[2040] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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[2391] | 5 | * Copyright (C) 2003-2007 |
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[2040] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_BIPARTITE_MATCHING |
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| 20 | #define LEMON_BIPARTITE_MATCHING |
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| 21 | |
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[2051] | 22 | #include <functional> |
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| 23 | |
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| 24 | #include <lemon/bin_heap.h> |
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| 25 | #include <lemon/maps.h> |
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[2040] | 26 | |
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| 27 | #include <iostream> |
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| 28 | |
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| 29 | ///\ingroup matching |
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| 30 | ///\file |
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| 31 | ///\brief Maximum matching algorithms in bipartite graphs. |
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[2462] | 32 | /// |
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| 33 | ///\note The pr_bipartite_matching.h file also contains algorithms to |
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| 34 | ///solve maximum cardinality bipartite matching problems. |
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[2040] | 35 | |
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| 36 | namespace lemon { |
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| 37 | |
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| 38 | /// \ingroup matching |
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| 39 | /// |
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| 40 | /// \brief Bipartite Max Cardinality Matching algorithm |
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| 41 | /// |
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| 42 | /// Bipartite Max Cardinality Matching algorithm. This class implements |
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[2051] | 43 | /// the Hopcroft-Karp algorithm which has \f$ O(e\sqrt{n}) \f$ time |
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[2040] | 44 | /// complexity. |
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[2462] | 45 | /// |
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| 46 | /// \note In several cases the push-relabel based algorithms have |
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| 47 | /// better runtime performance than the augmenting path based ones. |
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| 48 | /// |
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| 49 | /// \see PrBipartiteMatching |
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[2040] | 50 | template <typename BpUGraph> |
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| 51 | class MaxBipartiteMatching { |
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| 52 | protected: |
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| 53 | |
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| 54 | typedef BpUGraph Graph; |
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| 55 | |
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| 56 | typedef typename Graph::Node Node; |
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| 57 | typedef typename Graph::ANodeIt ANodeIt; |
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| 58 | typedef typename Graph::BNodeIt BNodeIt; |
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| 59 | typedef typename Graph::UEdge UEdge; |
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| 60 | typedef typename Graph::UEdgeIt UEdgeIt; |
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| 61 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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| 62 | |
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| 63 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
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| 64 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
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| 65 | |
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| 66 | |
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| 67 | public: |
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| 68 | |
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| 69 | /// \brief Constructor. |
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| 70 | /// |
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| 71 | /// Constructor of the algorithm. |
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| 72 | MaxBipartiteMatching(const BpUGraph& _graph) |
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| 73 | : anode_matching(_graph), bnode_matching(_graph), graph(&_graph) {} |
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| 74 | |
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| 75 | /// \name Execution control |
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| 76 | /// The simplest way to execute the algorithm is to use |
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| 77 | /// one of the member functions called \c run(). |
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| 78 | /// \n |
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| 79 | /// If you need more control on the execution, |
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| 80 | /// first you must call \ref init() or one alternative for it. |
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| 81 | /// Finally \ref start() will perform the matching computation or |
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| 82 | /// with step-by-step execution you can augment the solution. |
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| 83 | |
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| 84 | /// @{ |
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| 85 | |
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| 86 | /// \brief Initalize the data structures. |
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| 87 | /// |
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| 88 | /// It initalizes the data structures and creates an empty matching. |
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| 89 | void init() { |
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| 90 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 91 | anode_matching[it] = INVALID; |
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| 92 | } |
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| 93 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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| 94 | bnode_matching[it] = INVALID; |
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| 95 | } |
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[2051] | 96 | matching_size = 0; |
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[2040] | 97 | } |
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| 98 | |
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| 99 | /// \brief Initalize the data structures. |
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| 100 | /// |
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| 101 | /// It initalizes the data structures and creates a greedy |
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| 102 | /// matching. From this matching sometimes it is faster to get |
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| 103 | /// the matching than from the initial empty matching. |
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| 104 | void greedyInit() { |
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[2051] | 105 | matching_size = 0; |
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[2040] | 106 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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| 107 | bnode_matching[it] = INVALID; |
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| 108 | } |
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| 109 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 110 | anode_matching[it] = INVALID; |
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| 111 | for (IncEdgeIt jt(*graph, it); jt != INVALID; ++jt) { |
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| 112 | if (bnode_matching[graph->bNode(jt)] == INVALID) { |
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| 113 | anode_matching[it] = jt; |
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| 114 | bnode_matching[graph->bNode(jt)] = jt; |
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[2051] | 115 | ++matching_size; |
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[2040] | 116 | break; |
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| 117 | } |
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| 118 | } |
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| 119 | } |
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| 120 | } |
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| 121 | |
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| 122 | /// \brief Initalize the data structures with an initial matching. |
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| 123 | /// |
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| 124 | /// It initalizes the data structures with an initial matching. |
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| 125 | template <typename MatchingMap> |
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[2386] | 126 | void matchingInit(const MatchingMap& mm) { |
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[2040] | 127 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 128 | anode_matching[it] = INVALID; |
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| 129 | } |
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| 130 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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| 131 | bnode_matching[it] = INVALID; |
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| 132 | } |
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[2051] | 133 | matching_size = 0; |
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[2040] | 134 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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[2386] | 135 | if (mm[it]) { |
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[2051] | 136 | ++matching_size; |
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[2040] | 137 | anode_matching[graph->aNode(it)] = it; |
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| 138 | bnode_matching[graph->bNode(it)] = it; |
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| 139 | } |
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| 140 | } |
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| 141 | } |
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| 142 | |
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| 143 | /// \brief Initalize the data structures with an initial matching. |
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| 144 | /// |
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| 145 | /// It initalizes the data structures with an initial matching. |
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| 146 | /// \return %True when the given map contains really a matching. |
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| 147 | template <typename MatchingMap> |
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[2386] | 148 | void checkedMatchingInit(const MatchingMap& mm) { |
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[2040] | 149 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 150 | anode_matching[it] = INVALID; |
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| 151 | } |
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| 152 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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| 153 | bnode_matching[it] = INVALID; |
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| 154 | } |
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[2051] | 155 | matching_size = 0; |
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[2040] | 156 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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[2386] | 157 | if (mm[it]) { |
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[2051] | 158 | ++matching_size; |
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[2040] | 159 | if (anode_matching[graph->aNode(it)] != INVALID) { |
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| 160 | return false; |
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| 161 | } |
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| 162 | anode_matching[graph->aNode(it)] = it; |
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| 163 | if (bnode_matching[graph->aNode(it)] != INVALID) { |
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| 164 | return false; |
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| 165 | } |
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| 166 | bnode_matching[graph->bNode(it)] = it; |
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| 167 | } |
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| 168 | } |
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| 169 | return false; |
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| 170 | } |
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| 171 | |
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| 172 | /// \brief An augmenting phase of the Hopcroft-Karp algorithm |
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| 173 | /// |
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| 174 | /// It runs an augmenting phase of the Hopcroft-Karp |
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[2352] | 175 | /// algorithm. This phase finds maximum count of edge disjoint |
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[2040] | 176 | /// augmenting paths and augments on these paths. The algorithm |
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| 177 | /// consists at most of \f$ O(\sqrt{n}) \f$ phase and one phase is |
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| 178 | /// \f$ O(e) \f$ long. |
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| 179 | bool augment() { |
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| 180 | |
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| 181 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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| 182 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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| 183 | |
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| 184 | typename Graph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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| 185 | |
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| 186 | std::vector<Node> queue, bqueue; |
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| 187 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 188 | if (anode_matching[it] == INVALID) { |
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| 189 | queue.push_back(it); |
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| 190 | areached[it] = true; |
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| 191 | } |
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| 192 | } |
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| 193 | |
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| 194 | bool success = false; |
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| 195 | |
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| 196 | while (!success && !queue.empty()) { |
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| 197 | std::vector<Node> newqueue; |
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[2386] | 198 | for (int i = 0; i < int(queue.size()); ++i) { |
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[2040] | 199 | Node anode = queue[i]; |
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| 200 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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| 201 | Node bnode = graph->bNode(jt); |
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| 202 | if (breached[bnode]) continue; |
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| 203 | breached[bnode] = true; |
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| 204 | bpred[bnode] = jt; |
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| 205 | if (bnode_matching[bnode] == INVALID) { |
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| 206 | bqueue.push_back(bnode); |
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| 207 | success = true; |
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| 208 | } else { |
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| 209 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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| 210 | if (!areached[newanode]) { |
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| 211 | areached[newanode] = true; |
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| 212 | newqueue.push_back(newanode); |
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| 213 | } |
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| 214 | } |
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| 215 | } |
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| 216 | } |
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| 217 | queue.swap(newqueue); |
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| 218 | } |
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| 219 | |
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| 220 | if (success) { |
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| 221 | |
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| 222 | typename Graph::template ANodeMap<bool> aused(*graph, false); |
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| 223 | |
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[2386] | 224 | for (int i = 0; i < int(bqueue.size()); ++i) { |
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[2040] | 225 | Node bnode = bqueue[i]; |
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| 226 | |
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| 227 | bool used = false; |
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| 228 | |
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| 229 | while (bnode != INVALID) { |
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| 230 | UEdge uedge = bpred[bnode]; |
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| 231 | Node anode = graph->aNode(uedge); |
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| 232 | |
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| 233 | if (aused[anode]) { |
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| 234 | used = true; |
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| 235 | break; |
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| 236 | } |
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| 237 | |
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| 238 | bnode = anode_matching[anode] != INVALID ? |
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| 239 | graph->bNode(anode_matching[anode]) : INVALID; |
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| 240 | |
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| 241 | } |
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| 242 | |
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| 243 | if (used) continue; |
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| 244 | |
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| 245 | bnode = bqueue[i]; |
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| 246 | while (bnode != INVALID) { |
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| 247 | UEdge uedge = bpred[bnode]; |
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| 248 | Node anode = graph->aNode(uedge); |
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| 249 | |
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| 250 | bnode_matching[bnode] = uedge; |
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| 251 | |
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| 252 | bnode = anode_matching[anode] != INVALID ? |
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| 253 | graph->bNode(anode_matching[anode]) : INVALID; |
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| 254 | |
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| 255 | anode_matching[anode] = uedge; |
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| 256 | |
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| 257 | aused[anode] = true; |
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| 258 | } |
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[2051] | 259 | ++matching_size; |
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[2040] | 260 | |
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| 261 | } |
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| 262 | } |
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| 263 | return success; |
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| 264 | } |
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| 265 | |
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| 266 | /// \brief An augmenting phase of the Ford-Fulkerson algorithm |
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| 267 | /// |
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| 268 | /// It runs an augmenting phase of the Ford-Fulkerson |
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[2352] | 269 | /// algorithm. This phase finds only one augmenting path and |
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[2040] | 270 | /// augments only on this paths. The algorithm consists at most |
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| 271 | /// of \f$ O(n) \f$ simple phase and one phase is at most |
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| 272 | /// \f$ O(e) \f$ long. |
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| 273 | bool simpleAugment() { |
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| 274 | |
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| 275 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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| 276 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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| 277 | |
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| 278 | typename Graph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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| 279 | |
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| 280 | std::vector<Node> queue; |
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| 281 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 282 | if (anode_matching[it] == INVALID) { |
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| 283 | queue.push_back(it); |
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| 284 | areached[it] = true; |
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| 285 | } |
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| 286 | } |
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| 287 | |
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| 288 | while (!queue.empty()) { |
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| 289 | std::vector<Node> newqueue; |
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[2386] | 290 | for (int i = 0; i < int(queue.size()); ++i) { |
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[2040] | 291 | Node anode = queue[i]; |
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| 292 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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| 293 | Node bnode = graph->bNode(jt); |
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| 294 | if (breached[bnode]) continue; |
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| 295 | breached[bnode] = true; |
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| 296 | bpred[bnode] = jt; |
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| 297 | if (bnode_matching[bnode] == INVALID) { |
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| 298 | while (bnode != INVALID) { |
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| 299 | UEdge uedge = bpred[bnode]; |
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| 300 | anode = graph->aNode(uedge); |
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| 301 | |
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| 302 | bnode_matching[bnode] = uedge; |
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| 303 | |
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| 304 | bnode = anode_matching[anode] != INVALID ? |
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| 305 | graph->bNode(anode_matching[anode]) : INVALID; |
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| 306 | |
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| 307 | anode_matching[anode] = uedge; |
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| 308 | |
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| 309 | } |
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[2051] | 310 | ++matching_size; |
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[2040] | 311 | return true; |
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| 312 | } else { |
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| 313 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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| 314 | if (!areached[newanode]) { |
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| 315 | areached[newanode] = true; |
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| 316 | newqueue.push_back(newanode); |
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| 317 | } |
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| 318 | } |
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| 319 | } |
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| 320 | } |
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| 321 | queue.swap(newqueue); |
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| 322 | } |
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| 323 | |
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| 324 | return false; |
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| 325 | } |
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| 326 | |
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| 327 | /// \brief Starts the algorithm. |
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| 328 | /// |
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| 329 | /// Starts the algorithm. It runs augmenting phases until the optimal |
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| 330 | /// solution reached. |
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| 331 | void start() { |
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| 332 | while (augment()) {} |
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| 333 | } |
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| 334 | |
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| 335 | /// \brief Runs the algorithm. |
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| 336 | /// |
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| 337 | /// It just initalize the algorithm and then start it. |
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| 338 | void run() { |
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[2058] | 339 | greedyInit(); |
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[2040] | 340 | start(); |
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| 341 | } |
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| 342 | |
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| 343 | /// @} |
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| 344 | |
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| 345 | /// \name Query Functions |
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| 346 | /// The result of the %Matching algorithm can be obtained using these |
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| 347 | /// functions.\n |
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| 348 | /// Before the use of these functions, |
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| 349 | /// either run() or start() must be called. |
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| 350 | |
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| 351 | ///@{ |
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| 352 | |
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[2462] | 353 | /// \brief Set true all matching uedge in the map. |
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| 354 | /// |
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| 355 | /// Set true all matching uedge in the map. It does not change the |
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| 356 | /// value mapped to the other uedges. |
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| 357 | /// \return The number of the matching edges. |
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| 358 | template <typename MatchingMap> |
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| 359 | int quickMatching(MatchingMap& mm) const { |
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| 360 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 361 | if (anode_matching[it] != INVALID) { |
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| 362 | mm[anode_matching[it]] = true; |
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| 363 | } |
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| 364 | } |
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| 365 | return matching_size; |
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| 366 | } |
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| 367 | |
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| 368 | /// \brief Set true all matching uedge in the map and the others to false. |
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| 369 | /// |
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| 370 | /// Set true all matching uedge in the map and the others to false. |
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| 371 | /// \return The number of the matching edges. |
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| 372 | template <typename MatchingMap> |
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| 373 | int matching(MatchingMap& mm) const { |
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| 374 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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| 375 | mm[it] = it == anode_matching[graph->aNode(it)]; |
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| 376 | } |
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| 377 | return matching_size; |
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| 378 | } |
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| 379 | |
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| 380 | |
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| 381 | /// \brief Return true if the given uedge is in the matching. |
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| 382 | /// |
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| 383 | /// It returns true if the given uedge is in the matching. |
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| 384 | bool matchingEdge(const UEdge& edge) const { |
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| 385 | return anode_matching[graph->aNode(edge)] == edge; |
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| 386 | } |
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| 387 | |
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| 388 | /// \brief Returns the matching edge from the node. |
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| 389 | /// |
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| 390 | /// Returns the matching edge from the node. If there is not such |
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| 391 | /// edge it gives back \c INVALID. |
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| 392 | UEdge matchingEdge(const Node& node) const { |
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| 393 | if (graph->aNode(node)) { |
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| 394 | return anode_matching[node]; |
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| 395 | } else { |
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| 396 | return bnode_matching[node]; |
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| 397 | } |
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| 398 | } |
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| 399 | |
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| 400 | /// \brief Gives back the number of the matching edges. |
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| 401 | /// |
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| 402 | /// Gives back the number of the matching edges. |
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| 403 | int matchingSize() const { |
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| 404 | return matching_size; |
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| 405 | } |
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| 406 | |
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| 407 | /// \brief Returns a minimum covering of the nodes. |
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[2040] | 408 | /// |
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| 409 | /// The minimum covering set problem is the dual solution of the |
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[2462] | 410 | /// maximum bipartite matching. It provides a solution for this |
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[2040] | 411 | /// problem what is proof of the optimality of the matching. |
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| 412 | /// \return The size of the cover set. |
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| 413 | template <typename CoverMap> |
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[2058] | 414 | int coverSet(CoverMap& covering) const { |
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[2040] | 415 | |
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| 416 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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| 417 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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| 418 | |
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| 419 | std::vector<Node> queue; |
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| 420 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 421 | if (anode_matching[it] == INVALID) { |
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| 422 | queue.push_back(it); |
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| 423 | } |
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| 424 | } |
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| 425 | |
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| 426 | while (!queue.empty()) { |
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| 427 | std::vector<Node> newqueue; |
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[2386] | 428 | for (int i = 0; i < int(queue.size()); ++i) { |
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[2040] | 429 | Node anode = queue[i]; |
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| 430 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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| 431 | Node bnode = graph->bNode(jt); |
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| 432 | if (breached[bnode]) continue; |
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| 433 | breached[bnode] = true; |
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| 434 | if (bnode_matching[bnode] != INVALID) { |
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| 435 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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| 436 | if (!areached[newanode]) { |
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| 437 | areached[newanode] = true; |
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| 438 | newqueue.push_back(newanode); |
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| 439 | } |
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| 440 | } |
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| 441 | } |
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| 442 | } |
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| 443 | queue.swap(newqueue); |
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| 444 | } |
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| 445 | |
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| 446 | int size = 0; |
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| 447 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 448 | covering[it] = !areached[it] && anode_matching[it] != INVALID; |
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| 449 | if (!areached[it] && anode_matching[it] != INVALID) { |
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| 450 | ++size; |
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| 451 | } |
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| 452 | } |
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| 453 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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| 454 | covering[it] = breached[it]; |
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| 455 | if (breached[it]) { |
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| 456 | ++size; |
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| 457 | } |
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| 458 | } |
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| 459 | return size; |
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| 460 | } |
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| 461 | |
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[2462] | 462 | /// \brief Gives back a barrier on the A-nodes |
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| 463 | |
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| 464 | /// The barrier is s subset of the nodes on the same side of the |
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| 465 | /// graph, which size minus its neighbours is exactly the |
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| 466 | /// unmatched nodes on the A-side. |
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| 467 | /// \retval barrier A WriteMap on the ANodes with bool value. |
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| 468 | template <typename BarrierMap> |
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| 469 | void aBarrier(BarrierMap& barrier) const { |
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| 470 | |
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| 471 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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| 472 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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| 473 | |
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| 474 | std::vector<Node> queue; |
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[2040] | 475 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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[2462] | 476 | if (anode_matching[it] == INVALID) { |
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| 477 | queue.push_back(it); |
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[2040] | 478 | } |
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| 479 | } |
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| 480 | |
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[2462] | 481 | while (!queue.empty()) { |
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| 482 | std::vector<Node> newqueue; |
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| 483 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 484 | Node anode = queue[i]; |
---|
| 485 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
| 486 | Node bnode = graph->bNode(jt); |
---|
| 487 | if (breached[bnode]) continue; |
---|
| 488 | breached[bnode] = true; |
---|
| 489 | if (bnode_matching[bnode] != INVALID) { |
---|
| 490 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
| 491 | if (!areached[newanode]) { |
---|
| 492 | areached[newanode] = true; |
---|
| 493 | newqueue.push_back(newanode); |
---|
| 494 | } |
---|
| 495 | } |
---|
| 496 | } |
---|
| 497 | } |
---|
| 498 | queue.swap(newqueue); |
---|
[2040] | 499 | } |
---|
| 500 | |
---|
[2462] | 501 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 502 | barrier[it] = areached[it] || anode_matching[it] == INVALID; |
---|
[2040] | 503 | } |
---|
| 504 | } |
---|
| 505 | |
---|
[2462] | 506 | /// \brief Gives back a barrier on the B-nodes |
---|
| 507 | |
---|
| 508 | /// The barrier is s subset of the nodes on the same side of the |
---|
| 509 | /// graph, which size minus its neighbours is exactly the |
---|
| 510 | /// unmatched nodes on the B-side. |
---|
| 511 | /// \retval barrier A WriteMap on the BNodes with bool value. |
---|
| 512 | template <typename BarrierMap> |
---|
| 513 | void bBarrier(BarrierMap& barrier) const { |
---|
| 514 | |
---|
| 515 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
---|
| 516 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
---|
| 517 | |
---|
| 518 | std::vector<Node> queue; |
---|
| 519 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 520 | if (anode_matching[it] == INVALID) { |
---|
| 521 | queue.push_back(it); |
---|
| 522 | } |
---|
| 523 | } |
---|
| 524 | |
---|
| 525 | while (!queue.empty()) { |
---|
| 526 | std::vector<Node> newqueue; |
---|
| 527 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
| 528 | Node anode = queue[i]; |
---|
| 529 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
| 530 | Node bnode = graph->bNode(jt); |
---|
| 531 | if (breached[bnode]) continue; |
---|
| 532 | breached[bnode] = true; |
---|
| 533 | if (bnode_matching[bnode] != INVALID) { |
---|
| 534 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
| 535 | if (!areached[newanode]) { |
---|
| 536 | areached[newanode] = true; |
---|
| 537 | newqueue.push_back(newanode); |
---|
| 538 | } |
---|
| 539 | } |
---|
| 540 | } |
---|
| 541 | } |
---|
| 542 | queue.swap(newqueue); |
---|
| 543 | } |
---|
| 544 | |
---|
| 545 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 546 | barrier[it] = !breached[it]; |
---|
| 547 | } |
---|
[2040] | 548 | } |
---|
| 549 | |
---|
| 550 | /// @} |
---|
| 551 | |
---|
| 552 | private: |
---|
| 553 | |
---|
| 554 | ANodeMatchingMap anode_matching; |
---|
| 555 | BNodeMatchingMap bnode_matching; |
---|
| 556 | const Graph *graph; |
---|
| 557 | |
---|
[2051] | 558 | int matching_size; |
---|
| 559 | |
---|
| 560 | }; |
---|
| 561 | |
---|
[2058] | 562 | /// \ingroup matching |
---|
| 563 | /// |
---|
| 564 | /// \brief Maximum cardinality bipartite matching |
---|
| 565 | /// |
---|
| 566 | /// This function calculates the maximum cardinality matching |
---|
| 567 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
| 568 | /// edge map. |
---|
| 569 | /// |
---|
| 570 | /// \param graph The bipartite graph. |
---|
| 571 | /// \retval matching The undirected edge map which will be set to |
---|
| 572 | /// the matching. |
---|
| 573 | /// \return The size of the matching. |
---|
| 574 | template <typename BpUGraph, typename MatchingMap> |
---|
| 575 | int maxBipartiteMatching(const BpUGraph& graph, MatchingMap& matching) { |
---|
| 576 | MaxBipartiteMatching<BpUGraph> bpmatching(graph); |
---|
| 577 | bpmatching.run(); |
---|
| 578 | bpmatching.matching(matching); |
---|
| 579 | return bpmatching.matchingSize(); |
---|
| 580 | } |
---|
| 581 | |
---|
[2051] | 582 | /// \brief Default traits class for weighted bipartite matching algoritms. |
---|
| 583 | /// |
---|
| 584 | /// Default traits class for weighted bipartite matching algoritms. |
---|
| 585 | /// \param _BpUGraph The bipartite undirected graph type. |
---|
| 586 | /// \param _WeightMap Type of weight map. |
---|
| 587 | template <typename _BpUGraph, typename _WeightMap> |
---|
| 588 | struct WeightedBipartiteMatchingDefaultTraits { |
---|
| 589 | /// \brief The type of the weight of the undirected edges. |
---|
| 590 | typedef typename _WeightMap::Value Value; |
---|
| 591 | |
---|
| 592 | /// The undirected bipartite graph type the algorithm runs on. |
---|
| 593 | typedef _BpUGraph BpUGraph; |
---|
| 594 | |
---|
| 595 | /// The map of the edges weights |
---|
| 596 | typedef _WeightMap WeightMap; |
---|
| 597 | |
---|
| 598 | /// \brief The cross reference type used by heap. |
---|
| 599 | /// |
---|
| 600 | /// The cross reference type used by heap. |
---|
| 601 | /// Usually it is \c Graph::NodeMap<int>. |
---|
| 602 | typedef typename BpUGraph::template NodeMap<int> HeapCrossRef; |
---|
| 603 | |
---|
| 604 | /// \brief Instantiates a HeapCrossRef. |
---|
| 605 | /// |
---|
| 606 | /// This function instantiates a \ref HeapCrossRef. |
---|
| 607 | /// \param graph is the graph, to which we would like to define the |
---|
| 608 | /// HeapCrossRef. |
---|
| 609 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 610 | return new HeapCrossRef(graph); |
---|
| 611 | } |
---|
| 612 | |
---|
| 613 | /// \brief The heap type used by weighted matching algorithms. |
---|
| 614 | /// |
---|
| 615 | /// The heap type used by weighted matching algorithms. It should |
---|
| 616 | /// minimize the priorities and the heap's key type is the graph's |
---|
| 617 | /// anode graph's node. |
---|
| 618 | /// |
---|
| 619 | /// \sa BinHeap |
---|
[2263] | 620 | typedef BinHeap<Value, HeapCrossRef> Heap; |
---|
[2051] | 621 | |
---|
| 622 | /// \brief Instantiates a Heap. |
---|
| 623 | /// |
---|
| 624 | /// This function instantiates a \ref Heap. |
---|
| 625 | /// \param crossref The cross reference of the heap. |
---|
| 626 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
| 627 | return new Heap(crossref); |
---|
| 628 | } |
---|
| 629 | |
---|
| 630 | }; |
---|
| 631 | |
---|
| 632 | |
---|
| 633 | /// \ingroup matching |
---|
| 634 | /// |
---|
| 635 | /// \brief Bipartite Max Weighted Matching algorithm |
---|
| 636 | /// |
---|
| 637 | /// This class implements the bipartite Max Weighted Matching |
---|
| 638 | /// algorithm. It uses the successive shortest path algorithm to |
---|
| 639 | /// calculate the maximum weighted matching in the bipartite |
---|
| 640 | /// graph. The algorithm can be used also to calculate the maximum |
---|
| 641 | /// cardinality maximum weighted matching. The time complexity |
---|
| 642 | /// of the algorithm is \f$ O(ne\log(n)) \f$ with the default binary |
---|
| 643 | /// heap implementation but this can be improved to |
---|
| 644 | /// \f$ O(n^2\log(n)+ne) \f$ if we use fibonacci heaps. |
---|
| 645 | /// |
---|
| 646 | /// The algorithm also provides a potential function on the nodes |
---|
| 647 | /// which a dual solution of the matching algorithm and it can be |
---|
| 648 | /// used to proof the optimality of the given pimal solution. |
---|
| 649 | #ifdef DOXYGEN |
---|
| 650 | template <typename _BpUGraph, typename _WeightMap, typename _Traits> |
---|
| 651 | #else |
---|
| 652 | template <typename _BpUGraph, |
---|
| 653 | typename _WeightMap = typename _BpUGraph::template UEdgeMap<int>, |
---|
| 654 | typename _Traits = WeightedBipartiteMatchingDefaultTraits<_BpUGraph, _WeightMap> > |
---|
| 655 | #endif |
---|
| 656 | class MaxWeightedBipartiteMatching { |
---|
| 657 | public: |
---|
| 658 | |
---|
| 659 | typedef _Traits Traits; |
---|
| 660 | typedef typename Traits::BpUGraph BpUGraph; |
---|
| 661 | typedef typename Traits::WeightMap WeightMap; |
---|
| 662 | typedef typename Traits::Value Value; |
---|
| 663 | |
---|
| 664 | protected: |
---|
| 665 | |
---|
| 666 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
| 667 | typedef typename Traits::Heap Heap; |
---|
| 668 | |
---|
| 669 | |
---|
| 670 | typedef typename BpUGraph::Node Node; |
---|
| 671 | typedef typename BpUGraph::ANodeIt ANodeIt; |
---|
| 672 | typedef typename BpUGraph::BNodeIt BNodeIt; |
---|
| 673 | typedef typename BpUGraph::UEdge UEdge; |
---|
| 674 | typedef typename BpUGraph::UEdgeIt UEdgeIt; |
---|
| 675 | typedef typename BpUGraph::IncEdgeIt IncEdgeIt; |
---|
| 676 | |
---|
| 677 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
---|
| 678 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
---|
| 679 | |
---|
| 680 | typedef typename BpUGraph::template ANodeMap<Value> ANodePotentialMap; |
---|
| 681 | typedef typename BpUGraph::template BNodeMap<Value> BNodePotentialMap; |
---|
| 682 | |
---|
| 683 | |
---|
| 684 | public: |
---|
| 685 | |
---|
| 686 | /// \brief \ref Exception for uninitialized parameters. |
---|
| 687 | /// |
---|
| 688 | /// This error represents problems in the initialization |
---|
| 689 | /// of the parameters of the algorithms. |
---|
| 690 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
| 691 | public: |
---|
[2151] | 692 | virtual const char* what() const throw() { |
---|
[2051] | 693 | return "lemon::MaxWeightedBipartiteMatching::UninitializedParameter"; |
---|
| 694 | } |
---|
| 695 | }; |
---|
| 696 | |
---|
| 697 | ///\name Named template parameters |
---|
| 698 | |
---|
| 699 | ///@{ |
---|
| 700 | |
---|
| 701 | template <class H, class CR> |
---|
| 702 | struct DefHeapTraits : public Traits { |
---|
| 703 | typedef CR HeapCrossRef; |
---|
| 704 | typedef H Heap; |
---|
| 705 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &) { |
---|
| 706 | throw UninitializedParameter(); |
---|
| 707 | } |
---|
| 708 | static Heap *createHeap(HeapCrossRef &) { |
---|
| 709 | throw UninitializedParameter(); |
---|
| 710 | } |
---|
| 711 | }; |
---|
| 712 | |
---|
| 713 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
| 714 | /// and cross reference type |
---|
| 715 | /// |
---|
| 716 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 717 | /// reference type |
---|
| 718 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 719 | struct DefHeap |
---|
| 720 | : public MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 721 | DefHeapTraits<H, CR> > { |
---|
| 722 | typedef MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 723 | DefHeapTraits<H, CR> > Create; |
---|
| 724 | }; |
---|
| 725 | |
---|
| 726 | template <class H, class CR> |
---|
| 727 | struct DefStandardHeapTraits : public Traits { |
---|
| 728 | typedef CR HeapCrossRef; |
---|
| 729 | typedef H Heap; |
---|
| 730 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 731 | return new HeapCrossRef(graph); |
---|
| 732 | } |
---|
| 733 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
| 734 | return new Heap(crossref); |
---|
| 735 | } |
---|
| 736 | }; |
---|
| 737 | |
---|
| 738 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
| 739 | /// cross reference type with automatic allocation |
---|
| 740 | /// |
---|
| 741 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 742 | /// reference type. It can allocate the heap and the cross reference |
---|
| 743 | /// object if the cross reference's constructor waits for the graph as |
---|
| 744 | /// parameter and the heap's constructor waits for the cross reference. |
---|
| 745 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 746 | struct DefStandardHeap |
---|
| 747 | : public MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 748 | DefStandardHeapTraits<H, CR> > { |
---|
| 749 | typedef MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 750 | DefStandardHeapTraits<H, CR> > |
---|
| 751 | Create; |
---|
| 752 | }; |
---|
| 753 | |
---|
| 754 | ///@} |
---|
| 755 | |
---|
| 756 | |
---|
| 757 | /// \brief Constructor. |
---|
| 758 | /// |
---|
| 759 | /// Constructor of the algorithm. |
---|
| 760 | MaxWeightedBipartiteMatching(const BpUGraph& _graph, |
---|
| 761 | const WeightMap& _weight) |
---|
| 762 | : graph(&_graph), weight(&_weight), |
---|
| 763 | anode_matching(_graph), bnode_matching(_graph), |
---|
| 764 | anode_potential(_graph), bnode_potential(_graph), |
---|
| 765 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
| 766 | _heap(0), local_heap(0) {} |
---|
| 767 | |
---|
| 768 | /// \brief Destructor. |
---|
| 769 | /// |
---|
| 770 | /// Destructor of the algorithm. |
---|
| 771 | ~MaxWeightedBipartiteMatching() { |
---|
| 772 | destroyStructures(); |
---|
| 773 | } |
---|
| 774 | |
---|
| 775 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
| 776 | /// |
---|
| 777 | /// Sets the heap and the cross reference used by algorithm. |
---|
| 778 | /// If you don't use this function before calling \ref run(), |
---|
| 779 | /// it will allocate one. The destuctor deallocates this |
---|
| 780 | /// automatically allocated map, of course. |
---|
| 781 | /// \return \c (*this) |
---|
[2386] | 782 | MaxWeightedBipartiteMatching& heap(Heap& hp, HeapCrossRef &cr) { |
---|
[2051] | 783 | if(local_heap_cross_ref) { |
---|
| 784 | delete _heap_cross_ref; |
---|
| 785 | local_heap_cross_ref = false; |
---|
| 786 | } |
---|
[2386] | 787 | _heap_cross_ref = &cr; |
---|
[2051] | 788 | if(local_heap) { |
---|
| 789 | delete _heap; |
---|
| 790 | local_heap = false; |
---|
| 791 | } |
---|
[2386] | 792 | _heap = &hp; |
---|
[2051] | 793 | return *this; |
---|
| 794 | } |
---|
| 795 | |
---|
| 796 | /// \name Execution control |
---|
| 797 | /// The simplest way to execute the algorithm is to use |
---|
| 798 | /// one of the member functions called \c run(). |
---|
| 799 | /// \n |
---|
| 800 | /// If you need more control on the execution, |
---|
| 801 | /// first you must call \ref init() or one alternative for it. |
---|
| 802 | /// Finally \ref start() will perform the matching computation or |
---|
| 803 | /// with step-by-step execution you can augment the solution. |
---|
| 804 | |
---|
| 805 | /// @{ |
---|
| 806 | |
---|
| 807 | /// \brief Initalize the data structures. |
---|
| 808 | /// |
---|
| 809 | /// It initalizes the data structures and creates an empty matching. |
---|
| 810 | void init() { |
---|
| 811 | initStructures(); |
---|
| 812 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 813 | anode_matching[it] = INVALID; |
---|
| 814 | anode_potential[it] = 0; |
---|
| 815 | } |
---|
| 816 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 817 | bnode_matching[it] = INVALID; |
---|
| 818 | bnode_potential[it] = 0; |
---|
| 819 | for (IncEdgeIt jt(*graph, it); jt != INVALID; ++jt) { |
---|
[2058] | 820 | if ((*weight)[jt] > bnode_potential[it]) { |
---|
| 821 | bnode_potential[it] = (*weight)[jt]; |
---|
[2051] | 822 | } |
---|
| 823 | } |
---|
| 824 | } |
---|
| 825 | matching_value = 0; |
---|
| 826 | matching_size = 0; |
---|
| 827 | } |
---|
| 828 | |
---|
| 829 | |
---|
| 830 | /// \brief An augmenting phase of the weighted matching algorithm |
---|
| 831 | /// |
---|
| 832 | /// It runs an augmenting phase of the weighted matching |
---|
[2352] | 833 | /// algorithm. This phase finds the best augmenting path and |
---|
[2051] | 834 | /// augments only on this paths. |
---|
| 835 | /// |
---|
| 836 | /// The algorithm consists at most |
---|
| 837 | /// of \f$ O(n) \f$ phase and one phase is \f$ O(n\log(n)+e) \f$ |
---|
| 838 | /// long with Fibonacci heap or \f$ O((n+e)\log(n)) \f$ long |
---|
| 839 | /// with binary heap. |
---|
| 840 | /// \param decrease If the given parameter true the matching value |
---|
| 841 | /// can be decreased in the augmenting phase. If we would like |
---|
| 842 | /// to calculate the maximum cardinality maximum weighted matching |
---|
| 843 | /// then we should let the algorithm to decrease the matching |
---|
| 844 | /// value in order to increase the number of the matching edges. |
---|
| 845 | bool augment(bool decrease = false) { |
---|
| 846 | |
---|
| 847 | typename BpUGraph::template BNodeMap<Value> bdist(*graph); |
---|
| 848 | typename BpUGraph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
---|
| 849 | |
---|
| 850 | Node bestNode = INVALID; |
---|
| 851 | Value bestValue = 0; |
---|
| 852 | |
---|
| 853 | _heap->clear(); |
---|
| 854 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 855 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
---|
| 856 | } |
---|
| 857 | |
---|
| 858 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 859 | if (anode_matching[it] == INVALID) { |
---|
| 860 | _heap->push(it, 0); |
---|
| 861 | } |
---|
| 862 | } |
---|
| 863 | |
---|
| 864 | Value bdistMax = 0; |
---|
| 865 | while (!_heap->empty()) { |
---|
| 866 | Node anode = _heap->top(); |
---|
| 867 | Value avalue = _heap->prio(); |
---|
| 868 | _heap->pop(); |
---|
| 869 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
| 870 | if (jt == anode_matching[anode]) continue; |
---|
| 871 | Node bnode = graph->bNode(jt); |
---|
[2058] | 872 | Value bvalue = avalue - (*weight)[jt] + |
---|
| 873 | anode_potential[anode] + bnode_potential[bnode]; |
---|
[2051] | 874 | if (bpred[bnode] == INVALID || bvalue < bdist[bnode]) { |
---|
| 875 | bdist[bnode] = bvalue; |
---|
| 876 | bpred[bnode] = jt; |
---|
| 877 | } |
---|
| 878 | if (bvalue > bdistMax) { |
---|
| 879 | bdistMax = bvalue; |
---|
| 880 | } |
---|
| 881 | if (bnode_matching[bnode] != INVALID) { |
---|
| 882 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
| 883 | switch (_heap->state(newanode)) { |
---|
| 884 | case Heap::PRE_HEAP: |
---|
| 885 | _heap->push(newanode, bvalue); |
---|
| 886 | break; |
---|
| 887 | case Heap::IN_HEAP: |
---|
| 888 | if (bvalue < (*_heap)[newanode]) { |
---|
| 889 | _heap->decrease(newanode, bvalue); |
---|
| 890 | } |
---|
| 891 | break; |
---|
| 892 | case Heap::POST_HEAP: |
---|
| 893 | break; |
---|
| 894 | } |
---|
| 895 | } else { |
---|
| 896 | if (bestNode == INVALID || |
---|
[2058] | 897 | bnode_potential[bnode] - bvalue > bestValue) { |
---|
| 898 | bestValue = bnode_potential[bnode] - bvalue; |
---|
[2051] | 899 | bestNode = bnode; |
---|
| 900 | } |
---|
| 901 | } |
---|
| 902 | } |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | if (bestNode == INVALID || (!decrease && bestValue < 0)) { |
---|
| 906 | return false; |
---|
| 907 | } |
---|
| 908 | |
---|
| 909 | matching_value += bestValue; |
---|
| 910 | ++matching_size; |
---|
| 911 | |
---|
| 912 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 913 | if (bpred[it] != INVALID) { |
---|
[2058] | 914 | bnode_potential[it] -= bdist[it]; |
---|
[2051] | 915 | } else { |
---|
[2058] | 916 | bnode_potential[it] -= bdistMax; |
---|
[2051] | 917 | } |
---|
| 918 | } |
---|
| 919 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 920 | if (anode_matching[it] != INVALID) { |
---|
| 921 | Node bnode = graph->bNode(anode_matching[it]); |
---|
| 922 | if (bpred[bnode] != INVALID) { |
---|
| 923 | anode_potential[it] += bdist[bnode]; |
---|
| 924 | } else { |
---|
| 925 | anode_potential[it] += bdistMax; |
---|
| 926 | } |
---|
| 927 | } |
---|
| 928 | } |
---|
| 929 | |
---|
| 930 | while (bestNode != INVALID) { |
---|
| 931 | UEdge uedge = bpred[bestNode]; |
---|
| 932 | Node anode = graph->aNode(uedge); |
---|
| 933 | |
---|
| 934 | bnode_matching[bestNode] = uedge; |
---|
| 935 | if (anode_matching[anode] != INVALID) { |
---|
| 936 | bestNode = graph->bNode(anode_matching[anode]); |
---|
| 937 | } else { |
---|
| 938 | bestNode = INVALID; |
---|
| 939 | } |
---|
| 940 | anode_matching[anode] = uedge; |
---|
| 941 | } |
---|
| 942 | |
---|
| 943 | |
---|
| 944 | return true; |
---|
| 945 | } |
---|
| 946 | |
---|
| 947 | /// \brief Starts the algorithm. |
---|
| 948 | /// |
---|
| 949 | /// Starts the algorithm. It runs augmenting phases until the |
---|
| 950 | /// optimal solution reached. |
---|
| 951 | /// |
---|
| 952 | /// \param maxCardinality If the given value is true it will |
---|
| 953 | /// calculate the maximum cardinality maximum matching instead of |
---|
| 954 | /// the maximum matching. |
---|
| 955 | void start(bool maxCardinality = false) { |
---|
| 956 | while (augment(maxCardinality)) {} |
---|
| 957 | } |
---|
| 958 | |
---|
| 959 | /// \brief Runs the algorithm. |
---|
| 960 | /// |
---|
| 961 | /// It just initalize the algorithm and then start it. |
---|
| 962 | /// |
---|
| 963 | /// \param maxCardinality If the given value is true it will |
---|
| 964 | /// calculate the maximum cardinality maximum matching instead of |
---|
| 965 | /// the maximum matching. |
---|
| 966 | void run(bool maxCardinality = false) { |
---|
| 967 | init(); |
---|
| 968 | start(maxCardinality); |
---|
| 969 | } |
---|
| 970 | |
---|
| 971 | /// @} |
---|
| 972 | |
---|
| 973 | /// \name Query Functions |
---|
| 974 | /// The result of the %Matching algorithm can be obtained using these |
---|
| 975 | /// functions.\n |
---|
| 976 | /// Before the use of these functions, |
---|
| 977 | /// either run() or start() must be called. |
---|
| 978 | |
---|
| 979 | ///@{ |
---|
| 980 | |
---|
| 981 | /// \brief Gives back the potential in the NodeMap |
---|
| 982 | /// |
---|
[2058] | 983 | /// Gives back the potential in the NodeMap. The matching is optimal |
---|
| 984 | /// with the current number of edges if \f$ \pi(a) + \pi(b) - w(ab) = 0 \f$ |
---|
| 985 | /// for each matching edges and \f$ \pi(a) + \pi(b) - w(ab) \ge 0 \f$ |
---|
| 986 | /// for each edges. |
---|
[2051] | 987 | template <typename PotentialMap> |
---|
[2386] | 988 | void potential(PotentialMap& pt) const { |
---|
[2051] | 989 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
[2386] | 990 | pt[it] = anode_potential[it]; |
---|
[2051] | 991 | } |
---|
| 992 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
[2386] | 993 | pt[it] = bnode_potential[it]; |
---|
[2051] | 994 | } |
---|
| 995 | } |
---|
| 996 | |
---|
| 997 | /// \brief Set true all matching uedge in the map. |
---|
| 998 | /// |
---|
| 999 | /// Set true all matching uedge in the map. It does not change the |
---|
| 1000 | /// value mapped to the other uedges. |
---|
| 1001 | /// \return The number of the matching edges. |
---|
| 1002 | template <typename MatchingMap> |
---|
[2386] | 1003 | int quickMatching(MatchingMap& mm) const { |
---|
[2051] | 1004 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1005 | if (anode_matching[it] != INVALID) { |
---|
[2386] | 1006 | mm[anode_matching[it]] = true; |
---|
[2051] | 1007 | } |
---|
| 1008 | } |
---|
| 1009 | return matching_size; |
---|
| 1010 | } |
---|
| 1011 | |
---|
| 1012 | /// \brief Set true all matching uedge in the map and the others to false. |
---|
| 1013 | /// |
---|
| 1014 | /// Set true all matching uedge in the map and the others to false. |
---|
| 1015 | /// \return The number of the matching edges. |
---|
| 1016 | template <typename MatchingMap> |
---|
[2386] | 1017 | int matching(MatchingMap& mm) const { |
---|
[2051] | 1018 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
---|
[2386] | 1019 | mm[it] = it == anode_matching[graph->aNode(it)]; |
---|
[2051] | 1020 | } |
---|
| 1021 | return matching_size; |
---|
| 1022 | } |
---|
| 1023 | |
---|
| 1024 | |
---|
| 1025 | /// \brief Return true if the given uedge is in the matching. |
---|
| 1026 | /// |
---|
| 1027 | /// It returns true if the given uedge is in the matching. |
---|
[2058] | 1028 | bool matchingEdge(const UEdge& edge) const { |
---|
[2051] | 1029 | return anode_matching[graph->aNode(edge)] == edge; |
---|
| 1030 | } |
---|
| 1031 | |
---|
| 1032 | /// \brief Returns the matching edge from the node. |
---|
| 1033 | /// |
---|
| 1034 | /// Returns the matching edge from the node. If there is not such |
---|
| 1035 | /// edge it gives back \c INVALID. |
---|
[2058] | 1036 | UEdge matchingEdge(const Node& node) const { |
---|
[2051] | 1037 | if (graph->aNode(node)) { |
---|
| 1038 | return anode_matching[node]; |
---|
| 1039 | } else { |
---|
| 1040 | return bnode_matching[node]; |
---|
| 1041 | } |
---|
| 1042 | } |
---|
| 1043 | |
---|
| 1044 | /// \brief Gives back the sum of weights of the matching edges. |
---|
| 1045 | /// |
---|
| 1046 | /// Gives back the sum of weights of the matching edges. |
---|
| 1047 | Value matchingValue() const { |
---|
| 1048 | return matching_value; |
---|
| 1049 | } |
---|
| 1050 | |
---|
| 1051 | /// \brief Gives back the number of the matching edges. |
---|
| 1052 | /// |
---|
| 1053 | /// Gives back the number of the matching edges. |
---|
| 1054 | int matchingSize() const { |
---|
| 1055 | return matching_size; |
---|
| 1056 | } |
---|
| 1057 | |
---|
| 1058 | /// @} |
---|
| 1059 | |
---|
| 1060 | private: |
---|
| 1061 | |
---|
| 1062 | void initStructures() { |
---|
| 1063 | if (!_heap_cross_ref) { |
---|
| 1064 | local_heap_cross_ref = true; |
---|
| 1065 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
| 1066 | } |
---|
| 1067 | if (!_heap) { |
---|
| 1068 | local_heap = true; |
---|
| 1069 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
| 1070 | } |
---|
| 1071 | } |
---|
| 1072 | |
---|
| 1073 | void destroyStructures() { |
---|
| 1074 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
| 1075 | if (local_heap) delete _heap; |
---|
| 1076 | } |
---|
| 1077 | |
---|
| 1078 | |
---|
| 1079 | private: |
---|
| 1080 | |
---|
| 1081 | const BpUGraph *graph; |
---|
| 1082 | const WeightMap* weight; |
---|
| 1083 | |
---|
| 1084 | ANodeMatchingMap anode_matching; |
---|
| 1085 | BNodeMatchingMap bnode_matching; |
---|
| 1086 | |
---|
| 1087 | ANodePotentialMap anode_potential; |
---|
| 1088 | BNodePotentialMap bnode_potential; |
---|
| 1089 | |
---|
| 1090 | Value matching_value; |
---|
| 1091 | int matching_size; |
---|
| 1092 | |
---|
| 1093 | HeapCrossRef *_heap_cross_ref; |
---|
| 1094 | bool local_heap_cross_ref; |
---|
| 1095 | |
---|
| 1096 | Heap *_heap; |
---|
| 1097 | bool local_heap; |
---|
| 1098 | |
---|
| 1099 | }; |
---|
| 1100 | |
---|
[2058] | 1101 | /// \ingroup matching |
---|
| 1102 | /// |
---|
| 1103 | /// \brief Maximum weighted bipartite matching |
---|
| 1104 | /// |
---|
| 1105 | /// This function calculates the maximum weighted matching |
---|
| 1106 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
| 1107 | /// edge map. |
---|
| 1108 | /// |
---|
| 1109 | /// \param graph The bipartite graph. |
---|
| 1110 | /// \param weight The undirected edge map which contains the weights. |
---|
| 1111 | /// \retval matching The undirected edge map which will be set to |
---|
| 1112 | /// the matching. |
---|
| 1113 | /// \return The value of the matching. |
---|
| 1114 | template <typename BpUGraph, typename WeightMap, typename MatchingMap> |
---|
| 1115 | typename WeightMap::Value |
---|
| 1116 | maxWeightedBipartiteMatching(const BpUGraph& graph, const WeightMap& weight, |
---|
| 1117 | MatchingMap& matching) { |
---|
| 1118 | MaxWeightedBipartiteMatching<BpUGraph, WeightMap> |
---|
| 1119 | bpmatching(graph, weight); |
---|
| 1120 | bpmatching.run(); |
---|
| 1121 | bpmatching.matching(matching); |
---|
| 1122 | return bpmatching.matchingValue(); |
---|
| 1123 | } |
---|
| 1124 | |
---|
| 1125 | /// \ingroup matching |
---|
| 1126 | /// |
---|
| 1127 | /// \brief Maximum weighted maximum cardinality bipartite matching |
---|
| 1128 | /// |
---|
| 1129 | /// This function calculates the maximum weighted of the maximum cardinality |
---|
| 1130 | /// matchings of a bipartite graph. It gives back the matching in an |
---|
| 1131 | /// undirected edge map. |
---|
| 1132 | /// |
---|
| 1133 | /// \param graph The bipartite graph. |
---|
| 1134 | /// \param weight The undirected edge map which contains the weights. |
---|
| 1135 | /// \retval matching The undirected edge map which will be set to |
---|
| 1136 | /// the matching. |
---|
| 1137 | /// \return The value of the matching. |
---|
| 1138 | template <typename BpUGraph, typename WeightMap, typename MatchingMap> |
---|
| 1139 | typename WeightMap::Value |
---|
| 1140 | maxWeightedMaxBipartiteMatching(const BpUGraph& graph, |
---|
| 1141 | const WeightMap& weight, |
---|
| 1142 | MatchingMap& matching) { |
---|
| 1143 | MaxWeightedBipartiteMatching<BpUGraph, WeightMap> |
---|
| 1144 | bpmatching(graph, weight); |
---|
| 1145 | bpmatching.run(true); |
---|
| 1146 | bpmatching.matching(matching); |
---|
| 1147 | return bpmatching.matchingValue(); |
---|
| 1148 | } |
---|
| 1149 | |
---|
[2051] | 1150 | /// \brief Default traits class for minimum cost bipartite matching |
---|
| 1151 | /// algoritms. |
---|
| 1152 | /// |
---|
| 1153 | /// Default traits class for minimum cost bipartite matching |
---|
| 1154 | /// algoritms. |
---|
| 1155 | /// |
---|
| 1156 | /// \param _BpUGraph The bipartite undirected graph |
---|
| 1157 | /// type. |
---|
| 1158 | /// |
---|
| 1159 | /// \param _CostMap Type of cost map. |
---|
| 1160 | template <typename _BpUGraph, typename _CostMap> |
---|
| 1161 | struct MinCostMaxBipartiteMatchingDefaultTraits { |
---|
| 1162 | /// \brief The type of the cost of the undirected edges. |
---|
| 1163 | typedef typename _CostMap::Value Value; |
---|
| 1164 | |
---|
| 1165 | /// The undirected bipartite graph type the algorithm runs on. |
---|
| 1166 | typedef _BpUGraph BpUGraph; |
---|
| 1167 | |
---|
| 1168 | /// The map of the edges costs |
---|
| 1169 | typedef _CostMap CostMap; |
---|
| 1170 | |
---|
| 1171 | /// \brief The cross reference type used by heap. |
---|
| 1172 | /// |
---|
| 1173 | /// The cross reference type used by heap. |
---|
| 1174 | /// Usually it is \c Graph::NodeMap<int>. |
---|
| 1175 | typedef typename BpUGraph::template NodeMap<int> HeapCrossRef; |
---|
| 1176 | |
---|
| 1177 | /// \brief Instantiates a HeapCrossRef. |
---|
| 1178 | /// |
---|
| 1179 | /// This function instantiates a \ref HeapCrossRef. |
---|
| 1180 | /// \param graph is the graph, to which we would like to define the |
---|
| 1181 | /// HeapCrossRef. |
---|
| 1182 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 1183 | return new HeapCrossRef(graph); |
---|
| 1184 | } |
---|
| 1185 | |
---|
| 1186 | /// \brief The heap type used by costed matching algorithms. |
---|
| 1187 | /// |
---|
| 1188 | /// The heap type used by costed matching algorithms. It should |
---|
| 1189 | /// minimize the priorities and the heap's key type is the graph's |
---|
| 1190 | /// anode graph's node. |
---|
| 1191 | /// |
---|
| 1192 | /// \sa BinHeap |
---|
[2269] | 1193 | typedef BinHeap<Value, HeapCrossRef> Heap; |
---|
[2051] | 1194 | |
---|
| 1195 | /// \brief Instantiates a Heap. |
---|
| 1196 | /// |
---|
| 1197 | /// This function instantiates a \ref Heap. |
---|
| 1198 | /// \param crossref The cross reference of the heap. |
---|
| 1199 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
| 1200 | return new Heap(crossref); |
---|
| 1201 | } |
---|
| 1202 | |
---|
| 1203 | }; |
---|
| 1204 | |
---|
| 1205 | |
---|
| 1206 | /// \ingroup matching |
---|
| 1207 | /// |
---|
| 1208 | /// \brief Bipartite Min Cost Matching algorithm |
---|
| 1209 | /// |
---|
| 1210 | /// This class implements the bipartite Min Cost Matching algorithm. |
---|
| 1211 | /// It uses the successive shortest path algorithm to calculate the |
---|
| 1212 | /// minimum cost maximum matching in the bipartite graph. The time |
---|
| 1213 | /// complexity of the algorithm is \f$ O(ne\log(n)) \f$ with the |
---|
| 1214 | /// default binary heap implementation but this can be improved to |
---|
| 1215 | /// \f$ O(n^2\log(n)+ne) \f$ if we use fibonacci heaps. |
---|
| 1216 | /// |
---|
| 1217 | /// The algorithm also provides a potential function on the nodes |
---|
| 1218 | /// which a dual solution of the matching algorithm and it can be |
---|
| 1219 | /// used to proof the optimality of the given pimal solution. |
---|
| 1220 | #ifdef DOXYGEN |
---|
| 1221 | template <typename _BpUGraph, typename _CostMap, typename _Traits> |
---|
| 1222 | #else |
---|
| 1223 | template <typename _BpUGraph, |
---|
| 1224 | typename _CostMap = typename _BpUGraph::template UEdgeMap<int>, |
---|
| 1225 | typename _Traits = MinCostMaxBipartiteMatchingDefaultTraits<_BpUGraph, _CostMap> > |
---|
| 1226 | #endif |
---|
| 1227 | class MinCostMaxBipartiteMatching { |
---|
| 1228 | public: |
---|
| 1229 | |
---|
| 1230 | typedef _Traits Traits; |
---|
| 1231 | typedef typename Traits::BpUGraph BpUGraph; |
---|
| 1232 | typedef typename Traits::CostMap CostMap; |
---|
| 1233 | typedef typename Traits::Value Value; |
---|
| 1234 | |
---|
| 1235 | protected: |
---|
| 1236 | |
---|
| 1237 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
| 1238 | typedef typename Traits::Heap Heap; |
---|
| 1239 | |
---|
| 1240 | |
---|
| 1241 | typedef typename BpUGraph::Node Node; |
---|
| 1242 | typedef typename BpUGraph::ANodeIt ANodeIt; |
---|
| 1243 | typedef typename BpUGraph::BNodeIt BNodeIt; |
---|
| 1244 | typedef typename BpUGraph::UEdge UEdge; |
---|
| 1245 | typedef typename BpUGraph::UEdgeIt UEdgeIt; |
---|
| 1246 | typedef typename BpUGraph::IncEdgeIt IncEdgeIt; |
---|
| 1247 | |
---|
| 1248 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
---|
| 1249 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
---|
| 1250 | |
---|
| 1251 | typedef typename BpUGraph::template ANodeMap<Value> ANodePotentialMap; |
---|
| 1252 | typedef typename BpUGraph::template BNodeMap<Value> BNodePotentialMap; |
---|
| 1253 | |
---|
| 1254 | |
---|
| 1255 | public: |
---|
| 1256 | |
---|
| 1257 | /// \brief \ref Exception for uninitialized parameters. |
---|
| 1258 | /// |
---|
| 1259 | /// This error represents problems in the initialization |
---|
| 1260 | /// of the parameters of the algorithms. |
---|
| 1261 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
| 1262 | public: |
---|
[2151] | 1263 | virtual const char* what() const throw() { |
---|
[2051] | 1264 | return "lemon::MinCostMaxBipartiteMatching::UninitializedParameter"; |
---|
| 1265 | } |
---|
| 1266 | }; |
---|
| 1267 | |
---|
| 1268 | ///\name Named template parameters |
---|
| 1269 | |
---|
| 1270 | ///@{ |
---|
| 1271 | |
---|
| 1272 | template <class H, class CR> |
---|
| 1273 | struct DefHeapTraits : public Traits { |
---|
| 1274 | typedef CR HeapCrossRef; |
---|
| 1275 | typedef H Heap; |
---|
| 1276 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &) { |
---|
| 1277 | throw UninitializedParameter(); |
---|
| 1278 | } |
---|
| 1279 | static Heap *createHeap(HeapCrossRef &) { |
---|
| 1280 | throw UninitializedParameter(); |
---|
| 1281 | } |
---|
| 1282 | }; |
---|
| 1283 | |
---|
| 1284 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
| 1285 | /// and cross reference type |
---|
| 1286 | /// |
---|
| 1287 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 1288 | /// reference type |
---|
| 1289 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 1290 | struct DefHeap |
---|
| 1291 | : public MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1292 | DefHeapTraits<H, CR> > { |
---|
| 1293 | typedef MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1294 | DefHeapTraits<H, CR> > Create; |
---|
| 1295 | }; |
---|
| 1296 | |
---|
| 1297 | template <class H, class CR> |
---|
| 1298 | struct DefStandardHeapTraits : public Traits { |
---|
| 1299 | typedef CR HeapCrossRef; |
---|
| 1300 | typedef H Heap; |
---|
| 1301 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 1302 | return new HeapCrossRef(graph); |
---|
| 1303 | } |
---|
| 1304 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
| 1305 | return new Heap(crossref); |
---|
| 1306 | } |
---|
| 1307 | }; |
---|
| 1308 | |
---|
| 1309 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
| 1310 | /// cross reference type with automatic allocation |
---|
| 1311 | /// |
---|
| 1312 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 1313 | /// reference type. It can allocate the heap and the cross reference |
---|
| 1314 | /// object if the cross reference's constructor waits for the graph as |
---|
| 1315 | /// parameter and the heap's constructor waits for the cross reference. |
---|
| 1316 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 1317 | struct DefStandardHeap |
---|
| 1318 | : public MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1319 | DefStandardHeapTraits<H, CR> > { |
---|
| 1320 | typedef MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1321 | DefStandardHeapTraits<H, CR> > |
---|
| 1322 | Create; |
---|
| 1323 | }; |
---|
| 1324 | |
---|
| 1325 | ///@} |
---|
| 1326 | |
---|
| 1327 | |
---|
| 1328 | /// \brief Constructor. |
---|
| 1329 | /// |
---|
| 1330 | /// Constructor of the algorithm. |
---|
| 1331 | MinCostMaxBipartiteMatching(const BpUGraph& _graph, |
---|
| 1332 | const CostMap& _cost) |
---|
| 1333 | : graph(&_graph), cost(&_cost), |
---|
| 1334 | anode_matching(_graph), bnode_matching(_graph), |
---|
| 1335 | anode_potential(_graph), bnode_potential(_graph), |
---|
| 1336 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
| 1337 | _heap(0), local_heap(0) {} |
---|
| 1338 | |
---|
| 1339 | /// \brief Destructor. |
---|
| 1340 | /// |
---|
| 1341 | /// Destructor of the algorithm. |
---|
| 1342 | ~MinCostMaxBipartiteMatching() { |
---|
| 1343 | destroyStructures(); |
---|
| 1344 | } |
---|
| 1345 | |
---|
| 1346 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
| 1347 | /// |
---|
| 1348 | /// Sets the heap and the cross reference used by algorithm. |
---|
| 1349 | /// If you don't use this function before calling \ref run(), |
---|
| 1350 | /// it will allocate one. The destuctor deallocates this |
---|
| 1351 | /// automatically allocated map, of course. |
---|
| 1352 | /// \return \c (*this) |
---|
[2386] | 1353 | MinCostMaxBipartiteMatching& heap(Heap& hp, HeapCrossRef &cr) { |
---|
[2051] | 1354 | if(local_heap_cross_ref) { |
---|
| 1355 | delete _heap_cross_ref; |
---|
| 1356 | local_heap_cross_ref = false; |
---|
| 1357 | } |
---|
[2386] | 1358 | _heap_cross_ref = &cr; |
---|
[2051] | 1359 | if(local_heap) { |
---|
| 1360 | delete _heap; |
---|
| 1361 | local_heap = false; |
---|
| 1362 | } |
---|
[2386] | 1363 | _heap = &hp; |
---|
[2051] | 1364 | return *this; |
---|
| 1365 | } |
---|
| 1366 | |
---|
| 1367 | /// \name Execution control |
---|
| 1368 | /// The simplest way to execute the algorithm is to use |
---|
| 1369 | /// one of the member functions called \c run(). |
---|
| 1370 | /// \n |
---|
| 1371 | /// If you need more control on the execution, |
---|
| 1372 | /// first you must call \ref init() or one alternative for it. |
---|
| 1373 | /// Finally \ref start() will perform the matching computation or |
---|
| 1374 | /// with step-by-step execution you can augment the solution. |
---|
| 1375 | |
---|
| 1376 | /// @{ |
---|
| 1377 | |
---|
| 1378 | /// \brief Initalize the data structures. |
---|
| 1379 | /// |
---|
| 1380 | /// It initalizes the data structures and creates an empty matching. |
---|
| 1381 | void init() { |
---|
| 1382 | initStructures(); |
---|
| 1383 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1384 | anode_matching[it] = INVALID; |
---|
| 1385 | anode_potential[it] = 0; |
---|
| 1386 | } |
---|
| 1387 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1388 | bnode_matching[it] = INVALID; |
---|
| 1389 | bnode_potential[it] = 0; |
---|
| 1390 | } |
---|
| 1391 | matching_cost = 0; |
---|
| 1392 | matching_size = 0; |
---|
| 1393 | } |
---|
| 1394 | |
---|
| 1395 | |
---|
| 1396 | /// \brief An augmenting phase of the costed matching algorithm |
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| 1397 | /// |
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| 1398 | /// It runs an augmenting phase of the matching algorithm. The |
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| 1399 | /// phase finds the best augmenting path and augments only on this |
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| 1400 | /// paths. |
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| 1401 | /// |
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| 1402 | /// The algorithm consists at most |
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| 1403 | /// of \f$ O(n) \f$ phase and one phase is \f$ O(n\log(n)+e) \f$ |
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| 1404 | /// long with Fibonacci heap or \f$ O((n+e)\log(n)) \f$ long |
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| 1405 | /// with binary heap. |
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| 1406 | bool augment() { |
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| 1407 | |
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| 1408 | typename BpUGraph::template BNodeMap<Value> bdist(*graph); |
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| 1409 | typename BpUGraph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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| 1410 | |
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| 1411 | Node bestNode = INVALID; |
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| 1412 | Value bestValue = 0; |
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| 1413 | |
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| 1414 | _heap->clear(); |
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| 1415 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 1416 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
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| 1417 | } |
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| 1418 | |
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| 1419 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 1420 | if (anode_matching[it] == INVALID) { |
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| 1421 | _heap->push(it, 0); |
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| 1422 | } |
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| 1423 | } |
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[2136] | 1424 | Value bdistMax = 0; |
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[2051] | 1425 | |
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| 1426 | while (!_heap->empty()) { |
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| 1427 | Node anode = _heap->top(); |
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| 1428 | Value avalue = _heap->prio(); |
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| 1429 | _heap->pop(); |
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| 1430 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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| 1431 | if (jt == anode_matching[anode]) continue; |
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| 1432 | Node bnode = graph->bNode(jt); |
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| 1433 | Value bvalue = avalue + (*cost)[jt] + |
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| 1434 | anode_potential[anode] - bnode_potential[bnode]; |
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| 1435 | if (bpred[bnode] == INVALID || bvalue < bdist[bnode]) { |
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| 1436 | bdist[bnode] = bvalue; |
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| 1437 | bpred[bnode] = jt; |
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| 1438 | } |
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[2136] | 1439 | if (bvalue > bdistMax) { |
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| 1440 | bdistMax = bvalue; |
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| 1441 | } |
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[2051] | 1442 | if (bnode_matching[bnode] != INVALID) { |
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| 1443 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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| 1444 | switch (_heap->state(newanode)) { |
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| 1445 | case Heap::PRE_HEAP: |
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| 1446 | _heap->push(newanode, bvalue); |
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| 1447 | break; |
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| 1448 | case Heap::IN_HEAP: |
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| 1449 | if (bvalue < (*_heap)[newanode]) { |
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| 1450 | _heap->decrease(newanode, bvalue); |
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| 1451 | } |
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| 1452 | break; |
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| 1453 | case Heap::POST_HEAP: |
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| 1454 | break; |
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| 1455 | } |
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| 1456 | } else { |
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| 1457 | if (bestNode == INVALID || |
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| 1458 | bvalue + bnode_potential[bnode] < bestValue) { |
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| 1459 | bestValue = bvalue + bnode_potential[bnode]; |
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| 1460 | bestNode = bnode; |
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| 1461 | } |
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| 1462 | } |
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| 1463 | } |
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| 1464 | } |
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| 1465 | |
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| 1466 | if (bestNode == INVALID) { |
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| 1467 | return false; |
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| 1468 | } |
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| 1469 | |
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| 1470 | matching_cost += bestValue; |
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| 1471 | ++matching_size; |
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| 1472 | |
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| 1473 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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| 1474 | if (bpred[it] != INVALID) { |
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| 1475 | bnode_potential[it] += bdist[it]; |
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[2136] | 1476 | } else { |
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| 1477 | bnode_potential[it] += bdistMax; |
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[2051] | 1478 | } |
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| 1479 | } |
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| 1480 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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| 1481 | if (anode_matching[it] != INVALID) { |
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| 1482 | Node bnode = graph->bNode(anode_matching[it]); |
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| 1483 | if (bpred[bnode] != INVALID) { |
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| 1484 | anode_potential[it] += bdist[bnode]; |
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[2136] | 1485 | } else { |
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| 1486 | anode_potential[it] += bdistMax; |
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[2051] | 1487 | } |
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| 1488 | } |
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| 1489 | } |
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| 1490 | |
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| 1491 | while (bestNode != INVALID) { |
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| 1492 | UEdge uedge = bpred[bestNode]; |
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| 1493 | Node anode = graph->aNode(uedge); |
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| 1494 | |
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| 1495 | bnode_matching[bestNode] = uedge; |
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| 1496 | if (anode_matching[anode] != INVALID) { |
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| 1497 | bestNode = graph->bNode(anode_matching[anode]); |
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| 1498 | } else { |
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| 1499 | bestNode = INVALID; |
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| 1500 | } |
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| 1501 | anode_matching[anode] = uedge; |
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| 1502 | } |
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| 1503 | |
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| 1504 | |
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| 1505 | return true; |
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| 1506 | } |
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| 1507 | |
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| 1508 | /// \brief Starts the algorithm. |
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| 1509 | /// |
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| 1510 | /// Starts the algorithm. It runs augmenting phases until the |
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| 1511 | /// optimal solution reached. |
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| 1512 | void start() { |
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| 1513 | while (augment()) {} |
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| 1514 | } |
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| 1515 | |
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| 1516 | /// \brief Runs the algorithm. |
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| 1517 | /// |
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| 1518 | /// It just initalize the algorithm and then start it. |
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| 1519 | void run() { |
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| 1520 | init(); |
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| 1521 | start(); |
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| 1522 | } |
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| 1523 | |
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| 1524 | /// @} |
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| 1525 | |
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| 1526 | /// \name Query Functions |
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| 1527 | /// The result of the %Matching algorithm can be obtained using these |
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| 1528 | /// functions.\n |
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| 1529 | /// Before the use of these functions, |
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| 1530 | /// either run() or start() must be called. |
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| 1531 | |
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| 1532 | ///@{ |
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| 1533 | |
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| 1534 | /// \brief Gives back the potential in the NodeMap |
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| 1535 | /// |
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[2058] | 1536 | /// Gives back the potential in the NodeMap. The potential is optimal with |
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| 1537 | /// the current number of edges if \f$ \pi(a) - \pi(b) + w(ab) = 0 \f$ for |
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[2051] | 1538 | /// each matching edges and \f$ \pi(a) - \pi(b) + w(ab) \ge 0 \f$ |
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| 1539 | /// for each edges. |
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| 1540 | template <typename PotentialMap> |
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[2386] | 1541 | void potential(PotentialMap& pt) const { |
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[2051] | 1542 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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[2386] | 1543 | pt[it] = anode_potential[it]; |
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[2051] | 1544 | } |
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| 1545 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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[2386] | 1546 | pt[it] = bnode_potential[it]; |
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[2051] | 1547 | } |
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| 1548 | } |
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| 1549 | |
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| 1550 | /// \brief Set true all matching uedge in the map. |
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| 1551 | /// |
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| 1552 | /// Set true all matching uedge in the map. It does not change the |
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| 1553 | /// value mapped to the other uedges. |
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| 1554 | /// \return The number of the matching edges. |
---|
| 1555 | template <typename MatchingMap> |
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[2386] | 1556 | int quickMatching(MatchingMap& mm) const { |
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[2051] | 1557 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1558 | if (anode_matching[it] != INVALID) { |
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[2386] | 1559 | mm[anode_matching[it]] = true; |
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[2051] | 1560 | } |
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| 1561 | } |
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| 1562 | return matching_size; |
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| 1563 | } |
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| 1564 | |
---|
| 1565 | /// \brief Set true all matching uedge in the map and the others to false. |
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| 1566 | /// |
---|
| 1567 | /// Set true all matching uedge in the map and the others to false. |
---|
| 1568 | /// \return The number of the matching edges. |
---|
| 1569 | template <typename MatchingMap> |
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[2386] | 1570 | int matching(MatchingMap& mm) const { |
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[2051] | 1571 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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[2386] | 1572 | mm[it] = it == anode_matching[graph->aNode(it)]; |
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[2051] | 1573 | } |
---|
| 1574 | return matching_size; |
---|
| 1575 | } |
---|
| 1576 | |
---|
| 1577 | |
---|
| 1578 | /// \brief Return true if the given uedge is in the matching. |
---|
| 1579 | /// |
---|
| 1580 | /// It returns true if the given uedge is in the matching. |
---|
[2058] | 1581 | bool matchingEdge(const UEdge& edge) const { |
---|
[2051] | 1582 | return anode_matching[graph->aNode(edge)] == edge; |
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| 1583 | } |
---|
| 1584 | |
---|
| 1585 | /// \brief Returns the matching edge from the node. |
---|
| 1586 | /// |
---|
| 1587 | /// Returns the matching edge from the node. If there is not such |
---|
| 1588 | /// edge it gives back \c INVALID. |
---|
[2058] | 1589 | UEdge matchingEdge(const Node& node) const { |
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[2051] | 1590 | if (graph->aNode(node)) { |
---|
| 1591 | return anode_matching[node]; |
---|
| 1592 | } else { |
---|
| 1593 | return bnode_matching[node]; |
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| 1594 | } |
---|
| 1595 | } |
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| 1596 | |
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| 1597 | /// \brief Gives back the sum of costs of the matching edges. |
---|
| 1598 | /// |
---|
| 1599 | /// Gives back the sum of costs of the matching edges. |
---|
| 1600 | Value matchingCost() const { |
---|
| 1601 | return matching_cost; |
---|
| 1602 | } |
---|
| 1603 | |
---|
| 1604 | /// \brief Gives back the number of the matching edges. |
---|
| 1605 | /// |
---|
| 1606 | /// Gives back the number of the matching edges. |
---|
| 1607 | int matchingSize() const { |
---|
| 1608 | return matching_size; |
---|
| 1609 | } |
---|
| 1610 | |
---|
| 1611 | /// @} |
---|
| 1612 | |
---|
| 1613 | private: |
---|
| 1614 | |
---|
| 1615 | void initStructures() { |
---|
| 1616 | if (!_heap_cross_ref) { |
---|
| 1617 | local_heap_cross_ref = true; |
---|
| 1618 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
| 1619 | } |
---|
| 1620 | if (!_heap) { |
---|
| 1621 | local_heap = true; |
---|
| 1622 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
| 1623 | } |
---|
| 1624 | } |
---|
| 1625 | |
---|
| 1626 | void destroyStructures() { |
---|
| 1627 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
| 1628 | if (local_heap) delete _heap; |
---|
| 1629 | } |
---|
| 1630 | |
---|
| 1631 | |
---|
| 1632 | private: |
---|
| 1633 | |
---|
| 1634 | const BpUGraph *graph; |
---|
| 1635 | const CostMap* cost; |
---|
| 1636 | |
---|
| 1637 | ANodeMatchingMap anode_matching; |
---|
| 1638 | BNodeMatchingMap bnode_matching; |
---|
| 1639 | |
---|
| 1640 | ANodePotentialMap anode_potential; |
---|
| 1641 | BNodePotentialMap bnode_potential; |
---|
| 1642 | |
---|
| 1643 | Value matching_cost; |
---|
| 1644 | int matching_size; |
---|
| 1645 | |
---|
| 1646 | HeapCrossRef *_heap_cross_ref; |
---|
| 1647 | bool local_heap_cross_ref; |
---|
| 1648 | |
---|
| 1649 | Heap *_heap; |
---|
| 1650 | bool local_heap; |
---|
[2040] | 1651 | |
---|
| 1652 | }; |
---|
| 1653 | |
---|
[2058] | 1654 | /// \ingroup matching |
---|
| 1655 | /// |
---|
| 1656 | /// \brief Minimum cost maximum cardinality bipartite matching |
---|
| 1657 | /// |
---|
| 1658 | /// This function calculates the minimum cost matching of the maximum |
---|
| 1659 | /// cardinality matchings of a bipartite graph. It gives back the matching |
---|
| 1660 | /// in an undirected edge map. |
---|
| 1661 | /// |
---|
| 1662 | /// \param graph The bipartite graph. |
---|
| 1663 | /// \param cost The undirected edge map which contains the costs. |
---|
| 1664 | /// \retval matching The undirected edge map which will be set to |
---|
| 1665 | /// the matching. |
---|
| 1666 | /// \return The cost of the matching. |
---|
| 1667 | template <typename BpUGraph, typename CostMap, typename MatchingMap> |
---|
| 1668 | typename CostMap::Value |
---|
| 1669 | minCostMaxBipartiteMatching(const BpUGraph& graph, |
---|
| 1670 | const CostMap& cost, |
---|
| 1671 | MatchingMap& matching) { |
---|
| 1672 | MinCostMaxBipartiteMatching<BpUGraph, CostMap> |
---|
| 1673 | bpmatching(graph, cost); |
---|
| 1674 | bpmatching.run(); |
---|
| 1675 | bpmatching.matching(matching); |
---|
| 1676 | return bpmatching.matchingCost(); |
---|
| 1677 | } |
---|
| 1678 | |
---|
[2040] | 1679 | } |
---|
| 1680 | |
---|
| 1681 | #endif |
---|