[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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[2553] | 5 | * Copyright (C) 2003-2008 |
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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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[2466] | 72 | MaxBipartiteMatching(const BpUGraph& graph) |
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| 73 | : _matching(graph), _rmatching(graph), _reached(graph), _graph(&graph) {} |
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[2040] | 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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[2466] | 90 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 91 | _matching.set(it, INVALID); |
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[2040] | 92 | } |
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[2466] | 93 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 94 | _rmatching.set(it, INVALID); |
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| 95 | _reached.set(it, -1); |
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[2040] | 96 | } |
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[2466] | 97 | _size = 0; |
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| 98 | _phase = -1; |
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[2040] | 99 | } |
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| 100 | |
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| 101 | /// \brief Initalize the data structures. |
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| 102 | /// |
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| 103 | /// It initalizes the data structures and creates a greedy |
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| 104 | /// matching. From this matching sometimes it is faster to get |
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| 105 | /// the matching than from the initial empty matching. |
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| 106 | void greedyInit() { |
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[2466] | 107 | _size = 0; |
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| 108 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 109 | _rmatching.set(it, INVALID); |
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| 110 | _reached.set(it, 0); |
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[2040] | 111 | } |
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[2466] | 112 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 113 | _matching[it] = INVALID; |
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| 114 | for (IncEdgeIt jt(*_graph, it); jt != INVALID; ++jt) { |
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| 115 | if (_rmatching[_graph->bNode(jt)] == INVALID) { |
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| 116 | _matching.set(it, jt); |
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| 117 | _rmatching.set(_graph->bNode(jt), jt); |
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[2488] | 118 | _reached.set(_graph->bNode(jt), -1); |
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[2466] | 119 | ++_size; |
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[2040] | 120 | break; |
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| 121 | } |
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| 122 | } |
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| 123 | } |
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[2466] | 124 | _phase = 0; |
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[2040] | 125 | } |
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| 126 | |
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| 127 | /// \brief Initalize the data structures with an initial matching. |
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| 128 | /// |
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| 129 | /// It initalizes the data structures with an initial matching. |
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| 130 | template <typename MatchingMap> |
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[2386] | 131 | void matchingInit(const MatchingMap& mm) { |
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[2466] | 132 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 133 | _matching.set(it, INVALID); |
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[2040] | 134 | } |
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[2466] | 135 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 136 | _rmatching.set(it, INVALID); |
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| 137 | _reached.set(it, 0); |
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[2040] | 138 | } |
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[2466] | 139 | _size = 0; |
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| 140 | for (UEdgeIt it(*_graph); it != INVALID; ++it) { |
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[2386] | 141 | if (mm[it]) { |
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[2466] | 142 | ++_size; |
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| 143 | _matching.set(_graph->aNode(it), it); |
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| 144 | _rmatching.set(_graph->bNode(it), it); |
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| 145 | _reached.set(it, 0); |
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[2040] | 146 | } |
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| 147 | } |
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[2466] | 148 | _phase = 0; |
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[2040] | 149 | } |
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| 150 | |
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| 151 | /// \brief Initalize the data structures with an initial matching. |
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| 152 | /// |
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| 153 | /// It initalizes the data structures with an initial matching. |
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| 154 | /// \return %True when the given map contains really a matching. |
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| 155 | template <typename MatchingMap> |
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[2466] | 156 | bool checkedMatchingInit(const MatchingMap& mm) { |
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| 157 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 158 | _matching.set(it, INVALID); |
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[2040] | 159 | } |
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[2466] | 160 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 161 | _rmatching.set(it, INVALID); |
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| 162 | _reached.set(it, 0); |
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[2040] | 163 | } |
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[2466] | 164 | _size = 0; |
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| 165 | for (UEdgeIt it(*_graph); it != INVALID; ++it) { |
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[2386] | 166 | if (mm[it]) { |
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[2466] | 167 | ++_size; |
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| 168 | if (_matching[_graph->aNode(it)] != INVALID) { |
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[2040] | 169 | return false; |
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| 170 | } |
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[2466] | 171 | _matching.set(_graph->aNode(it), it); |
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| 172 | if (_matching[_graph->bNode(it)] != INVALID) { |
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[2040] | 173 | return false; |
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| 174 | } |
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[2466] | 175 | _matching.set(_graph->bNode(it), it); |
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| 176 | _reached.set(_graph->bNode(it), -1); |
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[2040] | 177 | } |
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| 178 | } |
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[2466] | 179 | _phase = 0; |
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| 180 | return true; |
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| 181 | } |
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| 182 | |
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| 183 | private: |
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| 184 | |
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| 185 | bool _find_path(Node anode, int maxlevel, |
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| 186 | typename Graph::template BNodeMap<int>& level) { |
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| 187 | for (IncEdgeIt it(*_graph, anode); it != INVALID; ++it) { |
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| 188 | Node bnode = _graph->bNode(it); |
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| 189 | if (level[bnode] == maxlevel) { |
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| 190 | level.set(bnode, -1); |
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| 191 | if (maxlevel == 0) { |
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| 192 | _matching.set(anode, it); |
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| 193 | _rmatching.set(bnode, it); |
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| 194 | return true; |
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| 195 | } else { |
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| 196 | Node nnode = _graph->aNode(_rmatching[bnode]); |
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| 197 | if (_find_path(nnode, maxlevel - 1, level)) { |
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| 198 | _matching.set(anode, it); |
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| 199 | _rmatching.set(bnode, it); |
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| 200 | return true; |
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| 201 | } |
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| 202 | } |
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| 203 | } |
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| 204 | } |
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[2040] | 205 | return false; |
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| 206 | } |
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| 207 | |
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[2466] | 208 | public: |
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| 209 | |
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[2040] | 210 | /// \brief An augmenting phase of the Hopcroft-Karp algorithm |
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| 211 | /// |
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| 212 | /// It runs an augmenting phase of the Hopcroft-Karp |
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[2466] | 213 | /// algorithm. This phase finds maximal edge disjoint augmenting |
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| 214 | /// paths and augments on these paths. The algorithm consists at |
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| 215 | /// most of \f$ O(\sqrt{n}) \f$ phase and one phase is \f$ O(e) |
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| 216 | /// \f$ long. |
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[2040] | 217 | bool augment() { |
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| 218 | |
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[2466] | 219 | ++_phase; |
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| 220 | |
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| 221 | typename Graph::template BNodeMap<int> _level(*_graph, -1); |
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| 222 | typename Graph::template ANodeMap<bool> _found(*_graph, false); |
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[2040] | 223 | |
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[2466] | 224 | std::vector<Node> queue, aqueue; |
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| 225 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 226 | if (_rmatching[it] == INVALID) { |
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[2040] | 227 | queue.push_back(it); |
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[2466] | 228 | _reached.set(it, _phase); |
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| 229 | _level.set(it, 0); |
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[2040] | 230 | } |
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| 231 | } |
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| 232 | |
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| 233 | bool success = false; |
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| 234 | |
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[2466] | 235 | int level = 0; |
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[2040] | 236 | while (!success && !queue.empty()) { |
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[2466] | 237 | std::vector<Node> nqueue; |
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[2386] | 238 | for (int i = 0; i < int(queue.size()); ++i) { |
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[2466] | 239 | Node bnode = queue[i]; |
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| 240 | for (IncEdgeIt jt(*_graph, bnode); jt != INVALID; ++jt) { |
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| 241 | Node anode = _graph->aNode(jt); |
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| 242 | if (_matching[anode] == INVALID) { |
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| 243 | |
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| 244 | if (!_found[anode]) { |
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| 245 | if (_find_path(anode, level, _level)) { |
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| 246 | ++_size; |
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| 247 | } |
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| 248 | _found.set(anode, true); |
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| 249 | } |
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[2040] | 250 | success = true; |
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| 251 | } else { |
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[2466] | 252 | Node nnode = _graph->bNode(_matching[anode]); |
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| 253 | if (_reached[nnode] != _phase) { |
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| 254 | _reached.set(nnode, _phase); |
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| 255 | nqueue.push_back(nnode); |
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| 256 | _level.set(nnode, level + 1); |
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[2040] | 257 | } |
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| 258 | } |
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| 259 | } |
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| 260 | } |
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[2466] | 261 | ++level; |
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| 262 | queue.swap(nqueue); |
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[2040] | 263 | } |
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[2466] | 264 | |
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[2040] | 265 | return success; |
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| 266 | } |
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[2466] | 267 | private: |
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| 268 | |
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| 269 | void _find_path_bfs(Node anode, |
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| 270 | typename Graph::template ANodeMap<UEdge>& pred) { |
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| 271 | while (true) { |
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| 272 | UEdge uedge = pred[anode]; |
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| 273 | Node bnode = _graph->bNode(uedge); |
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[2040] | 274 | |
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[2466] | 275 | UEdge nedge = _rmatching[bnode]; |
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| 276 | |
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| 277 | _matching.set(anode, uedge); |
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| 278 | _rmatching.set(bnode, uedge); |
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| 279 | |
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| 280 | if (nedge == INVALID) break; |
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| 281 | anode = _graph->aNode(nedge); |
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| 282 | } |
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| 283 | } |
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| 284 | |
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| 285 | public: |
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| 286 | |
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| 287 | /// \brief An augmenting phase with single path augementing |
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[2040] | 288 | /// |
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[2466] | 289 | /// This phase finds only one augmenting paths and augments on |
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| 290 | /// these paths. The algorithm consists at most of \f$ O(n) \f$ |
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| 291 | /// phase and one phase is \f$ O(e) \f$ long. |
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| 292 | bool simpleAugment() { |
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| 293 | ++_phase; |
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| 294 | |
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| 295 | typename Graph::template ANodeMap<UEdge> _pred(*_graph); |
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[2040] | 296 | |
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[2466] | 297 | std::vector<Node> queue, aqueue; |
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| 298 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 299 | if (_rmatching[it] == INVALID) { |
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[2040] | 300 | queue.push_back(it); |
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[2466] | 301 | _reached.set(it, _phase); |
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[2040] | 302 | } |
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| 303 | } |
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| 304 | |
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[2466] | 305 | bool success = false; |
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| 306 | |
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| 307 | int level = 0; |
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| 308 | while (!success && !queue.empty()) { |
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| 309 | std::vector<Node> nqueue; |
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[2386] | 310 | for (int i = 0; i < int(queue.size()); ++i) { |
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[2466] | 311 | Node bnode = queue[i]; |
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| 312 | for (IncEdgeIt jt(*_graph, bnode); jt != INVALID; ++jt) { |
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| 313 | Node anode = _graph->aNode(jt); |
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| 314 | if (_matching[anode] == INVALID) { |
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| 315 | _pred.set(anode, jt); |
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| 316 | _find_path_bfs(anode, _pred); |
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| 317 | ++_size; |
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| 318 | return true; |
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[2040] | 319 | } else { |
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[2466] | 320 | Node nnode = _graph->bNode(_matching[anode]); |
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| 321 | if (_reached[nnode] != _phase) { |
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| 322 | _pred.set(anode, jt); |
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| 323 | _reached.set(nnode, _phase); |
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| 324 | nqueue.push_back(nnode); |
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[2040] | 325 | } |
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| 326 | } |
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| 327 | } |
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| 328 | } |
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[2466] | 329 | ++level; |
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| 330 | queue.swap(nqueue); |
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[2040] | 331 | } |
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| 332 | |
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[2466] | 333 | return success; |
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[2040] | 334 | } |
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| 335 | |
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[2466] | 336 | |
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| 337 | |
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[2040] | 338 | /// \brief Starts the algorithm. |
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| 339 | /// |
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| 340 | /// Starts the algorithm. It runs augmenting phases until the optimal |
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| 341 | /// solution reached. |
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| 342 | void start() { |
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| 343 | while (augment()) {} |
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| 344 | } |
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| 345 | |
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| 346 | /// \brief Runs the algorithm. |
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| 347 | /// |
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| 348 | /// It just initalize the algorithm and then start it. |
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| 349 | void run() { |
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[2058] | 350 | greedyInit(); |
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[2040] | 351 | start(); |
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| 352 | } |
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| 353 | |
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| 354 | /// @} |
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| 355 | |
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| 356 | /// \name Query Functions |
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| 357 | /// The result of the %Matching algorithm can be obtained using these |
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| 358 | /// functions.\n |
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| 359 | /// Before the use of these functions, |
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| 360 | /// either run() or start() must be called. |
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| 361 | |
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| 362 | ///@{ |
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| 363 | |
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[2466] | 364 | /// \brief Return true if the given uedge is in the matching. |
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| 365 | /// |
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| 366 | /// It returns true if the given uedge is in the matching. |
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| 367 | bool matchingEdge(const UEdge& edge) const { |
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| 368 | return _matching[_graph->aNode(edge)] == edge; |
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| 369 | } |
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| 370 | |
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| 371 | /// \brief Returns the matching edge from the node. |
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| 372 | /// |
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| 373 | /// Returns the matching edge from the node. If there is not such |
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| 374 | /// edge it gives back \c INVALID. |
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| 375 | /// \note If the parameter node is a B-node then the running time is |
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| 376 | /// propotional to the degree of the node. |
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| 377 | UEdge matchingEdge(const Node& node) const { |
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| 378 | if (_graph->aNode(node)) { |
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| 379 | return _matching[node]; |
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| 380 | } else { |
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| 381 | return _rmatching[node]; |
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| 382 | } |
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| 383 | } |
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| 384 | |
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[2462] | 385 | /// \brief Set true all matching uedge in the map. |
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| 386 | /// |
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| 387 | /// Set true all matching uedge in the map. It does not change the |
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| 388 | /// value mapped to the other uedges. |
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| 389 | /// \return The number of the matching edges. |
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| 390 | template <typename MatchingMap> |
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| 391 | int quickMatching(MatchingMap& mm) const { |
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[2466] | 392 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 393 | if (_matching[it] != INVALID) { |
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| 394 | mm.set(_matching[it], true); |
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[2462] | 395 | } |
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| 396 | } |
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[2466] | 397 | return _size; |
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[2462] | 398 | } |
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| 399 | |
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| 400 | /// \brief Set true all matching uedge in the map and the others to false. |
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| 401 | /// |
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| 402 | /// Set true all matching uedge in the map and the others to false. |
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| 403 | /// \return The number of the matching edges. |
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| 404 | template <typename MatchingMap> |
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| 405 | int matching(MatchingMap& mm) const { |
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[2466] | 406 | for (UEdgeIt it(*_graph); it != INVALID; ++it) { |
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| 407 | mm.set(it, it == _matching[_graph->aNode(it)]); |
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[2462] | 408 | } |
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[2466] | 409 | return _size; |
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[2462] | 410 | } |
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| 411 | |
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[2463] | 412 | ///Gives back the matching in an ANodeMap. |
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| 413 | |
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| 414 | ///Gives back the matching in an ANodeMap. The parameter should |
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| 415 | ///be a write ANodeMap of UEdge values. |
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| 416 | ///\return The number of the matching edges. |
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| 417 | template<class MatchingMap> |
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| 418 | int aMatching(MatchingMap& mm) const { |
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[2466] | 419 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 420 | mm.set(it, _matching[it]); |
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[2463] | 421 | } |
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[2466] | 422 | return _size; |
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[2463] | 423 | } |
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| 424 | |
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| 425 | ///Gives back the matching in a BNodeMap. |
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| 426 | |
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| 427 | ///Gives back the matching in a BNodeMap. The parameter should |
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| 428 | ///be a write BNodeMap of UEdge values. |
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| 429 | ///\return The number of the matching edges. |
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| 430 | template<class MatchingMap> |
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| 431 | int bMatching(MatchingMap& mm) const { |
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[2466] | 432 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 433 | mm.set(it, _rmatching[it]); |
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[2463] | 434 | } |
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[2466] | 435 | return _size; |
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[2462] | 436 | } |
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| 437 | |
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| 438 | /// \brief Returns a minimum covering of the nodes. |
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[2040] | 439 | /// |
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| 440 | /// The minimum covering set problem is the dual solution of the |
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[2462] | 441 | /// maximum bipartite matching. It provides a solution for this |
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[2040] | 442 | /// problem what is proof of the optimality of the matching. |
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| 443 | /// \return The size of the cover set. |
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| 444 | template <typename CoverMap> |
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[2058] | 445 | int coverSet(CoverMap& covering) const { |
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[2040] | 446 | |
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[2466] | 447 | int size = 0; |
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| 448 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
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| 449 | bool cn = _matching[it] != INVALID && |
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| 450 | _reached[_graph->bNode(_matching[it])] == _phase; |
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| 451 | covering.set(it, cn); |
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| 452 | if (cn) ++size; |
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[2040] | 453 | } |
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[2466] | 454 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
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| 455 | bool cn = _reached[it] != _phase; |
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| 456 | covering.set(it, cn); |
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| 457 | if (cn) ++size; |
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[2040] | 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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[2466] | 463 | /// |
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[2462] | 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. |
---|
| 467 | /// \retval barrier A WriteMap on the ANodes with bool value. |
---|
| 468 | template <typename BarrierMap> |
---|
| 469 | void aBarrier(BarrierMap& barrier) const { |
---|
| 470 | |
---|
[2466] | 471 | for (ANodeIt it(*_graph); it != INVALID; ++it) { |
---|
| 472 | barrier.set(it, _matching[it] == INVALID || |
---|
| 473 | _reached[_graph->bNode(_matching[it])] != _phase); |
---|
[2040] | 474 | } |
---|
| 475 | } |
---|
| 476 | |
---|
[2462] | 477 | /// \brief Gives back a barrier on the B-nodes |
---|
[2466] | 478 | /// |
---|
[2462] | 479 | /// The barrier is s subset of the nodes on the same side of the |
---|
| 480 | /// graph, which size minus its neighbours is exactly the |
---|
| 481 | /// unmatched nodes on the B-side. |
---|
| 482 | /// \retval barrier A WriteMap on the BNodes with bool value. |
---|
| 483 | template <typename BarrierMap> |
---|
| 484 | void bBarrier(BarrierMap& barrier) const { |
---|
| 485 | |
---|
[2466] | 486 | for (BNodeIt it(*_graph); it != INVALID; ++it) { |
---|
| 487 | barrier.set(it, _reached[it] == _phase); |
---|
[2462] | 488 | } |
---|
[2466] | 489 | } |
---|
[2462] | 490 | |
---|
[2466] | 491 | /// \brief Gives back the number of the matching edges. |
---|
| 492 | /// |
---|
| 493 | /// Gives back the number of the matching edges. |
---|
| 494 | int matchingSize() const { |
---|
| 495 | return _size; |
---|
[2040] | 496 | } |
---|
| 497 | |
---|
| 498 | /// @} |
---|
| 499 | |
---|
| 500 | private: |
---|
| 501 | |
---|
[2466] | 502 | typename BpUGraph::template ANodeMap<UEdge> _matching; |
---|
| 503 | typename BpUGraph::template BNodeMap<UEdge> _rmatching; |
---|
[2040] | 504 | |
---|
[2466] | 505 | typename BpUGraph::template BNodeMap<int> _reached; |
---|
| 506 | |
---|
| 507 | int _phase; |
---|
| 508 | const Graph *_graph; |
---|
| 509 | |
---|
| 510 | int _size; |
---|
[2051] | 511 | |
---|
| 512 | }; |
---|
| 513 | |
---|
[2058] | 514 | /// \ingroup matching |
---|
| 515 | /// |
---|
| 516 | /// \brief Maximum cardinality bipartite matching |
---|
| 517 | /// |
---|
| 518 | /// This function calculates the maximum cardinality matching |
---|
| 519 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
| 520 | /// edge map. |
---|
| 521 | /// |
---|
| 522 | /// \param graph The bipartite graph. |
---|
[2463] | 523 | /// \return The size of the matching. |
---|
| 524 | template <typename BpUGraph> |
---|
| 525 | int maxBipartiteMatching(const BpUGraph& graph) { |
---|
| 526 | MaxBipartiteMatching<BpUGraph> bpmatching(graph); |
---|
| 527 | bpmatching.run(); |
---|
| 528 | return bpmatching.matchingSize(); |
---|
| 529 | } |
---|
| 530 | |
---|
| 531 | /// \ingroup matching |
---|
| 532 | /// |
---|
| 533 | /// \brief Maximum cardinality bipartite matching |
---|
| 534 | /// |
---|
| 535 | /// This function calculates the maximum cardinality matching |
---|
| 536 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
| 537 | /// edge map. |
---|
| 538 | /// |
---|
| 539 | /// \param graph The bipartite graph. |
---|
| 540 | /// \retval matching The ANodeMap of UEdges which will be set to covered |
---|
| 541 | /// matching undirected edge. |
---|
[2058] | 542 | /// \return The size of the matching. |
---|
| 543 | template <typename BpUGraph, typename MatchingMap> |
---|
| 544 | int maxBipartiteMatching(const BpUGraph& graph, MatchingMap& matching) { |
---|
| 545 | MaxBipartiteMatching<BpUGraph> bpmatching(graph); |
---|
| 546 | bpmatching.run(); |
---|
[2463] | 547 | bpmatching.aMatching(matching); |
---|
| 548 | return bpmatching.matchingSize(); |
---|
| 549 | } |
---|
| 550 | |
---|
| 551 | /// \ingroup matching |
---|
| 552 | /// |
---|
| 553 | /// \brief Maximum cardinality bipartite matching |
---|
| 554 | /// |
---|
| 555 | /// This function calculates the maximum cardinality matching |
---|
| 556 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
| 557 | /// edge map. |
---|
| 558 | /// |
---|
| 559 | /// \param graph The bipartite graph. |
---|
| 560 | /// \retval matching The ANodeMap of UEdges which will be set to covered |
---|
| 561 | /// matching undirected edge. |
---|
| 562 | /// \retval barrier The BNodeMap of bools which will be set to a barrier |
---|
| 563 | /// of the BNode-set. |
---|
| 564 | /// \return The size of the matching. |
---|
| 565 | template <typename BpUGraph, typename MatchingMap, typename BarrierMap> |
---|
| 566 | int maxBipartiteMatching(const BpUGraph& graph, |
---|
| 567 | MatchingMap& matching, BarrierMap& barrier) { |
---|
| 568 | MaxBipartiteMatching<BpUGraph> bpmatching(graph); |
---|
| 569 | bpmatching.run(); |
---|
| 570 | bpmatching.aMatching(matching); |
---|
| 571 | bpmatching.bBarrier(barrier); |
---|
[2058] | 572 | return bpmatching.matchingSize(); |
---|
| 573 | } |
---|
| 574 | |
---|
[2051] | 575 | /// \brief Default traits class for weighted bipartite matching algoritms. |
---|
| 576 | /// |
---|
| 577 | /// Default traits class for weighted bipartite matching algoritms. |
---|
| 578 | /// \param _BpUGraph The bipartite undirected graph type. |
---|
| 579 | /// \param _WeightMap Type of weight map. |
---|
| 580 | template <typename _BpUGraph, typename _WeightMap> |
---|
[2550] | 581 | struct MaxWeightedBipartiteMatchingDefaultTraits { |
---|
[2051] | 582 | /// \brief The type of the weight of the undirected edges. |
---|
| 583 | typedef typename _WeightMap::Value Value; |
---|
| 584 | |
---|
| 585 | /// The undirected bipartite graph type the algorithm runs on. |
---|
| 586 | typedef _BpUGraph BpUGraph; |
---|
| 587 | |
---|
| 588 | /// The map of the edges weights |
---|
| 589 | typedef _WeightMap WeightMap; |
---|
| 590 | |
---|
| 591 | /// \brief The cross reference type used by heap. |
---|
| 592 | /// |
---|
| 593 | /// The cross reference type used by heap. |
---|
[2550] | 594 | /// Usually it is \c Graph::ANodeMap<int>. |
---|
| 595 | typedef typename BpUGraph::template ANodeMap<int> HeapCrossRef; |
---|
[2051] | 596 | |
---|
| 597 | /// \brief Instantiates a HeapCrossRef. |
---|
| 598 | /// |
---|
| 599 | /// This function instantiates a \ref HeapCrossRef. |
---|
| 600 | /// \param graph is the graph, to which we would like to define the |
---|
| 601 | /// HeapCrossRef. |
---|
| 602 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 603 | return new HeapCrossRef(graph); |
---|
| 604 | } |
---|
| 605 | |
---|
| 606 | /// \brief The heap type used by weighted matching algorithms. |
---|
| 607 | /// |
---|
| 608 | /// The heap type used by weighted matching algorithms. It should |
---|
| 609 | /// minimize the priorities and the heap's key type is the graph's |
---|
| 610 | /// anode graph's node. |
---|
| 611 | /// |
---|
| 612 | /// \sa BinHeap |
---|
[2263] | 613 | typedef BinHeap<Value, HeapCrossRef> Heap; |
---|
[2051] | 614 | |
---|
| 615 | /// \brief Instantiates a Heap. |
---|
| 616 | /// |
---|
| 617 | /// This function instantiates a \ref Heap. |
---|
| 618 | /// \param crossref The cross reference of the heap. |
---|
| 619 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
| 620 | return new Heap(crossref); |
---|
| 621 | } |
---|
| 622 | |
---|
| 623 | }; |
---|
| 624 | |
---|
| 625 | |
---|
| 626 | /// \ingroup matching |
---|
| 627 | /// |
---|
| 628 | /// \brief Bipartite Max Weighted Matching algorithm |
---|
| 629 | /// |
---|
| 630 | /// This class implements the bipartite Max Weighted Matching |
---|
| 631 | /// algorithm. It uses the successive shortest path algorithm to |
---|
| 632 | /// calculate the maximum weighted matching in the bipartite |
---|
| 633 | /// graph. The algorithm can be used also to calculate the maximum |
---|
| 634 | /// cardinality maximum weighted matching. The time complexity |
---|
| 635 | /// of the algorithm is \f$ O(ne\log(n)) \f$ with the default binary |
---|
| 636 | /// heap implementation but this can be improved to |
---|
| 637 | /// \f$ O(n^2\log(n)+ne) \f$ if we use fibonacci heaps. |
---|
| 638 | /// |
---|
| 639 | /// The algorithm also provides a potential function on the nodes |
---|
| 640 | /// which a dual solution of the matching algorithm and it can be |
---|
| 641 | /// used to proof the optimality of the given pimal solution. |
---|
| 642 | #ifdef DOXYGEN |
---|
| 643 | template <typename _BpUGraph, typename _WeightMap, typename _Traits> |
---|
| 644 | #else |
---|
| 645 | template <typename _BpUGraph, |
---|
| 646 | typename _WeightMap = typename _BpUGraph::template UEdgeMap<int>, |
---|
[2550] | 647 | typename _Traits = |
---|
| 648 | MaxWeightedBipartiteMatchingDefaultTraits<_BpUGraph, _WeightMap> > |
---|
[2051] | 649 | #endif |
---|
| 650 | class MaxWeightedBipartiteMatching { |
---|
| 651 | public: |
---|
| 652 | |
---|
| 653 | typedef _Traits Traits; |
---|
| 654 | typedef typename Traits::BpUGraph BpUGraph; |
---|
| 655 | typedef typename Traits::WeightMap WeightMap; |
---|
| 656 | typedef typename Traits::Value Value; |
---|
| 657 | |
---|
| 658 | protected: |
---|
| 659 | |
---|
| 660 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
| 661 | typedef typename Traits::Heap Heap; |
---|
| 662 | |
---|
| 663 | |
---|
| 664 | typedef typename BpUGraph::Node Node; |
---|
| 665 | typedef typename BpUGraph::ANodeIt ANodeIt; |
---|
| 666 | typedef typename BpUGraph::BNodeIt BNodeIt; |
---|
| 667 | typedef typename BpUGraph::UEdge UEdge; |
---|
| 668 | typedef typename BpUGraph::UEdgeIt UEdgeIt; |
---|
| 669 | typedef typename BpUGraph::IncEdgeIt IncEdgeIt; |
---|
| 670 | |
---|
| 671 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
---|
| 672 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
---|
| 673 | |
---|
| 674 | typedef typename BpUGraph::template ANodeMap<Value> ANodePotentialMap; |
---|
| 675 | typedef typename BpUGraph::template BNodeMap<Value> BNodePotentialMap; |
---|
| 676 | |
---|
| 677 | |
---|
| 678 | public: |
---|
| 679 | |
---|
| 680 | /// \brief \ref Exception for uninitialized parameters. |
---|
| 681 | /// |
---|
| 682 | /// This error represents problems in the initialization |
---|
| 683 | /// of the parameters of the algorithms. |
---|
| 684 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
| 685 | public: |
---|
[2151] | 686 | virtual const char* what() const throw() { |
---|
[2051] | 687 | return "lemon::MaxWeightedBipartiteMatching::UninitializedParameter"; |
---|
| 688 | } |
---|
| 689 | }; |
---|
| 690 | |
---|
| 691 | ///\name Named template parameters |
---|
| 692 | |
---|
| 693 | ///@{ |
---|
| 694 | |
---|
| 695 | template <class H, class CR> |
---|
| 696 | struct DefHeapTraits : public Traits { |
---|
| 697 | typedef CR HeapCrossRef; |
---|
| 698 | typedef H Heap; |
---|
| 699 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &) { |
---|
| 700 | throw UninitializedParameter(); |
---|
| 701 | } |
---|
| 702 | static Heap *createHeap(HeapCrossRef &) { |
---|
| 703 | throw UninitializedParameter(); |
---|
| 704 | } |
---|
| 705 | }; |
---|
| 706 | |
---|
| 707 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
| 708 | /// and cross reference type |
---|
| 709 | /// |
---|
| 710 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 711 | /// reference type |
---|
| 712 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 713 | struct DefHeap |
---|
| 714 | : public MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 715 | DefHeapTraits<H, CR> > { |
---|
| 716 | typedef MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 717 | DefHeapTraits<H, CR> > Create; |
---|
| 718 | }; |
---|
| 719 | |
---|
| 720 | template <class H, class CR> |
---|
| 721 | struct DefStandardHeapTraits : public Traits { |
---|
| 722 | typedef CR HeapCrossRef; |
---|
| 723 | typedef H Heap; |
---|
| 724 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 725 | return new HeapCrossRef(graph); |
---|
| 726 | } |
---|
| 727 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
| 728 | return new Heap(crossref); |
---|
| 729 | } |
---|
| 730 | }; |
---|
| 731 | |
---|
| 732 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
| 733 | /// cross reference type with automatic allocation |
---|
| 734 | /// |
---|
| 735 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 736 | /// reference type. It can allocate the heap and the cross reference |
---|
| 737 | /// object if the cross reference's constructor waits for the graph as |
---|
| 738 | /// parameter and the heap's constructor waits for the cross reference. |
---|
| 739 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 740 | struct DefStandardHeap |
---|
| 741 | : public MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 742 | DefStandardHeapTraits<H, CR> > { |
---|
| 743 | typedef MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
| 744 | DefStandardHeapTraits<H, CR> > |
---|
| 745 | Create; |
---|
| 746 | }; |
---|
| 747 | |
---|
| 748 | ///@} |
---|
| 749 | |
---|
| 750 | |
---|
| 751 | /// \brief Constructor. |
---|
| 752 | /// |
---|
| 753 | /// Constructor of the algorithm. |
---|
| 754 | MaxWeightedBipartiteMatching(const BpUGraph& _graph, |
---|
| 755 | const WeightMap& _weight) |
---|
| 756 | : graph(&_graph), weight(&_weight), |
---|
| 757 | anode_matching(_graph), bnode_matching(_graph), |
---|
| 758 | anode_potential(_graph), bnode_potential(_graph), |
---|
| 759 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
| 760 | _heap(0), local_heap(0) {} |
---|
| 761 | |
---|
| 762 | /// \brief Destructor. |
---|
| 763 | /// |
---|
| 764 | /// Destructor of the algorithm. |
---|
| 765 | ~MaxWeightedBipartiteMatching() { |
---|
| 766 | destroyStructures(); |
---|
| 767 | } |
---|
| 768 | |
---|
| 769 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
| 770 | /// |
---|
| 771 | /// Sets the heap and the cross reference used by algorithm. |
---|
| 772 | /// If you don't use this function before calling \ref run(), |
---|
| 773 | /// it will allocate one. The destuctor deallocates this |
---|
| 774 | /// automatically allocated map, of course. |
---|
| 775 | /// \return \c (*this) |
---|
[2386] | 776 | MaxWeightedBipartiteMatching& heap(Heap& hp, HeapCrossRef &cr) { |
---|
[2051] | 777 | if(local_heap_cross_ref) { |
---|
| 778 | delete _heap_cross_ref; |
---|
| 779 | local_heap_cross_ref = false; |
---|
| 780 | } |
---|
[2386] | 781 | _heap_cross_ref = &cr; |
---|
[2051] | 782 | if(local_heap) { |
---|
| 783 | delete _heap; |
---|
| 784 | local_heap = false; |
---|
| 785 | } |
---|
[2386] | 786 | _heap = &hp; |
---|
[2051] | 787 | return *this; |
---|
| 788 | } |
---|
| 789 | |
---|
| 790 | /// \name Execution control |
---|
| 791 | /// The simplest way to execute the algorithm is to use |
---|
| 792 | /// one of the member functions called \c run(). |
---|
| 793 | /// \n |
---|
| 794 | /// If you need more control on the execution, |
---|
| 795 | /// first you must call \ref init() or one alternative for it. |
---|
| 796 | /// Finally \ref start() will perform the matching computation or |
---|
| 797 | /// with step-by-step execution you can augment the solution. |
---|
| 798 | |
---|
| 799 | /// @{ |
---|
| 800 | |
---|
| 801 | /// \brief Initalize the data structures. |
---|
| 802 | /// |
---|
| 803 | /// It initalizes the data structures and creates an empty matching. |
---|
| 804 | void init() { |
---|
| 805 | initStructures(); |
---|
| 806 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 807 | anode_matching[it] = INVALID; |
---|
| 808 | anode_potential[it] = 0; |
---|
| 809 | } |
---|
| 810 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 811 | bnode_matching[it] = INVALID; |
---|
| 812 | bnode_potential[it] = 0; |
---|
| 813 | for (IncEdgeIt jt(*graph, it); jt != INVALID; ++jt) { |
---|
[2058] | 814 | if ((*weight)[jt] > bnode_potential[it]) { |
---|
| 815 | bnode_potential[it] = (*weight)[jt]; |
---|
[2051] | 816 | } |
---|
| 817 | } |
---|
| 818 | } |
---|
| 819 | matching_value = 0; |
---|
| 820 | matching_size = 0; |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | |
---|
| 824 | /// \brief An augmenting phase of the weighted matching algorithm |
---|
| 825 | /// |
---|
| 826 | /// It runs an augmenting phase of the weighted matching |
---|
[2352] | 827 | /// algorithm. This phase finds the best augmenting path and |
---|
[2051] | 828 | /// augments only on this paths. |
---|
| 829 | /// |
---|
| 830 | /// The algorithm consists at most |
---|
| 831 | /// of \f$ O(n) \f$ phase and one phase is \f$ O(n\log(n)+e) \f$ |
---|
| 832 | /// long with Fibonacci heap or \f$ O((n+e)\log(n)) \f$ long |
---|
| 833 | /// with binary heap. |
---|
| 834 | /// \param decrease If the given parameter true the matching value |
---|
| 835 | /// can be decreased in the augmenting phase. If we would like |
---|
| 836 | /// to calculate the maximum cardinality maximum weighted matching |
---|
| 837 | /// then we should let the algorithm to decrease the matching |
---|
| 838 | /// value in order to increase the number of the matching edges. |
---|
| 839 | bool augment(bool decrease = false) { |
---|
| 840 | |
---|
| 841 | typename BpUGraph::template BNodeMap<Value> bdist(*graph); |
---|
| 842 | typename BpUGraph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
---|
| 843 | |
---|
| 844 | Node bestNode = INVALID; |
---|
| 845 | Value bestValue = 0; |
---|
| 846 | |
---|
| 847 | _heap->clear(); |
---|
| 848 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 849 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
---|
| 850 | } |
---|
| 851 | |
---|
| 852 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 853 | if (anode_matching[it] == INVALID) { |
---|
| 854 | _heap->push(it, 0); |
---|
| 855 | } |
---|
| 856 | } |
---|
| 857 | |
---|
| 858 | Value bdistMax = 0; |
---|
| 859 | while (!_heap->empty()) { |
---|
| 860 | Node anode = _heap->top(); |
---|
| 861 | Value avalue = _heap->prio(); |
---|
| 862 | _heap->pop(); |
---|
| 863 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
| 864 | if (jt == anode_matching[anode]) continue; |
---|
| 865 | Node bnode = graph->bNode(jt); |
---|
[2058] | 866 | Value bvalue = avalue - (*weight)[jt] + |
---|
| 867 | anode_potential[anode] + bnode_potential[bnode]; |
---|
[2550] | 868 | if (bvalue > bdistMax) { |
---|
| 869 | bdistMax = bvalue; |
---|
| 870 | } |
---|
[2051] | 871 | if (bpred[bnode] == INVALID || bvalue < bdist[bnode]) { |
---|
| 872 | bdist[bnode] = bvalue; |
---|
| 873 | bpred[bnode] = jt; |
---|
[2550] | 874 | } else continue; |
---|
[2051] | 875 | if (bnode_matching[bnode] != INVALID) { |
---|
| 876 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
| 877 | switch (_heap->state(newanode)) { |
---|
| 878 | case Heap::PRE_HEAP: |
---|
| 879 | _heap->push(newanode, bvalue); |
---|
| 880 | break; |
---|
| 881 | case Heap::IN_HEAP: |
---|
| 882 | if (bvalue < (*_heap)[newanode]) { |
---|
| 883 | _heap->decrease(newanode, bvalue); |
---|
| 884 | } |
---|
| 885 | break; |
---|
| 886 | case Heap::POST_HEAP: |
---|
| 887 | break; |
---|
| 888 | } |
---|
| 889 | } else { |
---|
| 890 | if (bestNode == INVALID || |
---|
[2058] | 891 | bnode_potential[bnode] - bvalue > bestValue) { |
---|
| 892 | bestValue = bnode_potential[bnode] - bvalue; |
---|
[2051] | 893 | bestNode = bnode; |
---|
| 894 | } |
---|
| 895 | } |
---|
| 896 | } |
---|
| 897 | } |
---|
| 898 | |
---|
| 899 | if (bestNode == INVALID || (!decrease && bestValue < 0)) { |
---|
| 900 | return false; |
---|
| 901 | } |
---|
| 902 | |
---|
| 903 | matching_value += bestValue; |
---|
| 904 | ++matching_size; |
---|
| 905 | |
---|
| 906 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 907 | if (bpred[it] != INVALID) { |
---|
[2058] | 908 | bnode_potential[it] -= bdist[it]; |
---|
[2051] | 909 | } else { |
---|
[2058] | 910 | bnode_potential[it] -= bdistMax; |
---|
[2051] | 911 | } |
---|
| 912 | } |
---|
| 913 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 914 | if (anode_matching[it] != INVALID) { |
---|
| 915 | Node bnode = graph->bNode(anode_matching[it]); |
---|
| 916 | if (bpred[bnode] != INVALID) { |
---|
| 917 | anode_potential[it] += bdist[bnode]; |
---|
| 918 | } else { |
---|
| 919 | anode_potential[it] += bdistMax; |
---|
| 920 | } |
---|
| 921 | } |
---|
| 922 | } |
---|
| 923 | |
---|
| 924 | while (bestNode != INVALID) { |
---|
| 925 | UEdge uedge = bpred[bestNode]; |
---|
| 926 | Node anode = graph->aNode(uedge); |
---|
| 927 | |
---|
| 928 | bnode_matching[bestNode] = uedge; |
---|
| 929 | if (anode_matching[anode] != INVALID) { |
---|
| 930 | bestNode = graph->bNode(anode_matching[anode]); |
---|
| 931 | } else { |
---|
| 932 | bestNode = INVALID; |
---|
| 933 | } |
---|
| 934 | anode_matching[anode] = uedge; |
---|
| 935 | } |
---|
| 936 | |
---|
| 937 | |
---|
| 938 | return true; |
---|
| 939 | } |
---|
| 940 | |
---|
| 941 | /// \brief Starts the algorithm. |
---|
| 942 | /// |
---|
| 943 | /// Starts the algorithm. It runs augmenting phases until the |
---|
| 944 | /// optimal solution reached. |
---|
| 945 | /// |
---|
| 946 | /// \param maxCardinality If the given value is true it will |
---|
| 947 | /// calculate the maximum cardinality maximum matching instead of |
---|
| 948 | /// the maximum matching. |
---|
| 949 | void start(bool maxCardinality = false) { |
---|
| 950 | while (augment(maxCardinality)) {} |
---|
| 951 | } |
---|
| 952 | |
---|
| 953 | /// \brief Runs the algorithm. |
---|
| 954 | /// |
---|
| 955 | /// It just initalize the algorithm and then start it. |
---|
| 956 | /// |
---|
| 957 | /// \param maxCardinality If the given value is true it will |
---|
| 958 | /// calculate the maximum cardinality maximum matching instead of |
---|
| 959 | /// the maximum matching. |
---|
| 960 | void run(bool maxCardinality = false) { |
---|
| 961 | init(); |
---|
| 962 | start(maxCardinality); |
---|
| 963 | } |
---|
| 964 | |
---|
| 965 | /// @} |
---|
| 966 | |
---|
| 967 | /// \name Query Functions |
---|
| 968 | /// The result of the %Matching algorithm can be obtained using these |
---|
| 969 | /// functions.\n |
---|
| 970 | /// Before the use of these functions, |
---|
| 971 | /// either run() or start() must be called. |
---|
| 972 | |
---|
| 973 | ///@{ |
---|
| 974 | |
---|
| 975 | /// \brief Gives back the potential in the NodeMap |
---|
| 976 | /// |
---|
[2058] | 977 | /// Gives back the potential in the NodeMap. The matching is optimal |
---|
| 978 | /// with the current number of edges if \f$ \pi(a) + \pi(b) - w(ab) = 0 \f$ |
---|
| 979 | /// for each matching edges and \f$ \pi(a) + \pi(b) - w(ab) \ge 0 \f$ |
---|
| 980 | /// for each edges. |
---|
[2051] | 981 | template <typename PotentialMap> |
---|
[2386] | 982 | void potential(PotentialMap& pt) const { |
---|
[2051] | 983 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
[2463] | 984 | pt.set(it, anode_potential[it]); |
---|
[2051] | 985 | } |
---|
| 986 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
[2463] | 987 | pt.set(it, bnode_potential[it]); |
---|
[2051] | 988 | } |
---|
| 989 | } |
---|
| 990 | |
---|
| 991 | /// \brief Set true all matching uedge in the map. |
---|
| 992 | /// |
---|
| 993 | /// Set true all matching uedge in the map. It does not change the |
---|
| 994 | /// value mapped to the other uedges. |
---|
| 995 | /// \return The number of the matching edges. |
---|
| 996 | template <typename MatchingMap> |
---|
[2386] | 997 | int quickMatching(MatchingMap& mm) const { |
---|
[2051] | 998 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 999 | if (anode_matching[it] != INVALID) { |
---|
[2463] | 1000 | mm.set(anode_matching[it], true); |
---|
[2051] | 1001 | } |
---|
| 1002 | } |
---|
| 1003 | return matching_size; |
---|
| 1004 | } |
---|
| 1005 | |
---|
| 1006 | /// \brief Set true all matching uedge in the map and the others to false. |
---|
| 1007 | /// |
---|
| 1008 | /// Set true all matching uedge in the map and the others to false. |
---|
| 1009 | /// \return The number of the matching edges. |
---|
| 1010 | template <typename MatchingMap> |
---|
[2386] | 1011 | int matching(MatchingMap& mm) const { |
---|
[2051] | 1012 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
---|
[2463] | 1013 | mm.set(it, it == anode_matching[graph->aNode(it)]); |
---|
| 1014 | } |
---|
| 1015 | return matching_size; |
---|
| 1016 | } |
---|
| 1017 | |
---|
| 1018 | ///Gives back the matching in an ANodeMap. |
---|
| 1019 | |
---|
| 1020 | ///Gives back the matching in an ANodeMap. The parameter should |
---|
| 1021 | ///be a write ANodeMap of UEdge values. |
---|
| 1022 | ///\return The number of the matching edges. |
---|
| 1023 | template<class MatchingMap> |
---|
| 1024 | int aMatching(MatchingMap& mm) const { |
---|
| 1025 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1026 | mm.set(it, anode_matching[it]); |
---|
| 1027 | } |
---|
| 1028 | return matching_size; |
---|
| 1029 | } |
---|
| 1030 | |
---|
| 1031 | ///Gives back the matching in a BNodeMap. |
---|
| 1032 | |
---|
| 1033 | ///Gives back the matching in a BNodeMap. The parameter should |
---|
| 1034 | ///be a write BNodeMap of UEdge values. |
---|
| 1035 | ///\return The number of the matching edges. |
---|
| 1036 | template<class MatchingMap> |
---|
| 1037 | int bMatching(MatchingMap& mm) const { |
---|
| 1038 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1039 | mm.set(it, bnode_matching[it]); |
---|
[2051] | 1040 | } |
---|
| 1041 | return matching_size; |
---|
| 1042 | } |
---|
| 1043 | |
---|
| 1044 | |
---|
| 1045 | /// \brief Return true if the given uedge is in the matching. |
---|
| 1046 | /// |
---|
| 1047 | /// It returns true if the given uedge is in the matching. |
---|
[2058] | 1048 | bool matchingEdge(const UEdge& edge) const { |
---|
[2051] | 1049 | return anode_matching[graph->aNode(edge)] == edge; |
---|
| 1050 | } |
---|
| 1051 | |
---|
| 1052 | /// \brief Returns the matching edge from the node. |
---|
| 1053 | /// |
---|
| 1054 | /// Returns the matching edge from the node. If there is not such |
---|
| 1055 | /// edge it gives back \c INVALID. |
---|
[2058] | 1056 | UEdge matchingEdge(const Node& node) const { |
---|
[2051] | 1057 | if (graph->aNode(node)) { |
---|
| 1058 | return anode_matching[node]; |
---|
| 1059 | } else { |
---|
| 1060 | return bnode_matching[node]; |
---|
| 1061 | } |
---|
| 1062 | } |
---|
| 1063 | |
---|
| 1064 | /// \brief Gives back the sum of weights of the matching edges. |
---|
| 1065 | /// |
---|
| 1066 | /// Gives back the sum of weights of the matching edges. |
---|
| 1067 | Value matchingValue() const { |
---|
| 1068 | return matching_value; |
---|
| 1069 | } |
---|
| 1070 | |
---|
| 1071 | /// \brief Gives back the number of the matching edges. |
---|
| 1072 | /// |
---|
| 1073 | /// Gives back the number of the matching edges. |
---|
| 1074 | int matchingSize() const { |
---|
| 1075 | return matching_size; |
---|
| 1076 | } |
---|
| 1077 | |
---|
| 1078 | /// @} |
---|
| 1079 | |
---|
| 1080 | private: |
---|
| 1081 | |
---|
| 1082 | void initStructures() { |
---|
| 1083 | if (!_heap_cross_ref) { |
---|
| 1084 | local_heap_cross_ref = true; |
---|
| 1085 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
| 1086 | } |
---|
| 1087 | if (!_heap) { |
---|
| 1088 | local_heap = true; |
---|
| 1089 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
| 1090 | } |
---|
| 1091 | } |
---|
| 1092 | |
---|
| 1093 | void destroyStructures() { |
---|
| 1094 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
| 1095 | if (local_heap) delete _heap; |
---|
| 1096 | } |
---|
| 1097 | |
---|
| 1098 | |
---|
| 1099 | private: |
---|
| 1100 | |
---|
| 1101 | const BpUGraph *graph; |
---|
| 1102 | const WeightMap* weight; |
---|
| 1103 | |
---|
| 1104 | ANodeMatchingMap anode_matching; |
---|
| 1105 | BNodeMatchingMap bnode_matching; |
---|
| 1106 | |
---|
| 1107 | ANodePotentialMap anode_potential; |
---|
| 1108 | BNodePotentialMap bnode_potential; |
---|
| 1109 | |
---|
| 1110 | Value matching_value; |
---|
| 1111 | int matching_size; |
---|
| 1112 | |
---|
| 1113 | HeapCrossRef *_heap_cross_ref; |
---|
| 1114 | bool local_heap_cross_ref; |
---|
| 1115 | |
---|
| 1116 | Heap *_heap; |
---|
| 1117 | bool local_heap; |
---|
| 1118 | |
---|
| 1119 | }; |
---|
| 1120 | |
---|
[2058] | 1121 | /// \ingroup matching |
---|
| 1122 | /// |
---|
| 1123 | /// \brief Maximum weighted bipartite matching |
---|
| 1124 | /// |
---|
| 1125 | /// This function calculates the maximum weighted matching |
---|
| 1126 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
| 1127 | /// edge map. |
---|
| 1128 | /// |
---|
| 1129 | /// \param graph The bipartite graph. |
---|
| 1130 | /// \param weight The undirected edge map which contains the weights. |
---|
| 1131 | /// \retval matching The undirected edge map which will be set to |
---|
| 1132 | /// the matching. |
---|
| 1133 | /// \return The value of the matching. |
---|
| 1134 | template <typename BpUGraph, typename WeightMap, typename MatchingMap> |
---|
| 1135 | typename WeightMap::Value |
---|
| 1136 | maxWeightedBipartiteMatching(const BpUGraph& graph, const WeightMap& weight, |
---|
| 1137 | MatchingMap& matching) { |
---|
| 1138 | MaxWeightedBipartiteMatching<BpUGraph, WeightMap> |
---|
| 1139 | bpmatching(graph, weight); |
---|
| 1140 | bpmatching.run(); |
---|
| 1141 | bpmatching.matching(matching); |
---|
| 1142 | return bpmatching.matchingValue(); |
---|
| 1143 | } |
---|
| 1144 | |
---|
| 1145 | /// \ingroup matching |
---|
| 1146 | /// |
---|
| 1147 | /// \brief Maximum weighted maximum cardinality bipartite matching |
---|
| 1148 | /// |
---|
| 1149 | /// This function calculates the maximum weighted of the maximum cardinality |
---|
| 1150 | /// matchings of a bipartite graph. It gives back the matching in an |
---|
| 1151 | /// undirected edge map. |
---|
| 1152 | /// |
---|
| 1153 | /// \param graph The bipartite graph. |
---|
| 1154 | /// \param weight The undirected edge map which contains the weights. |
---|
| 1155 | /// \retval matching The undirected edge map which will be set to |
---|
| 1156 | /// the matching. |
---|
| 1157 | /// \return The value of the matching. |
---|
| 1158 | template <typename BpUGraph, typename WeightMap, typename MatchingMap> |
---|
| 1159 | typename WeightMap::Value |
---|
| 1160 | maxWeightedMaxBipartiteMatching(const BpUGraph& graph, |
---|
| 1161 | const WeightMap& weight, |
---|
| 1162 | MatchingMap& matching) { |
---|
| 1163 | MaxWeightedBipartiteMatching<BpUGraph, WeightMap> |
---|
| 1164 | bpmatching(graph, weight); |
---|
| 1165 | bpmatching.run(true); |
---|
| 1166 | bpmatching.matching(matching); |
---|
| 1167 | return bpmatching.matchingValue(); |
---|
| 1168 | } |
---|
| 1169 | |
---|
[2051] | 1170 | /// \brief Default traits class for minimum cost bipartite matching |
---|
| 1171 | /// algoritms. |
---|
| 1172 | /// |
---|
| 1173 | /// Default traits class for minimum cost bipartite matching |
---|
| 1174 | /// algoritms. |
---|
| 1175 | /// |
---|
| 1176 | /// \param _BpUGraph The bipartite undirected graph |
---|
| 1177 | /// type. |
---|
| 1178 | /// |
---|
| 1179 | /// \param _CostMap Type of cost map. |
---|
| 1180 | template <typename _BpUGraph, typename _CostMap> |
---|
| 1181 | struct MinCostMaxBipartiteMatchingDefaultTraits { |
---|
| 1182 | /// \brief The type of the cost of the undirected edges. |
---|
| 1183 | typedef typename _CostMap::Value Value; |
---|
| 1184 | |
---|
| 1185 | /// The undirected bipartite graph type the algorithm runs on. |
---|
| 1186 | typedef _BpUGraph BpUGraph; |
---|
| 1187 | |
---|
| 1188 | /// The map of the edges costs |
---|
| 1189 | typedef _CostMap CostMap; |
---|
| 1190 | |
---|
| 1191 | /// \brief The cross reference type used by heap. |
---|
| 1192 | /// |
---|
| 1193 | /// The cross reference type used by heap. |
---|
| 1194 | /// Usually it is \c Graph::NodeMap<int>. |
---|
| 1195 | typedef typename BpUGraph::template NodeMap<int> HeapCrossRef; |
---|
| 1196 | |
---|
| 1197 | /// \brief Instantiates a HeapCrossRef. |
---|
| 1198 | /// |
---|
| 1199 | /// This function instantiates a \ref HeapCrossRef. |
---|
| 1200 | /// \param graph is the graph, to which we would like to define the |
---|
| 1201 | /// HeapCrossRef. |
---|
| 1202 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 1203 | return new HeapCrossRef(graph); |
---|
| 1204 | } |
---|
| 1205 | |
---|
| 1206 | /// \brief The heap type used by costed matching algorithms. |
---|
| 1207 | /// |
---|
| 1208 | /// The heap type used by costed matching algorithms. It should |
---|
| 1209 | /// minimize the priorities and the heap's key type is the graph's |
---|
| 1210 | /// anode graph's node. |
---|
| 1211 | /// |
---|
| 1212 | /// \sa BinHeap |
---|
[2269] | 1213 | typedef BinHeap<Value, HeapCrossRef> Heap; |
---|
[2051] | 1214 | |
---|
| 1215 | /// \brief Instantiates a Heap. |
---|
| 1216 | /// |
---|
| 1217 | /// This function instantiates a \ref Heap. |
---|
| 1218 | /// \param crossref The cross reference of the heap. |
---|
| 1219 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
| 1220 | return new Heap(crossref); |
---|
| 1221 | } |
---|
| 1222 | |
---|
| 1223 | }; |
---|
| 1224 | |
---|
| 1225 | |
---|
| 1226 | /// \ingroup matching |
---|
| 1227 | /// |
---|
| 1228 | /// \brief Bipartite Min Cost Matching algorithm |
---|
| 1229 | /// |
---|
| 1230 | /// This class implements the bipartite Min Cost Matching algorithm. |
---|
| 1231 | /// It uses the successive shortest path algorithm to calculate the |
---|
| 1232 | /// minimum cost maximum matching in the bipartite graph. The time |
---|
| 1233 | /// complexity of the algorithm is \f$ O(ne\log(n)) \f$ with the |
---|
| 1234 | /// default binary heap implementation but this can be improved to |
---|
| 1235 | /// \f$ O(n^2\log(n)+ne) \f$ if we use fibonacci heaps. |
---|
| 1236 | /// |
---|
| 1237 | /// The algorithm also provides a potential function on the nodes |
---|
| 1238 | /// which a dual solution of the matching algorithm and it can be |
---|
| 1239 | /// used to proof the optimality of the given pimal solution. |
---|
| 1240 | #ifdef DOXYGEN |
---|
| 1241 | template <typename _BpUGraph, typename _CostMap, typename _Traits> |
---|
| 1242 | #else |
---|
| 1243 | template <typename _BpUGraph, |
---|
| 1244 | typename _CostMap = typename _BpUGraph::template UEdgeMap<int>, |
---|
[2550] | 1245 | typename _Traits = |
---|
| 1246 | MinCostMaxBipartiteMatchingDefaultTraits<_BpUGraph, _CostMap> > |
---|
[2051] | 1247 | #endif |
---|
| 1248 | class MinCostMaxBipartiteMatching { |
---|
| 1249 | public: |
---|
| 1250 | |
---|
| 1251 | typedef _Traits Traits; |
---|
| 1252 | typedef typename Traits::BpUGraph BpUGraph; |
---|
| 1253 | typedef typename Traits::CostMap CostMap; |
---|
| 1254 | typedef typename Traits::Value Value; |
---|
| 1255 | |
---|
| 1256 | protected: |
---|
| 1257 | |
---|
| 1258 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
| 1259 | typedef typename Traits::Heap Heap; |
---|
| 1260 | |
---|
| 1261 | |
---|
| 1262 | typedef typename BpUGraph::Node Node; |
---|
| 1263 | typedef typename BpUGraph::ANodeIt ANodeIt; |
---|
| 1264 | typedef typename BpUGraph::BNodeIt BNodeIt; |
---|
| 1265 | typedef typename BpUGraph::UEdge UEdge; |
---|
| 1266 | typedef typename BpUGraph::UEdgeIt UEdgeIt; |
---|
| 1267 | typedef typename BpUGraph::IncEdgeIt IncEdgeIt; |
---|
| 1268 | |
---|
| 1269 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
---|
| 1270 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
---|
| 1271 | |
---|
| 1272 | typedef typename BpUGraph::template ANodeMap<Value> ANodePotentialMap; |
---|
| 1273 | typedef typename BpUGraph::template BNodeMap<Value> BNodePotentialMap; |
---|
| 1274 | |
---|
| 1275 | |
---|
| 1276 | public: |
---|
| 1277 | |
---|
| 1278 | /// \brief \ref Exception for uninitialized parameters. |
---|
| 1279 | /// |
---|
| 1280 | /// This error represents problems in the initialization |
---|
| 1281 | /// of the parameters of the algorithms. |
---|
| 1282 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
| 1283 | public: |
---|
[2151] | 1284 | virtual const char* what() const throw() { |
---|
[2051] | 1285 | return "lemon::MinCostMaxBipartiteMatching::UninitializedParameter"; |
---|
| 1286 | } |
---|
| 1287 | }; |
---|
| 1288 | |
---|
| 1289 | ///\name Named template parameters |
---|
| 1290 | |
---|
| 1291 | ///@{ |
---|
| 1292 | |
---|
| 1293 | template <class H, class CR> |
---|
| 1294 | struct DefHeapTraits : public Traits { |
---|
| 1295 | typedef CR HeapCrossRef; |
---|
| 1296 | typedef H Heap; |
---|
| 1297 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &) { |
---|
| 1298 | throw UninitializedParameter(); |
---|
| 1299 | } |
---|
| 1300 | static Heap *createHeap(HeapCrossRef &) { |
---|
| 1301 | throw UninitializedParameter(); |
---|
| 1302 | } |
---|
| 1303 | }; |
---|
| 1304 | |
---|
| 1305 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
| 1306 | /// and cross reference type |
---|
| 1307 | /// |
---|
| 1308 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 1309 | /// reference type |
---|
| 1310 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 1311 | struct DefHeap |
---|
| 1312 | : public MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1313 | DefHeapTraits<H, CR> > { |
---|
| 1314 | typedef MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1315 | DefHeapTraits<H, CR> > Create; |
---|
| 1316 | }; |
---|
| 1317 | |
---|
| 1318 | template <class H, class CR> |
---|
| 1319 | struct DefStandardHeapTraits : public Traits { |
---|
| 1320 | typedef CR HeapCrossRef; |
---|
| 1321 | typedef H Heap; |
---|
| 1322 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
| 1323 | return new HeapCrossRef(graph); |
---|
| 1324 | } |
---|
| 1325 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
| 1326 | return new Heap(crossref); |
---|
| 1327 | } |
---|
| 1328 | }; |
---|
| 1329 | |
---|
| 1330 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
| 1331 | /// cross reference type with automatic allocation |
---|
| 1332 | /// |
---|
| 1333 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
| 1334 | /// reference type. It can allocate the heap and the cross reference |
---|
| 1335 | /// object if the cross reference's constructor waits for the graph as |
---|
| 1336 | /// parameter and the heap's constructor waits for the cross reference. |
---|
| 1337 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
| 1338 | struct DefStandardHeap |
---|
| 1339 | : public MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1340 | DefStandardHeapTraits<H, CR> > { |
---|
| 1341 | typedef MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
| 1342 | DefStandardHeapTraits<H, CR> > |
---|
| 1343 | Create; |
---|
| 1344 | }; |
---|
| 1345 | |
---|
| 1346 | ///@} |
---|
| 1347 | |
---|
| 1348 | |
---|
| 1349 | /// \brief Constructor. |
---|
| 1350 | /// |
---|
| 1351 | /// Constructor of the algorithm. |
---|
| 1352 | MinCostMaxBipartiteMatching(const BpUGraph& _graph, |
---|
| 1353 | const CostMap& _cost) |
---|
| 1354 | : graph(&_graph), cost(&_cost), |
---|
| 1355 | anode_matching(_graph), bnode_matching(_graph), |
---|
| 1356 | anode_potential(_graph), bnode_potential(_graph), |
---|
| 1357 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
| 1358 | _heap(0), local_heap(0) {} |
---|
| 1359 | |
---|
| 1360 | /// \brief Destructor. |
---|
| 1361 | /// |
---|
| 1362 | /// Destructor of the algorithm. |
---|
| 1363 | ~MinCostMaxBipartiteMatching() { |
---|
| 1364 | destroyStructures(); |
---|
| 1365 | } |
---|
| 1366 | |
---|
| 1367 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
| 1368 | /// |
---|
| 1369 | /// Sets the heap and the cross reference used by algorithm. |
---|
| 1370 | /// If you don't use this function before calling \ref run(), |
---|
| 1371 | /// it will allocate one. The destuctor deallocates this |
---|
| 1372 | /// automatically allocated map, of course. |
---|
| 1373 | /// \return \c (*this) |
---|
[2386] | 1374 | MinCostMaxBipartiteMatching& heap(Heap& hp, HeapCrossRef &cr) { |
---|
[2051] | 1375 | if(local_heap_cross_ref) { |
---|
| 1376 | delete _heap_cross_ref; |
---|
| 1377 | local_heap_cross_ref = false; |
---|
| 1378 | } |
---|
[2386] | 1379 | _heap_cross_ref = &cr; |
---|
[2051] | 1380 | if(local_heap) { |
---|
| 1381 | delete _heap; |
---|
| 1382 | local_heap = false; |
---|
| 1383 | } |
---|
[2386] | 1384 | _heap = &hp; |
---|
[2051] | 1385 | return *this; |
---|
| 1386 | } |
---|
| 1387 | |
---|
| 1388 | /// \name Execution control |
---|
| 1389 | /// The simplest way to execute the algorithm is to use |
---|
| 1390 | /// one of the member functions called \c run(). |
---|
| 1391 | /// \n |
---|
| 1392 | /// If you need more control on the execution, |
---|
| 1393 | /// first you must call \ref init() or one alternative for it. |
---|
| 1394 | /// Finally \ref start() will perform the matching computation or |
---|
| 1395 | /// with step-by-step execution you can augment the solution. |
---|
| 1396 | |
---|
| 1397 | /// @{ |
---|
| 1398 | |
---|
| 1399 | /// \brief Initalize the data structures. |
---|
| 1400 | /// |
---|
| 1401 | /// It initalizes the data structures and creates an empty matching. |
---|
| 1402 | void init() { |
---|
| 1403 | initStructures(); |
---|
| 1404 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1405 | anode_matching[it] = INVALID; |
---|
| 1406 | anode_potential[it] = 0; |
---|
| 1407 | } |
---|
| 1408 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1409 | bnode_matching[it] = INVALID; |
---|
| 1410 | bnode_potential[it] = 0; |
---|
| 1411 | } |
---|
| 1412 | matching_cost = 0; |
---|
| 1413 | matching_size = 0; |
---|
| 1414 | } |
---|
| 1415 | |
---|
| 1416 | |
---|
| 1417 | /// \brief An augmenting phase of the costed matching algorithm |
---|
| 1418 | /// |
---|
| 1419 | /// It runs an augmenting phase of the matching algorithm. The |
---|
| 1420 | /// phase finds the best augmenting path and augments only on this |
---|
| 1421 | /// paths. |
---|
| 1422 | /// |
---|
| 1423 | /// The algorithm consists at most |
---|
| 1424 | /// of \f$ O(n) \f$ phase and one phase is \f$ O(n\log(n)+e) \f$ |
---|
| 1425 | /// long with Fibonacci heap or \f$ O((n+e)\log(n)) \f$ long |
---|
| 1426 | /// with binary heap. |
---|
| 1427 | bool augment() { |
---|
| 1428 | |
---|
| 1429 | typename BpUGraph::template BNodeMap<Value> bdist(*graph); |
---|
| 1430 | typename BpUGraph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
---|
| 1431 | |
---|
| 1432 | Node bestNode = INVALID; |
---|
| 1433 | Value bestValue = 0; |
---|
| 1434 | |
---|
| 1435 | _heap->clear(); |
---|
| 1436 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1437 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
---|
| 1438 | } |
---|
| 1439 | |
---|
| 1440 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1441 | if (anode_matching[it] == INVALID) { |
---|
| 1442 | _heap->push(it, 0); |
---|
| 1443 | } |
---|
| 1444 | } |
---|
[2136] | 1445 | Value bdistMax = 0; |
---|
[2051] | 1446 | |
---|
| 1447 | while (!_heap->empty()) { |
---|
| 1448 | Node anode = _heap->top(); |
---|
| 1449 | Value avalue = _heap->prio(); |
---|
| 1450 | _heap->pop(); |
---|
| 1451 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
| 1452 | if (jt == anode_matching[anode]) continue; |
---|
| 1453 | Node bnode = graph->bNode(jt); |
---|
| 1454 | Value bvalue = avalue + (*cost)[jt] + |
---|
| 1455 | anode_potential[anode] - bnode_potential[bnode]; |
---|
[2550] | 1456 | if (bvalue > bdistMax) { |
---|
| 1457 | bdistMax = bvalue; |
---|
| 1458 | } |
---|
[2051] | 1459 | if (bpred[bnode] == INVALID || bvalue < bdist[bnode]) { |
---|
| 1460 | bdist[bnode] = bvalue; |
---|
| 1461 | bpred[bnode] = jt; |
---|
[2550] | 1462 | } else continue; |
---|
[2051] | 1463 | if (bnode_matching[bnode] != INVALID) { |
---|
| 1464 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
| 1465 | switch (_heap->state(newanode)) { |
---|
| 1466 | case Heap::PRE_HEAP: |
---|
| 1467 | _heap->push(newanode, bvalue); |
---|
| 1468 | break; |
---|
| 1469 | case Heap::IN_HEAP: |
---|
| 1470 | if (bvalue < (*_heap)[newanode]) { |
---|
| 1471 | _heap->decrease(newanode, bvalue); |
---|
| 1472 | } |
---|
| 1473 | break; |
---|
| 1474 | case Heap::POST_HEAP: |
---|
| 1475 | break; |
---|
| 1476 | } |
---|
| 1477 | } else { |
---|
| 1478 | if (bestNode == INVALID || |
---|
| 1479 | bvalue + bnode_potential[bnode] < bestValue) { |
---|
| 1480 | bestValue = bvalue + bnode_potential[bnode]; |
---|
| 1481 | bestNode = bnode; |
---|
| 1482 | } |
---|
| 1483 | } |
---|
| 1484 | } |
---|
| 1485 | } |
---|
| 1486 | |
---|
| 1487 | if (bestNode == INVALID) { |
---|
| 1488 | return false; |
---|
| 1489 | } |
---|
| 1490 | |
---|
| 1491 | matching_cost += bestValue; |
---|
| 1492 | ++matching_size; |
---|
| 1493 | |
---|
| 1494 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1495 | if (bpred[it] != INVALID) { |
---|
| 1496 | bnode_potential[it] += bdist[it]; |
---|
[2136] | 1497 | } else { |
---|
| 1498 | bnode_potential[it] += bdistMax; |
---|
[2051] | 1499 | } |
---|
| 1500 | } |
---|
| 1501 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1502 | if (anode_matching[it] != INVALID) { |
---|
| 1503 | Node bnode = graph->bNode(anode_matching[it]); |
---|
| 1504 | if (bpred[bnode] != INVALID) { |
---|
| 1505 | anode_potential[it] += bdist[bnode]; |
---|
[2136] | 1506 | } else { |
---|
| 1507 | anode_potential[it] += bdistMax; |
---|
[2051] | 1508 | } |
---|
| 1509 | } |
---|
| 1510 | } |
---|
| 1511 | |
---|
| 1512 | while (bestNode != INVALID) { |
---|
| 1513 | UEdge uedge = bpred[bestNode]; |
---|
| 1514 | Node anode = graph->aNode(uedge); |
---|
| 1515 | |
---|
| 1516 | bnode_matching[bestNode] = uedge; |
---|
| 1517 | if (anode_matching[anode] != INVALID) { |
---|
| 1518 | bestNode = graph->bNode(anode_matching[anode]); |
---|
| 1519 | } else { |
---|
| 1520 | bestNode = INVALID; |
---|
| 1521 | } |
---|
| 1522 | anode_matching[anode] = uedge; |
---|
| 1523 | } |
---|
| 1524 | |
---|
| 1525 | |
---|
| 1526 | return true; |
---|
| 1527 | } |
---|
| 1528 | |
---|
| 1529 | /// \brief Starts the algorithm. |
---|
| 1530 | /// |
---|
| 1531 | /// Starts the algorithm. It runs augmenting phases until the |
---|
| 1532 | /// optimal solution reached. |
---|
| 1533 | void start() { |
---|
| 1534 | while (augment()) {} |
---|
| 1535 | } |
---|
| 1536 | |
---|
| 1537 | /// \brief Runs the algorithm. |
---|
| 1538 | /// |
---|
| 1539 | /// It just initalize the algorithm and then start it. |
---|
| 1540 | void run() { |
---|
| 1541 | init(); |
---|
| 1542 | start(); |
---|
| 1543 | } |
---|
| 1544 | |
---|
| 1545 | /// @} |
---|
| 1546 | |
---|
| 1547 | /// \name Query Functions |
---|
| 1548 | /// The result of the %Matching algorithm can be obtained using these |
---|
| 1549 | /// functions.\n |
---|
| 1550 | /// Before the use of these functions, |
---|
| 1551 | /// either run() or start() must be called. |
---|
| 1552 | |
---|
| 1553 | ///@{ |
---|
| 1554 | |
---|
| 1555 | /// \brief Gives back the potential in the NodeMap |
---|
| 1556 | /// |
---|
[2463] | 1557 | /// Gives back the potential in the NodeMap. The matching is optimal |
---|
| 1558 | /// with the current number of edges if \f$ \pi(a) + \pi(b) - w(ab) = 0 \f$ |
---|
| 1559 | /// for each matching edges and \f$ \pi(a) + \pi(b) - w(ab) \ge 0 \f$ |
---|
| 1560 | /// for each edges. |
---|
[2051] | 1561 | template <typename PotentialMap> |
---|
[2386] | 1562 | void potential(PotentialMap& pt) const { |
---|
[2051] | 1563 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
[2463] | 1564 | pt.set(it, anode_potential[it]); |
---|
[2051] | 1565 | } |
---|
| 1566 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
[2463] | 1567 | pt.set(it, bnode_potential[it]); |
---|
[2051] | 1568 | } |
---|
| 1569 | } |
---|
| 1570 | |
---|
| 1571 | /// \brief Set true all matching uedge in the map. |
---|
| 1572 | /// |
---|
| 1573 | /// Set true all matching uedge in the map. It does not change the |
---|
| 1574 | /// value mapped to the other uedges. |
---|
| 1575 | /// \return The number of the matching edges. |
---|
| 1576 | template <typename MatchingMap> |
---|
[2386] | 1577 | int quickMatching(MatchingMap& mm) const { |
---|
[2051] | 1578 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1579 | if (anode_matching[it] != INVALID) { |
---|
[2463] | 1580 | mm.set(anode_matching[it], true); |
---|
[2051] | 1581 | } |
---|
| 1582 | } |
---|
| 1583 | return matching_size; |
---|
| 1584 | } |
---|
| 1585 | |
---|
| 1586 | /// \brief Set true all matching uedge in the map and the others to false. |
---|
| 1587 | /// |
---|
| 1588 | /// Set true all matching uedge in the map and the others to false. |
---|
| 1589 | /// \return The number of the matching edges. |
---|
| 1590 | template <typename MatchingMap> |
---|
[2386] | 1591 | int matching(MatchingMap& mm) const { |
---|
[2051] | 1592 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
---|
[2463] | 1593 | mm.set(it, it == anode_matching[graph->aNode(it)]); |
---|
[2051] | 1594 | } |
---|
| 1595 | return matching_size; |
---|
| 1596 | } |
---|
| 1597 | |
---|
[2463] | 1598 | /// \brief Gives back the matching in an ANodeMap. |
---|
| 1599 | /// |
---|
| 1600 | /// Gives back the matching in an ANodeMap. The parameter should |
---|
| 1601 | /// be a write ANodeMap of UEdge values. |
---|
| 1602 | /// \return The number of the matching edges. |
---|
| 1603 | template<class MatchingMap> |
---|
| 1604 | int aMatching(MatchingMap& mm) const { |
---|
| 1605 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1606 | mm.set(it, anode_matching[it]); |
---|
| 1607 | } |
---|
| 1608 | return matching_size; |
---|
| 1609 | } |
---|
| 1610 | |
---|
| 1611 | /// \brief Gives back the matching in a BNodeMap. |
---|
| 1612 | /// |
---|
| 1613 | /// Gives back the matching in a BNodeMap. The parameter should |
---|
| 1614 | /// be a write BNodeMap of UEdge values. |
---|
| 1615 | /// \return The number of the matching edges. |
---|
| 1616 | template<class MatchingMap> |
---|
| 1617 | int bMatching(MatchingMap& mm) const { |
---|
| 1618 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
| 1619 | mm.set(it, bnode_matching[it]); |
---|
| 1620 | } |
---|
| 1621 | return matching_size; |
---|
| 1622 | } |
---|
[2051] | 1623 | |
---|
| 1624 | /// \brief Return true if the given uedge is in the matching. |
---|
| 1625 | /// |
---|
| 1626 | /// It returns true if the given uedge is in the matching. |
---|
[2058] | 1627 | bool matchingEdge(const UEdge& edge) const { |
---|
[2051] | 1628 | return anode_matching[graph->aNode(edge)] == edge; |
---|
| 1629 | } |
---|
| 1630 | |
---|
| 1631 | /// \brief Returns the matching edge from the node. |
---|
| 1632 | /// |
---|
| 1633 | /// Returns the matching edge from the node. If there is not such |
---|
| 1634 | /// edge it gives back \c INVALID. |
---|
[2058] | 1635 | UEdge matchingEdge(const Node& node) const { |
---|
[2051] | 1636 | if (graph->aNode(node)) { |
---|
| 1637 | return anode_matching[node]; |
---|
| 1638 | } else { |
---|
| 1639 | return bnode_matching[node]; |
---|
| 1640 | } |
---|
| 1641 | } |
---|
| 1642 | |
---|
| 1643 | /// \brief Gives back the sum of costs of the matching edges. |
---|
| 1644 | /// |
---|
| 1645 | /// Gives back the sum of costs of the matching edges. |
---|
| 1646 | Value matchingCost() const { |
---|
| 1647 | return matching_cost; |
---|
| 1648 | } |
---|
| 1649 | |
---|
| 1650 | /// \brief Gives back the number of the matching edges. |
---|
| 1651 | /// |
---|
| 1652 | /// Gives back the number of the matching edges. |
---|
| 1653 | int matchingSize() const { |
---|
| 1654 | return matching_size; |
---|
| 1655 | } |
---|
| 1656 | |
---|
| 1657 | /// @} |
---|
| 1658 | |
---|
| 1659 | private: |
---|
| 1660 | |
---|
| 1661 | void initStructures() { |
---|
| 1662 | if (!_heap_cross_ref) { |
---|
| 1663 | local_heap_cross_ref = true; |
---|
| 1664 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
| 1665 | } |
---|
| 1666 | if (!_heap) { |
---|
| 1667 | local_heap = true; |
---|
| 1668 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
| 1669 | } |
---|
| 1670 | } |
---|
| 1671 | |
---|
| 1672 | void destroyStructures() { |
---|
| 1673 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
| 1674 | if (local_heap) delete _heap; |
---|
| 1675 | } |
---|
| 1676 | |
---|
| 1677 | |
---|
| 1678 | private: |
---|
| 1679 | |
---|
| 1680 | const BpUGraph *graph; |
---|
| 1681 | const CostMap* cost; |
---|
| 1682 | |
---|
| 1683 | ANodeMatchingMap anode_matching; |
---|
| 1684 | BNodeMatchingMap bnode_matching; |
---|
| 1685 | |
---|
| 1686 | ANodePotentialMap anode_potential; |
---|
| 1687 | BNodePotentialMap bnode_potential; |
---|
| 1688 | |
---|
| 1689 | Value matching_cost; |
---|
| 1690 | int matching_size; |
---|
| 1691 | |
---|
| 1692 | HeapCrossRef *_heap_cross_ref; |
---|
| 1693 | bool local_heap_cross_ref; |
---|
| 1694 | |
---|
| 1695 | Heap *_heap; |
---|
| 1696 | bool local_heap; |
---|
[2040] | 1697 | |
---|
| 1698 | }; |
---|
| 1699 | |
---|
[2058] | 1700 | /// \ingroup matching |
---|
| 1701 | /// |
---|
| 1702 | /// \brief Minimum cost maximum cardinality bipartite matching |
---|
| 1703 | /// |
---|
[2463] | 1704 | /// This function calculates the maximum cardinality matching with |
---|
| 1705 | /// minimum cost of a bipartite graph. It gives back the matching in |
---|
| 1706 | /// an undirected edge map. |
---|
[2058] | 1707 | /// |
---|
| 1708 | /// \param graph The bipartite graph. |
---|
| 1709 | /// \param cost The undirected edge map which contains the costs. |
---|
| 1710 | /// \retval matching The undirected edge map which will be set to |
---|
| 1711 | /// the matching. |
---|
| 1712 | /// \return The cost of the matching. |
---|
| 1713 | template <typename BpUGraph, typename CostMap, typename MatchingMap> |
---|
| 1714 | typename CostMap::Value |
---|
| 1715 | minCostMaxBipartiteMatching(const BpUGraph& graph, |
---|
| 1716 | const CostMap& cost, |
---|
| 1717 | MatchingMap& matching) { |
---|
| 1718 | MinCostMaxBipartiteMatching<BpUGraph, CostMap> |
---|
| 1719 | bpmatching(graph, cost); |
---|
| 1720 | bpmatching.run(); |
---|
| 1721 | bpmatching.matching(matching); |
---|
| 1722 | return bpmatching.matchingCost(); |
---|
| 1723 | } |
---|
| 1724 | |
---|
[2040] | 1725 | } |
---|
| 1726 | |
---|
| 1727 | #endif |
---|