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