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<div class="title">cliques.cc</div> </div>
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<a href="cliques_8cc.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 2010-2018 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="preprocessor">#include "<a class="code" href="cliques_8h.html">ortools/graph/cliques.h</a>"</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  </div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <memory></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include <utility></span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  </div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "absl/container/flat_hash_set.h"</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="hash_8h.html">ortools/base/hash.h</a>"</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="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="keyword">namespace </span>{</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// Encapsulates graph() to make all nodes self-connected.</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> Connects(std::function<<span class="keywordtype">bool</span>(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph, <span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) {</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordflow">return</span> i == j || graph(i, j);</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</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="comment">// Implements the recursive step of the Bron-Kerbosch algorithm with pivoting.</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// - graph is a callback such that graph->Run(i, j) returns true iff there is an</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// arc between i and j.</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// - callback is a callback called for all maximal cliques discovered by the</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// algorithm.</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// - input_candidates is an array that contains the list of nodes connected to</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// all nodes in the current clique. It is composed of two parts; the first</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// part contains the "not" set (nodes that were already processed and must not</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// be added to the clique - see the description of the algorithm in the</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// paper), and nodes that are candidates for addition. The candidates from the</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// "not" set are at the beginning of the array.</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// - first_candidate_index elements is the index of the first candidate that is</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// not in the "not" set (which is also the number of candidates in the "not"</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// set).</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// - num_input_candidates is the number of elements in input_candidates,</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// including both the "not" set and the actual candidates.</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// - current_clique is the current clique discovered by the algorithm.</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// - stop is a stopping condition for the algorithm; if the value it points to</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// is true, the algorithm stops further exploration and returns.</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// TODO(user) : rewrite this algorithm without recursion.</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">void</span> Search(std::function<<span class="keywordtype">bool</span>(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  std::function<<span class="keywordtype">bool</span>(<span class="keyword">const</span> std::vector<int>&)> <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>,</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordtype">int</span>* input_candidates, <span class="keywordtype">int</span> first_candidate_index,</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">int</span> num_input_candidates, std::vector<int>* current_clique,</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">bool</span>* stop) {</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// The pivot is a node from input_candidates that is disconnected from the</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// minimal number of nodes in the actual candidates (excluding the "not" set);</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// the algorithm then selects only candidates that are disconnected from the</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// pivot (and the pivot itself), to reach the termination condition as quickly</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// as possible (see the original paper for more details).</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordtype">int</span> pivot = 0;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// A node that is disconnected from the selected pivot. This node is selected</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">// during the pivot matching phase to speed up the first iteration of the</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// recursive call.</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">int</span> disconnected_node = 0;</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// The number of candidates (that are not in "not") disconnected from the</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// selected pivot. The value is computed during pivot selection. In the</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// "recursive" phase, we only need to do explore num_disconnected_candidates</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// nodes, because after this step, all remaining candidates will all be</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// connected to the pivot node (which is in "not"), so they can't form a</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// maximal clique.</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordtype">int</span> num_disconnected_candidates = num_input_candidates;</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>  <span class="comment">// If the selected pivot is not in "not", we need to process one more</span></div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// candidate (the pivot itself). pre_increment is added to</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// num_disconnected_candidates to compensate for this fact.</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordtype">int</span> pre_increment = 0;</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  </div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">// Find Pivot.</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_input_candidates && num_disconnected_candidates != 0;</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  ++i) {</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">int</span> pivot_candidate = input_candidates[i];</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  </div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">// Count is the number of candidates (not including nodes in the "not" set)</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="comment">// that are disconnected from the pivot candidate.</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordtype">int</span> count = 0;</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// The index of a candidate node that is not connected to pivot_candidate.</span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// This node will be used to quickly start the nested iteration (we keep</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// track of the index so that we don't have to find a node that is</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// disconnected from the pivot later in the iteration).</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordtype">int</span> disconnected_node_candidate = 0;</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// Compute the number of candidate nodes that are disconnected from</span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// pivot_candidate. Note that this computation is the same for the "not"</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// candidates and the normal candidates.</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = first_candidate_index;</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  j < num_input_candidates && count < num_disconnected_candidates; ++j) {</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">if</span> (!Connects(graph, pivot_candidate, input_candidates[j])) {</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  count++;</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  disconnected_node_candidate = j;</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  }</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  </div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// Update the pivot candidate if we found a new minimum for</span></div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// num_disconnected_candidates.</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">if</span> (count < num_disconnected_candidates) {</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  pivot = pivot_candidate;</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  num_disconnected_candidates = count;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">if</span> (i < first_candidate_index) {</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  disconnected_node = disconnected_node_candidate;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  disconnected_node = i;</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// The pivot candidate is not in the "not" set. We need to pre-increment</span></div>
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|
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// the counter for the node to compensate for that.</span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  pre_increment = 1;</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  }</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  }</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  std::vector<int> new_candidates;</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  new_candidates.reserve(num_input_candidates);</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> remaining_candidates = num_disconnected_candidates + pre_increment;</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  remaining_candidates >= 1; remaining_candidates--) {</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// Swap a node that is disconnected from the pivot (or the pivot itself)</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// with the first candidate, so that we can later move it to "not" simply by</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">// increasing the index of the first candidate that is not in "not".</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> selected = input_candidates[disconnected_node];</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  std::swap(input_candidates[disconnected_node],</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  input_candidates[first_candidate_index]);</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  </div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">// Fill the list of candidates and the "not" set for the recursive call:</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  new_candidates.clear();</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < first_candidate_index; ++i) {</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">if</span> (Connects(graph, selected, input_candidates[i])) {</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  new_candidates.push_back(input_candidates[i]);</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  }</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  }</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> new_first_candidate_index = new_candidates.size();</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = first_candidate_index + 1; i < num_input_candidates; ++i) {</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">if</span> (Connects(graph, selected, input_candidates[i])) {</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  new_candidates.push_back(input_candidates[i]);</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  }</div>
|
|
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  }</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> new_candidate_size = new_candidates.size();</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  </div>
|
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">// Add the selected candidate to the current clique.</span></div>
|
|
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  current_clique->push_back(selected);</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  </div>
|
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// If there are no remaining candidates, we have found a maximal clique.</span></div>
|
|
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// Otherwise, do the recursive step.</span></div>
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|
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">if</span> (new_candidate_size == 0) {</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  *stop = <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>(*current_clique);</div>
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|
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">if</span> (new_first_candidate_index < new_candidate_size) {</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  Search(graph, <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>, new_candidates.data(),</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  new_first_candidate_index, new_candidate_size, current_clique,</div>
|
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  stop);</div>
|
|
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">if</span> (*stop) {</div>
|
|
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  }</div>
|
|
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div>
|
|
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  }</div>
|
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div>
|
|
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="comment">// Remove the selected candidate from the current clique.</span></div>
|
|
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  current_clique->pop_back();</div>
|
|
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// Add the selected candidate to the set "not" - we've already processed</span></div>
|
|
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// all possible maximal cliques that use this node in 'current_clique'. The</span></div>
|
|
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="comment">// current candidate is the element of the new candidate set, so we can move</span></div>
|
|
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">// it to "not" simply by increasing first_candidate_index.</span></div>
|
|
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  first_candidate_index++;</div>
|
|
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  </div>
|
|
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="comment">// Find the next candidate that is disconnected from the pivot.</span></div>
|
|
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">if</span> (remaining_candidates > 1) {</div>
|
|
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  disconnected_node = first_candidate_index;</div>
|
|
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">while</span> (disconnected_node < num_input_candidates &&</div>
|
|
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  Connects(graph, pivot, input_candidates[disconnected_node])) {</div>
|
|
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  disconnected_node++;</div>
|
|
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  }</div>
|
|
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  }</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> }</div>
|
|
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
|
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="keyword">class </span>FindAndEliminate {</div>
|
|
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keyword">public</span>:</div>
|
|
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  FindAndEliminate(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>
|
|
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  std::function<<span class="keywordtype">bool</span>(<span class="keyword">const</span> std::vector<int>&)> <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>)</div>
|
|
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  : graph_(graph), node_count_(node_count), callback_(<a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>) {}</div>
|
|
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div>
|
|
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordtype">bool</span> GraphCallback(<span class="keywordtype">int</span> node1, <span class="keywordtype">int</span> node2) {</div>
|
|
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">if</span> (visited_.find(</div>
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|
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  std::make_pair(<a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">std::min</a>(node1, node2), <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(node1, node2))) !=</div>
|
|
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  visited_.end()) {</div>
|
|
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
|
|
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</div>
|
|
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">return</span> Connects(graph_, node1, node2);</div>
|
|
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  }</div>
|
|
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  </div>
|
|
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordtype">bool</span> SolutionCallback(<span class="keyword">const</span> std::vector<int>& solution) {</div>
|
|
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> size = solution.size();</div>
|
|
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">if</span> (size > 1) {</div>
|
|
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size - 1; ++i) {</div>
|
|
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < size; ++j) {</div>
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|
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  visited_.insert(std::make_pair(<a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">std::min</a>(solution[i], solution[j]),</div>
|
|
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(solution[i], solution[j])));</div>
|
|
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  }</div>
|
|
<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>  callback_(solution);</div>
|
|
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  }</div>
|
|
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
|
|
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  }</div>
|
|
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  </div>
|
|
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keyword">private</span>:</div>
|
|
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  std::function<bool(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph_;</div>
|
|
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordtype">int</span> node_count_;</div>
|
|
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  std::function<bool(<span class="keyword">const</span> std::vector<int>&)> callback_;</div>
|
|
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  absl::flat_hash_set<std::pair<int, int>> visited_;</div>
|
|
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> };</div>
|
|
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> } <span class="comment">// namespace</span></div>
|
|
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  </div>
|
|
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment">// This method implements the 'version2' of the Bron-Kerbosch</span></div>
|
|
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment">// algorithm to find all maximal cliques in a undirected graph.</span></div>
|
|
<div class="line"><a name="l00226"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#af7f3504c258b748227551a4d7b7bf036"> 226</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#af7f3504c258b748227551a4d7b7bf036">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>
|
|
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  std::function<<span class="keywordtype">bool</span>(<span class="keyword">const</span> std::vector<int>&)> <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>) {</div>
|
|
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  std::unique_ptr<int[]> initial_candidates(<span class="keyword">new</span> <span class="keywordtype">int</span>[node_count]);</div>
|
|
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  std::vector<int> actual;</div>
|
|
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div>
|
|
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 0; c < node_count; ++c) {</div>
|
|
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  initial_candidates[c] = c;</div>
|
|
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  }</div>
|
|
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  </div>
|
|
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordtype">bool</span> stop = <span class="keyword">false</span>;</div>
|
|
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <a class="code" href="classoperations__research_1_1_search.html">Search</a>(graph, <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>, initial_candidates.get(), 0, node_count, &actual,</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  &stop);</div>
|
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> }</div>
|
|
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  </div>
|
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<div class="line"><a name="l00240"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a5986867bcb6d1470fd6c27438d289fcd"> 240</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#a5986867bcb6d1470fd6c27438d289fcd">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>
|
|
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  std::function<<span class="keywordtype">bool</span>(<span class="keyword">const</span> std::vector<int>&)> <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>) {</div>
|
|
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  FindAndEliminate cache(graph, node_count, <a class="code" href="gurobi__interface_8cc.html#a6627a3800ac768bb5528ef54c9cace36">callback</a>);</div>
|
|
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  std::unique_ptr<int[]> initial_candidates(<span class="keyword">new</span> <span class="keywordtype">int</span>[node_count]);</div>
|
|
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  std::vector<int> actual;</div>
|
|
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  </div>
|
|
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  std::function<bool(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> cached_graph = [&cache](<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) {</div>
|
|
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">return</span> cache.GraphCallback(i, j);</div>
|
|
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  };</div>
|
|
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  std::function<bool(<span class="keyword">const</span> std::vector<int>&)> cached_callback =</div>
|
|
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  [&cache](<span class="keyword">const</span> std::vector<int>& res) {</div>
|
|
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">return</span> cache.SolutionCallback(res);</div>
|
|
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  };</div>
|
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<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  </div>
|
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<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 0; c < node_count; ++c) {</div>
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<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  initial_candidates[c] = c;</div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  }</div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  </div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordtype">bool</span> stop = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <a class="code" href="classoperations__research_1_1_search.html">Search</a>(cached_graph, cached_callback, initial_candidates.get(), 0, node_count,</div>
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  &actual, &stop);</div>
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<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> }</div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  </div>
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<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a021e695f54a13bd809c34b2f4ca87c37"><div class="ttname"><a href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a></div><div class="ttdeci">int64 min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00138">alldiff_cst.cc:138</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a9d0c202d5fdd62f4fa2c613339ff168a"><div class="ttname"><a href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a></div><div class="ttdeci">int64 max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_search_html"><div class="ttname"><a href="classoperations__research_1_1_search.html">operations_research::Search</a></div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_8cc_source.html#l00953">constraint_solver.cc:953</a></div></div>
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<div class="ttc" id="acliques_8h_html"><div class="ttname"><a href="cliques_8h.html">cliques.h</a></div></div>
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<div class="ttc" id="ahash_8h_html"><div class="ttname"><a href="hash_8h.html">hash.h</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="ttdoc">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a5986867bcb6d1470fd6c27438d289fcd"><div class="ttname"><a href="namespaceoperations__research.html#a5986867bcb6d1470fd6c27438d289fcd">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 class="ttdef"><b>Definition:</b> <a href="cliques_8cc_source.html#l00240">cliques.cc:240</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_af7f3504c258b748227551a4d7b7bf036"><div class="ttname"><a href="namespaceoperations__research.html#af7f3504c258b748227551a4d7b7bf036">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 class="ttdef"><b>Definition:</b> <a href="cliques_8cc_source.html#l00226">cliques.cc:226</a></div></div>
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