>
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<div class="line"><a name="l00164"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a18c56882f1ab1cfb8a93b0c3c23f1e77"> 164</a></span>  <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a18c56882f1ab1cfb8a93b0c3c23f1e77">BronKerboschAlgorithm</a>(<a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#ab7e6d525ff89ae730a1c917f3dccc3f0">IsArcCallback</a> is_arc, <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> num_nodes,</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#aff90108523eb5a8ec3549adc67355aa1">CliqueCallback</a> clique_callback)</div>
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|
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  : is_arc_(std::move(is_arc)),</div>
|
|
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  clique_callback_(std::move(clique_callback)),</div>
|
|
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  num_nodes_(num_nodes) {}</div>
|
|
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  </div>
|
|
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// Runs the Bron-Kerbosch algorithm for kint64max iterations. In practice,</span></div>
|
|
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// this is equivalent to running until completion or until the clique callback</span></div>
|
|
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="comment">// returns BronKerboschAlgorithmStatus::STOP. If the method returned because</span></div>
|
|
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">// the search is finished, it will return COMPLETED; otherwise, it will return</span></div>
|
|
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// INTERRUPTED and it can be resumed by calling this method again.</span></div>
|
|
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a14ad57c326955d7c5be67f0e444ff9eb">Run</a>();</div>
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|
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  </div>
|
|
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="comment">// Runs at most 'max_num_iterations' iterations of the Bron-Kerbosch</span></div>
|
|
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">// algorithm. When this function returns INTERRUPTED, there is still work to</span></div>
|
|
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// be done to process all the cliques in the graph. In such case the method</span></div>
|
|
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="comment">// can be called again and it will resume the work where the previous call had</span></div>
|
|
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="comment">// stopped. When it returns COMPLETED any subsequent call to the method will</span></div>
|
|
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="comment">// resume the search from the beginning.</span></div>
|
|
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a2f5f0a127dbe36c5518b68872efd8ad1">RunIterations</a>(int64_t max_num_iterations);</div>
|
|
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  </div>
|
|
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="comment">// Runs at most 'max_num_iterations' iterations of the Bron-Kerbosch</span></div>
|
|
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="comment">// algorithm, until the time limit is exceeded or until all cliques are</span></div>
|
|
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="comment">// enumerated. When this function returns INTERRUPTED, there is still work to</span></div>
|
|
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="comment">// be done to process all the cliques in the graph. In such case the method</span></div>
|
|
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="comment">// can be called again and it will resume the work where the previous call had</span></div>
|
|
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">// stopped. When it returns COMPLETED any subsequent call to the method will</span></div>
|
|
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="comment">// resume the search from the beginning.</span></div>
|
|
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a4eb3c164e162e27f2d6ca3dd0b7355d4">RunWithTimeLimit</a>(int64_t max_num_iterations,</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  TimeLimit* time_limit);</div>
|
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  </div>
|
|
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="comment">// Runs the Bron-Kerbosch algorithm for at most kint64max iterations, until</span></div>
|
|
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// the time limit is excceded or until all cliques are enumerated. In</span></div>
|
|
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="comment">// practice, running the algorithm for kint64max iterations is equivalent to</span></div>
|
|
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// running until completion or until the other stopping conditions apply. When</span></div>
|
|
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// this function returns INTERRUPTED, there is still work to be done to</span></div>
|
|
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// process all the cliques in the graph. In such case the method can be called</span></div>
|
|
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// again and it will resume the work where the previous call had stopped. When</span></div>
|
|
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// it returns COMPLETED any subsequent call to the method will resume the</span></div>
|
|
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="comment">// search from the beginning.</span></div>
|
|
<div class="line"><a name="l00204"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a8594a59f12eedf7ed0d8f8d2e56ca751"> 204</a></span>  <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a8594a59f12eedf7ed0d8f8d2e56ca751">RunWithTimeLimit</a>(TimeLimit* time_limit) {</div>
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|
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a4eb3c164e162e27f2d6ca3dd0b7355d4">RunWithTimeLimit</a>(kint64max, time_limit);</div>
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|
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  }</div>
|
|
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
|
|
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">private</span>:</div>
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|
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  DEFINE_INT_TYPE(CandidateIndex, ptrdiff_t);</div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  </div>
|
|
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// A data structure that maintains the variables of one "iteration" of the</span></div>
|
|
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="comment">// search algorithm. These are the variables that would normally be allocated</span></div>
|
|
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">// on the stack in the recursive implementation.</span></div>
|
|
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">// Note that most of the variables in the structure are explicitly left</span></div>
|
|
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// uninitialized by the constructor to avoid wasting resources on values that</span></div>
|
|
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="comment">// will be overwritten anyway. Most of the initialization is done in</span></div>
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|
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">// BronKerboschAlgorithm::InitializeState.</span></div>
|
|
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">struct </span>State {</div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  State() {}</div>
|
|
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  State(<span class="keyword">const</span> State& other)</div>
|
|
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  : pivot(other.pivot),</div>
|
|
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  num_remaining_candidates(other.num_remaining_candidates),</div>
|
|
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  candidates(other.candidates),</div>
|
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  first_candidate_index(other.first_candidate_index),</div>
|
|
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  candidate_for_recursion(other.candidate_for_recursion) {}</div>
|
|
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  </div>
|
|
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  State& operator=(<span class="keyword">const</span> State& other) {</div>
|
|
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  pivot = other.pivot;</div>
|
|
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  num_remaining_candidates = other.num_remaining_candidates;</div>
|
|
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  candidates = other.candidates;</div>
|
|
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  first_candidate_index = other.first_candidate_index;</div>
|
|
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  candidate_for_recursion = other.candidate_for_recursion;</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
|
|
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  }</div>
|
|
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  </div>
|
|
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">// Moves the first candidate in the state to the "not" set. Assumes that the</span></div>
|
|
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// first candidate is also the pivot or a candidate disconnected from the</span></div>
|
|
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// pivot (as done by RunIteration).</span></div>
|
|
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> MoveFirstCandidateToNotSet() {</div>
|
|
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  ++first_candidate_index;</div>
|
|
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  --num_remaining_candidates;</div>
|
|
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  }</div>
|
|
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  </div>
|
|
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="comment">// Creates a human-readable representation of the current state.</span></div>
|
|
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  std::string DebugString() {</div>
|
|
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  std::string buffer;</div>
|
|
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  absl::StrAppend(&buffer, <span class="stringliteral">"pivot = "</span>, pivot,</div>
|
|
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="stringliteral">"\nnum_remaining_candidates = "</span>, num_remaining_candidates,</div>
|
|
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="stringliteral">"\ncandidates = ["</span>);</div>
|
|
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">for</span> (CandidateIndex i(0); i < candidates.size(); ++i) {</div>
|
|
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keywordflow">if</span> (i > 0) buffer += <span class="stringliteral">", "</span>;</div>
|
|
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  absl::StrAppend(&buffer, candidates[i]);</div>
|
|
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  }</div>
|
|
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  absl::StrAppend(</div>
|
|
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  &buffer, <span class="stringliteral">"]\nfirst_candidate_index = "</span>, first_candidate_index.value(),</div>
|
|
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="stringliteral">"\ncandidate_for_recursion = "</span>, candidate_for_recursion.value());</div>
|
|
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">return</span> buffer;</div>
|
|
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  }</div>
|
|
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  </div>
|
|
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="comment">// The pivot node selected for the given level of the recursion.</span></div>
|
|
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> pivot;</div>
|
|
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="comment">// The number of remaining candidates to be explored at the given level of</span></div>
|
|
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="comment">// the recursion; the number is computed as num_disconnected_nodes +</span></div>
|
|
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="comment">// pre_increment in the original algorithm.</span></div>
|
|
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordtype">int</span> num_remaining_candidates;</div>
|
|
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="comment">// The list of nodes that are candidates for extending the current clique.</span></div>
|
|
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="comment">// This vector has the format proposed in the paper by Bron-Kerbosch; the</span></div>
|
|
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="comment">// first 'first_candidate_index' elements of the vector represent the</span></div>
|
|
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">// "not" set of nodes that were already visited by the algorithm. The</span></div>
|
|
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">// remaining elements are the actual candidates for extending the current</span></div>
|
|
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="comment">// clique.</span></div>
|
|
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="comment">// NOTE(user): We could store the delta between the iterations; however,</span></div>
|
|
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="comment">// we need to evaluate the impact this would have on the performance.</span></div>
|
|
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  absl::StrongVector<CandidateIndex, NodeIndex> candidates;</div>
|
|
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="comment">// The index of the first actual candidate in 'candidates'. This number is</span></div>
|
|
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// also the number of elements of the "not" set stored at the beginning of</span></div>
|
|
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="comment">// 'candidates'.</span></div>
|
|
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  CandidateIndex first_candidate_index;</div>
|
|
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  </div>
|
|
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="comment">// The current position in candidates when looking for the pivot and/or the</span></div>
|
|
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">// next candidate disconnected from the pivot.</span></div>
|
|
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  CandidateIndex candidate_for_recursion;</div>
|
|
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  };</div>
|
|
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  </div>
|
|
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// The deterministic time coefficients for the push and pop operations of the</span></div>
|
|
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="comment">// Bron-Kerbosch algorithm. The coefficients are set to match approximately</span></div>
|
|
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// the running time in seconds on a recent workstation on the random graph</span></div>
|
|
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// benchmark.</span></div>
|
|
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="comment">// NOTE(user): PushState is not the only source of complexity in the</span></div>
|
|
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="comment">// algorithm, but non-negative linear least squares produced zero coefficients</span></div>
|
|
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="comment">// for all other deterministic counters tested during the benchmarking. When</span></div>
|
|
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="comment">// we optimize the algorithm, we might need to add deterministic time to the</span></div>
|
|
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="comment">// other places that may produce complexity, namely InitializeState, PopState</span></div>
|
|
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="comment">// and SelectCandidateIndexForRecursion.</span></div>
|
|
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> kPushStateDeterministicTimeSecondsPerCandidate;</div>
|
|
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  </div>
|
|
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// Initializes the root state of the algorithm.</span></div>
|
|
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordtype">void</span> Initialize();</div>
|
|
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  </div>
|
|
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="comment">// Removes the top state from the state stack. This is equivalent to returning</span></div>
|
|
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="comment">// in the recursive implementation of the algorithm.</span></div>
|
|
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keywordtype">void</span> PopState();</div>
|
|
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  </div>
|
|
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// Adds a new state to the top of the stack, adding the node 'selected' to the</span></div>
|
|
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="comment">// current clique. This is equivalent to making a recurisve call in the</span></div>
|
|
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="comment">// recursive implementation of the algorithm.</span></div>
|
|
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordtype">void</span> PushState(<a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> selected);</div>
|
|
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  </div>
|
|
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// Initializes the given state. Runs the pivot selection algorithm in the</span></div>
|
|
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="comment">// state.</span></div>
|
|
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordtype">void</span> InitializeState(State* state);</div>
|
|
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  </div>
|
|
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// Returns true if (node1, node2) is an arc in the graph or if node1 == node2.</span></div>
|
|
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> IsArc(<a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node1, <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node2)<span class="keyword"> const </span>{</div>
|
|
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">return</span> node1 == node2 || is_arc_(node1, node2);</div>
|
|
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  }</div>
|
|
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  </div>
|
|
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="comment">// Selects the next node for recursion. The selected node is either the pivot</span></div>
|
|
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="comment">// (if it is not in the set "not") or a node that is disconnected from the</span></div>
|
|
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="comment">// pivot.</span></div>
|
|
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  CandidateIndex SelectCandidateIndexForRecursion(State* state);</div>
|
|
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  </div>
|
|
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="comment">// Returns a human-readable string representation of the clique.</span></div>
|
|
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  std::string CliqueDebugString(<span class="keyword">const</span> std::vector<NodeIndex>& clique);</div>
|
|
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  </div>
|
|
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="comment">// The callback called when the algorithm needs to determine if (node1, node2)</span></div>
|
|
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="comment">// is an arc in the graph.</span></div>
|
|
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#ab7e6d525ff89ae730a1c917f3dccc3f0">IsArcCallback</a> is_arc_;</div>
|
|
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  </div>
|
|
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="comment">// The callback called when the algorithm discovers a maximal clique. The</span></div>
|
|
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="comment">// return value of the callback controls how the algorithm proceeds with the</span></div>
|
|
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="comment">// clique search.</span></div>
|
|
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#aff90108523eb5a8ec3549adc67355aa1">CliqueCallback</a> clique_callback_;</div>
|
|
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  </div>
|
|
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="comment">// The number of nodes in the graph.</span></div>
|
|
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> num_nodes_;</div>
|
|
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  </div>
|
|
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">// Contains the state of the aglorithm. The vector serves as an external stack</span></div>
|
|
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="comment">// for the recursive part of the algorithm - instead of using the C++ stack</span></div>
|
|
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="comment">// and natural recursion, it is implemented as a loop and new states are added</span></div>
|
|
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="comment">// to the top of the stack. The algorithm ends when the stack is empty.</span></div>
|
|
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  std::vector<State> states_;</div>
|
|
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  </div>
|
|
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// A vector that receives the current clique found by the algorithm.</span></div>
|
|
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  std::vector<NodeIndex> current_clique_;</div>
|
|
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  </div>
|
|
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// Set to true if the algorithm is active (it was not stopped by an the clique</span></div>
|
|
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">// callback).</span></div>
|
|
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  int64_t num_remaining_iterations_;</div>
|
|
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  </div>
|
|
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="comment">// The current time limit used by the solver. The time limit is assigned by</span></div>
|
|
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">// the Run methods and it can be different for each call to run.</span></div>
|
|
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  TimeLimit* time_limit_;</div>
|
|
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> };</div>
|
|
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  </div>
|
|
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="keywordtype">void</span> BronKerboschAlgorithm<NodeIndex>::InitializeState(State* state) {</div>
|
|
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  DCHECK(state != <span class="keyword">nullptr</span>);</div>
|
|
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_candidates = state->candidates.size();</div>
|
|
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keywordtype">int</span> num_disconnected_candidates = num_candidates;</div>
|
|
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  state->pivot = 0;</div>
|
|
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  CandidateIndex pivot_index(-1);</div>
|
|
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="keywordflow">for</span> (CandidateIndex pivot_candidate_index(0);</div>
|
|
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  pivot_candidate_index < num_candidates &&</div>
|
|
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  num_disconnected_candidates > 0;</div>
|
|
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  ++pivot_candidate_index) {</div>
|
|
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> pivot_candidate = state->candidates[pivot_candidate_index];</div>
|
|
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordtype">int</span> count = 0;</div>
|
|
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keywordflow">for</span> (CandidateIndex i(state->first_candidate_index); i < num_candidates;</div>
|
|
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  ++i) {</div>
|
|
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keywordflow">if</span> (!IsArc(pivot_candidate, state->candidates[i])) {</div>
|
|
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  ++count;</div>
|
|
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  }</div>
|
|
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  }</div>
|
|
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keywordflow">if</span> (count < num_disconnected_candidates) {</div>
|
|
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  pivot_index = pivot_candidate_index;</div>
|
|
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  state->pivot = pivot_candidate;</div>
|
|
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  num_disconnected_candidates = count;</div>
|
|
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  }</div>
|
|
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  }</div>
|
|
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  state->num_remaining_candidates = num_disconnected_candidates;</div>
|
|
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordflow">if</span> (pivot_index >= state->first_candidate_index) {</div>
|
|
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  std::swap(state->candidates[pivot_index],</div>
|
|
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  state->candidates[state->first_candidate_index]);</div>
|
|
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  ++state->num_remaining_candidates;</div>
|
|
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  }</div>
|
|
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> }</div>
|
|
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  </div>
|
|
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="keyword">typename</span> BronKerboschAlgorithm<NodeIndex>::CandidateIndex</div>
|
|
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> BronKerboschAlgorithm<NodeIndex>::SelectCandidateIndexForRecursion(</div>
|
|
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  State* state) {</div>
|
|
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  DCHECK(state != <span class="keyword">nullptr</span>);</div>
|
|
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  CandidateIndex disconnected_node_index =</div>
|
|
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  std::max(state->first_candidate_index, state->candidate_for_recursion);</div>
|
|
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordflow">while</span> (disconnected_node_index < state->candidates.size() &&</div>
|
|
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  state->candidates[disconnected_node_index] != state->pivot &&</div>
|
|
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  IsArc(state->pivot, state->candidates[disconnected_node_index])) {</div>
|
|
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  ++disconnected_node_index;</div>
|
|
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  }</div>
|
|
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  state->candidate_for_recursion = disconnected_node_index;</div>
|
|
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">return</span> disconnected_node_index;</div>
|
|
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span> }</div>
|
|
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  </div>
|
|
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="keywordtype">void</span> BronKerboschAlgorithm<NodeIndex>::Initialize() {</div>
|
|
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  DCHECK(states_.empty());</div>
|
|
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  states_.reserve(num_nodes_);</div>
|
|
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  states_.emplace_back();</div>
|
|
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  </div>
|
|
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  State* <span class="keyword">const</span> root_state = &states_.back();</div>
|
|
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  root_state->first_candidate_index = 0;</div>
|
|
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  root_state->candidate_for_recursion = 0;</div>
|
|
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  root_state->candidates.resize(num_nodes_, 0);</div>
|
|
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  std::iota(root_state->candidates.begin(), root_state->candidates.end(), 0);</div>
|
|
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  root_state->num_remaining_candidates = num_nodes_;</div>
|
|
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  InitializeState(root_state);</div>
|
|
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  </div>
|
|
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  DVLOG(2) << <span class="stringliteral">"Initialized"</span>;</div>
|
|
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> }</div>
|
|
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  </div>
|
|
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="keywordtype">void</span> BronKerboschAlgorithm<NodeIndex>::PopState() {</div>
|
|
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  DCHECK(!states_.empty());</div>
|
|
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  states_.pop_back();</div>
|
|
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <span class="keywordflow">if</span> (!states_.empty()) {</div>
|
|
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  State* <span class="keyword">const</span> state = &states_.back();</div>
|
|
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  current_clique_.pop_back();</div>
|
|
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  state->MoveFirstCandidateToNotSet();</div>
|
|
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  }</div>
|
|
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> }</div>
|
|
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  </div>
|
|
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> std::string BronKerboschAlgorithm<NodeIndex>::CliqueDebugString(</div>
|
|
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keyword">const</span> std::vector<NodeIndex>& clique) {</div>
|
|
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  std::string message = <span class="stringliteral">"Clique: [ "</span>;</div>
|
|
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node : clique) {</div>
|
|
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  absl::StrAppend(&message, node, <span class="stringliteral">" "</span>);</div>
|
|
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  }</div>
|
|
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  message += <span class="stringliteral">"]"</span>;</div>
|
|
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">return</span> message;</div>
|
|
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> }</div>
|
|
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  </div>
|
|
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="keywordtype">void</span> BronKerboschAlgorithm<NodeIndex>::PushState(<a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> selected) {</div>
|
|
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  DCHECK(!states_.empty());</div>
|
|
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  DCHECK(time_limit_ != <span class="keyword">nullptr</span>);</div>
|
|
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  DVLOG(2) << <span class="stringliteral">"PushState: New depth = "</span> << states_.size() + 1</div>
|
|
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  << <span class="stringliteral">", selected node = "</span> << selected;</div>
|
|
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  absl::StrongVector<CandidateIndex, NodeIndex> new_candidates;</div>
|
|
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  </div>
|
|
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  State* <span class="keyword">const</span> previous_state = &states_.back();</div>
|
|
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> deterministic_time =</div>
|
|
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  kPushStateDeterministicTimeSecondsPerCandidate *</div>
|
|
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  previous_state->candidates.size();</div>
|
|
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  time_limit_->AdvanceDeterministicTime(deterministic_time, <span class="stringliteral">"PushState"</span>);</div>
|
|
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  </div>
|
|
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="comment">// Add all candidates from previous_state->candidates that are connected to</span></div>
|
|
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">// 'selected' in the graph to the vector 'new_candidates', skipping the node</span></div>
|
|
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="comment">// 'selected'; this node is always at the position</span></div>
|
|
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="comment">// 'previous_state->first_candidate_index', so we can skip it by skipping the</span></div>
|
|
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="comment">// element at this particular index.</span></div>
|
|
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  new_candidates.reserve(previous_state->candidates.size());</div>
|
|
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">for</span> (CandidateIndex i(0); i < previous_state->first_candidate_index; ++i) {</div>
|
|
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> candidate = previous_state->candidates[i];</div>
|
|
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordflow">if</span> (IsArc(selected, candidate)) {</div>
|
|
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  new_candidates.push_back(candidate);</div>
|
|
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  }</div>
|
|
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  }</div>
|
|
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <span class="keyword">const</span> CandidateIndex new_first_candidate_index(new_candidates.size());</div>
|
|
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keywordflow">for</span> (CandidateIndex i = previous_state->first_candidate_index + 1;</div>
|
|
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  i < previous_state->candidates.size(); ++i) {</div>
|
|
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> candidate = previous_state->candidates[i];</div>
|
|
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">if</span> (IsArc(selected, candidate)) {</div>
|
|
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  new_candidates.push_back(candidate);</div>
|
|
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  }</div>
|
|
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  }</div>
|
|
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  </div>
|
|
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  current_clique_.push_back(selected);</div>
|
|
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">if</span> (new_candidates.empty()) {</div>
|
|
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="comment">// We've found a clique. Report it to the user, but do not push the state</span></div>
|
|
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="comment">// because it would be popped immediately anyway.</span></div>
|
|
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  DVLOG(2) << CliqueDebugString(current_clique_);</div>
|
|
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119c">CliqueResponse</a> response = clique_callback_(current_clique_);</div>
|
|
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <span class="keywordflow">if</span> (response == <a class="code" href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119ca615a46af313786fc4e349f34118be111">CliqueResponse::STOP</a>) {</div>
|
|
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="comment">// The number of remaining iterations will be decremented at the end of</span></div>
|
|
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="comment">// the loop in RunIterations; setting it to 0 here would make it -1 at</span></div>
|
|
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="comment">// the end of the main loop.</span></div>
|
|
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  num_remaining_iterations_ = 1;</div>
|
|
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  }</div>
|
|
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  current_clique_.pop_back();</div>
|
|
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  previous_state->MoveFirstCandidateToNotSet();</div>
|
|
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  }</div>
|
|
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  </div>
|
|
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="comment">// NOTE(user): The following line may invalidate previous_state (if the</span></div>
|
|
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="comment">// vector data was re-allocated in the process). We must avoid using</span></div>
|
|
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="comment">// previous_state below here.</span></div>
|
|
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  states_.emplace_back();</div>
|
|
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  State* <span class="keyword">const</span> new_state = &states_.back();</div>
|
|
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  new_state->candidates.swap(new_candidates);</div>
|
|
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  new_state->first_candidate_index = new_first_candidate_index;</div>
|
|
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  </div>
|
|
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  InitializeState(new_state);</div>
|
|
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> }</div>
|
|
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  </div>
|
|
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
|
|
<div class="line"><a name="l00509"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a4eb3c164e162e27f2d6ca3dd0b7355d4"> 509</a></span> <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a4eb3c164e162e27f2d6ca3dd0b7355d4">BronKerboschAlgorithm<NodeIndex>::RunWithTimeLimit</a>(</div>
|
|
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  int64_t max_num_iterations, TimeLimit* time_limit) {</div>
|
|
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  CHECK(time_limit != <span class="keyword">nullptr</span>);</div>
|
|
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  time_limit_ = time_limit;</div>
|
|
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keywordflow">if</span> (states_.empty()) {</div>
|
|
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  Initialize();</div>
|
|
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  }</div>
|
|
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keywordflow">for</span> (num_remaining_iterations_ = max_num_iterations;</div>
|
|
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  !states_.empty() && num_remaining_iterations_ > 0 &&</div>
|
|
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  !time_limit->LimitReached();</div>
|
|
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  --num_remaining_iterations_) {</div>
|
|
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  State* <span class="keyword">const</span> state = &states_.back();</div>
|
|
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  DVLOG(2) << <span class="stringliteral">"Loop: "</span> << states_.size() << <span class="stringliteral">" states, "</span></div>
|
|
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  << state->num_remaining_candidates << <span class="stringliteral">" candidate to explore\n"</span></div>
|
|
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  << state->DebugString();</div>
|
|
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordflow">if</span> (state->num_remaining_candidates == 0) {</div>
|
|
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  PopState();</div>
|
|
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">continue</span>;</div>
|
|
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  }</div>
|
|
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  </div>
|
|
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keyword">const</span> CandidateIndex selected_index =</div>
|
|
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  SelectCandidateIndexForRecursion(state);</div>
|
|
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  DVLOG(2) << <span class="stringliteral">"selected_index = "</span> << selected_index;</div>
|
|
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> selected = state->candidates[selected_index];</div>
|
|
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  DVLOG(2) << <span class="stringliteral">"Selected candidate = "</span> << selected;</div>
|
|
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  </div>
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<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>& f = state->candidates[state->first_candidate_index];</div>
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<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>& s = state->candidates[selected_index];</div>
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<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  std::swap(f, s);</div>
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<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  </div>
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<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  PushState(selected);</div>
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<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  }</div>
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<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  time_limit_ = <span class="keyword">nullptr</span>;</div>
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<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keywordflow">return</span> states_.empty() ? <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8a8f7afecbc8fbc4cd0f50a57d1172482e">BronKerboschAlgorithmStatus::COMPLETED</a></div>
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<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  : <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8a658f2cadfdf09b6046246e9314f7cd43">BronKerboschAlgorithmStatus::INTERRUPTED</a>;</div>
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<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> }</div>
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<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  </div>
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<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
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<div class="line"><a name="l00547"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a2f5f0a127dbe36c5518b68872efd8ad1"> 547</a></span> <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a2f5f0a127dbe36c5518b68872efd8ad1">BronKerboschAlgorithm<NodeIndex>::RunIterations</a>(</div>
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<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  int64_t max_num_iterations) {</div>
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<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  TimeLimit time_limit(std::numeric_limits<double>::infinity());</div>
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<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keywordflow">return</span> RunWithTimeLimit(max_num_iterations, &time_limit);</div>
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<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> }</div>
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<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  </div>
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<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
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<div class="line"><a name="l00554"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a14ad57c326955d7c5be67f0e444ff9eb"> 554</a></span> <a class="code" href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">BronKerboschAlgorithmStatus</a> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a14ad57c326955d7c5be67f0e444ff9eb">BronKerboschAlgorithm<NodeIndex>::Run</a>() {</div>
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<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">return</span> RunIterations(kint64max);</div>
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<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> }</div>
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<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  </div>
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<div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
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<div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="classoperations__research_1_1_bron_kerbosch_algorithm.html">BronKerboschAlgorithm</a><</div>
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<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>>::kPushStateDeterministicTimeSecondsPerCandidate = 0.54663e-7;</div>
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<div class="line"><a name="l00561"></a><span class="lineno"> 561</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  </div>
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<div class="line"><a name="l00563"></a><span class="lineno"> 563</span> <span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_GRAPH_CLIQUES_H_</span></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html">operations_research::BronKerboschAlgorithm</a></div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00144">cliques.h:144</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_a14ad57c326955d7c5be67f0e444ff9eb"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a14ad57c326955d7c5be67f0e444ff9eb">operations_research::BronKerboschAlgorithm::Run</a></div><div class="ttdeci">BronKerboschAlgorithmStatus Run()</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00554">cliques.h:554</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_a18c56882f1ab1cfb8a93b0c3c23f1e77"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a18c56882f1ab1cfb8a93b0c3c23f1e77">operations_research::BronKerboschAlgorithm::BronKerboschAlgorithm</a></div><div class="ttdeci">BronKerboschAlgorithm(IsArcCallback is_arc, NodeIndex num_nodes, CliqueCallback clique_callback)</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00164">cliques.h:164</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_a2f5f0a127dbe36c5518b68872efd8ad1"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a2f5f0a127dbe36c5518b68872efd8ad1">operations_research::BronKerboschAlgorithm::RunIterations</a></div><div class="ttdeci">BronKerboschAlgorithmStatus RunIterations(int64_t max_num_iterations)</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00547">cliques.h:547</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_a4eb3c164e162e27f2d6ca3dd0b7355d4"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a4eb3c164e162e27f2d6ca3dd0b7355d4">operations_research::BronKerboschAlgorithm::RunWithTimeLimit</a></div><div class="ttdeci">BronKerboschAlgorithmStatus RunWithTimeLimit(int64_t max_num_iterations, TimeLimit *time_limit)</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00509">cliques.h:509</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_a8594a59f12eedf7ed0d8f8d2e56ca751"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#a8594a59f12eedf7ed0d8f8d2e56ca751">operations_research::BronKerboschAlgorithm::RunWithTimeLimit</a></div><div class="ttdeci">BronKerboschAlgorithmStatus RunWithTimeLimit(TimeLimit *time_limit)</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00204">cliques.h:204</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_ab7e6d525ff89ae730a1c917f3dccc3f0"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#ab7e6d525ff89ae730a1c917f3dccc3f0">operations_research::BronKerboschAlgorithm::IsArcCallback</a></div><div class="ttdeci">std::function< bool(NodeIndex, NodeIndex)> IsArcCallback</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00150">cliques.h:150</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bron_kerbosch_algorithm_html_aff90108523eb5a8ec3549adc67355aa1"><div class="ttname"><a href="classoperations__research_1_1_bron_kerbosch_algorithm.html#aff90108523eb5a8ec3549adc67355aa1">operations_research::BronKerboschAlgorithm::CliqueCallback</a></div><div class="ttdeci">std::function< CliqueResponse(const std::vector< NodeIndex > &)> CliqueCallback</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00159">cliques.h:160</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdef"><b>Definition:</b> <a href="christofides_8h_source.html#l00035">christofides.h:35</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a509097448ff5705cf3e64d889362bdec"><div class="ttname"><a href="namespaceoperations__research.html#a509097448ff5705cf3e64d889362bdec">operations_research::FindCliques</a></div><div class="ttdeci">void FindCliques(std::function< bool(int, int)> graph, int node_count, std::function< bool(const std::vector< int > &)> callback)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a7ffcae041a5d746371436101400cdb6b"><div class="ttname"><a href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">operations_research::NodeIndex</a></div><div class="ttdeci">int32_t NodeIndex</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00200">ebert_graph.h:192</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_abd4e546b0e3afb0208c7a44ee6ab4ea8"><div class="ttname"><a href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8">operations_research::BronKerboschAlgorithmStatus</a></div><div class="ttdeci">BronKerboschAlgorithmStatus</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00068">cliques.h:68</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_abd4e546b0e3afb0208c7a44ee6ab4ea8a658f2cadfdf09b6046246e9314f7cd43"><div class="ttname"><a href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8a658f2cadfdf09b6046246e9314f7cd43">operations_research::BronKerboschAlgorithmStatus::INTERRUPTED</a></div><div class="ttdeci">@ INTERRUPTED</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_abd4e546b0e3afb0208c7a44ee6ab4ea8a8f7afecbc8fbc4cd0f50a57d1172482e"><div class="ttname"><a href="namespaceoperations__research.html#abd4e546b0e3afb0208c7a44ee6ab4ea8a8f7afecbc8fbc4cd0f50a57d1172482e">operations_research::BronKerboschAlgorithmStatus::COMPLETED</a></div><div class="ttdeci">@ COMPLETED</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ae6df4b4cb7c39ca06812199bbee9119c"><div class="ttname"><a href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119c">operations_research::CliqueResponse</a></div><div class="ttdeci">CliqueResponse</div><div class="ttdef"><b>Definition:</b> <a href="cliques_8h_source.html#l00058">cliques.h:58</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ae6df4b4cb7c39ca06812199bbee9119ca2f453cfe638e57e27bb0c9512436111e"><div class="ttname"><a href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119ca2f453cfe638e57e27bb0c9512436111e">operations_research::CliqueResponse::CONTINUE</a></div><div class="ttdeci">@ CONTINUE</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ae6df4b4cb7c39ca06812199bbee9119ca615a46af313786fc4e349f34118be111"><div class="ttname"><a href="namespaceoperations__research.html#ae6df4b4cb7c39ca06812199bbee9119ca615a46af313786fc4e349f34118be111">operations_research::CliqueResponse::STOP</a></div><div class="ttdeci">@ STOP</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_afe4b5a6c0e4019314f288e3f4307c114"><div class="ttname"><a href="namespaceoperations__research.html#afe4b5a6c0e4019314f288e3f4307c114">operations_research::CoverArcsByCliques</a></div><div class="ttdeci">void CoverArcsByCliques(std::function< bool(int, int)> graph, int node_count, std::function< bool(const std::vector< int > &)> callback)</div></div>
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