194 lines
20 KiB
HTML
194 lines
20 KiB
HTML
<!-- HTML header for doxygen 1.8.18-->
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
|
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
|
|
<meta name="generator" content="Doxygen 1.9.1"/>
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
|
<title>OR-Tools: symmetry_util.h Source File</title>
|
|
<link href="tabs.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="jquery.js"></script>
|
|
<script type="text/javascript" src="dynsections.js"></script>
|
|
<link href="navtree.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="resize.js"></script>
|
|
<script type="text/javascript" src="navtreedata.js"></script>
|
|
<script type="text/javascript" src="navtree.js"></script>
|
|
<link href="search/search.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="search/searchdata.js"></script>
|
|
<script type="text/javascript" src="search/search.js"></script>
|
|
<link href="doxygen.css" rel="stylesheet" type="text/css" />
|
|
<link href="styleSheet.tmp.css" rel="stylesheet" type="text/css"/>
|
|
</head>
|
|
<body>
|
|
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
|
|
<div id="titlearea">
|
|
<table cellspacing="0" cellpadding="0">
|
|
<tbody>
|
|
<tr style="height: 56px;">
|
|
<td id="projectlogo"><img alt="Logo" src="orLogo.png"/></td>
|
|
<td id="projectalign" style="padding-left: 0.5em;">
|
|
<div id="projectname">OR-Tools
|
|
 <span id="projectnumber">8.2</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<!-- end header part -->
|
|
<!-- Generated by Doxygen 1.9.1 -->
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
|
|
/* @license-end */
|
|
</script>
|
|
<script type="text/javascript" src="menudata.js"></script>
|
|
<script type="text/javascript" src="menu.js"></script>
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(function() {
|
|
initMenu('',true,false,'search.php','Search');
|
|
$(document).ready(function() { init_search(); });
|
|
});
|
|
/* @license-end */</script>
|
|
<div id="main-nav"></div>
|
|
</div><!-- top -->
|
|
<div id="side-nav" class="ui-resizable side-nav-resizable">
|
|
<div id="nav-tree">
|
|
<div id="nav-tree-contents">
|
|
<div id="nav-sync" class="sync"></div>
|
|
</div>
|
|
</div>
|
|
<div id="splitbar" style="-moz-user-select:none;"
|
|
class="ui-resizable-handle">
|
|
</div>
|
|
</div>
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(document).ready(function(){initNavTree('symmetry__util_8h_source.html',''); initResizable(); });
|
|
/* @license-end */
|
|
</script>
|
|
<div id="doc-content">
|
|
<!-- window showing the filter options -->
|
|
<div id="MSearchSelectWindow"
|
|
onmouseover="return searchBox.OnSearchSelectShow()"
|
|
onmouseout="return searchBox.OnSearchSelectHide()"
|
|
onkeydown="return searchBox.OnSearchSelectKey(event)">
|
|
</div>
|
|
|
|
<!-- iframe showing the search results (closed by default) -->
|
|
<div id="MSearchResultsWindow">
|
|
<iframe src="javascript:void(0)" frameborder="0"
|
|
name="MSearchResults" id="MSearchResults">
|
|
</iframe>
|
|
</div>
|
|
|
|
<div class="header">
|
|
<div class="headertitle">
|
|
<div class="title">symmetry_util.h</div> </div>
|
|
</div><!--header-->
|
|
<div class="contents">
|
|
<a href="symmetry__util_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
|
|
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
|
|
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
|
|
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
|
|
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
|
|
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
|
|
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
|
|
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
|
|
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
|
|
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
|
|
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
|
|
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_SAT_SYMMETRY_UTIL_H_</span></div>
|
|
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_SAT_SYMMETRY_UTIL_H_</span></div>
|
|
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
|
|
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include "<a class="code" href="sparse__permutation_8h.html">ortools/algorithms/sparse_permutation.h</a>"</span></div>
|
|
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
|
|
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
|
|
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">namespace </span>sat {</div>
|
|
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  </div>
|
|
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// Given the generator for a permutation group of [0, n-1], tries to identify</span></div>
|
|
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// a grouping of the variables in an p x q matrix such that any permutations</span></div>
|
|
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// of the columns of this matrix is in the given group.</span></div>
|
|
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// The name comes from: "Packing and Partitioning Orbitopes", Volker Kaibel,</span></div>
|
|
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// Marc E. Pfetsch, https://arxiv.org/abs/math/0603678 . Here we just detect it,</span></div>
|
|
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// independently of the constraints on the variables in this matrix. We can also</span></div>
|
|
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// detect non-Boolean orbitope.</span></div>
|
|
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// In order to detect orbitope, this basic algorithm requires that the</span></div>
|
|
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// generators of the orbitope must only contain one or more 2-cyle (i.e</span></div>
|
|
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// transpositions). Thus they must be involutions. The list of transpositions in</span></div>
|
|
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// the SparsePermutation must also be listed in a canonical order.</span></div>
|
|
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// TODO(user): Detect more than one orbitope? Note that once detected, the</span></div>
|
|
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// structure can be exploited efficiently, but for now, a more "generic"</span></div>
|
|
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// algorithm based on stabilizator should achieve the same preprocessing power,</span></div>
|
|
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// so I don't know how hard we need to invest in orbitope detection.</span></div>
|
|
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// TODO(user): The heuristic is quite limited for now, but this works on</span></div>
|
|
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// graph20-20-1rand.mps.gz. I suspect the generators provided by the detection</span></div>
|
|
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// code follow our preconditions.</span></div>
|
|
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> std::vector<std::vector<int>> <a class="code" href="namespaceoperations__research_1_1sat.html#ae4be5fcdd40601e7d3862a5c9ab06915">BasicOrbitopeExtraction</a>(</div>
|
|
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators);</div>
|
|
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
|
|
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Returns a vector of size n such that</span></div>
|
|
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// - orbits[i] == -1 iff i is never touched by the generators (singleton orbit).</span></div>
|
|
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// - orbits[i] = orbit_index, where orbits are numbered from 0 to num_orbits - 1</span></div>
|
|
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// TODO(user): We could reuse the internal memory if needed.</span></div>
|
|
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> std::vector<int> <a class="code" href="namespaceoperations__research_1_1sat.html#ae75c184235d68cd4b3019cfba09b764d">GetOrbits</a>(</div>
|
|
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators);</div>
|
|
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  </div>
|
|
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// Returns the orbits under the given orbitope action.</span></div>
|
|
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// Same results format as in GetOrbits(). Note that here, the orbit index</span></div>
|
|
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// is simply the row index of an element in the orbitope matrix.</span></div>
|
|
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> std::vector<int> <a class="code" href="namespaceoperations__research_1_1sat.html#a34d8ec706e23b38d955a1c902a03208e">GetOrbitopeOrbits</a>(</div>
|
|
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::vector<int>>& orbitope);</div>
|
|
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
|
|
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Given the generators for a permutation group of [0, n-1], update it to</span></div>
|
|
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// a set of generators of the group stabilizing the given element.</span></div>
|
|
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// Note that one can add symmetry breaking constraints by repeatedly doing:</span></div>
|
|
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// 1/ Call GetOrbits() using the current set of generators.</span></div>
|
|
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// 2/ Choose an element x0 in a large orbit (x0, .. xi ..) , and add x0 >= xi</span></div>
|
|
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// for all i.</span></div>
|
|
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// 3/ Update the set of generators to the one stabilizing x0.</span></div>
|
|
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// This is more or less what is described in "Symmetry Breaking Inequalities</span></div>
|
|
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// from the Schreier-Sims Table", Domenico Salvagnin,</span></div>
|
|
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// https://link.springer.com/chapter/10.1007/978-3-319-93031-2_37</span></div>
|
|
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// TODO(user): Implement!</span></div>
|
|
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a7d18360f794498374dd75058bc040e58"> 75</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a7d18360f794498374dd75058bc040e58">TransformToGeneratorOfStabilizer</a>(</div>
|
|
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">int</span> to_stabilize,</div>
|
|
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  std::vector<std::unique_ptr<SparsePermutation>>* generators) {}</div>
|
|
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  </div>
|
|
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> } <span class="comment">// namespace sat</span></div>
|
|
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> } <span class="comment">// namespace operations_research</span></div>
|
|
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  </div>
|
|
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_SYMMETRY_UTIL_H_</span></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a34d8ec706e23b38d955a1c902a03208e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a34d8ec706e23b38d955a1c902a03208e">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#l00176">symmetry_util.cc:176</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a7d18360f794498374dd75058bc040e58"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a7d18360f794498374dd75058bc040e58">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#l00075">symmetry_util.h:75</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae4be5fcdd40601e7d3862a5c9ab06915"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae4be5fcdd40601e7d3862a5c9ab06915">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#l00021">symmetry_util.cc:21</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae75c184235d68cd4b3019cfba09b764d"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae75c184235d68cd4b3019cfba09b764d">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#l00144">symmetry_util.cc:144</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
|
|
<div class="ttc" id="asparse__permutation_8h_html"><div class="ttname"><a href="sparse__permutation_8h.html">sparse_permutation.h</a></div></div>
|
|
</div><!-- fragment --></div><!-- contents -->
|
|
</div><!-- doc-content -->
|
|
<!-- HTML footer for doxygen 1.8.18-->
|
|
<!-- start footer part -->
|
|
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
|
|
<ul>
|
|
<li class="navelem"><a class="el" href="dir_a7cc1eeded8f693d0da6c729bc88c45a.html">ortools</a></li><li class="navelem"><a class="el" href="dir_dddac007a45022d9da6ea1dee012c3b9.html">sat</a></li><li class="navelem"><a class="el" href="symmetry__util_8h.html">symmetry_util.h</a></li>
|
|
<li class="footer">Generated by
|
|
<a href="http://www.doxygen.org/index.html">
|
|
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.9.1 </li>
|
|
</ul>
|
|
</div>
|
|
</body>
|
|
</html>
|