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) 2003-2006 |
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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 | namespace lemon { |
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34 | |
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35 | /// \ingroup matching |
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36 | /// |
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37 | /// \brief Bipartite Max Cardinality Matching algorithm |
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38 | /// |
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39 | /// Bipartite Max Cardinality Matching algorithm. This class implements |
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40 | /// the Hopcroft-Karp algorithm which has \f$ O(e\sqrt{n}) \f$ time |
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41 | /// complexity. |
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42 | template <typename BpUGraph> |
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43 | class MaxBipartiteMatching { |
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44 | protected: |
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45 | |
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46 | typedef BpUGraph Graph; |
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47 | |
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48 | typedef typename Graph::Node Node; |
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49 | typedef typename Graph::ANodeIt ANodeIt; |
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50 | typedef typename Graph::BNodeIt BNodeIt; |
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51 | typedef typename Graph::UEdge UEdge; |
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52 | typedef typename Graph::UEdgeIt UEdgeIt; |
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53 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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54 | |
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55 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
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56 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
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57 | |
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58 | |
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59 | public: |
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60 | |
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61 | /// \brief Constructor. |
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62 | /// |
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63 | /// Constructor of the algorithm. |
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64 | MaxBipartiteMatching(const BpUGraph& _graph) |
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65 | : anode_matching(_graph), bnode_matching(_graph), graph(&_graph) {} |
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66 | |
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67 | /// \name Execution control |
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68 | /// The simplest way to execute the algorithm is to use |
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69 | /// one of the member functions called \c run(). |
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70 | /// \n |
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71 | /// If you need more control on the execution, |
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72 | /// first you must call \ref init() or one alternative for it. |
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73 | /// Finally \ref start() will perform the matching computation or |
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74 | /// with step-by-step execution you can augment the solution. |
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75 | |
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76 | /// @{ |
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77 | |
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78 | /// \brief Initalize the data structures. |
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79 | /// |
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80 | /// It initalizes the data structures and creates an empty matching. |
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81 | void init() { |
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82 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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83 | anode_matching[it] = INVALID; |
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84 | } |
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85 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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86 | bnode_matching[it] = INVALID; |
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87 | } |
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88 | matching_size = 0; |
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89 | } |
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90 | |
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91 | /// \brief Initalize the data structures. |
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92 | /// |
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93 | /// It initalizes the data structures and creates a greedy |
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94 | /// matching. From this matching sometimes it is faster to get |
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95 | /// the matching than from the initial empty matching. |
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96 | void greedyInit() { |
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97 | matching_size = 0; |
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98 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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99 | bnode_matching[it] = INVALID; |
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100 | } |
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101 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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102 | anode_matching[it] = INVALID; |
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103 | for (IncEdgeIt jt(*graph, it); jt != INVALID; ++jt) { |
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104 | if (bnode_matching[graph->bNode(jt)] == INVALID) { |
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105 | anode_matching[it] = jt; |
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106 | bnode_matching[graph->bNode(jt)] = jt; |
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107 | ++matching_size; |
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108 | break; |
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109 | } |
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110 | } |
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111 | } |
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112 | } |
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113 | |
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114 | /// \brief Initalize the data structures with an initial matching. |
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115 | /// |
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116 | /// It initalizes the data structures with an initial matching. |
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117 | template <typename MatchingMap> |
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118 | void matchingInit(const MatchingMap& matching) { |
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119 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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120 | anode_matching[it] = INVALID; |
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121 | } |
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122 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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123 | bnode_matching[it] = INVALID; |
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124 | } |
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125 | matching_size = 0; |
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126 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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127 | if (matching[it]) { |
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128 | ++matching_size; |
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129 | anode_matching[graph->aNode(it)] = it; |
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130 | bnode_matching[graph->bNode(it)] = it; |
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131 | } |
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132 | } |
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133 | } |
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134 | |
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135 | /// \brief Initalize the data structures with an initial matching. |
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136 | /// |
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137 | /// It initalizes the data structures with an initial matching. |
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138 | /// \return %True when the given map contains really a matching. |
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139 | template <typename MatchingMap> |
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140 | void checkedMatchingInit(const MatchingMap& matching) { |
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141 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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142 | anode_matching[it] = INVALID; |
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143 | } |
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144 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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145 | bnode_matching[it] = INVALID; |
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146 | } |
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147 | matching_size = 0; |
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148 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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149 | if (matching[it]) { |
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150 | ++matching_size; |
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151 | if (anode_matching[graph->aNode(it)] != INVALID) { |
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152 | return false; |
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153 | } |
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154 | anode_matching[graph->aNode(it)] = it; |
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155 | if (bnode_matching[graph->aNode(it)] != INVALID) { |
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156 | return false; |
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157 | } |
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158 | bnode_matching[graph->bNode(it)] = it; |
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159 | } |
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160 | } |
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161 | return false; |
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162 | } |
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163 | |
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164 | /// \brief An augmenting phase of the Hopcroft-Karp algorithm |
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165 | /// |
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166 | /// It runs an augmenting phase of the Hopcroft-Karp |
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167 | /// algorithm. This phase finds maximum count of edge disjoint |
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168 | /// augmenting paths and augments on these paths. The algorithm |
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169 | /// consists at most of \f$ O(\sqrt{n}) \f$ phase and one phase is |
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170 | /// \f$ O(e) \f$ long. |
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171 | bool augment() { |
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172 | |
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173 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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174 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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175 | |
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176 | typename Graph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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177 | |
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178 | std::vector<Node> queue, bqueue; |
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179 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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180 | if (anode_matching[it] == INVALID) { |
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181 | queue.push_back(it); |
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182 | areached[it] = true; |
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183 | } |
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184 | } |
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185 | |
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186 | bool success = false; |
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187 | |
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188 | while (!success && !queue.empty()) { |
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189 | std::vector<Node> newqueue; |
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190 | for (int i = 0; i < (int)queue.size(); ++i) { |
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191 | Node anode = queue[i]; |
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192 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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193 | Node bnode = graph->bNode(jt); |
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194 | if (breached[bnode]) continue; |
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195 | breached[bnode] = true; |
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196 | bpred[bnode] = jt; |
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197 | if (bnode_matching[bnode] == INVALID) { |
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198 | bqueue.push_back(bnode); |
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199 | success = true; |
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200 | } else { |
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201 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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202 | if (!areached[newanode]) { |
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203 | areached[newanode] = true; |
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204 | newqueue.push_back(newanode); |
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205 | } |
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206 | } |
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207 | } |
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208 | } |
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209 | queue.swap(newqueue); |
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210 | } |
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211 | |
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212 | if (success) { |
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213 | |
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214 | typename Graph::template ANodeMap<bool> aused(*graph, false); |
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215 | |
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216 | for (int i = 0; i < (int)bqueue.size(); ++i) { |
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217 | Node bnode = bqueue[i]; |
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218 | |
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219 | bool used = false; |
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220 | |
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221 | while (bnode != INVALID) { |
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222 | UEdge uedge = bpred[bnode]; |
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223 | Node anode = graph->aNode(uedge); |
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224 | |
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225 | if (aused[anode]) { |
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226 | used = true; |
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227 | break; |
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228 | } |
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229 | |
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230 | bnode = anode_matching[anode] != INVALID ? |
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231 | graph->bNode(anode_matching[anode]) : INVALID; |
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232 | |
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233 | } |
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234 | |
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235 | if (used) continue; |
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236 | |
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237 | bnode = bqueue[i]; |
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238 | while (bnode != INVALID) { |
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239 | UEdge uedge = bpred[bnode]; |
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240 | Node anode = graph->aNode(uedge); |
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241 | |
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242 | bnode_matching[bnode] = uedge; |
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243 | |
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244 | bnode = anode_matching[anode] != INVALID ? |
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245 | graph->bNode(anode_matching[anode]) : INVALID; |
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246 | |
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247 | anode_matching[anode] = uedge; |
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248 | |
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249 | aused[anode] = true; |
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250 | } |
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251 | ++matching_size; |
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252 | |
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253 | } |
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254 | } |
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255 | return success; |
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256 | } |
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257 | |
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258 | /// \brief An augmenting phase of the Ford-Fulkerson algorithm |
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259 | /// |
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260 | /// It runs an augmenting phase of the Ford-Fulkerson |
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261 | /// algorithm. This phase finds only one augmenting path and |
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262 | /// augments only on this paths. The algorithm consists at most |
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263 | /// of \f$ O(n) \f$ simple phase and one phase is at most |
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264 | /// \f$ O(e) \f$ long. |
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265 | bool simpleAugment() { |
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266 | |
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267 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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268 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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269 | |
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270 | typename Graph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
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271 | |
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272 | std::vector<Node> queue; |
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273 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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274 | if (anode_matching[it] == INVALID) { |
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275 | queue.push_back(it); |
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276 | areached[it] = true; |
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277 | } |
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278 | } |
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279 | |
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280 | while (!queue.empty()) { |
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281 | std::vector<Node> newqueue; |
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282 | for (int i = 0; i < (int)queue.size(); ++i) { |
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283 | Node anode = queue[i]; |
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284 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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285 | Node bnode = graph->bNode(jt); |
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286 | if (breached[bnode]) continue; |
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287 | breached[bnode] = true; |
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288 | bpred[bnode] = jt; |
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289 | if (bnode_matching[bnode] == INVALID) { |
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290 | while (bnode != INVALID) { |
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291 | UEdge uedge = bpred[bnode]; |
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292 | anode = graph->aNode(uedge); |
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293 | |
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294 | bnode_matching[bnode] = uedge; |
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295 | |
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296 | bnode = anode_matching[anode] != INVALID ? |
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297 | graph->bNode(anode_matching[anode]) : INVALID; |
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298 | |
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299 | anode_matching[anode] = uedge; |
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300 | |
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301 | } |
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302 | ++matching_size; |
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303 | return true; |
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304 | } else { |
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305 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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306 | if (!areached[newanode]) { |
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307 | areached[newanode] = true; |
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308 | newqueue.push_back(newanode); |
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309 | } |
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310 | } |
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311 | } |
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312 | } |
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313 | queue.swap(newqueue); |
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314 | } |
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315 | |
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316 | return false; |
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317 | } |
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318 | |
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319 | /// \brief Starts the algorithm. |
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320 | /// |
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321 | /// Starts the algorithm. It runs augmenting phases until the optimal |
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322 | /// solution reached. |
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323 | void start() { |
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324 | while (augment()) {} |
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325 | } |
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326 | |
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327 | /// \brief Runs the algorithm. |
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328 | /// |
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329 | /// It just initalize the algorithm and then start it. |
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330 | void run() { |
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331 | greedyInit(); |
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332 | start(); |
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333 | } |
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334 | |
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335 | /// @} |
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336 | |
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337 | /// \name Query Functions |
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338 | /// The result of the %Matching algorithm can be obtained using these |
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339 | /// functions.\n |
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340 | /// Before the use of these functions, |
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341 | /// either run() or start() must be called. |
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342 | |
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343 | ///@{ |
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344 | |
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345 | /// \brief Returns an minimum covering of the nodes. |
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346 | /// |
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347 | /// The minimum covering set problem is the dual solution of the |
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348 | /// maximum bipartite matching. It provides an solution for this |
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349 | /// problem what is proof of the optimality of the matching. |
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350 | /// \return The size of the cover set. |
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351 | template <typename CoverMap> |
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352 | int coverSet(CoverMap& covering) const { |
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353 | |
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354 | typename Graph::template ANodeMap<bool> areached(*graph, false); |
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355 | typename Graph::template BNodeMap<bool> breached(*graph, false); |
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356 | |
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357 | std::vector<Node> queue; |
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358 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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359 | if (anode_matching[it] == INVALID) { |
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360 | queue.push_back(it); |
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361 | } |
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362 | } |
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363 | |
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364 | while (!queue.empty()) { |
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365 | std::vector<Node> newqueue; |
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366 | for (int i = 0; i < (int)queue.size(); ++i) { |
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367 | Node anode = queue[i]; |
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368 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
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369 | Node bnode = graph->bNode(jt); |
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370 | if (breached[bnode]) continue; |
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371 | breached[bnode] = true; |
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372 | if (bnode_matching[bnode] != INVALID) { |
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373 | Node newanode = graph->aNode(bnode_matching[bnode]); |
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374 | if (!areached[newanode]) { |
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375 | areached[newanode] = true; |
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376 | newqueue.push_back(newanode); |
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377 | } |
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378 | } |
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379 | } |
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380 | } |
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381 | queue.swap(newqueue); |
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382 | } |
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383 | |
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384 | int size = 0; |
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385 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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386 | covering[it] = !areached[it] && anode_matching[it] != INVALID; |
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387 | if (!areached[it] && anode_matching[it] != INVALID) { |
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388 | ++size; |
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389 | } |
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390 | } |
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391 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
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392 | covering[it] = breached[it]; |
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393 | if (breached[it]) { |
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394 | ++size; |
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395 | } |
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396 | } |
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397 | return size; |
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398 | } |
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399 | |
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400 | /// \brief Set true all matching uedge in the map. |
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401 | /// |
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402 | /// Set true all matching uedge in the map. It does not change the |
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403 | /// value mapped to the other uedges. |
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404 | /// \return The number of the matching edges. |
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405 | template <typename MatchingMap> |
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406 | int quickMatching(MatchingMap& matching) const { |
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407 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
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408 | if (anode_matching[it] != INVALID) { |
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409 | matching[anode_matching[it]] = true; |
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410 | } |
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411 | } |
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412 | return matching_size; |
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413 | } |
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414 | |
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415 | /// \brief Set true all matching uedge in the map and the others to false. |
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416 | /// |
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417 | /// Set true all matching uedge in the map and the others to false. |
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418 | /// \return The number of the matching edges. |
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419 | template <typename MatchingMap> |
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420 | int matching(MatchingMap& matching) const { |
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421 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
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422 | matching[it] = it == anode_matching[graph->aNode(it)]; |
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423 | } |
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424 | return matching_size; |
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425 | } |
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426 | |
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427 | |
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428 | /// \brief Return true if the given uedge is in the matching. |
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429 | /// |
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430 | /// It returns true if the given uedge is in the matching. |
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431 | bool matchingEdge(const UEdge& edge) const { |
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432 | return anode_matching[graph->aNode(edge)] == edge; |
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433 | } |
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434 | |
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435 | /// \brief Returns the matching edge from the node. |
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436 | /// |
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437 | /// Returns the matching edge from the node. If there is not such |
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438 | /// edge it gives back \c INVALID. |
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439 | UEdge matchingEdge(const Node& node) const { |
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440 | if (graph->aNode(node)) { |
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441 | return anode_matching[node]; |
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442 | } else { |
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443 | return bnode_matching[node]; |
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444 | } |
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445 | } |
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446 | |
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447 | /// \brief Gives back the number of the matching edges. |
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448 | /// |
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449 | /// Gives back the number of the matching edges. |
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450 | int matchingSize() const { |
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451 | return matching_size; |
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452 | } |
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453 | |
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454 | /// @} |
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455 | |
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456 | private: |
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457 | |
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458 | ANodeMatchingMap anode_matching; |
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459 | BNodeMatchingMap bnode_matching; |
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460 | const Graph *graph; |
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461 | |
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462 | int matching_size; |
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463 | |
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464 | }; |
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465 | |
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466 | /// \ingroup matching |
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467 | /// |
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468 | /// \brief Maximum cardinality bipartite matching |
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469 | /// |
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470 | /// This function calculates the maximum cardinality matching |
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471 | /// in a bipartite graph. It gives back the matching in an undirected |
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472 | /// edge map. |
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473 | /// |
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474 | /// \param graph The bipartite graph. |
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475 | /// \retval matching The undirected edge map which will be set to |
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476 | /// the matching. |
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477 | /// \return The size of the matching. |
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478 | template <typename BpUGraph, typename MatchingMap> |
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479 | int maxBipartiteMatching(const BpUGraph& graph, MatchingMap& matching) { |
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480 | MaxBipartiteMatching<BpUGraph> bpmatching(graph); |
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481 | bpmatching.run(); |
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482 | bpmatching.matching(matching); |
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483 | return bpmatching.matchingSize(); |
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484 | } |
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485 | |
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486 | /// \brief Default traits class for weighted bipartite matching algoritms. |
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487 | /// |
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488 | /// Default traits class for weighted bipartite matching algoritms. |
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489 | /// \param _BpUGraph The bipartite undirected graph type. |
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490 | /// \param _WeightMap Type of weight map. |
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491 | template <typename _BpUGraph, typename _WeightMap> |
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492 | struct WeightedBipartiteMatchingDefaultTraits { |
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493 | /// \brief The type of the weight of the undirected edges. |
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494 | typedef typename _WeightMap::Value Value; |
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495 | |
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496 | /// The undirected bipartite graph type the algorithm runs on. |
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497 | typedef _BpUGraph BpUGraph; |
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498 | |
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499 | /// The map of the edges weights |
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500 | typedef _WeightMap WeightMap; |
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501 | |
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502 | /// \brief The cross reference type used by heap. |
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503 | /// |
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504 | /// The cross reference type used by heap. |
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505 | /// Usually it is \c Graph::NodeMap<int>. |
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506 | typedef typename BpUGraph::template NodeMap<int> HeapCrossRef; |
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507 | |
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508 | /// \brief Instantiates a HeapCrossRef. |
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509 | /// |
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510 | /// This function instantiates a \ref HeapCrossRef. |
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511 | /// \param graph is the graph, to which we would like to define the |
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512 | /// HeapCrossRef. |
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513 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
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514 | return new HeapCrossRef(graph); |
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515 | } |
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516 | |
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517 | /// \brief The heap type used by weighted matching algorithms. |
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518 | /// |
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519 | /// The heap type used by weighted matching algorithms. It should |
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520 | /// minimize the priorities and the heap's key type is the graph's |
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521 | /// anode graph's node. |
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522 | /// |
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523 | /// \sa BinHeap |
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524 | typedef BinHeap<Value, HeapCrossRef> Heap; |
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525 | |
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526 | /// \brief Instantiates a Heap. |
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527 | /// |
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528 | /// This function instantiates a \ref Heap. |
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529 | /// \param crossref The cross reference of the heap. |
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530 | static Heap *createHeap(HeapCrossRef& crossref) { |
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531 | return new Heap(crossref); |
---|
532 | } |
---|
533 | |
---|
534 | }; |
---|
535 | |
---|
536 | |
---|
537 | /// \ingroup matching |
---|
538 | /// |
---|
539 | /// \brief Bipartite Max Weighted Matching algorithm |
---|
540 | /// |
---|
541 | /// This class implements the bipartite Max Weighted Matching |
---|
542 | /// algorithm. It uses the successive shortest path algorithm to |
---|
543 | /// calculate the maximum weighted matching in the bipartite |
---|
544 | /// graph. The algorithm can be used also to calculate the maximum |
---|
545 | /// cardinality maximum weighted matching. The time complexity |
---|
546 | /// of the algorithm is \f$ O(ne\log(n)) \f$ with the default binary |
---|
547 | /// heap implementation but this can be improved to |
---|
548 | /// \f$ O(n^2\log(n)+ne) \f$ if we use fibonacci heaps. |
---|
549 | /// |
---|
550 | /// The algorithm also provides a potential function on the nodes |
---|
551 | /// which a dual solution of the matching algorithm and it can be |
---|
552 | /// used to proof the optimality of the given pimal solution. |
---|
553 | #ifdef DOXYGEN |
---|
554 | template <typename _BpUGraph, typename _WeightMap, typename _Traits> |
---|
555 | #else |
---|
556 | template <typename _BpUGraph, |
---|
557 | typename _WeightMap = typename _BpUGraph::template UEdgeMap<int>, |
---|
558 | typename _Traits = WeightedBipartiteMatchingDefaultTraits<_BpUGraph, _WeightMap> > |
---|
559 | #endif |
---|
560 | class MaxWeightedBipartiteMatching { |
---|
561 | public: |
---|
562 | |
---|
563 | typedef _Traits Traits; |
---|
564 | typedef typename Traits::BpUGraph BpUGraph; |
---|
565 | typedef typename Traits::WeightMap WeightMap; |
---|
566 | typedef typename Traits::Value Value; |
---|
567 | |
---|
568 | protected: |
---|
569 | |
---|
570 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
571 | typedef typename Traits::Heap Heap; |
---|
572 | |
---|
573 | |
---|
574 | typedef typename BpUGraph::Node Node; |
---|
575 | typedef typename BpUGraph::ANodeIt ANodeIt; |
---|
576 | typedef typename BpUGraph::BNodeIt BNodeIt; |
---|
577 | typedef typename BpUGraph::UEdge UEdge; |
---|
578 | typedef typename BpUGraph::UEdgeIt UEdgeIt; |
---|
579 | typedef typename BpUGraph::IncEdgeIt IncEdgeIt; |
---|
580 | |
---|
581 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
---|
582 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
---|
583 | |
---|
584 | typedef typename BpUGraph::template ANodeMap<Value> ANodePotentialMap; |
---|
585 | typedef typename BpUGraph::template BNodeMap<Value> BNodePotentialMap; |
---|
586 | |
---|
587 | |
---|
588 | public: |
---|
589 | |
---|
590 | /// \brief \ref Exception for uninitialized parameters. |
---|
591 | /// |
---|
592 | /// This error represents problems in the initialization |
---|
593 | /// of the parameters of the algorithms. |
---|
594 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
595 | public: |
---|
596 | virtual const char* what() const throw() { |
---|
597 | return "lemon::MaxWeightedBipartiteMatching::UninitializedParameter"; |
---|
598 | } |
---|
599 | }; |
---|
600 | |
---|
601 | ///\name Named template parameters |
---|
602 | |
---|
603 | ///@{ |
---|
604 | |
---|
605 | template <class H, class CR> |
---|
606 | struct DefHeapTraits : public Traits { |
---|
607 | typedef CR HeapCrossRef; |
---|
608 | typedef H Heap; |
---|
609 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &) { |
---|
610 | throw UninitializedParameter(); |
---|
611 | } |
---|
612 | static Heap *createHeap(HeapCrossRef &) { |
---|
613 | throw UninitializedParameter(); |
---|
614 | } |
---|
615 | }; |
---|
616 | |
---|
617 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
618 | /// and cross reference type |
---|
619 | /// |
---|
620 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
621 | /// reference type |
---|
622 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
623 | struct DefHeap |
---|
624 | : public MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
625 | DefHeapTraits<H, CR> > { |
---|
626 | typedef MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
627 | DefHeapTraits<H, CR> > Create; |
---|
628 | }; |
---|
629 | |
---|
630 | template <class H, class CR> |
---|
631 | struct DefStandardHeapTraits : public Traits { |
---|
632 | typedef CR HeapCrossRef; |
---|
633 | typedef H Heap; |
---|
634 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
635 | return new HeapCrossRef(graph); |
---|
636 | } |
---|
637 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
638 | return new Heap(crossref); |
---|
639 | } |
---|
640 | }; |
---|
641 | |
---|
642 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
643 | /// cross reference type with automatic allocation |
---|
644 | /// |
---|
645 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
646 | /// reference type. It can allocate the heap and the cross reference |
---|
647 | /// object if the cross reference's constructor waits for the graph as |
---|
648 | /// parameter and the heap's constructor waits for the cross reference. |
---|
649 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
650 | struct DefStandardHeap |
---|
651 | : public MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
652 | DefStandardHeapTraits<H, CR> > { |
---|
653 | typedef MaxWeightedBipartiteMatching<BpUGraph, WeightMap, |
---|
654 | DefStandardHeapTraits<H, CR> > |
---|
655 | Create; |
---|
656 | }; |
---|
657 | |
---|
658 | ///@} |
---|
659 | |
---|
660 | |
---|
661 | /// \brief Constructor. |
---|
662 | /// |
---|
663 | /// Constructor of the algorithm. |
---|
664 | MaxWeightedBipartiteMatching(const BpUGraph& _graph, |
---|
665 | const WeightMap& _weight) |
---|
666 | : graph(&_graph), weight(&_weight), |
---|
667 | anode_matching(_graph), bnode_matching(_graph), |
---|
668 | anode_potential(_graph), bnode_potential(_graph), |
---|
669 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
670 | _heap(0), local_heap(0) {} |
---|
671 | |
---|
672 | /// \brief Destructor. |
---|
673 | /// |
---|
674 | /// Destructor of the algorithm. |
---|
675 | ~MaxWeightedBipartiteMatching() { |
---|
676 | destroyStructures(); |
---|
677 | } |
---|
678 | |
---|
679 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
680 | /// |
---|
681 | /// Sets the heap and the cross reference used by algorithm. |
---|
682 | /// If you don't use this function before calling \ref run(), |
---|
683 | /// it will allocate one. The destuctor deallocates this |
---|
684 | /// automatically allocated map, of course. |
---|
685 | /// \return \c (*this) |
---|
686 | MaxWeightedBipartiteMatching& heap(Heap& heap, HeapCrossRef &crossRef) { |
---|
687 | if(local_heap_cross_ref) { |
---|
688 | delete _heap_cross_ref; |
---|
689 | local_heap_cross_ref = false; |
---|
690 | } |
---|
691 | _heap_cross_ref = &crossRef; |
---|
692 | if(local_heap) { |
---|
693 | delete _heap; |
---|
694 | local_heap = false; |
---|
695 | } |
---|
696 | _heap = &heap; |
---|
697 | return *this; |
---|
698 | } |
---|
699 | |
---|
700 | /// \name Execution control |
---|
701 | /// The simplest way to execute the algorithm is to use |
---|
702 | /// one of the member functions called \c run(). |
---|
703 | /// \n |
---|
704 | /// If you need more control on the execution, |
---|
705 | /// first you must call \ref init() or one alternative for it. |
---|
706 | /// Finally \ref start() will perform the matching computation or |
---|
707 | /// with step-by-step execution you can augment the solution. |
---|
708 | |
---|
709 | /// @{ |
---|
710 | |
---|
711 | /// \brief Initalize the data structures. |
---|
712 | /// |
---|
713 | /// It initalizes the data structures and creates an empty matching. |
---|
714 | void init() { |
---|
715 | initStructures(); |
---|
716 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
717 | anode_matching[it] = INVALID; |
---|
718 | anode_potential[it] = 0; |
---|
719 | } |
---|
720 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
721 | bnode_matching[it] = INVALID; |
---|
722 | bnode_potential[it] = 0; |
---|
723 | for (IncEdgeIt jt(*graph, it); jt != INVALID; ++jt) { |
---|
724 | if ((*weight)[jt] > bnode_potential[it]) { |
---|
725 | bnode_potential[it] = (*weight)[jt]; |
---|
726 | } |
---|
727 | } |
---|
728 | } |
---|
729 | matching_value = 0; |
---|
730 | matching_size = 0; |
---|
731 | } |
---|
732 | |
---|
733 | |
---|
734 | /// \brief An augmenting phase of the weighted matching algorithm |
---|
735 | /// |
---|
736 | /// It runs an augmenting phase of the weighted matching |
---|
737 | /// algorithm. This phase finds the best augmenting path and |
---|
738 | /// augments only on this paths. |
---|
739 | /// |
---|
740 | /// The algorithm consists at most |
---|
741 | /// of \f$ O(n) \f$ phase and one phase is \f$ O(n\log(n)+e) \f$ |
---|
742 | /// long with Fibonacci heap or \f$ O((n+e)\log(n)) \f$ long |
---|
743 | /// with binary heap. |
---|
744 | /// \param decrease If the given parameter true the matching value |
---|
745 | /// can be decreased in the augmenting phase. If we would like |
---|
746 | /// to calculate the maximum cardinality maximum weighted matching |
---|
747 | /// then we should let the algorithm to decrease the matching |
---|
748 | /// value in order to increase the number of the matching edges. |
---|
749 | bool augment(bool decrease = false) { |
---|
750 | |
---|
751 | typename BpUGraph::template BNodeMap<Value> bdist(*graph); |
---|
752 | typename BpUGraph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
---|
753 | |
---|
754 | Node bestNode = INVALID; |
---|
755 | Value bestValue = 0; |
---|
756 | |
---|
757 | _heap->clear(); |
---|
758 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
759 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
---|
760 | } |
---|
761 | |
---|
762 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
763 | if (anode_matching[it] == INVALID) { |
---|
764 | _heap->push(it, 0); |
---|
765 | } |
---|
766 | } |
---|
767 | |
---|
768 | Value bdistMax = 0; |
---|
769 | while (!_heap->empty()) { |
---|
770 | Node anode = _heap->top(); |
---|
771 | Value avalue = _heap->prio(); |
---|
772 | _heap->pop(); |
---|
773 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
774 | if (jt == anode_matching[anode]) continue; |
---|
775 | Node bnode = graph->bNode(jt); |
---|
776 | Value bvalue = avalue - (*weight)[jt] + |
---|
777 | anode_potential[anode] + bnode_potential[bnode]; |
---|
778 | if (bpred[bnode] == INVALID || bvalue < bdist[bnode]) { |
---|
779 | bdist[bnode] = bvalue; |
---|
780 | bpred[bnode] = jt; |
---|
781 | } |
---|
782 | if (bvalue > bdistMax) { |
---|
783 | bdistMax = bvalue; |
---|
784 | } |
---|
785 | if (bnode_matching[bnode] != INVALID) { |
---|
786 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
787 | switch (_heap->state(newanode)) { |
---|
788 | case Heap::PRE_HEAP: |
---|
789 | _heap->push(newanode, bvalue); |
---|
790 | break; |
---|
791 | case Heap::IN_HEAP: |
---|
792 | if (bvalue < (*_heap)[newanode]) { |
---|
793 | _heap->decrease(newanode, bvalue); |
---|
794 | } |
---|
795 | break; |
---|
796 | case Heap::POST_HEAP: |
---|
797 | break; |
---|
798 | } |
---|
799 | } else { |
---|
800 | if (bestNode == INVALID || |
---|
801 | bnode_potential[bnode] - bvalue > bestValue) { |
---|
802 | bestValue = bnode_potential[bnode] - bvalue; |
---|
803 | bestNode = bnode; |
---|
804 | } |
---|
805 | } |
---|
806 | } |
---|
807 | } |
---|
808 | |
---|
809 | if (bestNode == INVALID || (!decrease && bestValue < 0)) { |
---|
810 | return false; |
---|
811 | } |
---|
812 | |
---|
813 | matching_value += bestValue; |
---|
814 | ++matching_size; |
---|
815 | |
---|
816 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
817 | if (bpred[it] != INVALID) { |
---|
818 | bnode_potential[it] -= bdist[it]; |
---|
819 | } else { |
---|
820 | bnode_potential[it] -= bdistMax; |
---|
821 | } |
---|
822 | } |
---|
823 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
824 | if (anode_matching[it] != INVALID) { |
---|
825 | Node bnode = graph->bNode(anode_matching[it]); |
---|
826 | if (bpred[bnode] != INVALID) { |
---|
827 | anode_potential[it] += bdist[bnode]; |
---|
828 | } else { |
---|
829 | anode_potential[it] += bdistMax; |
---|
830 | } |
---|
831 | } |
---|
832 | } |
---|
833 | |
---|
834 | while (bestNode != INVALID) { |
---|
835 | UEdge uedge = bpred[bestNode]; |
---|
836 | Node anode = graph->aNode(uedge); |
---|
837 | |
---|
838 | bnode_matching[bestNode] = uedge; |
---|
839 | if (anode_matching[anode] != INVALID) { |
---|
840 | bestNode = graph->bNode(anode_matching[anode]); |
---|
841 | } else { |
---|
842 | bestNode = INVALID; |
---|
843 | } |
---|
844 | anode_matching[anode] = uedge; |
---|
845 | } |
---|
846 | |
---|
847 | |
---|
848 | return true; |
---|
849 | } |
---|
850 | |
---|
851 | /// \brief Starts the algorithm. |
---|
852 | /// |
---|
853 | /// Starts the algorithm. It runs augmenting phases until the |
---|
854 | /// optimal solution reached. |
---|
855 | /// |
---|
856 | /// \param maxCardinality If the given value is true it will |
---|
857 | /// calculate the maximum cardinality maximum matching instead of |
---|
858 | /// the maximum matching. |
---|
859 | void start(bool maxCardinality = false) { |
---|
860 | while (augment(maxCardinality)) {} |
---|
861 | } |
---|
862 | |
---|
863 | /// \brief Runs the algorithm. |
---|
864 | /// |
---|
865 | /// It just initalize the algorithm and then start it. |
---|
866 | /// |
---|
867 | /// \param maxCardinality If the given value is true it will |
---|
868 | /// calculate the maximum cardinality maximum matching instead of |
---|
869 | /// the maximum matching. |
---|
870 | void run(bool maxCardinality = false) { |
---|
871 | init(); |
---|
872 | start(maxCardinality); |
---|
873 | } |
---|
874 | |
---|
875 | /// @} |
---|
876 | |
---|
877 | /// \name Query Functions |
---|
878 | /// The result of the %Matching algorithm can be obtained using these |
---|
879 | /// functions.\n |
---|
880 | /// Before the use of these functions, |
---|
881 | /// either run() or start() must be called. |
---|
882 | |
---|
883 | ///@{ |
---|
884 | |
---|
885 | /// \brief Gives back the potential in the NodeMap |
---|
886 | /// |
---|
887 | /// Gives back the potential in the NodeMap. The matching is optimal |
---|
888 | /// with the current number of edges if \f$ \pi(a) + \pi(b) - w(ab) = 0 \f$ |
---|
889 | /// for each matching edges and \f$ \pi(a) + \pi(b) - w(ab) \ge 0 \f$ |
---|
890 | /// for each edges. |
---|
891 | template <typename PotentialMap> |
---|
892 | void potential(PotentialMap& potential) const { |
---|
893 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
894 | potential[it] = anode_potential[it]; |
---|
895 | } |
---|
896 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
897 | potential[it] = bnode_potential[it]; |
---|
898 | } |
---|
899 | } |
---|
900 | |
---|
901 | /// \brief Set true all matching uedge in the map. |
---|
902 | /// |
---|
903 | /// Set true all matching uedge in the map. It does not change the |
---|
904 | /// value mapped to the other uedges. |
---|
905 | /// \return The number of the matching edges. |
---|
906 | template <typename MatchingMap> |
---|
907 | int quickMatching(MatchingMap& matching) const { |
---|
908 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
909 | if (anode_matching[it] != INVALID) { |
---|
910 | matching[anode_matching[it]] = true; |
---|
911 | } |
---|
912 | } |
---|
913 | return matching_size; |
---|
914 | } |
---|
915 | |
---|
916 | /// \brief Set true all matching uedge in the map and the others to false. |
---|
917 | /// |
---|
918 | /// Set true all matching uedge in the map and the others to false. |
---|
919 | /// \return The number of the matching edges. |
---|
920 | template <typename MatchingMap> |
---|
921 | int matching(MatchingMap& matching) const { |
---|
922 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
---|
923 | matching[it] = it == anode_matching[graph->aNode(it)]; |
---|
924 | } |
---|
925 | return matching_size; |
---|
926 | } |
---|
927 | |
---|
928 | |
---|
929 | /// \brief Return true if the given uedge is in the matching. |
---|
930 | /// |
---|
931 | /// It returns true if the given uedge is in the matching. |
---|
932 | bool matchingEdge(const UEdge& edge) const { |
---|
933 | return anode_matching[graph->aNode(edge)] == edge; |
---|
934 | } |
---|
935 | |
---|
936 | /// \brief Returns the matching edge from the node. |
---|
937 | /// |
---|
938 | /// Returns the matching edge from the node. If there is not such |
---|
939 | /// edge it gives back \c INVALID. |
---|
940 | UEdge matchingEdge(const Node& node) const { |
---|
941 | if (graph->aNode(node)) { |
---|
942 | return anode_matching[node]; |
---|
943 | } else { |
---|
944 | return bnode_matching[node]; |
---|
945 | } |
---|
946 | } |
---|
947 | |
---|
948 | /// \brief Gives back the sum of weights of the matching edges. |
---|
949 | /// |
---|
950 | /// Gives back the sum of weights of the matching edges. |
---|
951 | Value matchingValue() const { |
---|
952 | return matching_value; |
---|
953 | } |
---|
954 | |
---|
955 | /// \brief Gives back the number of the matching edges. |
---|
956 | /// |
---|
957 | /// Gives back the number of the matching edges. |
---|
958 | int matchingSize() const { |
---|
959 | return matching_size; |
---|
960 | } |
---|
961 | |
---|
962 | /// @} |
---|
963 | |
---|
964 | private: |
---|
965 | |
---|
966 | void initStructures() { |
---|
967 | if (!_heap_cross_ref) { |
---|
968 | local_heap_cross_ref = true; |
---|
969 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
970 | } |
---|
971 | if (!_heap) { |
---|
972 | local_heap = true; |
---|
973 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
974 | } |
---|
975 | } |
---|
976 | |
---|
977 | void destroyStructures() { |
---|
978 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
979 | if (local_heap) delete _heap; |
---|
980 | } |
---|
981 | |
---|
982 | |
---|
983 | private: |
---|
984 | |
---|
985 | const BpUGraph *graph; |
---|
986 | const WeightMap* weight; |
---|
987 | |
---|
988 | ANodeMatchingMap anode_matching; |
---|
989 | BNodeMatchingMap bnode_matching; |
---|
990 | |
---|
991 | ANodePotentialMap anode_potential; |
---|
992 | BNodePotentialMap bnode_potential; |
---|
993 | |
---|
994 | Value matching_value; |
---|
995 | int matching_size; |
---|
996 | |
---|
997 | HeapCrossRef *_heap_cross_ref; |
---|
998 | bool local_heap_cross_ref; |
---|
999 | |
---|
1000 | Heap *_heap; |
---|
1001 | bool local_heap; |
---|
1002 | |
---|
1003 | }; |
---|
1004 | |
---|
1005 | /// \ingroup matching |
---|
1006 | /// |
---|
1007 | /// \brief Maximum weighted bipartite matching |
---|
1008 | /// |
---|
1009 | /// This function calculates the maximum weighted matching |
---|
1010 | /// in a bipartite graph. It gives back the matching in an undirected |
---|
1011 | /// edge map. |
---|
1012 | /// |
---|
1013 | /// \param graph The bipartite graph. |
---|
1014 | /// \param weight The undirected edge map which contains the weights. |
---|
1015 | /// \retval matching The undirected edge map which will be set to |
---|
1016 | /// the matching. |
---|
1017 | /// \return The value of the matching. |
---|
1018 | template <typename BpUGraph, typename WeightMap, typename MatchingMap> |
---|
1019 | typename WeightMap::Value |
---|
1020 | maxWeightedBipartiteMatching(const BpUGraph& graph, const WeightMap& weight, |
---|
1021 | MatchingMap& matching) { |
---|
1022 | MaxWeightedBipartiteMatching<BpUGraph, WeightMap> |
---|
1023 | bpmatching(graph, weight); |
---|
1024 | bpmatching.run(); |
---|
1025 | bpmatching.matching(matching); |
---|
1026 | return bpmatching.matchingValue(); |
---|
1027 | } |
---|
1028 | |
---|
1029 | /// \ingroup matching |
---|
1030 | /// |
---|
1031 | /// \brief Maximum weighted maximum cardinality bipartite matching |
---|
1032 | /// |
---|
1033 | /// This function calculates the maximum weighted of the maximum cardinality |
---|
1034 | /// matchings of a bipartite graph. It gives back the matching in an |
---|
1035 | /// undirected edge map. |
---|
1036 | /// |
---|
1037 | /// \param graph The bipartite graph. |
---|
1038 | /// \param weight The undirected edge map which contains the weights. |
---|
1039 | /// \retval matching The undirected edge map which will be set to |
---|
1040 | /// the matching. |
---|
1041 | /// \return The value of the matching. |
---|
1042 | template <typename BpUGraph, typename WeightMap, typename MatchingMap> |
---|
1043 | typename WeightMap::Value |
---|
1044 | maxWeightedMaxBipartiteMatching(const BpUGraph& graph, |
---|
1045 | const WeightMap& weight, |
---|
1046 | MatchingMap& matching) { |
---|
1047 | MaxWeightedBipartiteMatching<BpUGraph, WeightMap> |
---|
1048 | bpmatching(graph, weight); |
---|
1049 | bpmatching.run(true); |
---|
1050 | bpmatching.matching(matching); |
---|
1051 | return bpmatching.matchingValue(); |
---|
1052 | } |
---|
1053 | |
---|
1054 | /// \brief Default traits class for minimum cost bipartite matching |
---|
1055 | /// algoritms. |
---|
1056 | /// |
---|
1057 | /// Default traits class for minimum cost bipartite matching |
---|
1058 | /// algoritms. |
---|
1059 | /// |
---|
1060 | /// \param _BpUGraph The bipartite undirected graph |
---|
1061 | /// type. |
---|
1062 | /// |
---|
1063 | /// \param _CostMap Type of cost map. |
---|
1064 | template <typename _BpUGraph, typename _CostMap> |
---|
1065 | struct MinCostMaxBipartiteMatchingDefaultTraits { |
---|
1066 | /// \brief The type of the cost of the undirected edges. |
---|
1067 | typedef typename _CostMap::Value Value; |
---|
1068 | |
---|
1069 | /// The undirected bipartite graph type the algorithm runs on. |
---|
1070 | typedef _BpUGraph BpUGraph; |
---|
1071 | |
---|
1072 | /// The map of the edges costs |
---|
1073 | typedef _CostMap CostMap; |
---|
1074 | |
---|
1075 | /// \brief The cross reference type used by heap. |
---|
1076 | /// |
---|
1077 | /// The cross reference type used by heap. |
---|
1078 | /// Usually it is \c Graph::NodeMap<int>. |
---|
1079 | typedef typename BpUGraph::template NodeMap<int> HeapCrossRef; |
---|
1080 | |
---|
1081 | /// \brief Instantiates a HeapCrossRef. |
---|
1082 | /// |
---|
1083 | /// This function instantiates a \ref HeapCrossRef. |
---|
1084 | /// \param graph is the graph, to which we would like to define the |
---|
1085 | /// HeapCrossRef. |
---|
1086 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
1087 | return new HeapCrossRef(graph); |
---|
1088 | } |
---|
1089 | |
---|
1090 | /// \brief The heap type used by costed matching algorithms. |
---|
1091 | /// |
---|
1092 | /// The heap type used by costed matching algorithms. It should |
---|
1093 | /// minimize the priorities and the heap's key type is the graph's |
---|
1094 | /// anode graph's node. |
---|
1095 | /// |
---|
1096 | /// \sa BinHeap |
---|
1097 | typedef BinHeap<Value, HeapCrossRef> Heap; |
---|
1098 | |
---|
1099 | /// \brief Instantiates a Heap. |
---|
1100 | /// |
---|
1101 | /// This function instantiates a \ref Heap. |
---|
1102 | /// \param crossref The cross reference of the heap. |
---|
1103 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
1104 | return new Heap(crossref); |
---|
1105 | } |
---|
1106 | |
---|
1107 | }; |
---|
1108 | |
---|
1109 | |
---|
1110 | /// \ingroup matching |
---|
1111 | /// |
---|
1112 | /// \brief Bipartite Min Cost Matching algorithm |
---|
1113 | /// |
---|
1114 | /// This class implements the bipartite Min Cost Matching algorithm. |
---|
1115 | /// It uses the successive shortest path algorithm to calculate the |
---|
1116 | /// minimum cost maximum matching in the bipartite graph. The time |
---|
1117 | /// complexity of the algorithm is \f$ O(ne\log(n)) \f$ with the |
---|
1118 | /// default binary heap implementation but this can be improved to |
---|
1119 | /// \f$ O(n^2\log(n)+ne) \f$ if we use fibonacci heaps. |
---|
1120 | /// |
---|
1121 | /// The algorithm also provides a potential function on the nodes |
---|
1122 | /// which a dual solution of the matching algorithm and it can be |
---|
1123 | /// used to proof the optimality of the given pimal solution. |
---|
1124 | #ifdef DOXYGEN |
---|
1125 | template <typename _BpUGraph, typename _CostMap, typename _Traits> |
---|
1126 | #else |
---|
1127 | template <typename _BpUGraph, |
---|
1128 | typename _CostMap = typename _BpUGraph::template UEdgeMap<int>, |
---|
1129 | typename _Traits = MinCostMaxBipartiteMatchingDefaultTraits<_BpUGraph, _CostMap> > |
---|
1130 | #endif |
---|
1131 | class MinCostMaxBipartiteMatching { |
---|
1132 | public: |
---|
1133 | |
---|
1134 | typedef _Traits Traits; |
---|
1135 | typedef typename Traits::BpUGraph BpUGraph; |
---|
1136 | typedef typename Traits::CostMap CostMap; |
---|
1137 | typedef typename Traits::Value Value; |
---|
1138 | |
---|
1139 | protected: |
---|
1140 | |
---|
1141 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
1142 | typedef typename Traits::Heap Heap; |
---|
1143 | |
---|
1144 | |
---|
1145 | typedef typename BpUGraph::Node Node; |
---|
1146 | typedef typename BpUGraph::ANodeIt ANodeIt; |
---|
1147 | typedef typename BpUGraph::BNodeIt BNodeIt; |
---|
1148 | typedef typename BpUGraph::UEdge UEdge; |
---|
1149 | typedef typename BpUGraph::UEdgeIt UEdgeIt; |
---|
1150 | typedef typename BpUGraph::IncEdgeIt IncEdgeIt; |
---|
1151 | |
---|
1152 | typedef typename BpUGraph::template ANodeMap<UEdge> ANodeMatchingMap; |
---|
1153 | typedef typename BpUGraph::template BNodeMap<UEdge> BNodeMatchingMap; |
---|
1154 | |
---|
1155 | typedef typename BpUGraph::template ANodeMap<Value> ANodePotentialMap; |
---|
1156 | typedef typename BpUGraph::template BNodeMap<Value> BNodePotentialMap; |
---|
1157 | |
---|
1158 | |
---|
1159 | public: |
---|
1160 | |
---|
1161 | /// \brief \ref Exception for uninitialized parameters. |
---|
1162 | /// |
---|
1163 | /// This error represents problems in the initialization |
---|
1164 | /// of the parameters of the algorithms. |
---|
1165 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
1166 | public: |
---|
1167 | virtual const char* what() const throw() { |
---|
1168 | return "lemon::MinCostMaxBipartiteMatching::UninitializedParameter"; |
---|
1169 | } |
---|
1170 | }; |
---|
1171 | |
---|
1172 | ///\name Named template parameters |
---|
1173 | |
---|
1174 | ///@{ |
---|
1175 | |
---|
1176 | template <class H, class CR> |
---|
1177 | struct DefHeapTraits : public Traits { |
---|
1178 | typedef CR HeapCrossRef; |
---|
1179 | typedef H Heap; |
---|
1180 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &) { |
---|
1181 | throw UninitializedParameter(); |
---|
1182 | } |
---|
1183 | static Heap *createHeap(HeapCrossRef &) { |
---|
1184 | throw UninitializedParameter(); |
---|
1185 | } |
---|
1186 | }; |
---|
1187 | |
---|
1188 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
1189 | /// and cross reference type |
---|
1190 | /// |
---|
1191 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
1192 | /// reference type |
---|
1193 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
1194 | struct DefHeap |
---|
1195 | : public MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
1196 | DefHeapTraits<H, CR> > { |
---|
1197 | typedef MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
1198 | DefHeapTraits<H, CR> > Create; |
---|
1199 | }; |
---|
1200 | |
---|
1201 | template <class H, class CR> |
---|
1202 | struct DefStandardHeapTraits : public Traits { |
---|
1203 | typedef CR HeapCrossRef; |
---|
1204 | typedef H Heap; |
---|
1205 | static HeapCrossRef *createHeapCrossRef(const BpUGraph &graph) { |
---|
1206 | return new HeapCrossRef(graph); |
---|
1207 | } |
---|
1208 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
1209 | return new Heap(crossref); |
---|
1210 | } |
---|
1211 | }; |
---|
1212 | |
---|
1213 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
1214 | /// cross reference type with automatic allocation |
---|
1215 | /// |
---|
1216 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
1217 | /// reference type. It can allocate the heap and the cross reference |
---|
1218 | /// object if the cross reference's constructor waits for the graph as |
---|
1219 | /// parameter and the heap's constructor waits for the cross reference. |
---|
1220 | template <class H, class CR = typename BpUGraph::template NodeMap<int> > |
---|
1221 | struct DefStandardHeap |
---|
1222 | : public MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
1223 | DefStandardHeapTraits<H, CR> > { |
---|
1224 | typedef MinCostMaxBipartiteMatching<BpUGraph, CostMap, |
---|
1225 | DefStandardHeapTraits<H, CR> > |
---|
1226 | Create; |
---|
1227 | }; |
---|
1228 | |
---|
1229 | ///@} |
---|
1230 | |
---|
1231 | |
---|
1232 | /// \brief Constructor. |
---|
1233 | /// |
---|
1234 | /// Constructor of the algorithm. |
---|
1235 | MinCostMaxBipartiteMatching(const BpUGraph& _graph, |
---|
1236 | const CostMap& _cost) |
---|
1237 | : graph(&_graph), cost(&_cost), |
---|
1238 | anode_matching(_graph), bnode_matching(_graph), |
---|
1239 | anode_potential(_graph), bnode_potential(_graph), |
---|
1240 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1241 | _heap(0), local_heap(0) {} |
---|
1242 | |
---|
1243 | /// \brief Destructor. |
---|
1244 | /// |
---|
1245 | /// Destructor of the algorithm. |
---|
1246 | ~MinCostMaxBipartiteMatching() { |
---|
1247 | destroyStructures(); |
---|
1248 | } |
---|
1249 | |
---|
1250 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
1251 | /// |
---|
1252 | /// Sets the heap and the cross reference used by algorithm. |
---|
1253 | /// If you don't use this function before calling \ref run(), |
---|
1254 | /// it will allocate one. The destuctor deallocates this |
---|
1255 | /// automatically allocated map, of course. |
---|
1256 | /// \return \c (*this) |
---|
1257 | MinCostMaxBipartiteMatching& heap(Heap& heap, HeapCrossRef &crossRef) { |
---|
1258 | if(local_heap_cross_ref) { |
---|
1259 | delete _heap_cross_ref; |
---|
1260 | local_heap_cross_ref = false; |
---|
1261 | } |
---|
1262 | _heap_cross_ref = &crossRef; |
---|
1263 | if(local_heap) { |
---|
1264 | delete _heap; |
---|
1265 | local_heap = false; |
---|
1266 | } |
---|
1267 | _heap = &heap; |
---|
1268 | return *this; |
---|
1269 | } |
---|
1270 | |
---|
1271 | /// \name Execution control |
---|
1272 | /// The simplest way to execute the algorithm is to use |
---|
1273 | /// one of the member functions called \c run(). |
---|
1274 | /// \n |
---|
1275 | /// If you need more control on the execution, |
---|
1276 | /// first you must call \ref init() or one alternative for it. |
---|
1277 | /// Finally \ref start() will perform the matching computation or |
---|
1278 | /// with step-by-step execution you can augment the solution. |
---|
1279 | |
---|
1280 | /// @{ |
---|
1281 | |
---|
1282 | /// \brief Initalize the data structures. |
---|
1283 | /// |
---|
1284 | /// It initalizes the data structures and creates an empty matching. |
---|
1285 | void init() { |
---|
1286 | initStructures(); |
---|
1287 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
1288 | anode_matching[it] = INVALID; |
---|
1289 | anode_potential[it] = 0; |
---|
1290 | } |
---|
1291 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
1292 | bnode_matching[it] = INVALID; |
---|
1293 | bnode_potential[it] = 0; |
---|
1294 | } |
---|
1295 | matching_cost = 0; |
---|
1296 | matching_size = 0; |
---|
1297 | } |
---|
1298 | |
---|
1299 | |
---|
1300 | /// \brief An augmenting phase of the costed matching algorithm |
---|
1301 | /// |
---|
1302 | /// It runs an augmenting phase of the matching algorithm. The |
---|
1303 | /// phase finds the best augmenting path and augments only on this |
---|
1304 | /// paths. |
---|
1305 | /// |
---|
1306 | /// The algorithm consists at most |
---|
1307 | /// of \f$ O(n) \f$ phase and one phase is \f$ O(n\log(n)+e) \f$ |
---|
1308 | /// long with Fibonacci heap or \f$ O((n+e)\log(n)) \f$ long |
---|
1309 | /// with binary heap. |
---|
1310 | bool augment() { |
---|
1311 | |
---|
1312 | typename BpUGraph::template BNodeMap<Value> bdist(*graph); |
---|
1313 | typename BpUGraph::template BNodeMap<UEdge> bpred(*graph, INVALID); |
---|
1314 | |
---|
1315 | Node bestNode = INVALID; |
---|
1316 | Value bestValue = 0; |
---|
1317 | |
---|
1318 | _heap->clear(); |
---|
1319 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
1320 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
---|
1321 | } |
---|
1322 | |
---|
1323 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
1324 | if (anode_matching[it] == INVALID) { |
---|
1325 | _heap->push(it, 0); |
---|
1326 | } |
---|
1327 | } |
---|
1328 | Value bdistMax = 0; |
---|
1329 | |
---|
1330 | while (!_heap->empty()) { |
---|
1331 | Node anode = _heap->top(); |
---|
1332 | Value avalue = _heap->prio(); |
---|
1333 | _heap->pop(); |
---|
1334 | for (IncEdgeIt jt(*graph, anode); jt != INVALID; ++jt) { |
---|
1335 | if (jt == anode_matching[anode]) continue; |
---|
1336 | Node bnode = graph->bNode(jt); |
---|
1337 | Value bvalue = avalue + (*cost)[jt] + |
---|
1338 | anode_potential[anode] - bnode_potential[bnode]; |
---|
1339 | if (bpred[bnode] == INVALID || bvalue < bdist[bnode]) { |
---|
1340 | bdist[bnode] = bvalue; |
---|
1341 | bpred[bnode] = jt; |
---|
1342 | } |
---|
1343 | if (bvalue > bdistMax) { |
---|
1344 | bdistMax = bvalue; |
---|
1345 | } |
---|
1346 | if (bnode_matching[bnode] != INVALID) { |
---|
1347 | Node newanode = graph->aNode(bnode_matching[bnode]); |
---|
1348 | switch (_heap->state(newanode)) { |
---|
1349 | case Heap::PRE_HEAP: |
---|
1350 | _heap->push(newanode, bvalue); |
---|
1351 | break; |
---|
1352 | case Heap::IN_HEAP: |
---|
1353 | if (bvalue < (*_heap)[newanode]) { |
---|
1354 | _heap->decrease(newanode, bvalue); |
---|
1355 | } |
---|
1356 | break; |
---|
1357 | case Heap::POST_HEAP: |
---|
1358 | break; |
---|
1359 | } |
---|
1360 | } else { |
---|
1361 | if (bestNode == INVALID || |
---|
1362 | bvalue + bnode_potential[bnode] < bestValue) { |
---|
1363 | bestValue = bvalue + bnode_potential[bnode]; |
---|
1364 | bestNode = bnode; |
---|
1365 | } |
---|
1366 | } |
---|
1367 | } |
---|
1368 | } |
---|
1369 | |
---|
1370 | if (bestNode == INVALID) { |
---|
1371 | return false; |
---|
1372 | } |
---|
1373 | |
---|
1374 | matching_cost += bestValue; |
---|
1375 | ++matching_size; |
---|
1376 | |
---|
1377 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
1378 | if (bpred[it] != INVALID) { |
---|
1379 | bnode_potential[it] += bdist[it]; |
---|
1380 | } else { |
---|
1381 | bnode_potential[it] += bdistMax; |
---|
1382 | } |
---|
1383 | } |
---|
1384 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
1385 | if (anode_matching[it] != INVALID) { |
---|
1386 | Node bnode = graph->bNode(anode_matching[it]); |
---|
1387 | if (bpred[bnode] != INVALID) { |
---|
1388 | anode_potential[it] += bdist[bnode]; |
---|
1389 | } else { |
---|
1390 | anode_potential[it] += bdistMax; |
---|
1391 | } |
---|
1392 | } |
---|
1393 | } |
---|
1394 | |
---|
1395 | while (bestNode != INVALID) { |
---|
1396 | UEdge uedge = bpred[bestNode]; |
---|
1397 | Node anode = graph->aNode(uedge); |
---|
1398 | |
---|
1399 | bnode_matching[bestNode] = uedge; |
---|
1400 | if (anode_matching[anode] != INVALID) { |
---|
1401 | bestNode = graph->bNode(anode_matching[anode]); |
---|
1402 | } else { |
---|
1403 | bestNode = INVALID; |
---|
1404 | } |
---|
1405 | anode_matching[anode] = uedge; |
---|
1406 | } |
---|
1407 | |
---|
1408 | |
---|
1409 | return true; |
---|
1410 | } |
---|
1411 | |
---|
1412 | /// \brief Starts the algorithm. |
---|
1413 | /// |
---|
1414 | /// Starts the algorithm. It runs augmenting phases until the |
---|
1415 | /// optimal solution reached. |
---|
1416 | void start() { |
---|
1417 | while (augment()) {} |
---|
1418 | } |
---|
1419 | |
---|
1420 | /// \brief Runs the algorithm. |
---|
1421 | /// |
---|
1422 | /// It just initalize the algorithm and then start it. |
---|
1423 | void run() { |
---|
1424 | init(); |
---|
1425 | start(); |
---|
1426 | } |
---|
1427 | |
---|
1428 | /// @} |
---|
1429 | |
---|
1430 | /// \name Query Functions |
---|
1431 | /// The result of the %Matching algorithm can be obtained using these |
---|
1432 | /// functions.\n |
---|
1433 | /// Before the use of these functions, |
---|
1434 | /// either run() or start() must be called. |
---|
1435 | |
---|
1436 | ///@{ |
---|
1437 | |
---|
1438 | /// \brief Gives back the potential in the NodeMap |
---|
1439 | /// |
---|
1440 | /// Gives back the potential in the NodeMap. The potential is optimal with |
---|
1441 | /// the current number of edges if \f$ \pi(a) - \pi(b) + w(ab) = 0 \f$ for |
---|
1442 | /// each matching edges and \f$ \pi(a) - \pi(b) + w(ab) \ge 0 \f$ |
---|
1443 | /// for each edges. |
---|
1444 | template <typename PotentialMap> |
---|
1445 | void potential(PotentialMap& potential) const { |
---|
1446 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
1447 | potential[it] = anode_potential[it]; |
---|
1448 | } |
---|
1449 | for (BNodeIt it(*graph); it != INVALID; ++it) { |
---|
1450 | potential[it] = bnode_potential[it]; |
---|
1451 | } |
---|
1452 | } |
---|
1453 | |
---|
1454 | /// \brief Set true all matching uedge in the map. |
---|
1455 | /// |
---|
1456 | /// Set true all matching uedge in the map. It does not change the |
---|
1457 | /// value mapped to the other uedges. |
---|
1458 | /// \return The number of the matching edges. |
---|
1459 | template <typename MatchingMap> |
---|
1460 | int quickMatching(MatchingMap& matching) const { |
---|
1461 | for (ANodeIt it(*graph); it != INVALID; ++it) { |
---|
1462 | if (anode_matching[it] != INVALID) { |
---|
1463 | matching[anode_matching[it]] = true; |
---|
1464 | } |
---|
1465 | } |
---|
1466 | return matching_size; |
---|
1467 | } |
---|
1468 | |
---|
1469 | /// \brief Set true all matching uedge in the map and the others to false. |
---|
1470 | /// |
---|
1471 | /// Set true all matching uedge in the map and the others to false. |
---|
1472 | /// \return The number of the matching edges. |
---|
1473 | template <typename MatchingMap> |
---|
1474 | int matching(MatchingMap& matching) const { |
---|
1475 | for (UEdgeIt it(*graph); it != INVALID; ++it) { |
---|
1476 | matching[it] = it == anode_matching[graph->aNode(it)]; |
---|
1477 | } |
---|
1478 | return matching_size; |
---|
1479 | } |
---|
1480 | |
---|
1481 | |
---|
1482 | /// \brief Return true if the given uedge is in the matching. |
---|
1483 | /// |
---|
1484 | /// It returns true if the given uedge is in the matching. |
---|
1485 | bool matchingEdge(const UEdge& edge) const { |
---|
1486 | return anode_matching[graph->aNode(edge)] == edge; |
---|
1487 | } |
---|
1488 | |
---|
1489 | /// \brief Returns the matching edge from the node. |
---|
1490 | /// |
---|
1491 | /// Returns the matching edge from the node. If there is not such |
---|
1492 | /// edge it gives back \c INVALID. |
---|
1493 | UEdge matchingEdge(const Node& node) const { |
---|
1494 | if (graph->aNode(node)) { |
---|
1495 | return anode_matching[node]; |
---|
1496 | } else { |
---|
1497 | return bnode_matching[node]; |
---|
1498 | } |
---|
1499 | } |
---|
1500 | |
---|
1501 | /// \brief Gives back the sum of costs of the matching edges. |
---|
1502 | /// |
---|
1503 | /// Gives back the sum of costs of the matching edges. |
---|
1504 | Value matchingCost() const { |
---|
1505 | return matching_cost; |
---|
1506 | } |
---|
1507 | |
---|
1508 | /// \brief Gives back the number of the matching edges. |
---|
1509 | /// |
---|
1510 | /// Gives back the number of the matching edges. |
---|
1511 | int matchingSize() const { |
---|
1512 | return matching_size; |
---|
1513 | } |
---|
1514 | |
---|
1515 | /// @} |
---|
1516 | |
---|
1517 | private: |
---|
1518 | |
---|
1519 | void initStructures() { |
---|
1520 | if (!_heap_cross_ref) { |
---|
1521 | local_heap_cross_ref = true; |
---|
1522 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
---|
1523 | } |
---|
1524 | if (!_heap) { |
---|
1525 | local_heap = true; |
---|
1526 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
1527 | } |
---|
1528 | } |
---|
1529 | |
---|
1530 | void destroyStructures() { |
---|
1531 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
1532 | if (local_heap) delete _heap; |
---|
1533 | } |
---|
1534 | |
---|
1535 | |
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1536 | private: |
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1537 | |
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1538 | const BpUGraph *graph; |
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1539 | const CostMap* cost; |
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1540 | |
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1541 | ANodeMatchingMap anode_matching; |
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1542 | BNodeMatchingMap bnode_matching; |
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1543 | |
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1544 | ANodePotentialMap anode_potential; |
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1545 | BNodePotentialMap bnode_potential; |
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1546 | |
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1547 | Value matching_cost; |
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1548 | int matching_size; |
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1549 | |
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1550 | HeapCrossRef *_heap_cross_ref; |
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1551 | bool local_heap_cross_ref; |
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1552 | |
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1553 | Heap *_heap; |
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1554 | bool local_heap; |
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1555 | |
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1556 | }; |
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1557 | |
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1558 | /// \ingroup matching |
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1559 | /// |
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1560 | /// \brief Minimum cost maximum cardinality bipartite matching |
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1561 | /// |
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1562 | /// This function calculates the minimum cost matching of the maximum |
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1563 | /// cardinality matchings of a bipartite graph. It gives back the matching |
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1564 | /// in an undirected edge map. |
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1565 | /// |
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1566 | /// \param graph The bipartite graph. |
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1567 | /// \param cost The undirected edge map which contains the costs. |
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1568 | /// \retval matching The undirected edge map which will be set to |
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1569 | /// the matching. |
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1570 | /// \return The cost of the matching. |
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1571 | template <typename BpUGraph, typename CostMap, typename MatchingMap> |
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1572 | typename CostMap::Value |
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1573 | minCostMaxBipartiteMatching(const BpUGraph& graph, |
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1574 | const CostMap& cost, |
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1575 | MatchingMap& matching) { |
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1576 | MinCostMaxBipartiteMatching<BpUGraph, CostMap> |
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1577 | bpmatching(graph, cost); |
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1578 | bpmatching.run(); |
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1579 | bpmatching.matching(matching); |
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1580 | return bpmatching.matchingCost(); |
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1581 | } |
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1582 | |
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1583 | } |
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1584 | |
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1585 | #endif |
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