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<a href="symmetry__util_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="preprocessor">#ifndef OR_TOOLS_SAT_SYMMETRY_UTIL_H_</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_SAT_SYMMETRY_UTIL_H_</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <memory></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include "<a class="code" href="sparse__permutation_8h.html">ortools/algorithms/sparse_permutation.h</a>"</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</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="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="keyword">namespace </span>sat {</div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// Given the generator for a permutation group of [0, n-1], tries to identify</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// a grouping of the variables in an p x q matrix such that any permutations</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// of the columns of this matrix is in the given group.</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">//</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// The name comes from: "Packing and Partitioning Orbitopes", Volker Kaibel,</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// Marc E. Pfetsch, https://arxiv.org/abs/math/0603678 . Here we just detect it,</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// independently of the constraints on the variables in this matrix. We can also</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// detect non-Boolean orbitope.</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">//</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// In order to detect orbitope, this basic algorithm requires that the</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// generators of the orbitope must only contain one or more 2-cyle (i.e</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// transpositions). Thus they must be involutions. The list of transpositions in</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// the SparsePermutation must also be listed in a canonical order.</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">//</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// TODO(user): Detect more than one orbitope? Note that once detected, the</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// structure can be exploited efficiently, but for now, a more "generic"</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// algorithm based on stabilizator should achieve the same preprocessing power,</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// so I don't know how hard we need to invest in orbitope detection.</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">//</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// TODO(user): The heuristic is quite limited for now, but this works on</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// graph20-20-1rand.mps.gz. I suspect the generators provided by the detection</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// code follow our preconditions.</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span>std::vector<std::vector<int>> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ae1ba8d73886e6e6403805d215aa0fd16">BasicOrbitopeExtraction</a>(</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators);</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// Returns a vector of size n such that</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// - orbits[i] == -1 iff i is never touched by the generators (singleton orbit).</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// - orbits[i] = orbit_index, where orbits are numbered from 0 to num_orbits - 1</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">// TODO(user): We could reuse the internal memory if needed.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span>std::vector<int> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ae177cbcee937152b1230499662441902">GetOrbits</a>(</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators);</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// Returns the orbits under the given orbitope action.</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// Same results format as in GetOrbits(). Note that here, the orbit index</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// is simply the row index of an element in the orbitope matrix.</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>std::vector<int> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a1e331438c0fc60e8b00aebd0b66ce658">GetOrbitopeOrbits</a>(</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::vector<int>>& orbitope);</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// Given the generators for a permutation group of [0, n-1], update it to</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">// a set of generators of the group stabilizing the given element.</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">//</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// Note that one can add symmetry breaking constraints by repeatedly doing:</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// 1/ Call GetOrbits() using the current set of generators.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// 2/ Choose an element x0 in a large orbit (x0, .. xi ..) , and add x0 >= xi</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// for all i.</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// 3/ Update the set of generators to the one stabilizing x0.</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 is more or less what is described in "Symmetry Breaking Inequalities</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">// from the Schreier-Sims Table", Domenico Salvagnin,</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment">// https://link.springer.com/chapter/10.1007/978-3-319-93031-2_37</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">//</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): Implement!</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a8fc9e60de9ebec04b0d8e62c0bcd7aa1"> 78</a></span><span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a8fc9e60de9ebec04b0d8e62c0bcd7aa1">TransformToGeneratorOfStabilizer</a>(</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordtype">int</span> to_stabilize,</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> std::vector<std::unique_ptr<SparsePermutation>>* generators) {}</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span>} <span class="comment">// namespace sat</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_SYMMETRY_UTIL_H_</span></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a1e331438c0fc60e8b00aebd0b66ce658"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a1e331438c0fc60e8b00aebd0b66ce658">operations_research::sat::GetOrbitopeOrbits</a></div><div class="ttdeci">std::vector< int > GetOrbitopeOrbits(int n, const std::vector< std::vector< int > > &orbitope)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8cc_source.html#l00183">symmetry_util.cc:183</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a8fc9e60de9ebec04b0d8e62c0bcd7aa1"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a8fc9e60de9ebec04b0d8e62c0bcd7aa1">operations_research::sat::TransformToGeneratorOfStabilizer</a></div><div class="ttdeci">void TransformToGeneratorOfStabilizer(int to_stabilize, std::vector< std::unique_ptr< SparsePermutation > > *generators)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8h_source.html#l00078">symmetry_util.h:78</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae177cbcee937152b1230499662441902"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae177cbcee937152b1230499662441902">operations_research::sat::GetOrbits</a></div><div class="ttdeci">std::vector< int > GetOrbits(int n, const std::vector< std::unique_ptr< SparsePermutation > > &generators)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8cc_source.html#l00151">symmetry_util.cc:151</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae1ba8d73886e6e6403805d215aa0fd16"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae1ba8d73886e6e6403805d215aa0fd16">operations_research::sat::BasicOrbitopeExtraction</a></div><div class="ttdeci">std::vector< std::vector< int > > BasicOrbitopeExtraction(const std::vector< std::unique_ptr< SparsePermutation > > &generators)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8cc_source.html#l00028">symmetry_util.cc:28</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">Collection of objects used to extend the Constraint Solver library.</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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