<ahref="lp__decomposer_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aid="l00001"name="l00001"></a><spanclass="lineno"> 1</span><spanclass="comment">// Copyright 2010-2021 Google LLC</span></div>
<divclass="line"><aid="l00002"name="l00002"></a><spanclass="lineno"> 2</span><spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aid="l00003"name="l00003"></a><spanclass="lineno"> 3</span><spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aid="l00004"name="l00004"></a><spanclass="lineno"> 4</span><spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aid="l00008"name="l00008"></a><spanclass="lineno"> 8</span><spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aid="l00009"name="l00009"></a><spanclass="lineno"> 9</span><spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aid="l00010"name="l00010"></a><spanclass="lineno"> 10</span><spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aid="l00011"name="l00011"></a><spanclass="lineno"> 11</span><spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aid="l00012"name="l00012"></a><spanclass="lineno"> 12</span><spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aid="l00027"name="l00027"></a><spanclass="lineno"> 27</span><spanclass="comment">// This class is used to decompose an existing LinearProgram into several</span></div>
<divclass="line"><aid="l00028"name="l00028"></a><spanclass="lineno"> 28</span><spanclass="comment">// independent LinearPrograms. Problems are independent when none of their</span></div>
<divclass="line"><aid="l00029"name="l00029"></a><spanclass="lineno"> 29</span><spanclass="comment">// variables are connected, i.e. appear in the same constraints.</span></div>
<divclass="line"><aid="l00030"name="l00030"></a><spanclass="lineno"> 30</span><spanclass="comment">// Consider for instance the following problem:</span></div>
<divclass="line"><aid="l00031"name="l00031"></a><spanclass="lineno"> 31</span><spanclass="comment">// min: x + 2 y + 3 z + 4 t + 5 u</span></div>
<divclass="line"><aid="l00032"name="l00032"></a><spanclass="lineno"> 32</span><spanclass="comment">// c1: 0 <= x + z <= 1;</span></div>
<divclass="line"><aid="l00033"name="l00033"></a><spanclass="lineno"> 33</span><spanclass="comment">// c2: 0 <= y + t <= 1;</span></div>
<divclass="line"><aid="l00034"name="l00034"></a><spanclass="lineno"> 34</span><spanclass="comment">// c3: 0 <= x + u <= 1;</span></div>
<divclass="line"><aid="l00035"name="l00035"></a><spanclass="lineno"> 35</span><spanclass="comment">// int: x, y, z, t, u</span></div>
<divclass="line"><aid="l00036"name="l00036"></a><spanclass="lineno"> 36</span><spanclass="comment">// Variables x, z and u are connected by constraints c1 and c3.</span></div>
<divclass="line"><aid="l00037"name="l00037"></a><spanclass="lineno"> 37</span><spanclass="comment">// Variables y and t are connected by constraints c2.</span></div>
<divclass="line"><aid="l00038"name="l00038"></a><spanclass="lineno"> 38</span><spanclass="comment">// The problem can be decomposed into two independent problems:</span></div>
<divclass="line"><aid="l00039"name="l00039"></a><spanclass="lineno"> 39</span><spanclass="comment">// min: x + 3 z + 5 u</span></div>
<divclass="line"><aid="l00040"name="l00040"></a><spanclass="lineno"> 40</span><spanclass="comment">// c1: 0 <= x + z <= 1;</span></div>
<divclass="line"><aid="l00041"name="l00041"></a><spanclass="lineno"> 41</span><spanclass="comment">// c3: 0 <= x + u <= 1;</span></div>
<divclass="line"><aid="l00048"name="l00048"></a><spanclass="lineno"> 48</span><spanclass="comment">// Note that a solution to those two independent problems is a solution to the</span></div>
<divclass="line"><aid="l00049"name="l00049"></a><spanclass="lineno"> 49</span><spanclass="comment">// original problem.</span></div>
<divclass="line"><aid="l00054"name="l00054"></a><spanclass="lineno"> 54</span><spanclass="comment">// Decomposes the problem into independent problems.</span></div>
<divclass="line"><aid="l00055"name="l00055"></a><spanclass="lineno"> 55</span><spanclass="comment">// Note that a pointer is kept (no copy) on the linear_problem, so the problem</span></div>
<divclass="line"><aid="l00056"name="l00056"></a><spanclass="lineno"> 56</span><spanclass="comment">// should not change during the life of the LPDecomposer object.</span></div>
<divclass="line"><aid="l00060"name="l00060"></a><spanclass="lineno"> 60</span><spanclass="comment">// Returns the number of independent problems generated by Decompose().</span></div>
<divclass="line"><aid="l00063"name="l00063"></a><spanclass="lineno"> 63</span><spanclass="comment">// Returns the original problem, i.e. as it was before any decomposition.</span></div>
<divclass="line"><aid="l00066"name="l00066"></a><spanclass="lineno"> 66</span><spanclass="comment">// Fills lp with the problem_index^th independent problem generated by</span></div>
<divclass="line"><aid="l00068"name="l00068"></a><spanclass="lineno"> 68</span><spanclass="comment">// Note that this method runs in O(num-entries-in-generated-problem).</span></div>
<divclass="line"><aid="l00072"name="l00072"></a><spanclass="lineno"> 72</span><spanclass="comment">// Returns an assignment to the original problem based on the assignments</span></div>
<divclass="line"><aid="l00073"name="l00073"></a><spanclass="lineno"> 73</span><spanclass="comment">// to the independent problems. Requires Decompose() to have been called.</span></div>
<divclass="line"><aid="l00077"name="l00077"></a><spanclass="lineno"> 77</span><spanclass="comment">// Returns an assignment to the given subproblem based on the assignment to</span></div>
<divclass="line"><aid="l00078"name="l00078"></a><spanclass="lineno"> 78</span><spanclass="comment">// the original problem. Requires Decompose() to have been called.</span></div>
<divclass="ttc"id="anamespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><divclass="ttdef"><b>Definition:</b><ahref="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
