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<div class="headertitle"><div class="title">find_graph_symmetries.h</div></div>
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<a href="find__graph__symmetries_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" 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 id="l00002" 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 id="l00003" 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 id="l00004" 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 id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" 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 id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" 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 id="l00009" 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 id="l00010" 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 id="l00011" 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 id="l00012" 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 id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// This class solves the graph automorphism problem</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// (https://en.wikipedia.org/wiki/Graph_automorphism), a variant of the famous</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// graph isomorphism problem (https://en.wikipedia.org/wiki/Graph_isomorphism).</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">//</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// The algorithm is largely based on the following article, published in 2008:</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// "Faster Symmetry Discovery using Sparsity of Symmetries" by Darga, Sakallah</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// and Markov. http://web.eecs.umich.edu/~imarkov/pubs/conf/dac08-sym.pdf.</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">//</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// See the comments on the class below for more details.</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#ifndef OR_TOOLS_ALGORITHMS_FIND_GRAPH_SYMMETRIES_H_</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#define OR_TOOLS_ALGORITHMS_FIND_GRAPH_SYMMETRIES_H_</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include <memory></span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include "absl/numeric/int128.h"</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="preprocessor">#include "absl/status/status.h"</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include "absl/time/time.h"</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include "<a class="code" href="dynamic__partition_8h.html">ortools/algorithms/dynamic_partition.h</a>"</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#include "<a class="code" href="dynamic__permutation_8h.html">ortools/algorithms/dynamic_permutation.h</a>"</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="preprocessor">#include "<a class="code" href="graph_8h.html">ortools/graph/graph.h</a>"</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include "<a class="code" href="iterators_8h.html">ortools/graph/iterators.h</a>"</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="preprocessor">#include "<a class="code" href="stats_8h.html">ortools/util/stats.h</a>"</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include "<a class="code" href="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">class </span>SparsePermutation;</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_graph_symmetry_finder.html"> 44</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_graph_symmetry_finder.html">GraphSymmetryFinder</a> {</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_graph_symmetry_finder.html#a84f705240fd04d39747187079208d4bf"> 46</a></span> typedef ::util::StaticGraph<> <a class="code hl_typedef" href="classoperations__research_1_1_graph_symmetry_finder.html#a84f705240fd04d39747187079208d4bf">Graph</a>;</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// If the Graph passed to the GraphSymmetryFinder is undirected, i.e.</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// for every arc a->b, b->a is also present, then you should set</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// "is_undirected" to true.</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// This will, in effect, DCHECK() that the graph is indeed undirected,</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// and bypass the need for reverse adjacency lists.</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// If you don't know this in advance, you may use GraphIsSymmetric() from</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// ortools/graph/util.h.</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// "graph" must not have multi-arcs.</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// TODO(user): support multi-arcs.</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_function" href="classoperations__research_1_1_graph_symmetry_finder.html#af0ae1a4d86cfcf11128fe60ea0f8d20b">GraphSymmetryFinder</a>(<span class="keyword">const</span> <a class="code hl_class" href="classutil_1_1_static_graph.html">Graph</a>& graph, <span class="keywordtype">bool</span> is_undirected);</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Whether the given permutation is an automorphism of the graph given at</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// construction. This costs O(sum(degree(x))) (the sum is over all nodes x</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// that are displaced by the permutation).</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1_graph_symmetry_finder.html#a998043f7ad1e35dc5f6cb23e18f6e7dd">IsGraphAutomorphism</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_dynamic_permutation.html">DynamicPermutation</a>& permutation) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// Find a set of generators of the automorphism subgroup of the graph that</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// respects the given node equivalence classes. The generators are themselves</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// permutations of the nodes: see http://en.wikipedia.org/wiki/Automorphism.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// These permutations may only map a node onto a node of its equivalence</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// class: two nodes i and j are in the same equivalence class iff</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// node_equivalence_classes_io[i] == node_equivalence_classes_io[j];</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// This set of generators is not necessarily the smallest possible (neither in</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// the number of generators, nor in the size of these generators), but it is</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// minimal in that no generator can be removed while keeping the generated</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// group intact.</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// TODO(user): verify the minimality in unit tests.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Note that if "generators" is empty, then the graph has no symmetry: the</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// only automorphism is the identity.</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// The equivalence classes are actually an input/output: they are refined</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// according to all asymmetries found. In the end, n1 and n2 will be</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// considered equivalent (i.e. node_equivalence_classes_io[n1] ==</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// node_equivalence_classes_io[n2]) if and only if there exists a</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// permutation of nodes that:</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// - keeps the graph invariant</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// - maps n1 onto n2</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// - maps each node to a node of its original equivalence class.</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// This method also outputs the size of the automorphism group, expressed as</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// a factorized product of integers (note that the size itself may be as</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// large as N!).</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// DEADLINE AND PARTIAL COMPLETION:</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// If the deadline passed as argument (via TimeLimit) is reached, this method</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// will return quickly (within a few milliseconds of the limit). The outputs</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// may be partially filled:</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// - Each element of "generators", if non-empty, will be a valid permutation.</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// - "node_equivalence_classes_io" will contain the equivalence classes</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// corresponding to the orbits under all the generators in "generators".</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// - "factorized_automorphism_group_size" will also be incomplete, and</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// partially valid: its last element may be undervalued. But all prior</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// elements are valid factors of the automorphism group size.</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> absl::Status <a class="code hl_function" href="classoperations__research_1_1_graph_symmetry_finder.html#ad1f88654797ab9271206d6a4c013a94e">FindSymmetries</a>(</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::vector<int>* node_equivalence_classes_io,</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> std::vector<std::unique_ptr<SparsePermutation> >* generators,</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::vector<int>* factorized_automorphism_group_size,</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_class" href="classoperations__research_1_1_time_limit.html">TimeLimit</a>* <a class="code hl_variable" href="cp__model__solver_8cc.html#aec8af5c1be4e1b6d4330e1161028de21">time_limit</a> = <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Fully refine the partition of nodes, using the graph as symmetry breaker.</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// This means applying the following steps on each part P of the partition:</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// - Compute the aggregated in-degree of all nodes of the graph, only looking</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// at arcs originating from nodes in P.</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// - For each in-degree d=1...max_in_degree, refine the partition by the set</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// of nodes with in-degree d.</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// And recursively applying it on all new or modified parts.</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// In our use cases, we may call this in a scenario where the partition was</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// already partially refined on all parts #0...#K, then you should set</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// "first_unrefined_part_index" to K+1.</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_graph_symmetry_finder.html#a651a63b1943d8b8fa2346df1d1a2f55c">RecursivelyRefinePartitionByAdjacency</a>(<span class="keywordtype">int</span> first_unrefined_part_index,</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_class" href="classoperations__research_1_1_dynamic_partition.html">DynamicPartition</a>* partition);</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// **** Methods below are public FOR TESTING ONLY. ****</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// Special wrapper of the above method: assuming that partition is already</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// fully refined, further refine it by {node}, and propagate by adjacency.</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// Also, optionally collect all the new singletons of the partition in</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// "new_singletons", sorted by their part number in the partition.</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_graph_symmetry_finder.html#acb28211fa0581e72d3dcb6b43ebe857a">DistinguishNodeInPartition</a>(<span class="keywordtype">int</span> node, <a class="code hl_class" href="classoperations__research_1_1_dynamic_partition.html">DynamicPartition</a>* partition,</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> std::vector<int>* new_singletons_or_null);</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keyword">const</span> <a class="code hl_class" href="classutil_1_1_static_graph.html">Graph</a>& graph_;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> NumNodes()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> graph_.num_nodes(); }</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// If the graph isn't symmetric, then we store the reverse adjacency lists</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// here: for each i in 0..NumNodes()-1, the list of nodes that have an</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// outgoing arc to i is stored (sorted by node) in:</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// flattened_reverse_adj_lists_[reverse_adj_list_index_[i] ...</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// reverse_adj_list_index_[i + 1]]</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// and can be iterated on easily with:</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// for (const int tail : TailsOfIncomingArcsTo(node)) ...</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// If the graph was specified as symmetric upon construction, both these</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="comment">// vectors are empty, and TailsOfIncomingArcsTo() crashes.</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> std::vector<int> flattened_reverse_adj_lists_;</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> std::vector<int> reverse_adj_list_index_;</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <a class="code hl_class" href="classutil_1_1_begin_end_wrapper.html">util::BeginEndWrapper<std::vector<int>::const_iterator</a>> TailsOfIncomingArcsTo(</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordtype">int</span> node) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// Deadline management. Populated upon FindSymmetries(). If the passed</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// time limit is nullptr, time_limit_ will point to dummy_time_limit_ which</span></div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="comment">// is an object with infinite limits by default.</span></div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_class" href="classoperations__research_1_1_time_limit.html">TimeLimit</a> dummy_time_limit_;</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <a class="code hl_class" href="classoperations__research_1_1_time_limit.html">TimeLimit</a>* time_limit_;</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// Internal search code used in FindSymmetries(), split out for readability:</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="comment">// find one permutation (if it exists) that maps root_node to root_image_node</span></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// and such that the image of "base_partition" by that permutation is equal to</span></div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// the "image_partition". If no such permutation exists, returns nullptr.</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// "generators_found_so_far" and "permutations_displacing_node" are used for</span></div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// pruning in the search. The former is just the "generators" vector of</span></div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// FindGraphSymmetries(), with the permutations found so far; and the latter</span></div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// is an inverted index from each node to all permutations (that we found)</span></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="comment">// that displace it.</span></div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> std::unique_ptr<SparsePermutation> FindOneSuitablePermutation(</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keywordtype">int</span> root_node, <span class="keywordtype">int</span> root_image_node, <a class="code hl_class" href="classoperations__research_1_1_dynamic_partition.html">DynamicPartition</a>* base_partition,</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <a class="code hl_class" href="classoperations__research_1_1_dynamic_partition.html">DynamicPartition</a>* image_partition,</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation> >&</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> generators_found_so_far,</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">const</span> std::vector<std::vector<int> >& permutations_displacing_node);</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// Data structure used by FindOneSuitablePermutation(). See the .cc</span></div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keyword">struct </span>SearchState {</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordtype">int</span> base_node;</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// We're tentatively mapping "base_node" to some image node. At first, we</span></div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// just pick a single candidate: we fill "first_image_node". If this</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// candidate doesn't work out, we'll select all other candidates in the same</span></div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// image part, prune them by the symmetries we found already, and put them</span></div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// in "remaining_pruned_image_nodes" (and set "first_image_node" to -1).</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordtype">int</span> first_image_node;</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> std::vector<int> remaining_pruned_image_nodes;</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keywordtype">int</span> num_parts_before_trying_to_map_base_node;</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> </div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// Only parts that are at or beyond this index, or their parent parts, may</span></div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="comment">// be mismatching between the base and the image partitions.</span></div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordtype">int</span> min_potential_mismatching_part_index;</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> SearchState(<span class="keywordtype">int</span> bn, <span class="keywordtype">int</span> in, <span class="keywordtype">int</span> np, <span class="keywordtype">int</span> mi)</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> : base_node(bn),</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> first_image_node(in),</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> num_parts_before_trying_to_map_base_node(np),</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> min_potential_mismatching_part_index(mi) {}</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> std::string DebugString() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> };</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> std::vector<SearchState> search_states_;</div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> </div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// Subroutine of FindOneSuitablePermutation(), split out for modularity:</span></div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// With the partial candidate mapping given by "base_partition",</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// "image_partition" and "current_permutation_candidate", determine whether</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// we have a full match (eg. the permutation is a valid candidate).</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// If so, simply return true. If not, return false but also fill</span></div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="comment">// "next_base_node" and "next_image_node" with what should be the next mapping</span></div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="comment">// decision.</span></div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="comment">// This also uses and updates "min_potential_mismatching_part_index_io"</span></div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="comment">// to incrementally search for mismatching parts along the partitions.</span></div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// Note(user): there may be false positives, i.e. this method may return true</span></div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="comment">// even if the partitions aren't actually a full match, because it uses</span></div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="comment">// fingerprints to compare part. This should almost never happen.</span></div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keywordtype">bool</span> ConfirmFullMatchOrFindNextMappingDecision(</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">const</span> DynamicPartition& base_partition,</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keyword">const</span> DynamicPartition& image_partition,</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">const</span> DynamicPermutation& current_permutation_candidate,</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keywordtype">int</span>* min_potential_mismatching_part_index_io, <span class="keywordtype">int</span>* next_base_node,</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <span class="keywordtype">int</span>* next_image_node) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> </div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="comment">// Subroutine of FindOneSuitablePermutation(), split out for modularity:</span></div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// Keep only one node of "nodes" per orbit, where the orbits are described</span></div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="comment">// by a subset of "all_permutations": the ones with indices in</span></div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="comment">// "permutation_indices" and that are compatible with "partition".</span></div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="comment">// For each orbit, keep the first node that appears in "nodes".</span></div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordtype">void</span> PruneOrbitsUnderPermutationsCompatibleWithPartition(</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">const</span> DynamicPartition& partition,</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation> >& all_permutations,</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keyword">const</span> std::vector<int>& permutation_indices, std::vector<int>* <a class="code hl_variable" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>);</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// Temporary objects used by some of the class methods, and owned by the</span></div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="comment">// class to avoid (costly) re-allocation. Their resting states are described</span></div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="comment">// in the side comments; with N = NumNodes().</span></div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> DynamicPermutation tmp_dynamic_permutation_; <span class="comment">// Identity(N)</span></div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">mutable</span> std::vector<bool> tmp_node_mask_; <span class="comment">// [0..N-1] = false</span></div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> std::vector<int> tmp_degree_; <span class="comment">// [0..N-1] = 0.</span></div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> std::vector<int> tmp_stack_; <span class="comment">// Empty.</span></div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> std::vector<std::vector<int> > tmp_nodes_with_degree_; <span class="comment">// [0..N-1] = [].</span></div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> MergingPartition tmp_partition_; <span class="comment">// Reset(N).</span></div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> std::vector<const SparsePermutation*> tmp_compatible_permutations_; <span class="comment">// Empty.</span></div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> </div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="comment">// Internal statistics, used for performance tuning and debugging.</span></div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="keyword">struct </span>Stats : <span class="keyword">public</span> StatsGroup {</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> Stats()</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> : <a class="code hl_function" href="classoperations__research_1_1_stats_group.html#ad3718c845372a46a063163204783b7ca">StatsGroup</a>(<span class="stringliteral">"GraphSymmetryFinder"</span>),</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> initialization_time(<span class="stringliteral">"a Initialization"</span>, this),</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> initialization_refine_time(<span class="stringliteral">"b ┗╸Refine"</span>, this),</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> invariant_dive_time(<span class="stringliteral">"c Invariant Dive"</span>, this),</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> main_search_time(<span class="stringliteral">"d Main Search"</span>, this),</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> invariant_unroll_time(<span class="stringliteral">"e ┣╸Dive unroll"</span>, this),</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> permutation_output_time(<span class="stringliteral">"f ┣╸Permutation output"</span>, this),</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> search_time(<span class="stringliteral">"g ┗╸FindOneSuitablePermutation()"</span>, this),</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> search_time_fail(<span class="stringliteral">"h ┣╸Fail"</span>, this),</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> search_time_success(<span class="stringliteral">"i ┣╸Success"</span>, this),</div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> initial_search_refine_time(<span class="stringliteral">"j ┣╸Initial refine"</span>, this),</div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> search_refine_time(<span class="stringliteral">"k ┣╸Further refines"</span>, this),</div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> quick_compatibility_time(<span class="stringliteral">"l ┣╸Compatibility checks"</span>, this),</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> quick_compatibility_fail_time(<span class="stringliteral">"m ┃ ┣╸Fail"</span>, this),</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> quick_compatibility_success_time(<span class="stringliteral">"n ┃ ┗╸Success"</span>, this),</div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> dynamic_permutation_refinement_time(</div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="stringliteral">"o ┣╸Dynamic permutation refinement"</span>, this),</div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> map_election_std_time(</div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="stringliteral">"p ┣╸Mapping election / full match detection"</span>, this),</div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> map_election_std_mapping_time(<span class="stringliteral">"q ┃ ┣╸Mapping elected"</span>, this),</div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> map_election_std_full_match_time(<span class="stringliteral">"r ┃ ┗╸Full Match"</span>, this),</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> automorphism_test_time(<span class="stringliteral">"s ┣╸[Upon full match] Automorphism check"</span>,</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> this),</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> automorphism_test_fail_time(<span class="stringliteral">"t ┃ ┣╸Fail"</span>, this),</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> automorphism_test_success_time(<span class="stringliteral">"u ┃ ┗╸Success"</span>, this),</div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> search_finalize_time(<span class="stringliteral">"v ┣╸[Upon auto success] Finalization"</span>, this),</div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> dynamic_permutation_undo_time(</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="stringliteral">"w ┣╸[Upon auto fail, full] Dynamic permutation undo"</span>, this),</div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> map_reelection_time(</div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="stringliteral">"x ┣╸[Upon auto fail, partial] Mapping re-election"</span>, this),</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> non_singleton_search_time(<span class="stringliteral">"y ┃ ┗╸Non-singleton search"</span>, this),</div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> backtracking_time(<span class="stringliteral">"z ┗╸Backtracking"</span>, this),</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> pruning_time(<span class="stringliteral">"{ ┗╸Pruning"</span>, this),</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> search_depth(<span class="stringliteral">"~ Search Stats: search_depth"</span>, this) {}</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> </div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> TimeDistribution initialization_time;</div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> TimeDistribution initialization_refine_time;</div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> TimeDistribution invariant_dive_time;</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> TimeDistribution main_search_time;</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> TimeDistribution invariant_unroll_time;</div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> TimeDistribution permutation_output_time;</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> TimeDistribution search_time;</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> TimeDistribution search_time_fail;</div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> TimeDistribution search_time_success;</div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> TimeDistribution initial_search_refine_time;</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> TimeDistribution search_refine_time;</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> TimeDistribution quick_compatibility_time;</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> TimeDistribution quick_compatibility_fail_time;</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> TimeDistribution quick_compatibility_success_time;</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> TimeDistribution dynamic_permutation_refinement_time;</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> TimeDistribution map_election_std_time;</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> TimeDistribution map_election_std_mapping_time;</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> TimeDistribution map_election_std_full_match_time;</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> TimeDistribution automorphism_test_time;</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> TimeDistribution automorphism_test_fail_time;</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> TimeDistribution automorphism_test_success_time;</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> TimeDistribution search_finalize_time;</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> TimeDistribution dynamic_permutation_undo_time;</div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> TimeDistribution map_reelection_time;</div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> TimeDistribution non_singleton_search_time;</div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> TimeDistribution backtracking_time;</div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> TimeDistribution pruning_time;</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> </div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> IntegerDistribution search_depth;</div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> };</div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="keyword">mutable</span> Stats stats_;</div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span>};</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> </div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> </div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_ALGORITHMS_FIND_GRAPH_SYMMETRIES_H_</span></div>
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<div class="ttc" id="aclassoperations__research_1_1_dynamic_partition_html"><div class="ttname"><a href="classoperations__research_1_1_dynamic_partition.html">operations_research::DynamicPartition</a></div><div class="ttdef"><b>Definition:</b> <a href="dynamic__partition_8h_source.html#l00050">dynamic_partition.h:50</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_dynamic_permutation_html"><div class="ttname"><a href="classoperations__research_1_1_dynamic_permutation.html">operations_research::DynamicPermutation</a></div><div class="ttdef"><b>Definition:</b> <a href="dynamic__permutation_8h_source.html#l00033">dynamic_permutation.h:33</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html">operations_research::GraphSymmetryFinder</a></div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8h_source.html#l00044">find_graph_symmetries.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html_a651a63b1943d8b8fa2346df1d1a2f55c"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html#a651a63b1943d8b8fa2346df1d1a2f55c">operations_research::GraphSymmetryFinder::RecursivelyRefinePartitionByAdjacency</a></div><div class="ttdeci">void RecursivelyRefinePartitionByAdjacency(int first_unrefined_part_index, DynamicPartition *partition)</div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8cc_source.html#l00199">find_graph_symmetries.cc:199</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html_a84f705240fd04d39747187079208d4bf"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html#a84f705240fd04d39747187079208d4bf">operations_research::GraphSymmetryFinder::Graph</a></div><div class="ttdeci">::util::StaticGraph Graph</div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8h_source.html#l00046">find_graph_symmetries.h:46</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html_a998043f7ad1e35dc5f6cb23e18f6e7dd"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html#a998043f7ad1e35dc5f6cb23e18f6e7dd">operations_research::GraphSymmetryFinder::IsGraphAutomorphism</a></div><div class="ttdeci">bool IsGraphAutomorphism(const DynamicPermutation &permutation) const</div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8cc_source.html#l00155">find_graph_symmetries.cc:155</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html_acb28211fa0581e72d3dcb6b43ebe857a"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html#acb28211fa0581e72d3dcb6b43ebe857a">operations_research::GraphSymmetryFinder::DistinguishNodeInPartition</a></div><div class="ttdeci">void DistinguishNodeInPartition(int node, DynamicPartition *partition, std::vector< int > *new_singletons_or_null)</div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8cc_source.html#l00276">find_graph_symmetries.cc:276</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html_ad1f88654797ab9271206d6a4c013a94e"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html#ad1f88654797ab9271206d6a4c013a94e">operations_research::GraphSymmetryFinder::FindSymmetries</a></div><div class="ttdeci">absl::Status FindSymmetries(std::vector< int > *node_equivalence_classes_io, std::vector< std::unique_ptr< SparsePermutation > > *generators, std::vector< int > *factorized_automorphism_group_size, TimeLimit *time_limit=nullptr)</div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8cc_source.html#l00383">find_graph_symmetries.cc:383</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_graph_symmetry_finder_html_af0ae1a4d86cfcf11128fe60ea0f8d20b"><div class="ttname"><a href="classoperations__research_1_1_graph_symmetry_finder.html#af0ae1a4d86cfcf11128fe60ea0f8d20b">operations_research::GraphSymmetryFinder::GraphSymmetryFinder</a></div><div class="ttdeci">GraphSymmetryFinder(const Graph &graph, bool is_undirected)</div><div class="ttdef"><b>Definition:</b> <a href="find__graph__symmetries_8cc_source.html#l00108">find_graph_symmetries.cc:108</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_stats_group_html_ad3718c845372a46a063163204783b7ca"><div class="ttname"><a href="classoperations__research_1_1_stats_group.html#ad3718c845372a46a063163204783b7ca">operations_research::StatsGroup::StatsGroup</a></div><div class="ttdeci">StatsGroup(const std::string &name)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00138">stats.h:138</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_time_limit_html"><div class="ttname"><a href="classoperations__research_1_1_time_limit.html">operations_research::TimeLimit</a></div><div class="ttdoc">A simple class to enforce both an elapsed time limit and a deterministic time limit in the same threa...</div><div class="ttdef"><b>Definition:</b> <a href="time__limit_8h_source.html#l00106">time_limit.h:106</a></div></div>
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<div class="ttc" id="aclassutil_1_1_begin_end_wrapper_html"><div class="ttname"><a href="classutil_1_1_begin_end_wrapper.html">util::BeginEndWrapper</a></div><div class="ttdef"><b>Definition:</b> <a href="iterators_8h_source.html#l00038">iterators.h:38</a></div></div>
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<div class="ttc" id="aclassutil_1_1_static_graph_html"><div class="ttname"><a href="classutil_1_1_static_graph.html">util::StaticGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00399">graph.h:399</a></div></div>
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<div class="ttc" id="acp__model__solver_8cc_html_aec8af5c1be4e1b6d4330e1161028de21"><div class="ttname"><a href="cp__model__solver_8cc.html#aec8af5c1be4e1b6d4330e1161028de21">time_limit</a></div><div class="ttdeci">ModelSharedTimeLimit * time_limit</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l02050">cp_model_solver.cc:2050</a></div></div>
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