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< a href = "christofides_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 = "comment" > // ChristofidesPathSolver computes an approximate solution to the Traveling< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "comment" > // Salesman Problen using the Christofides algorithm (c.f.< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < span class = "comment" > // https://en.wikipedia.org/wiki/Christofides_algorithm).< / span > < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "comment" > // Note that the algorithm guarantees finding a solution within 3/2 of the< / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < span class = "comment" > // optimum. Its complexity is O(n^2 * log(n)) where n is the number of nodes.< / span > < / div >
< div class = "line" > < a name = "l00019" > < / a > < span class = "lineno" > 19< / span >   < / div >
< div class = "line" > < a name = "l00020" > < / a > < span class = "lineno" > 20< / span >   < span class = "preprocessor" > #ifndef OR_TOOLS_GRAPH_CHRISTOFIDES_H_< / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < span class = "preprocessor" > #define OR_TOOLS_GRAPH_CHRISTOFIDES_H_< / span > < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "preprocessor" > #include " ortools/base/integral_types.h" < / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < span class = "preprocessor" > #include " ortools/base/logging.h" < / span > < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "eulerian__path_8h.html" > ortools/graph/eulerian_path.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "graph_8h.html" > ortools/graph/graph.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "minimum__spanning__tree_8h.html" > ortools/graph/minimum_spanning_tree.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < span class = "preprocessor" > #include " ortools/graph/perfect_matching.h" < / span > < / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < span class = "preprocessor" > #include " ortools/linear_solver/linear_solver.h" < / span > < / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "preprocessor" > #include " ortools/linear_solver/linear_solver.pb.h" < / span > < / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "preprocessor" > #include " ortools/util/saturated_arithmetic.h" < / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html" > 33< / a > < / span >   < span class = "keyword" > namespace < / span > < a class = "code" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < / div >
< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   using ::util::CompleteGraph;< / div >
< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType, < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > = int64,< / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > = int32,< / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   < span class = "keyword" > typename< / span > CostFunction = std::function< CostType(< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > , < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > )> > < / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ChristofidesPathSolver.html" > 40< / a > < / span >   < span class = "keyword" > class < / span > < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html" > ChristofidesPathSolver< / a > {< / div >
< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   < span class = "keyword" > public< / span > :< / div >
< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7" > 42< / a > < / span >   < span class = "keyword" > enum class< / span > < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7" > MatchingAlgorithm< / a > {< / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7ab66d0823917c9351a4cb68dff77f445a" > MINIMUM_WEIGHT_MATCHING< / a > ,< / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "preprocessor" > #if defined(USE_CBC) || defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7a201b88f6589fa1271207fe29f583dc96" > MINIMUM_WEIGHT_MATCHING_WITH_MIP< / a > ,< / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   < span class = "preprocessor" > #endif // defined(USE_CBC) || defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7a99c5fe202c37dcd8ed9cc60926a4f525" > MINIMAL_WEIGHT_MATCHING< / a > ,< / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   };< / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a87145cf1f5a36d27fd856596a23d495a" > ChristofidesPathSolver< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > num_nodes, CostFunction costs);< / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "comment" > // Sets the matching algorith to use. A minimum weight perfect matching< / span > < / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "comment" > // (MINIMUM_WEIGHT_MATCHING) guarantees the 3/2 upper bound to the optimal< / span > < / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   < span class = "comment" > // solution. A minimal weight perfect matching (MINIMAL_WEIGHT_MATCHING)< / span > < / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   < span class = "comment" > // finds a locally minimal weight matching which does not offer any bound< / span > < / div >
< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   < span class = "comment" > // guarantee but, as of 1/2017, is orders of magnitude faster than the< / span > < / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   < span class = "comment" > // minimum matching.< / span > < / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   < span class = "comment" > // By default, MINIMAL_WEIGHT_MATCHING is selected.< / span > < / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "comment" > // TODO(user): Change the default when minimum matching gets faster.< / span > < / div >
< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ChristofidesPathSolver.html#ae2b64dddd58baf1bc5e01cb14971e52e" > 59< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#ae2b64dddd58baf1bc5e01cb14971e52e" > SetMatchingAlgorithm< / a > (< a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7" > MatchingAlgorithm< / a > matching) {< / div >
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< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   matching_ = matching;< / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   }< / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < span class = "comment" > // Returns the cost of the approximate TSP tour.< / span > < / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   CostType < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#ab558649a26fef3a74f0909ef5af45e90" > TravelingSalesmanCost< / a > ();< / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   < / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   < span class = "comment" > // Returns the approximate TSP tour.< / span > < / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   std::vector< NodeIndex> < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a3076d9001536ea98d419faa81e7d8a47" > TravelingSalesmanPath< / a > ();< / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   < / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   < span class = "keyword" > private< / span > :< / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < span class = "comment" > // Runs the Christofides algorithm.< / span > < / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   < span class = "keywordtype" > void< / span > Solve();< / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   < / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   < span class = "comment" > // Safe addition operator to avoid overflows when possible.< / span > < / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > 74< / span >   < span class = "comment" > // template < typename T> < / span > < / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   < span class = "comment" > // T SafeAdd(T a, T b) {< / span > < / div >
< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   < span class = "comment" > // return a + b;< / span > < / div >
< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < span class = "comment" > // }< / span > < / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   < span class = "comment" > //template < > < / span > < / div >
< div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > 79< / span >   int64 SafeAdd(int64 a, int64 b) {< / div >
< div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   < span class = "keywordflow" > return< / span > CapAdd(a, b);< / 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 >   < / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   < span class = "comment" > // Matching algorithm to use.< / span > < / div >
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7" > MatchingAlgorithm< / a > matching_;< / div >
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < / div >
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "comment" > // The complete graph on the nodes of the problem.< / span > < / div >
< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   CompleteGraph< NodeIndex, ArcIndex> graph_;< / div >
< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   < span class = "comment" > // Function returning the cost between nodes of the problem.< / span > < / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < span class = "keyword" > const< / span > CostFunction costs_;< / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   < / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "comment" > // The cost of the computed TSP path.< / span > < / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   CostType tsp_cost_;< / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   < / div >
< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > 95< / span >   < span class = "comment" > // The path of the computed TSP,< / span > < / div >
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   std::vector< NodeIndex> tsp_path_;< / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   < / div >
< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   < span class = "comment" > // True if the TSP has been solved, false otherwise.< / span > < / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   < span class = "keywordtype" > bool< / span > solved_;< / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   };< / div >
< div class = "line" > < a name = "l00101" > < / a > < span class = "lineno" > 101< / span >   < / div >
< div class = "line" > < a name = "l00102" > < / a > < span class = "lineno" > 102< / span >   < span class = "comment" > // Computes a minimum weight perfect matching on an undirected graph.< / span > < / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > WeightFunctionType, < span class = "keyword" > typename< / span > GraphType> < / div >
< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   std::vector< < / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   std::pair< typename GraphType::NodeIndex, typename GraphType::NodeIndex> > < / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a3174292e878ea613e33ac86334fde459" > 106< / a > < / span >   < a class = "code" href = "namespaceoperations__research.html#a3174292e878ea613e33ac86334fde459" > ComputeMinimumWeightMatching< / a > (< span class = "keyword" > const< / span > GraphType& graph,< / div >
< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > 107< / span >   < span class = "keyword" > const< / span > WeightFunctionType& weight) {< / div >
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > GraphType::ArcIndex< / a > ;< / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > GraphType::NodeIndex< / a > ;< / div >
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   MinCostPerfectMatching matching(graph.num_nodes());< / div >
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : graph.OutgoingArcs(tail)) {< / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head = graph.Head(arc);< / div >
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   < span class = "comment" > // Adding both arcs is redudant for MinCostPerfectMatching.< / span > < / div >
< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < span class = "keywordflow" > if< / span > (tail < head) {< / div >
< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > 116< / span >   matching.AddEdgeWithCost(tail, head, weight(arc));< / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > 117< / span >   }< / div >
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   }< / div >
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > 119< / span >   }< / div >
< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   MinCostPerfectMatching::Status status = matching.Solve();< / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   DCHECK_EQ(status, MinCostPerfectMatching::OPTIMAL);< / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   std::vector< std::pair< NodeIndex, NodeIndex> > match;< / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > 123< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > 124< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head = matching.Match(tail);< / div >
< div class = "line" > < a name = "l00125" > < / a > < span class = "lineno" > 125< / span >   < span class = "keywordflow" > if< / span > (tail < head) { < span class = "comment" > // Both arcs are matched for a given edge, we keep one.< / span > < / div >
< div class = "line" > < a name = "l00126" > < / a > < span class = "lineno" > 126< / span >   match.emplace_back(tail, head);< / div >
< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   }< / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > 128< / span >   }< / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > 129< / span >   < span class = "keywordflow" > return< / span > match;< / div >
< div class = "line" > < a name = "l00130" > < / a > < span class = "lineno" > 130< / span >   }< / div >
< div class = "line" > < a name = "l00131" > < / a > < span class = "lineno" > 131< / span >   < / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < span class = "preprocessor" > #if defined(USE_CBC) || defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   < span class = "comment" > // Computes a minimum weight perfect matching on an undirected graph using a< / span > < / div >
< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   < span class = "comment" > // Mixed Integer Programming model.< / span > < / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   < span class = "comment" > // TODO(user): Handle infeasible cases if this algorithm is used outside of< / span > < / div >
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   < span class = "comment" > // Christofides.< / span > < / div >
< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > WeightFunctionType, < span class = "keyword" > typename< / span > GraphType> < / div >
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > 138< / span >   std::vector< < / div >
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   std::pair< typename GraphType::NodeIndex, typename GraphType::NodeIndex> > < / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a48f6892917d77639f011cd780ce88bde" > 140< / a > < / span >   < a class = "code" href = "namespaceoperations__research.html#a48f6892917d77639f011cd780ce88bde" > ComputeMinimumWeightMatchingWithMIP< / a > (< span class = "keyword" > const< / span > GraphType& graph,< / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   < span class = "keyword" > const< / span > WeightFunctionType& weight) {< / div >
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > GraphType::ArcIndex< / a > ;< / div >
< div class = "line" > < a name = "l00143" > < / a > < span class = "lineno" > 143< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > GraphType::NodeIndex< / a > ;< / div >
< div class = "line" > < a name = "l00144" > < / a > < span class = "lineno" > 144< / span >   MPModelProto model;< / div >
< div class = "line" > < a name = "l00145" > < / a > < span class = "lineno" > 145< / span >   model.set_maximize(< span class = "keyword" > false< / span > );< / div >
< div class = "line" > < a name = "l00146" > < / a > < span class = "lineno" > 146< / span >   < span class = "comment" > // The model is composed of Boolean decision variables to select matching arcs< / span > < / div >
< div class = "line" > < a name = "l00147" > < / a > < span class = "lineno" > 147< / span >   < span class = "comment" > // and constraints ensuring that each node appears in exactly one selected< / span > < / div >
< div class = "line" > < a name = "l00148" > < / a > < span class = "lineno" > 148< / span >   < span class = "comment" > // arc. The objective is to minimize the sum of the weights of selected arcs.< / span > < / div >
< div class = "line" > < a name = "l00149" > < / a > < span class = "lineno" > 149< / span >   < span class = "comment" > // It is assumed the graph is symmetrical.< / span > < / div >
< div class = "line" > < a name = "l00150" > < / a > < span class = "lineno" > 150< / span >   std::vector< int> variable_indices(graph.num_arcs(), -1);< / div >
< div class = "line" > < a name = "l00151" > < / a > < span class = "lineno" > 151< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00152" > < / a > < span class = "lineno" > 152< / span >   < span class = "comment" > // Creating arc-selection Boolean variable.< / span > < / div >
< div class = "line" > < a name = "l00153" > < / a > < span class = "lineno" > 153< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : graph.OutgoingArcs(node)) {< / div >
< div class = "line" > < a name = "l00154" > < / a > < span class = "lineno" > 154< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head = graph.Head(arc);< / div >
< div class = "line" > < a name = "l00155" > < / a > < span class = "lineno" > 155< / span >   < span class = "keywordflow" > if< / span > (node < head) {< / div >
< div class = "line" > < a name = "l00156" > < / a > < span class = "lineno" > 156< / span >   variable_indices[arc] = model.variable_size();< / div >
< div class = "line" > < a name = "l00157" > < / a > < span class = "lineno" > 157< / span >   MPVariableProto* < span class = "keyword" > const< / span > arc_var = model.add_variable();< / div >
< div class = "line" > < a name = "l00158" > < / a > < span class = "lineno" > 158< / span >   arc_var-> set_lower_bound(0);< / div >
< div class = "line" > < a name = "l00159" > < / a > < span class = "lineno" > 159< / span >   arc_var-> set_upper_bound(1);< / div >
< div class = "line" > < a name = "l00160" > < / a > < span class = "lineno" > 160< / span >   arc_var-> set_is_integer(< span class = "keyword" > true< / span > );< / div >
< div class = "line" > < a name = "l00161" > < / a > < span class = "lineno" > 161< / span >   arc_var-> set_objective_coefficient(weight(arc));< / div >
< div class = "line" > < a name = "l00162" > < / a > < span class = "lineno" > 162< / span >   }< / div >
< div class = "line" > < a name = "l00163" > < / a > < span class = "lineno" > 163< / span >   }< / div >
< div class = "line" > < a name = "l00164" > < / a > < span class = "lineno" > 164< / span >   < span class = "comment" > // Creating matching constraint:< / span > < / div >
< div class = "line" > < a name = "l00165" > < / a > < span class = "lineno" > 165< / span >   < span class = "comment" > // for all node i, sum(j) arc(i,j) + sum(j) arc(j,i) = 1< / span > < / div >
< div class = "line" > < a name = "l00166" > < / a > < span class = "lineno" > 166< / span >   MPConstraintProto* < span class = "keyword" > const< / span > one_of_ct = model.add_constraint();< / div >
< div class = "line" > < a name = "l00167" > < / a > < span class = "lineno" > 167< / span >   one_of_ct-> set_lower_bound(1);< / div >
< div class = "line" > < a name = "l00168" > < / a > < span class = "lineno" > 168< / span >   one_of_ct-> set_upper_bound(1);< / div >
< div class = "line" > < a name = "l00169" > < / a > < span class = "lineno" > 169< / span >   }< / div >
< div class = "line" > < a name = "l00170" > < / a > < span class = "lineno" > 170< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00171" > < / a > < span class = "lineno" > 171< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : graph.OutgoingArcs(node)) {< / div >
< div class = "line" > < a name = "l00172" > < / a > < span class = "lineno" > 172< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head = graph.Head(arc);< / div >
< div class = "line" > < a name = "l00173" > < / a > < span class = "lineno" > 173< / span >   < span class = "keywordflow" > if< / span > (node < head) {< / div >
< div class = "line" > < a name = "l00174" > < / a > < span class = "lineno" > 174< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > arc_var = variable_indices[arc];< / div >
< div class = "line" > < a name = "l00175" > < / a > < span class = "lineno" > 175< / span >   DCHECK_GE(arc_var, 0);< / div >
< div class = "line" > < a name = "l00176" > < / a > < span class = "lineno" > 176< / span >   MPConstraintProto* one_of_ct = model.mutable_constraint(node);< / div >
< div class = "line" > < a name = "l00177" > < / a > < span class = "lineno" > 177< / span >   one_of_ct-> add_var_index(arc_var);< / div >
< div class = "line" > < a name = "l00178" > < / a > < span class = "lineno" > 178< / span >   one_of_ct-> add_coefficient(1);< / div >
< div class = "line" > < a name = "l00179" > < / a > < span class = "lineno" > 179< / span >   one_of_ct = model.mutable_constraint(head);< / div >
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< div class = "line" > < a name = "l00180" > < / a > < span class = "lineno" > 180< / span >   one_of_ct-> add_var_index(arc_var);< / div >
< div class = "line" > < a name = "l00181" > < / a > < span class = "lineno" > 181< / span >   one_of_ct-> add_coefficient(1);< / div >
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< div class = "line" > < a name = "l00182" > < / a > < span class = "lineno" > 182< / span >   }< / div >
< div class = "line" > < a name = "l00183" > < / a > < span class = "lineno" > 183< / span >   }< / div >
< div class = "line" > < a name = "l00184" > < / a > < span class = "lineno" > 184< / span >   }< / div >
< div class = "line" > < a name = "l00185" > < / a > < span class = "lineno" > 185< / span >   < span class = "preprocessor" > #if defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00186" > < / a > < span class = "lineno" > 186< / span >   MPSolver mp_solver(< span class = "stringliteral" > " MatchingWithSCIP" < / span > ,< / div >
< div class = "line" > < a name = "l00187" > < / a > < span class = "lineno" > 187< / span >   MPSolver::SCIP_MIXED_INTEGER_PROGRAMMING);< / div >
< div class = "line" > < a name = "l00188" > < / a > < span class = "lineno" > 188< / span >   < span class = "preprocessor" > #elif defined(USE_CBC)< / span > < / div >
< div class = "line" > < a name = "l00189" > < / a > < span class = "lineno" > 189< / span >   MPSolver mp_solver(< span class = "stringliteral" > " MatchingWithCBC" < / span > ,< / div >
< div class = "line" > < a name = "l00190" > < / a > < span class = "lineno" > 190< / span >   MPSolver::CBC_MIXED_INTEGER_PROGRAMMING);< / div >
< div class = "line" > < a name = "l00191" > < / a > < span class = "lineno" > 191< / span >   < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a name = "l00192" > < / a > < span class = "lineno" > 192< / span >   std::string error;< / div >
< div class = "line" > < a name = "l00193" > < / a > < span class = "lineno" > 193< / span >   mp_solver.LoadModelFromProto(model, & error);< / div >
< div class = "line" > < a name = "l00194" > < / a > < span class = "lineno" > 194< / span >   MPSolver::ResultStatus status = mp_solver.Solve();< / div >
< div class = "line" > < a name = "l00195" > < / a > < span class = "lineno" > 195< / span >   CHECK_EQ(status, MPSolver::OPTIMAL);< / div >
< div class = "line" > < a name = "l00196" > < / a > < span class = "lineno" > 196< / span >   MPSolutionResponse response;< / div >
< div class = "line" > < a name = "l00197" > < / a > < span class = "lineno" > 197< / span >   mp_solver.FillSolutionResponseProto(& response);< / div >
< div class = "line" > < a name = "l00198" > < / a > < span class = "lineno" > 198< / span >   std::vector< std::pair< NodeIndex, NodeIndex> > matching;< / div >
< div class = "line" > < a name = "l00199" > < / a > < span class = "lineno" > 199< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc = 0; arc < variable_indices.size(); ++arc) {< / div >
< div class = "line" > < a name = "l00200" > < / a > < span class = "lineno" > 200< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > arc_var = variable_indices[arc];< / div >
< div class = "line" > < a name = "l00201" > < / a > < span class = "lineno" > 201< / span >   < span class = "keywordflow" > if< / span > (arc_var > = 0 & & response.variable_value(arc_var) > .9) {< / div >
< div class = "line" > < a name = "l00202" > < / a > < span class = "lineno" > 202< / span >   DCHECK_GE(response.variable_value(arc_var), 1.0 - 1e-4);< / div >
< div class = "line" > < a name = "l00203" > < / a > < span class = "lineno" > 203< / span >   matching.emplace_back(graph.Tail(arc), graph.Head(arc));< / div >
< div class = "line" > < a name = "l00204" > < / a > < span class = "lineno" > 204< / span >   }< / div >
< div class = "line" > < a name = "l00205" > < / a > < span class = "lineno" > 205< / span >   }< / div >
< div class = "line" > < a name = "l00206" > < / a > < span class = "lineno" > 206< / span >   < span class = "keywordflow" > return< / span > matching;< / div >
< div class = "line" > < a name = "l00207" > < / a > < span class = "lineno" > 207< / span >   }< / div >
< div class = "line" > < a name = "l00208" > < / a > < span class = "lineno" > 208< / span >   < span class = "preprocessor" > #endif // defined(USE_CBC) || defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00209" > < / a > < span class = "lineno" > 209< / span >   < / div >
< div class = "line" > < a name = "l00210" > < / a > < span class = "lineno" > 210< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType, < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ,< / div >
< div class = "line" > < a name = "l00211" > < / a > < span class = "lineno" > 211< / span >   < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00212" > < / a > < span class = "lineno" > 212< / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a87145cf1f5a36d27fd856596a23d495a" > ChristofidesPathSolver< CostType, ArcIndex, NodeIndex, CostFunction> ::< / a > < / div >
< div class = "line" > < a name = "l00213" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ChristofidesPathSolver.html#a87145cf1f5a36d27fd856596a23d495a" > 213< / a > < / span >   < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a87145cf1f5a36d27fd856596a23d495a" > ChristofidesPathSolver< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > num_nodes, CostFunction costs)< / div >
< div class = "line" > < a name = "l00214" > < / a > < span class = "lineno" > 214< / span >   : matching_(< a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7" > MatchingAlgorithm< / a > ::MINIMAL_WEIGHT_MATCHING),< / div >
< div class = "line" > < a name = "l00215" > < / a > < span class = "lineno" > 215< / span >   graph_(num_nodes),< / div >
< div class = "line" > < a name = "l00216" > < / a > < span class = "lineno" > 216< / span >   costs_(std::move(costs)),< / div >
< div class = "line" > < a name = "l00217" > < / a > < span class = "lineno" > 217< / span >   tsp_cost_(0),< / div >
< div class = "line" > < a name = "l00218" > < / a > < span class = "lineno" > 218< / span >   solved_(false) {}< / div >
< div class = "line" > < a name = "l00219" > < / a > < span class = "lineno" > 219< / span >   < / div >
< div class = "line" > < a name = "l00220" > < / a > < span class = "lineno" > 220< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType, < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ,< / div >
< div class = "line" > < a name = "l00221" > < / a > < span class = "lineno" > 221< / span >   < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00222" > < / a > < span class = "lineno" > 222< / span >   CostType < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html" > ChristofidesPathSolver< / a > < CostType, < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ,< / div >
< div class = "line" > < a name = "l00223" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ChristofidesPathSolver.html#ab558649a26fef3a74f0909ef5af45e90" > 223< / a > < / span >   CostFunction> ::TravelingSalesmanCost() {< / div >
< div class = "line" > < a name = "l00224" > < / a > < span class = "lineno" > 224< / span >   < span class = "keywordflow" > if< / span > (!solved_) {< / div >
< div class = "line" > < a name = "l00225" > < / a > < span class = "lineno" > 225< / span >   Solve();< / div >
< div class = "line" > < a name = "l00226" > < / a > < span class = "lineno" > 226< / span >   }< / div >
< div class = "line" > < a name = "l00227" > < / a > < span class = "lineno" > 227< / span >   < span class = "keywordflow" > return< / span > tsp_cost_;< / div >
< div class = "line" > < a name = "l00228" > < / a > < span class = "lineno" > 228< / span >   }< / div >
< div class = "line" > < a name = "l00229" > < / a > < span class = "lineno" > 229< / span >   < / div >
< div class = "line" > < a name = "l00230" > < / a > < span class = "lineno" > 230< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType, < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ,< / div >
< div class = "line" > < a name = "l00231" > < / a > < span class = "lineno" > 231< / span >   < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00232" > < / a > < span class = "lineno" > 232< / span >   std::vector< NodeIndex> < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html" > ChristofidesPathSolver< / a > < < / div >
< div class = "line" > < a name = "l00233" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ChristofidesPathSolver.html#a3076d9001536ea98d419faa81e7d8a47" > 233< / a > < / span >   CostType, < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > , CostFunction> ::TravelingSalesmanPath() {< / div >
< div class = "line" > < a name = "l00234" > < / a > < span class = "lineno" > 234< / span >   < span class = "keywordflow" > if< / span > (!solved_) {< / div >
< div class = "line" > < a name = "l00235" > < / a > < span class = "lineno" > 235< / span >   Solve();< / div >
< div class = "line" > < a name = "l00236" > < / a > < span class = "lineno" > 236< / span >   }< / div >
< div class = "line" > < a name = "l00237" > < / a > < span class = "lineno" > 237< / span >   < span class = "keywordflow" > return< / span > tsp_path_;< / div >
< div class = "line" > < a name = "l00238" > < / a > < span class = "lineno" > 238< / span >   }< / div >
< div class = "line" > < a name = "l00239" > < / a > < span class = "lineno" > 239< / span >   < / div >
< div class = "line" > < a name = "l00240" > < / a > < span class = "lineno" > 240< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType, < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ,< / div >
< div class = "line" > < a name = "l00241" > < / a > < span class = "lineno" > 241< / span >   < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00242" > < / a > < span class = "lineno" > 242< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1ChristofidesPathSolver.html" > ChristofidesPathSolver< / a > < CostType, < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > , < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ,< / div >
< div class = "line" > < a name = "l00243" > < / a > < span class = "lineno" > 243< / span >   CostFunction> ::Solve() {< / div >
< div class = "line" > < a name = "l00244" > < / a > < span class = "lineno" > 244< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > num_nodes = graph_.num_nodes();< / div >
< div class = "line" > < a name = "l00245" > < / a > < span class = "lineno" > 245< / span >   tsp_path_.clear();< / div >
< div class = "line" > < a name = "l00246" > < / a > < span class = "lineno" > 246< / span >   tsp_cost_ = 0;< / div >
< div class = "line" > < a name = "l00247" > < / a > < span class = "lineno" > 247< / span >   < span class = "keywordflow" > if< / span > (num_nodes == 1) {< / div >
< div class = "line" > < a name = "l00248" > < / a > < span class = "lineno" > 248< / span >   tsp_path_ = {0, 0};< / div >
< div class = "line" > < a name = "l00249" > < / a > < span class = "lineno" > 249< / span >   }< / div >
< div class = "line" > < a name = "l00250" > < / a > < span class = "lineno" > 250< / span >   < span class = "keywordflow" > if< / span > (num_nodes < = 1) {< / div >
< div class = "line" > < a name = "l00251" > < / a > < span class = "lineno" > 251< / span >   < span class = "keywordflow" > return< / span > ;< / div >
2019-11-14 13:52:51 -08:00
< div class = "line" > < a name = "l00252" > < / a > < span class = "lineno" > 252< / span >   }< / div >
2020-01-27 13:48:26 +01:00
< div class = "line" > < a name = "l00253" > < / a > < span class = "lineno" > 253< / span >   < span class = "comment" > // Compute Minimum Spanning Tree.< / span > < / div >
< div class = "line" > < a name = "l00254" > < / a > < span class = "lineno" > 254< / span >   < span class = "keyword" > const< / span > std::vector< ArcIndex> mst =< / div >
< div class = "line" > < a name = "l00255" > < / a > < span class = "lineno" > 255< / span >   < a class = "code" href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > BuildPrimMinimumSpanningTree< / a > (graph_, [< span class = "keyword" > this< / span > ](< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc) {< / div >
< div class = "line" > < a name = "l00256" > < / a > < span class = "lineno" > 256< / span >   < span class = "keywordflow" > return< / span > costs_(graph_.Tail(arc), graph_.Head(arc));< / div >
< div class = "line" > < a name = "l00257" > < / a > < span class = "lineno" > 257< / span >   });< / div >
< div class = "line" > < a name = "l00258" > < / a > < span class = "lineno" > 258< / span >   < span class = "comment" > // Detect odd degree nodes.< / span > < / div >
< div class = "line" > < a name = "l00259" > < / a > < span class = "lineno" > 259< / span >   std::vector< NodeIndex> degrees(num_nodes, 0);< / div >
< div class = "line" > < a name = "l00260" > < / a > < span class = "lineno" > 260< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : mst) {< / div >
< div class = "line" > < a name = "l00261" > < / a > < span class = "lineno" > 261< / span >   degrees[graph_.Tail(arc)]++;< / div >
< div class = "line" > < a name = "l00262" > < / a > < span class = "lineno" > 262< / span >   degrees[graph_.Head(arc)]++;< / div >
< div class = "line" > < a name = "l00263" > < / a > < span class = "lineno" > 263< / span >   }< / div >
< div class = "line" > < a name = "l00264" > < / a > < span class = "lineno" > 264< / span >   std::vector< NodeIndex> odd_degree_nodes;< / div >
< div class = "line" > < a name = "l00265" > < / a > < span class = "lineno" > 265< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > i = 0; i < degrees.size(); ++i) {< / div >
< div class = "line" > < a name = "l00266" > < / a > < span class = "lineno" > 266< / span >   < span class = "keywordflow" > if< / span > (degrees[i] % 2 != 0) {< / div >
< div class = "line" > < a name = "l00267" > < / a > < span class = "lineno" > 267< / span >   odd_degree_nodes.push_back(i);< / div >
< div class = "line" > < a name = "l00268" > < / a > < span class = "lineno" > 268< / span >   }< / div >
< div class = "line" > < a name = "l00269" > < / a > < span class = "lineno" > 269< / span >   }< / div >
< div class = "line" > < a name = "l00270" > < / a > < span class = "lineno" > 270< / span >   < span class = "comment" > // Find minimum-weight perfect matching on odd-degree-node complete graph.< / span > < / div >
< div class = "line" > < a name = "l00271" > < / a > < span class = "lineno" > 271< / span >   < span class = "comment" > // TODO(user): Make this code available as an independent algorithm.< / span > < / div >
< div class = "line" > < a name = "l00272" > < / a > < span class = "lineno" > 272< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > reduced_size = odd_degree_nodes.size();< / div >
< div class = "line" > < a name = "l00273" > < / a > < span class = "lineno" > 273< / span >   DCHECK_NE(0, reduced_size);< / div >
< div class = "line" > < a name = "l00274" > < / a > < span class = "lineno" > 274< / span >   CompleteGraph< NodeIndex, ArcIndex> reduced_graph(reduced_size);< / div >
< div class = "line" > < a name = "l00275" > < / a > < span class = "lineno" > 275< / span >   std::vector< std::pair< NodeIndex, NodeIndex> > closure_arcs;< / div >
< div class = "line" > < a name = "l00276" > < / a > < span class = "lineno" > 276< / span >   < span class = "keywordflow" > switch< / span > (matching_) {< / div >
< div class = "line" > < a name = "l00277" > < / a > < span class = "lineno" > 277< / span >   < span class = "keywordflow" > case< / span > MatchingAlgorithm::MINIMUM_WEIGHT_MATCHING: {< / div >
< div class = "line" > < a name = "l00278" > < / a > < span class = "lineno" > 278< / span >   closure_arcs = < a class = "code" href = "namespaceoperations__research.html#a3174292e878ea613e33ac86334fde459" > ComputeMinimumWeightMatching< / a > (< / div >
< div class = "line" > < a name = "l00279" > < / a > < span class = "lineno" > 279< / span >   reduced_graph, [< span class = "keyword" > this< / span > , & reduced_graph,< / div >
< div class = "line" > < a name = "l00280" > < / a > < span class = "lineno" > 280< / span >   & odd_degree_nodes](< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > CompleteGraph< > ::ArcIndex< / a > arc) {< / div >
< div class = "line" > < a name = "l00281" > < / a > < span class = "lineno" > 281< / span >   < span class = "keywordflow" > return< / span > costs_(odd_degree_nodes[reduced_graph.Tail(arc)],< / div >
< div class = "line" > < a name = "l00282" > < / a > < span class = "lineno" > 282< / span >   odd_degree_nodes[reduced_graph.Head(arc)]);< / div >
< div class = "line" > < a name = "l00283" > < / a > < span class = "lineno" > 283< / span >   });< / div >
< div class = "line" > < a name = "l00284" > < / a > < span class = "lineno" > 284< / span >   < span class = "keywordflow" > break< / span > ;< / div >
< div class = "line" > < a name = "l00285" > < / a > < span class = "lineno" > 285< / span >   }< / div >
< div class = "line" > < a name = "l00286" > < / a > < span class = "lineno" > 286< / span >   < span class = "preprocessor" > #if defined(USE_CBC) || defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00287" > < / a > < span class = "lineno" > 287< / span >   < span class = "keywordflow" > case< / span > MatchingAlgorithm::MINIMUM_WEIGHT_MATCHING_WITH_MIP: {< / div >
< div class = "line" > < a name = "l00288" > < / a > < span class = "lineno" > 288< / span >   closure_arcs = < a class = "code" href = "namespaceoperations__research.html#a48f6892917d77639f011cd780ce88bde" > ComputeMinimumWeightMatchingWithMIP< / a > (< / div >
< div class = "line" > < a name = "l00289" > < / a > < span class = "lineno" > 289< / span >   reduced_graph, [< span class = "keyword" > this< / span > , & reduced_graph,< / div >
< div class = "line" > < a name = "l00290" > < / a > < span class = "lineno" > 290< / span >   & odd_degree_nodes](< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > CompleteGraph< > ::ArcIndex< / a > arc) {< / div >
< div class = "line" > < a name = "l00291" > < / a > < span class = "lineno" > 291< / span >   < span class = "keywordflow" > return< / span > costs_(odd_degree_nodes[reduced_graph.Tail(arc)],< / div >
< div class = "line" > < a name = "l00292" > < / a > < span class = "lineno" > 292< / span >   odd_degree_nodes[reduced_graph.Head(arc)]);< / div >
< div class = "line" > < a name = "l00293" > < / a > < span class = "lineno" > 293< / span >   });< / div >
< div class = "line" > < a name = "l00294" > < / a > < span class = "lineno" > 294< / span >   < span class = "keywordflow" > break< / span > ;< / div >
< div class = "line" > < a name = "l00295" > < / a > < span class = "lineno" > 295< / span >   }< / div >
< div class = "line" > < a name = "l00296" > < / a > < span class = "lineno" > 296< / span >   < span class = "preprocessor" > #endif // defined(USE_CBC) || defined(USE_SCIP)< / span > < / div >
< div class = "line" > < a name = "l00297" > < / a > < span class = "lineno" > 297< / span >   < span class = "keywordflow" > case< / span > MatchingAlgorithm::MINIMAL_WEIGHT_MATCHING: {< / div >
< div class = "line" > < a name = "l00298" > < / a > < span class = "lineno" > 298< / span >   < span class = "comment" > // TODO(user): Cost caching was added and can gain up to 20% but< / span > < / div >
< div class = "line" > < a name = "l00299" > < / a > < span class = "lineno" > 299< / span >   < span class = "comment" > // increases memory usage; see if we can avoid caching.< / span > < / div >
< div class = "line" > < a name = "l00300" > < / a > < span class = "lineno" > 300< / span >   std::vector< ArcIndex> ordered_arcs(reduced_graph.num_arcs());< / div >
< div class = "line" > < a name = "l00301" > < / a > < span class = "lineno" > 301< / span >   std::vector< CostType> ordered_arc_costs(reduced_graph.num_arcs(), 0);< / div >
< div class = "line" > < a name = "l00302" > < / a > < span class = "lineno" > 302< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : reduced_graph.AllForwardArcs()) {< / div >
< div class = "line" > < a name = "l00303" > < / a > < span class = "lineno" > 303< / span >   ordered_arcs[arc] = arc;< / div >
< div class = "line" > < a name = "l00304" > < / a > < span class = "lineno" > 304< / span >   ordered_arc_costs[arc] =< / div >
< div class = "line" > < a name = "l00305" > < / a > < span class = "lineno" > 305< / span >   costs_(odd_degree_nodes[reduced_graph.Tail(arc)],< / div >
< div class = "line" > < a name = "l00306" > < / a > < span class = "lineno" > 306< / span >   odd_degree_nodes[reduced_graph.Head(arc)]);< / div >
< div class = "line" > < a name = "l00307" > < / a > < span class = "lineno" > 307< / span >   }< / div >
< div class = "line" > < a name = "l00308" > < / a > < span class = "lineno" > 308< / span >   std::sort(ordered_arcs.begin(), ordered_arcs.end(),< / div >
< div class = "line" > < a name = "l00309" > < / a > < span class = "lineno" > 309< / span >   [& ordered_arc_costs](< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc_a, < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc_b) {< / div >
2020-04-23 15:34:43 +02:00
< div class = "line" > < a name = "l00310" > < / a > < span class = "lineno" > 310< / span >   < span class = "keywordflow" > return< / span > ordered_arc_costs[arc_a] < ordered_arc_costs[arc_b];< / div >
2020-01-27 13:48:26 +01:00
< div class = "line" > < a name = "l00311" > < / a > < span class = "lineno" > 311< / span >   });< / div >
< div class = "line" > < a name = "l00312" > < / a > < span class = "lineno" > 312< / span >   std::vector< bool> touched_nodes(reduced_size, < span class = "keyword" > false< / span > );< / div >
< div class = "line" > < a name = "l00313" > < / a > < span class = "lineno" > 313< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc_index = 0; closure_arcs.size() * 2 < reduced_size;< / div >
< div class = "line" > < a name = "l00314" > < / a > < span class = "lineno" > 314< / span >   ++arc_index) {< / div >
< div class = "line" > < a name = "l00315" > < / a > < span class = "lineno" > 315< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc = ordered_arcs[arc_index];< / div >
< div class = "line" > < a name = "l00316" > < / a > < span class = "lineno" > 316< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail = reduced_graph.Tail(arc);< / div >
< div class = "line" > < a name = "l00317" > < / a > < span class = "lineno" > 317< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head = reduced_graph.Head(arc);< / div >
< div class = "line" > < a name = "l00318" > < / a > < span class = "lineno" > 318< / span >   < span class = "keywordflow" > if< / span > (head != tail & & !touched_nodes[tail] & & !touched_nodes[head]) {< / div >
< div class = "line" > < a name = "l00319" > < / a > < span class = "lineno" > 319< / span >   touched_nodes[tail] = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00320" > < / a > < span class = "lineno" > 320< / span >   touched_nodes[head] = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00321" > < / a > < span class = "lineno" > 321< / span >   closure_arcs.emplace_back(tail, head);< / div >
< div class = "line" > < a name = "l00322" > < / a > < span class = "lineno" > 322< / span >   }< / div >
< div class = "line" > < a name = "l00323" > < / a > < span class = "lineno" > 323< / span >   }< / div >
< div class = "line" > < a name = "l00324" > < / a > < span class = "lineno" > 324< / span >   < span class = "keywordflow" > break< / span > ;< / div >
< div class = "line" > < a name = "l00325" > < / a > < span class = "lineno" > 325< / span >   }< / div >
< div class = "line" > < a name = "l00326" > < / a > < span class = "lineno" > 326< / span >   }< / div >
< div class = "line" > < a name = "l00327" > < / a > < span class = "lineno" > 327< / span >   < span class = "comment" > // Build Eulerian path on minimum spanning tree + closing edges from matching< / span > < / div >
< div class = "line" > < a name = "l00328" > < / a > < span class = "lineno" > 328< / span >   < span class = "comment" > // and extract a solution to the Traveling Salesman from the path by skipping< / span > < / div >
< div class = "line" > < a name = "l00329" > < / a > < span class = "lineno" > 329< / span >   < span class = "comment" > // duplicate nodes.< / span > < / div >
< div class = "line" > < a name = "l00330" > < / a > < span class = "lineno" > 330< / span >   < a class = "code" href = "classutil_1_1ReverseArcListGraph.html" > ::util::ReverseArcListGraph< NodeIndex, ArcIndex> < / a > egraph(< / div >
< div class = "line" > < a name = "l00331" > < / a > < span class = "lineno" > 331< / span >   num_nodes, closure_arcs.size() + mst.size());< / div >
< div class = "line" > < a name = "l00332" > < / a > < span class = "lineno" > 332< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : mst) {< / div >
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< div class = "line" > < a name = "l00333" > < / a > < span class = "lineno" > 333< / span >   egraph.< a class = "code" href = "classutil_1_1ReverseArcListGraph.html#a7b505ba4a01bce342d049f5a8674da72" > AddArc< / a > (graph_.Tail(arc), graph_.Head(arc));< / div >
2020-01-27 13:48:26 +01:00
< div class = "line" > < a name = "l00334" > < / a > < span class = "lineno" > 334< / span >   }< / div >
< div class = "line" > < a name = "l00335" > < / a > < span class = "lineno" > 335< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > arc : closure_arcs) {< / div >
< div class = "line" > < a name = "l00336" > < / a > < span class = "lineno" > 336< / span >   egraph.AddArc(odd_degree_nodes[arc.first], odd_degree_nodes[arc.second]);< / div >
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< div class = "line" > < a name = "l00337" > < / a > < span class = "lineno" > 337< / span >   }< / div >
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< div class = "line" > < a name = "l00338" > < / a > < span class = "lineno" > 338< / span >   std::vector< bool> touched(num_nodes, < span class = "keyword" > false< / span > );< / div >
< div class = "line" > < a name = "l00339" > < / a > < span class = "lineno" > 339< / span >   DCHECK(< a class = "code" href = "namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89" > IsEulerianGraph< / a > (egraph));< / div >
< div class = "line" > < a name = "l00340" > < / a > < span class = "lineno" > 340< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : < a class = "code" href = "namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180" > BuildEulerianTourFromNode< / a > (egraph, 0)) {< / div >
< div class = "line" > < a name = "l00341" > < / a > < span class = "lineno" > 341< / span >   < span class = "keywordflow" > if< / span > (touched[node]) < span class = "keywordflow" > continue< / span > ;< / div >
< div class = "line" > < a name = "l00342" > < / a > < span class = "lineno" > 342< / span >   touched[node] = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00343" > < / a > < span class = "lineno" > 343< / span >   tsp_cost_ = SafeAdd(tsp_cost_,< / div >
< div class = "line" > < a name = "l00344" > < / a > < span class = "lineno" > 344< / span >   tsp_path_.empty() ? 0 : costs_(tsp_path_.back(), node));< / div >
< div class = "line" > < a name = "l00345" > < / a > < span class = "lineno" > 345< / span >   tsp_path_.push_back(node);< / div >
< div class = "line" > < a name = "l00346" > < / a > < span class = "lineno" > 346< / span >   }< / div >
< div class = "line" > < a name = "l00347" > < / a > < span class = "lineno" > 347< / span >   tsp_cost_ =< / div >
< div class = "line" > < a name = "l00348" > < / a > < span class = "lineno" > 348< / span >   SafeAdd(tsp_cost_, tsp_path_.empty() ? 0 : costs_(tsp_path_.back(), 0));< / div >
< div class = "line" > < a name = "l00349" > < / a > < span class = "lineno" > 349< / span >   tsp_path_.push_back(0);< / div >
< div class = "line" > < a name = "l00350" > < / a > < span class = "lineno" > 350< / span >   solved_ = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00351" > < / a > < span class = "lineno" > 351< / span >   }< / div >
< div class = "line" > < a name = "l00352" > < / a > < span class = "lineno" > 352< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00353" > < / a > < span class = "lineno" > 353< / span >   < / div >
< div class = "line" > < a name = "l00354" > < / a > < span class = "lineno" > 354< / span >   < span class = "preprocessor" > #endif // OR_TOOLS_GRAPH_CHRISTOFIDES_H_< / span > < / div >
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< / div > <!-- fragment --> < / div > <!-- contents -->
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< div class = "ttc" id = "aeulerian__path_8h_html" > < div class = "ttname" > < a href = "eulerian__path_8h.html" > eulerian_path.h< / a > < / div > < / div >
< div class = "ttc" id = "aclassutil_1_1ReverseArcListGraph_html" > < div class = "ttname" > < a href = "classutil_1_1ReverseArcListGraph.html" > util::ReverseArcListGraph< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l00459" > graph.h:459< / a > < / div > < / div >
2020-04-23 15:34:43 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_a1d4f082de5fc3eed348d65eb30b5f3e7a201b88f6589fa1271207fe29f583dc96" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7a201b88f6589fa1271207fe29f583dc96" > operations_research::ChristofidesPathSolver::MatchingAlgorithm::MINIMUM_WEIGHT_MATCHING_WITH_MIP< / a > < / div > < / div >
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "anamespaceoperations__research_html_ab1cf773de0cae72d0c44efe5b8f4bb89" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89" > operations_research::IsEulerianGraph< / a > < / div > < div class = "ttdeci" > bool IsEulerianGraph(const Graph & graph)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00040" > eulerian_path.h:40< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_ae2b64dddd58baf1bc5e01cb14971e52e" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#ae2b64dddd58baf1bc5e01cb14971e52e" > operations_research::ChristofidesPathSolver::SetMatchingAlgorithm< / a > < / div > < div class = "ttdeci" > void SetMatchingAlgorithm(MatchingAlgorithm matching)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00059" > christofides.h:59< / a > < / div > < / div >
2020-01-27 13:48:26 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html_a48f6892917d77639f011cd780ce88bde" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a48f6892917d77639f011cd780ce88bde" > operations_research::ComputeMinimumWeightMatchingWithMIP< / a > < / div > < div class = "ttdeci" > std::vector< std::pair< typename GraphType::NodeIndex, typename GraphType::NodeIndex > > ComputeMinimumWeightMatchingWithMIP(const GraphType & graph, const WeightFunctionType & weight)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00140" > christofides.h:140< / a > < / div > < / div >
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "anamespaceoperations__research_html" > < div class = "ttname" > < a href = "namespaceoperations__research.html" > operations_research< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00033" > christofides.h:33< / a > < / div > < / div >
< div class = "ttc" id = "aminimum__spanning__tree_8h_html" > < div class = "ttname" > < a href = "minimum__spanning__tree_8h.html" > minimum_spanning_tree.h< / a > < / div > < / div >
2020-01-27 13:48:26 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html_a3174292e878ea613e33ac86334fde459" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a3174292e878ea613e33ac86334fde459" > operations_research::ComputeMinimumWeightMatching< / a > < / div > < div class = "ttdeci" > std::vector< std::pair< typename GraphType::NodeIndex, typename GraphType::NodeIndex > > ComputeMinimumWeightMatching(const GraphType & graph, const WeightFunctionType & weight)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00106" > christofides.h:106< / a > < / div > < / div >
2020-04-23 15:34:43 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_a1d4f082de5fc3eed348d65eb30b5f3e7ab66d0823917c9351a4cb68dff77f445a" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7ab66d0823917c9351a4cb68dff77f445a" > operations_research::ChristofidesPathSolver::MatchingAlgorithm::MINIMUM_WEIGHT_MATCHING< / a > < / div > < / div >
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< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html" > operations_research::ChristofidesPathSolver< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00040" > christofides.h:40< / a > < / div > < / div >
2020-04-23 15:34:43 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_a1d4f082de5fc3eed348d65eb30b5f3e7a99c5fe202c37dcd8ed9cc60926a4f525" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7a99c5fe202c37dcd8ed9cc60926a4f525" > operations_research::ChristofidesPathSolver::MatchingAlgorithm::MINIMAL_WEIGHT_MATCHING< / a > < / div > < / div >
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "anamespaceoperations__research_html_a33a2f4c26fd60cd0fa98257b571c974f" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > operations_research::BuildPrimMinimumSpanningTree< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::ArcIndex > BuildPrimMinimumSpanningTree(const Graph & graph, const ArcValue & arc_value)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "minimum__spanning__tree_8h_source.html#l00117" > minimum_spanning_tree.h:117< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_ad90a9fc7d16bb2c98a088a4162bbbc9d" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > operations_research::ArcIndex< / a > < / div > < div class = "ttdeci" > int32 ArcIndex< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "ebert__graph_8h_source.html#l00201" > ebert_graph.h:201< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aa63055860fc53f8eed56d23d2571c180" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180" > operations_research::BuildEulerianTourFromNode< / a > < / div > < div class = "ttdeci" > std::vector< NodeIndex > BuildEulerianTourFromNode(const Graph & graph, NodeIndex root)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00116" > eulerian_path.h:116< / a > < / div > < / div >
2020-04-23 15:34:43 +02:00
< div class = "ttc" id = "aclassutil_1_1ReverseArcListGraph_html_a7b505ba4a01bce342d049f5a8674da72" > < div class = "ttname" > < a href = "classutil_1_1ReverseArcListGraph.html#a7b505ba4a01bce342d049f5a8674da72" > util::ReverseArcListGraph::AddArc< / a > < / div > < div class = "ttdeci" > ArcIndexType AddArc(NodeIndexType tail, NodeIndexType head)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l01500" > graph.h:1500< / a > < / div > < / div >
2020-01-27 13:48:26 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_a3076d9001536ea98d419faa81e7d8a47" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#a3076d9001536ea98d419faa81e7d8a47" > operations_research::ChristofidesPathSolver::TravelingSalesmanPath< / a > < / div > < div class = "ttdeci" > std::vector< NodeIndex > TravelingSalesmanPath()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00233" > christofides.h:233< / a > < / div > < / div >
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_a1d4f082de5fc3eed348d65eb30b5f3e7" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#a1d4f082de5fc3eed348d65eb30b5f3e7" > operations_research::ChristofidesPathSolver::MatchingAlgorithm< / a > < / div > < div class = "ttdeci" > MatchingAlgorithm< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00042" > christofides.h:42< / a > < / div > < / div >
< div class = "ttc" id = "agraph_8h_html" > < div class = "ttname" > < a href = "graph_8h.html" > graph.h< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a272bcc4d6ee0e87a7fc430a5cb13c582" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > operations_research::NodeIndex< / a > < / div > < div class = "ttdeci" > int32 NodeIndex< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "ebert__graph_8h_source.html#l00192" > ebert_graph.h:192< / a > < / div > < / div >
2020-01-27 13:48:26 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_ab558649a26fef3a74f0909ef5af45e90" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#ab558649a26fef3a74f0909ef5af45e90" > operations_research::ChristofidesPathSolver::TravelingSalesmanCost< / a > < / div > < div class = "ttdeci" > CostType TravelingSalesmanCost()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00223" > christofides.h:223< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1ChristofidesPathSolver_html_a87145cf1f5a36d27fd856596a23d495a" > < div class = "ttname" > < a href = "classoperations__research_1_1ChristofidesPathSolver.html#a87145cf1f5a36d27fd856596a23d495a" > operations_research::ChristofidesPathSolver::ChristofidesPathSolver< / a > < / div > < div class = "ttdeci" > ChristofidesPathSolver(NodeIndex num_nodes, CostFunction costs)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00213" > christofides.h:213< / a > < / div > < / div >
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