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_MAX_MATCHING_H |
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20 | #define LEMON_MAX_MATCHING_H |
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21 | |
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22 | #include <vector> |
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23 | #include <queue> |
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24 | #include <set> |
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25 | |
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26 | #include <lemon/bits/invalid.h> |
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27 | #include <lemon/unionfind.h> |
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28 | #include <lemon/graph_utils.h> |
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29 | #include <lemon/bin_heap.h> |
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30 | |
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31 | ///\ingroup matching |
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32 | ///\file |
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33 | ///\brief Maximum matching algorithm in undirected graph. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | ///\ingroup matching |
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38 | /// |
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39 | ///\brief Edmonds' alternating forest maximum matching algorithm. |
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40 | /// |
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41 | ///This class provides Edmonds' alternating forest matching |
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42 | ///algorithm. The starting matching (if any) can be passed to the |
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43 | ///algorithm using some of init functions. |
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44 | /// |
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45 | ///The dual side of a matching is a map of the nodes to |
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46 | ///MaxMatching::DecompType, having values \c D, \c A and \c C |
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47 | ///showing the Gallai-Edmonds decomposition of the graph. The nodes |
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48 | ///in \c D induce a graph with factor-critical components, the nodes |
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49 | ///in \c A form the barrier, and the nodes in \c C induce a graph |
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50 | ///having a perfect matching. This decomposition can be attained by |
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51 | ///calling \c decomposition() after running the algorithm. |
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52 | /// |
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53 | ///\param Graph The undirected graph type the algorithm runs on. |
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54 | /// |
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55 | ///\author Jacint Szabo |
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56 | template <typename Graph> |
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57 | class MaxMatching { |
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58 | |
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59 | protected: |
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60 | |
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61 | typedef typename Graph::Node Node; |
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62 | typedef typename Graph::Edge Edge; |
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63 | typedef typename Graph::UEdge UEdge; |
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64 | typedef typename Graph::UEdgeIt UEdgeIt; |
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65 | typedef typename Graph::NodeIt NodeIt; |
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66 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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67 | |
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68 | typedef typename Graph::template NodeMap<int> UFECrossRef; |
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69 | typedef UnionFindEnum<UFECrossRef> UFE; |
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70 | typedef std::vector<Node> NV; |
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71 | |
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72 | typedef typename Graph::template NodeMap<int> EFECrossRef; |
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73 | typedef ExtendFindEnum<EFECrossRef> EFE; |
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74 | |
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75 | public: |
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76 | |
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77 | ///\brief Indicates the Gallai-Edmonds decomposition of the graph. |
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78 | /// |
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79 | ///Indicates the Gallai-Edmonds decomposition of the graph, which |
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80 | ///shows an upper bound on the size of a maximum matching. The |
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81 | ///nodes with DecompType \c D induce a graph with factor-critical |
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82 | ///components, the nodes in \c A form the canonical barrier, and the |
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83 | ///nodes in \c C induce a graph having a perfect matching. |
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84 | enum DecompType { |
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85 | D=0, |
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86 | A=1, |
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87 | C=2 |
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88 | }; |
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89 | |
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90 | protected: |
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91 | |
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92 | static const int HEUR_density=2; |
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93 | const Graph& g; |
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94 | typename Graph::template NodeMap<Node> _mate; |
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95 | typename Graph::template NodeMap<DecompType> position; |
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96 | |
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97 | public: |
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98 | |
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99 | MaxMatching(const Graph& _g) |
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100 | : g(_g), _mate(_g), position(_g) {} |
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101 | |
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102 | ///\brief Sets the actual matching to the empty matching. |
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103 | /// |
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104 | ///Sets the actual matching to the empty matching. |
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105 | /// |
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106 | void init() { |
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107 | for(NodeIt v(g); v!=INVALID; ++v) { |
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108 | _mate.set(v,INVALID); |
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109 | position.set(v,C); |
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110 | } |
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111 | } |
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112 | |
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113 | ///\brief Finds a greedy matching for initial matching. |
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114 | /// |
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115 | ///For initial matchig it finds a maximal greedy matching. |
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116 | void greedyInit() { |
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117 | for(NodeIt v(g); v!=INVALID; ++v) { |
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118 | _mate.set(v,INVALID); |
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119 | position.set(v,C); |
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120 | } |
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121 | for(NodeIt v(g); v!=INVALID; ++v) |
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122 | if ( _mate[v]==INVALID ) { |
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123 | for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) { |
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124 | Node y=g.runningNode(e); |
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125 | if ( _mate[y]==INVALID && y!=v ) { |
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126 | _mate.set(v,y); |
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127 | _mate.set(y,v); |
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128 | break; |
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129 | } |
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130 | } |
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131 | } |
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132 | } |
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133 | |
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134 | ///\brief Initialize the matching from each nodes' mate. |
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135 | /// |
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136 | ///Initialize the matching from a \c Node valued \c Node map. This |
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137 | ///map must be \e symmetric, i.e. if \c map[u]==v then \c |
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138 | ///map[v]==u must hold, and \c uv will be an edge of the initial |
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139 | ///matching. |
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140 | template <typename MateMap> |
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141 | void mateMapInit(MateMap& map) { |
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142 | for(NodeIt v(g); v!=INVALID; ++v) { |
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143 | _mate.set(v,map[v]); |
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144 | position.set(v,C); |
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145 | } |
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146 | } |
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147 | |
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148 | ///\brief Initialize the matching from a node map with the |
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149 | ///incident matching edges. |
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150 | /// |
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151 | ///Initialize the matching from an \c UEdge valued \c Node map. \c |
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152 | ///map[v] must be an \c UEdge incident to \c v. This map must have |
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153 | ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c |
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154 | ///g.oppositeNode(v,map[v])==u holds, and now some edge joining \c |
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155 | ///u to \c v will be an edge of the matching. |
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156 | template<typename MatchingMap> |
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157 | void matchingMapInit(MatchingMap& map) { |
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158 | for(NodeIt v(g); v!=INVALID; ++v) { |
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159 | position.set(v,C); |
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160 | UEdge e=map[v]; |
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161 | if ( e!=INVALID ) |
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162 | _mate.set(v,g.oppositeNode(v,e)); |
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163 | else |
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164 | _mate.set(v,INVALID); |
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165 | } |
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166 | } |
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167 | |
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168 | ///\brief Initialize the matching from the map containing the |
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169 | ///undirected matching edges. |
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170 | /// |
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171 | ///Initialize the matching from a \c bool valued \c UEdge map. This |
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172 | ///map must have the property that there are no two incident edges |
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173 | ///\c e, \c f with \c map[e]==map[f]==true. The edges \c e with \c |
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174 | ///map[e]==true form the matching. |
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175 | template <typename MatchingMap> |
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176 | void matchingInit(MatchingMap& map) { |
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177 | for(NodeIt v(g); v!=INVALID; ++v) { |
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178 | _mate.set(v,INVALID); |
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179 | position.set(v,C); |
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180 | } |
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181 | for(UEdgeIt e(g); e!=INVALID; ++e) { |
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182 | if ( map[e] ) { |
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183 | Node u=g.source(e); |
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184 | Node v=g.target(e); |
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185 | _mate.set(u,v); |
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186 | _mate.set(v,u); |
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187 | } |
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188 | } |
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189 | } |
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190 | |
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191 | |
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192 | ///\brief Runs Edmonds' algorithm. |
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193 | /// |
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194 | ///Runs Edmonds' algorithm for sparse graphs (number of edges < |
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195 | ///2*number of nodes), and a heuristical Edmonds' algorithm with a |
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196 | ///heuristic of postponing shrinks for dense graphs. |
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197 | void run() { |
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198 | if (countUEdges(g) < HEUR_density * countNodes(g)) { |
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199 | greedyInit(); |
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200 | startSparse(); |
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201 | } else { |
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202 | init(); |
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203 | startDense(); |
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204 | } |
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205 | } |
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206 | |
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207 | |
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208 | ///\brief Starts Edmonds' algorithm. |
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209 | /// |
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210 | ///If runs the original Edmonds' algorithm. |
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211 | void startSparse() { |
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212 | |
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213 | typename Graph::template NodeMap<Node> ear(g,INVALID); |
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214 | //undefined for the base nodes of the blossoms (i.e. for the |
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215 | //representative elements of UFE blossom) and for the nodes in C |
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216 | |
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217 | UFECrossRef blossom_base(g); |
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218 | UFE blossom(blossom_base); |
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219 | NV rep(countNodes(g)); |
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220 | |
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221 | EFECrossRef tree_base(g); |
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222 | EFE tree(tree_base); |
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223 | |
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224 | //If these UFE's would be members of the class then also |
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225 | //blossom_base and tree_base should be a member. |
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226 | |
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227 | //We build only one tree and the other vertices uncovered by the |
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228 | //matching belong to C. (They can be considered as singleton |
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229 | //trees.) If this tree can be augmented or no more |
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230 | //grow/augmentation/shrink is possible then we return to this |
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231 | //"for" cycle. |
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232 | for(NodeIt v(g); v!=INVALID; ++v) { |
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233 | if (position[v]==C && _mate[v]==INVALID) { |
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234 | rep[blossom.insert(v)] = v; |
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235 | tree.insert(v); |
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236 | position.set(v,D); |
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237 | normShrink(v, ear, blossom, rep, tree); |
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238 | } |
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239 | } |
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240 | } |
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241 | |
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242 | ///\brief Starts Edmonds' algorithm. |
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243 | /// |
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244 | ///It runs Edmonds' algorithm with a heuristic of postponing |
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245 | ///shrinks, giving a faster algorithm for dense graphs. |
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246 | void startDense() { |
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247 | |
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248 | typename Graph::template NodeMap<Node> ear(g,INVALID); |
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249 | //undefined for the base nodes of the blossoms (i.e. for the |
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250 | //representative elements of UFE blossom) and for the nodes in C |
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251 | |
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252 | UFECrossRef blossom_base(g); |
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253 | UFE blossom(blossom_base); |
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254 | NV rep(countNodes(g)); |
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255 | |
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256 | EFECrossRef tree_base(g); |
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257 | EFE tree(tree_base); |
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258 | |
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259 | //If these UFE's would be members of the class then also |
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260 | //blossom_base and tree_base should be a member. |
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261 | |
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262 | //We build only one tree and the other vertices uncovered by the |
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263 | //matching belong to C. (They can be considered as singleton |
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264 | //trees.) If this tree can be augmented or no more |
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265 | //grow/augmentation/shrink is possible then we return to this |
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266 | //"for" cycle. |
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267 | for(NodeIt v(g); v!=INVALID; ++v) { |
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268 | if ( position[v]==C && _mate[v]==INVALID ) { |
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269 | rep[blossom.insert(v)] = v; |
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270 | tree.insert(v); |
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271 | position.set(v,D); |
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272 | lateShrink(v, ear, blossom, rep, tree); |
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273 | } |
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274 | } |
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275 | } |
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276 | |
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277 | |
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278 | |
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279 | ///\brief Returns the size of the actual matching stored. |
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280 | /// |
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281 | ///Returns the size of the actual matching stored. After \ref |
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282 | ///run() it returns the size of a maximum matching in the graph. |
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283 | int size() const { |
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284 | int s=0; |
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285 | for(NodeIt v(g); v!=INVALID; ++v) { |
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286 | if ( _mate[v]!=INVALID ) { |
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287 | ++s; |
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288 | } |
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289 | } |
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290 | return s/2; |
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291 | } |
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292 | |
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293 | |
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294 | ///\brief Returns the mate of a node in the actual matching. |
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295 | /// |
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296 | ///Returns the mate of a \c node in the actual matching. |
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297 | ///Returns INVALID if the \c node is not covered by the actual matching. |
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298 | Node mate(const Node& node) const { |
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299 | return _mate[node]; |
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300 | } |
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301 | |
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302 | ///\brief Returns the matching edge incident to the given node. |
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303 | /// |
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304 | ///Returns the matching edge of a \c node in the actual matching. |
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305 | ///Returns INVALID if the \c node is not covered by the actual matching. |
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306 | UEdge matchingEdge(const Node& node) const { |
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307 | if (_mate[node] == INVALID) return INVALID; |
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308 | Node n = node < _mate[node] ? node : _mate[node]; |
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309 | for (IncEdgeIt e(g, n); e != INVALID; ++e) { |
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310 | if (g.oppositeNode(n, e) == _mate[n]) { |
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311 | return e; |
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312 | } |
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313 | } |
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314 | return INVALID; |
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315 | } |
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316 | |
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317 | /// \brief Returns the class of the node in the Edmonds-Gallai |
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318 | /// decomposition. |
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319 | /// |
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320 | /// Returns the class of the node in the Edmonds-Gallai |
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321 | /// decomposition. |
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322 | DecompType decomposition(const Node& n) { |
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323 | return position[n] == A; |
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324 | } |
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325 | |
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326 | /// \brief Returns true when the node is in the barrier. |
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327 | /// |
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328 | /// Returns true when the node is in the barrier. |
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329 | bool barrier(const Node& n) { |
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330 | return position[n] == A; |
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331 | } |
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332 | |
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333 | ///\brief Gives back the matching in a \c Node of mates. |
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334 | /// |
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335 | ///Writes the stored matching to a \c Node valued \c Node map. The |
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336 | ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c |
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337 | ///map[v]==u will hold, and now \c uv is an edge of the matching. |
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338 | template <typename MateMap> |
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339 | void mateMap(MateMap& map) const { |
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340 | for(NodeIt v(g); v!=INVALID; ++v) { |
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341 | map.set(v,_mate[v]); |
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342 | } |
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343 | } |
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344 | |
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345 | ///\brief Gives back the matching in an \c UEdge valued \c Node |
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346 | ///map. |
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347 | /// |
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348 | ///Writes the stored matching to an \c UEdge valued \c Node |
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349 | ///map. \c map[v] will be an \c UEdge incident to \c v. This |
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350 | ///map will have the property that if \c g.oppositeNode(u,map[u]) |
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351 | ///== v then \c map[u]==map[v] holds, and now this edge is an edge |
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352 | ///of the matching. |
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353 | template <typename MatchingMap> |
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354 | void matchingMap(MatchingMap& map) const { |
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355 | typename Graph::template NodeMap<bool> todo(g,true); |
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356 | for(NodeIt v(g); v!=INVALID; ++v) { |
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357 | if (_mate[v]!=INVALID && v < _mate[v]) { |
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358 | Node u=_mate[v]; |
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359 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
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360 | if ( g.runningNode(e) == u ) { |
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361 | map.set(u,e); |
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362 | map.set(v,e); |
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363 | todo.set(u,false); |
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364 | todo.set(v,false); |
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365 | break; |
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366 | } |
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367 | } |
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368 | } |
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369 | } |
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370 | } |
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371 | |
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372 | |
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373 | ///\brief Gives back the matching in a \c bool valued \c UEdge |
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374 | ///map. |
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375 | /// |
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376 | ///Writes the matching stored to a \c bool valued \c Edge |
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377 | ///map. This map will have the property that there are no two |
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378 | ///incident edges \c e, \c f with \c map[e]==map[f]==true. The |
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379 | ///edges \c e with \c map[e]==true form the matching. |
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380 | template<typename MatchingMap> |
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381 | void matching(MatchingMap& map) const { |
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382 | for(UEdgeIt e(g); e!=INVALID; ++e) map.set(e,false); |
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383 | |
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384 | typename Graph::template NodeMap<bool> todo(g,true); |
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385 | for(NodeIt v(g); v!=INVALID; ++v) { |
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386 | if ( todo[v] && _mate[v]!=INVALID ) { |
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387 | Node u=_mate[v]; |
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388 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
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389 | if ( g.runningNode(e) == u ) { |
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390 | map.set(e,true); |
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391 | todo.set(u,false); |
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392 | todo.set(v,false); |
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393 | break; |
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394 | } |
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395 | } |
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396 | } |
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397 | } |
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398 | } |
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399 | |
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400 | |
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401 | ///\brief Returns the canonical decomposition of the graph after running |
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402 | ///the algorithm. |
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403 | /// |
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404 | ///After calling any run methods of the class, it writes the |
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405 | ///Gallai-Edmonds canonical decomposition of the graph. \c map |
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406 | ///must be a node map of \ref DecompType 's. |
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407 | template <typename DecompositionMap> |
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408 | void decomposition(DecompositionMap& map) const { |
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409 | for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]); |
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410 | } |
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411 | |
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412 | ///\brief Returns a barrier on the nodes. |
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413 | /// |
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414 | ///After calling any run methods of the class, it writes a |
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415 | ///canonical barrier on the nodes. The odd component number of the |
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416 | ///remaining graph minus the barrier size is a lower bound for the |
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417 | ///uncovered nodes in the graph. The \c map must be a node map of |
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418 | ///bools. |
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419 | template <typename BarrierMap> |
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420 | void barrier(BarrierMap& barrier) { |
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421 | for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A); |
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422 | } |
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423 | |
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424 | private: |
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425 | |
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426 | |
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427 | void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
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428 | UFE& blossom, NV& rep, EFE& tree) { |
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429 | //We have one tree which we grow, and also shrink but only if it |
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430 | //cannot be postponed. If we augment then we return to the "for" |
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431 | //cycle of runEdmonds(). |
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432 | |
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433 | std::queue<Node> Q; //queue of the totally unscanned nodes |
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434 | Q.push(v); |
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435 | std::queue<Node> R; |
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436 | //queue of the nodes which must be scanned for a possible shrink |
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437 | |
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438 | while ( !Q.empty() ) { |
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439 | Node x=Q.front(); |
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440 | Q.pop(); |
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441 | for( IncEdgeIt e(g,x); e!= INVALID; ++e ) { |
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442 | Node y=g.runningNode(e); |
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443 | //growOrAugment grows if y is covered by the matching and |
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444 | //augments if not. In this latter case it returns 1. |
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445 | if (position[y]==C && |
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446 | growOrAugment(y, x, ear, blossom, rep, tree, Q)) return; |
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447 | } |
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448 | R.push(x); |
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449 | } |
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450 | |
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451 | while ( !R.empty() ) { |
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452 | Node x=R.front(); |
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453 | R.pop(); |
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454 | |
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455 | for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) { |
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456 | Node y=g.runningNode(e); |
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457 | |
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458 | if ( position[y] == D && blossom.find(x) != blossom.find(y) ) |
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459 | //Recall that we have only one tree. |
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460 | shrink( x, y, ear, blossom, rep, tree, Q); |
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461 | |
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462 | while ( !Q.empty() ) { |
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463 | Node z=Q.front(); |
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464 | Q.pop(); |
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465 | for( IncEdgeIt f(g,z); f!= INVALID; ++f ) { |
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466 | Node w=g.runningNode(f); |
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467 | //growOrAugment grows if y is covered by the matching and |
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468 | //augments if not. In this latter case it returns 1. |
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469 | if (position[w]==C && |
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470 | growOrAugment(w, z, ear, blossom, rep, tree, Q)) return; |
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471 | } |
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472 | R.push(z); |
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473 | } |
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474 | } //for e |
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475 | } // while ( !R.empty() ) |
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476 | } |
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477 | |
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478 | void normShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
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479 | UFE& blossom, NV& rep, EFE& tree) { |
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480 | //We have one tree, which we grow and shrink. If we augment then we |
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481 | //return to the "for" cycle of runEdmonds(). |
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482 | |
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483 | std::queue<Node> Q; //queue of the unscanned nodes |
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484 | Q.push(v); |
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485 | while ( !Q.empty() ) { |
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486 | |
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487 | Node x=Q.front(); |
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488 | Q.pop(); |
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489 | |
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490 | for( IncEdgeIt e(g,x); e!=INVALID; ++e ) { |
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491 | Node y=g.runningNode(e); |
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492 | |
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493 | switch ( position[y] ) { |
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494 | case D: //x and y must be in the same tree |
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495 | if ( blossom.find(x) != blossom.find(y)) |
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496 | //x and y are in the same tree |
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497 | shrink(x, y, ear, blossom, rep, tree, Q); |
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498 | break; |
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499 | case C: |
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500 | //growOrAugment grows if y is covered by the matching and |
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501 | //augments if not. In this latter case it returns 1. |
---|
502 | if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return; |
---|
503 | break; |
---|
504 | default: break; |
---|
505 | } |
---|
506 | } |
---|
507 | } |
---|
508 | } |
---|
509 | |
---|
510 | void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear, |
---|
511 | UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) { |
---|
512 | //x and y are the two adjacent vertices in two blossoms. |
---|
513 | |
---|
514 | typename Graph::template NodeMap<bool> path(g,false); |
---|
515 | |
---|
516 | Node b=rep[blossom.find(x)]; |
---|
517 | path.set(b,true); |
---|
518 | b=_mate[b]; |
---|
519 | while ( b!=INVALID ) { |
---|
520 | b=rep[blossom.find(ear[b])]; |
---|
521 | path.set(b,true); |
---|
522 | b=_mate[b]; |
---|
523 | } //we go until the root through bases of blossoms and odd vertices |
---|
524 | |
---|
525 | Node top=y; |
---|
526 | Node middle=rep[blossom.find(top)]; |
---|
527 | Node bottom=x; |
---|
528 | while ( !path[middle] ) |
---|
529 | shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q); |
---|
530 | //Until we arrive to a node on the path, we update blossom, tree |
---|
531 | //and the positions of the odd nodes. |
---|
532 | |
---|
533 | Node base=middle; |
---|
534 | top=x; |
---|
535 | middle=rep[blossom.find(top)]; |
---|
536 | bottom=y; |
---|
537 | Node blossom_base=rep[blossom.find(base)]; |
---|
538 | while ( middle!=blossom_base ) |
---|
539 | shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q); |
---|
540 | //Until we arrive to a node on the path, we update blossom, tree |
---|
541 | //and the positions of the odd nodes. |
---|
542 | |
---|
543 | rep[blossom.find(base)] = base; |
---|
544 | } |
---|
545 | |
---|
546 | void shrinkStep(Node& top, Node& middle, Node& bottom, |
---|
547 | typename Graph::template NodeMap<Node>& ear, |
---|
548 | UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) { |
---|
549 | //We traverse a blossom and update everything. |
---|
550 | |
---|
551 | ear.set(top,bottom); |
---|
552 | Node t=top; |
---|
553 | while ( t!=middle ) { |
---|
554 | Node u=_mate[t]; |
---|
555 | t=ear[u]; |
---|
556 | ear.set(t,u); |
---|
557 | } |
---|
558 | bottom=_mate[middle]; |
---|
559 | position.set(bottom,D); |
---|
560 | Q.push(bottom); |
---|
561 | top=ear[bottom]; |
---|
562 | Node oldmiddle=middle; |
---|
563 | middle=rep[blossom.find(top)]; |
---|
564 | tree.erase(bottom); |
---|
565 | tree.erase(oldmiddle); |
---|
566 | blossom.insert(bottom); |
---|
567 | blossom.join(bottom, oldmiddle); |
---|
568 | blossom.join(top, oldmiddle); |
---|
569 | } |
---|
570 | |
---|
571 | |
---|
572 | |
---|
573 | bool growOrAugment(Node& y, Node& x, typename Graph::template |
---|
574 | NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree, |
---|
575 | std::queue<Node>& Q) { |
---|
576 | //x is in a blossom in the tree, y is outside. If y is covered by |
---|
577 | //the matching we grow, otherwise we augment. In this case we |
---|
578 | //return 1. |
---|
579 | |
---|
580 | if ( _mate[y]!=INVALID ) { //grow |
---|
581 | ear.set(y,x); |
---|
582 | Node w=_mate[y]; |
---|
583 | rep[blossom.insert(w)] = w; |
---|
584 | position.set(y,A); |
---|
585 | position.set(w,D); |
---|
586 | int t = tree.find(rep[blossom.find(x)]); |
---|
587 | tree.insert(y,t); |
---|
588 | tree.insert(w,t); |
---|
589 | Q.push(w); |
---|
590 | } else { //augment |
---|
591 | augment(x, ear, blossom, rep, tree); |
---|
592 | _mate.set(x,y); |
---|
593 | _mate.set(y,x); |
---|
594 | return true; |
---|
595 | } |
---|
596 | return false; |
---|
597 | } |
---|
598 | |
---|
599 | void augment(Node x, typename Graph::template NodeMap<Node>& ear, |
---|
600 | UFE& blossom, NV& rep, EFE& tree) { |
---|
601 | Node v=_mate[x]; |
---|
602 | while ( v!=INVALID ) { |
---|
603 | |
---|
604 | Node u=ear[v]; |
---|
605 | _mate.set(v,u); |
---|
606 | Node tmp=v; |
---|
607 | v=_mate[u]; |
---|
608 | _mate.set(u,tmp); |
---|
609 | } |
---|
610 | int y = tree.find(rep[blossom.find(x)]); |
---|
611 | for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) { |
---|
612 | if ( position[tit] == D ) { |
---|
613 | int b = blossom.find(tit); |
---|
614 | for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) { |
---|
615 | position.set(bit, C); |
---|
616 | } |
---|
617 | blossom.eraseClass(b); |
---|
618 | } else position.set(tit, C); |
---|
619 | } |
---|
620 | tree.eraseClass(y); |
---|
621 | |
---|
622 | } |
---|
623 | |
---|
624 | }; |
---|
625 | |
---|
626 | /// \ingroup matching |
---|
627 | /// |
---|
628 | /// \brief Weighted matching in general undirected graphs |
---|
629 | /// |
---|
630 | /// This class provides an efficient implementation of Edmond's |
---|
631 | /// maximum weighted matching algorithm. The implementation is based |
---|
632 | /// on extensive use of priority queues and provides |
---|
633 | /// \f$O(nm\log(n))\f$ time complexity. |
---|
634 | /// |
---|
635 | /// The maximum weighted matching problem is to find undirected |
---|
636 | /// edges in the graph with maximum overall weight and no two of |
---|
637 | /// them shares their endpoints. The problem can be formulated with |
---|
638 | /// the next linear program: |
---|
639 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
640 | ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f] |
---|
641 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
642 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
643 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
644 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both endpoints in |
---|
645 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of |
---|
646 | /// the nodes. |
---|
647 | /// |
---|
648 | /// The algorithm calculates an optimal matching and a proof of the |
---|
649 | /// optimality. The solution of the dual problem can be used to check |
---|
650 | /// the result of the algorithm. The dual linear problem is the next: |
---|
651 | /// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f] |
---|
652 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
653 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
654 | /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f] |
---|
655 | /// |
---|
656 | /// The algorithm can be executed with \c run() or the \c init() and |
---|
657 | /// then the \c start() member functions. After it the matching can |
---|
658 | /// be asked with \c matching() or mate() functions. The dual |
---|
659 | /// solution can be get with \c nodeValue(), \c blossomNum() and \c |
---|
660 | /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt |
---|
661 | /// "BlossomIt" nested class which is able to iterate on the nodes |
---|
662 | /// of a blossom. If the value type is integral then the dual |
---|
663 | /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4". |
---|
664 | /// |
---|
665 | /// \author Balazs Dezso |
---|
666 | template <typename _UGraph, |
---|
667 | typename _WeightMap = typename _UGraph::template UEdgeMap<int> > |
---|
668 | class MaxWeightedMatching { |
---|
669 | public: |
---|
670 | |
---|
671 | typedef _UGraph UGraph; |
---|
672 | typedef _WeightMap WeightMap; |
---|
673 | typedef typename WeightMap::Value Value; |
---|
674 | |
---|
675 | /// \brief Scaling factor for dual solution |
---|
676 | /// |
---|
677 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
678 | /// according to the value type. |
---|
679 | static const int dualScale = |
---|
680 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
681 | |
---|
682 | typedef typename UGraph::template NodeMap<typename UGraph::Edge> |
---|
683 | MatchingMap; |
---|
684 | |
---|
685 | private: |
---|
686 | |
---|
687 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
688 | |
---|
689 | typedef typename UGraph::template NodeMap<Value> NodePotential; |
---|
690 | typedef std::vector<Node> BlossomNodeList; |
---|
691 | |
---|
692 | struct BlossomVariable { |
---|
693 | int begin, end; |
---|
694 | Value value; |
---|
695 | |
---|
696 | BlossomVariable(int _begin, int _end, Value _value) |
---|
697 | : begin(_begin), end(_end), value(_value) {} |
---|
698 | |
---|
699 | }; |
---|
700 | |
---|
701 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
702 | |
---|
703 | const UGraph& _ugraph; |
---|
704 | const WeightMap& _weight; |
---|
705 | |
---|
706 | MatchingMap* _matching; |
---|
707 | |
---|
708 | NodePotential* _node_potential; |
---|
709 | |
---|
710 | BlossomPotential _blossom_potential; |
---|
711 | BlossomNodeList _blossom_node_list; |
---|
712 | |
---|
713 | int _node_num; |
---|
714 | int _blossom_num; |
---|
715 | |
---|
716 | typedef typename UGraph::template NodeMap<int> NodeIntMap; |
---|
717 | typedef typename UGraph::template EdgeMap<int> EdgeIntMap; |
---|
718 | typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap; |
---|
719 | typedef IntegerMap<int> IntIntMap; |
---|
720 | |
---|
721 | enum Status { |
---|
722 | EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2 |
---|
723 | }; |
---|
724 | |
---|
725 | typedef HeapUnionFind<Value, NodeIntMap> BlossomSet; |
---|
726 | struct BlossomData { |
---|
727 | int tree; |
---|
728 | Status status; |
---|
729 | Edge pred, next; |
---|
730 | Value pot, offset; |
---|
731 | Node base; |
---|
732 | }; |
---|
733 | |
---|
734 | NodeIntMap *_blossom_index; |
---|
735 | BlossomSet *_blossom_set; |
---|
736 | IntegerMap<BlossomData>* _blossom_data; |
---|
737 | |
---|
738 | NodeIntMap *_node_index; |
---|
739 | EdgeIntMap *_node_heap_index; |
---|
740 | |
---|
741 | struct NodeData { |
---|
742 | |
---|
743 | NodeData(EdgeIntMap& node_heap_index) |
---|
744 | : heap(node_heap_index) {} |
---|
745 | |
---|
746 | int blossom; |
---|
747 | Value pot; |
---|
748 | BinHeap<Value, EdgeIntMap> heap; |
---|
749 | std::map<int, Edge> heap_index; |
---|
750 | |
---|
751 | int tree; |
---|
752 | }; |
---|
753 | |
---|
754 | IntegerMap<NodeData>* _node_data; |
---|
755 | |
---|
756 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
757 | |
---|
758 | IntIntMap *_tree_set_index; |
---|
759 | TreeSet *_tree_set; |
---|
760 | |
---|
761 | NodeIntMap *_delta1_index; |
---|
762 | BinHeap<Value, NodeIntMap> *_delta1; |
---|
763 | |
---|
764 | IntIntMap *_delta2_index; |
---|
765 | BinHeap<Value, IntIntMap> *_delta2; |
---|
766 | |
---|
767 | UEdgeIntMap *_delta3_index; |
---|
768 | BinHeap<Value, UEdgeIntMap> *_delta3; |
---|
769 | |
---|
770 | IntIntMap *_delta4_index; |
---|
771 | BinHeap<Value, IntIntMap> *_delta4; |
---|
772 | |
---|
773 | Value _delta_sum; |
---|
774 | |
---|
775 | void createStructures() { |
---|
776 | _node_num = countNodes(_ugraph); |
---|
777 | _blossom_num = _node_num * 3 / 2; |
---|
778 | |
---|
779 | if (!_matching) { |
---|
780 | _matching = new MatchingMap(_ugraph); |
---|
781 | } |
---|
782 | if (!_node_potential) { |
---|
783 | _node_potential = new NodePotential(_ugraph); |
---|
784 | } |
---|
785 | if (!_blossom_set) { |
---|
786 | _blossom_index = new NodeIntMap(_ugraph); |
---|
787 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
788 | _blossom_data = new IntegerMap<BlossomData>(_blossom_num); |
---|
789 | } |
---|
790 | |
---|
791 | if (!_node_index) { |
---|
792 | _node_index = new NodeIntMap(_ugraph); |
---|
793 | _node_heap_index = new EdgeIntMap(_ugraph); |
---|
794 | _node_data = new IntegerMap<NodeData>(_node_num, |
---|
795 | NodeData(*_node_heap_index)); |
---|
796 | } |
---|
797 | |
---|
798 | if (!_tree_set) { |
---|
799 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
800 | _tree_set = new TreeSet(*_tree_set_index); |
---|
801 | } |
---|
802 | if (!_delta1) { |
---|
803 | _delta1_index = new NodeIntMap(_ugraph); |
---|
804 | _delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index); |
---|
805 | } |
---|
806 | if (!_delta2) { |
---|
807 | _delta2_index = new IntIntMap(_blossom_num); |
---|
808 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
809 | } |
---|
810 | if (!_delta3) { |
---|
811 | _delta3_index = new UEdgeIntMap(_ugraph); |
---|
812 | _delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index); |
---|
813 | } |
---|
814 | if (!_delta4) { |
---|
815 | _delta4_index = new IntIntMap(_blossom_num); |
---|
816 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
817 | } |
---|
818 | } |
---|
819 | |
---|
820 | void destroyStructures() { |
---|
821 | _node_num = countNodes(_ugraph); |
---|
822 | _blossom_num = _node_num * 3 / 2; |
---|
823 | |
---|
824 | if (_matching) { |
---|
825 | delete _matching; |
---|
826 | } |
---|
827 | if (_node_potential) { |
---|
828 | delete _node_potential; |
---|
829 | } |
---|
830 | if (_blossom_set) { |
---|
831 | delete _blossom_index; |
---|
832 | delete _blossom_set; |
---|
833 | delete _blossom_data; |
---|
834 | } |
---|
835 | |
---|
836 | if (_node_index) { |
---|
837 | delete _node_index; |
---|
838 | delete _node_heap_index; |
---|
839 | delete _node_data; |
---|
840 | } |
---|
841 | |
---|
842 | if (_tree_set) { |
---|
843 | delete _tree_set_index; |
---|
844 | delete _tree_set; |
---|
845 | } |
---|
846 | if (_delta1) { |
---|
847 | delete _delta1_index; |
---|
848 | delete _delta1; |
---|
849 | } |
---|
850 | if (_delta2) { |
---|
851 | delete _delta2_index; |
---|
852 | delete _delta2; |
---|
853 | } |
---|
854 | if (_delta3) { |
---|
855 | delete _delta3_index; |
---|
856 | delete _delta3; |
---|
857 | } |
---|
858 | if (_delta4) { |
---|
859 | delete _delta4_index; |
---|
860 | delete _delta4; |
---|
861 | } |
---|
862 | } |
---|
863 | |
---|
864 | void matchedToEven(int blossom, int tree) { |
---|
865 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
866 | _delta2->erase(blossom); |
---|
867 | } |
---|
868 | |
---|
869 | if (!_blossom_set->trivial(blossom)) { |
---|
870 | (*_blossom_data)[blossom].pot -= |
---|
871 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
872 | } |
---|
873 | |
---|
874 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
875 | n != INVALID; ++n) { |
---|
876 | |
---|
877 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
878 | int ni = (*_node_index)[n]; |
---|
879 | |
---|
880 | (*_node_data)[ni].heap.clear(); |
---|
881 | (*_node_data)[ni].heap_index.clear(); |
---|
882 | |
---|
883 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
884 | |
---|
885 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
886 | |
---|
887 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
888 | Node v = _ugraph.source(e); |
---|
889 | int vb = _blossom_set->find(v); |
---|
890 | int vi = (*_node_index)[v]; |
---|
891 | |
---|
892 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
893 | dualScale * _weight[e]; |
---|
894 | |
---|
895 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
896 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
897 | _delta3->push(e, rw / 2); |
---|
898 | } |
---|
899 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
900 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
901 | _delta3->push(e, rw); |
---|
902 | } |
---|
903 | } else { |
---|
904 | typename std::map<int, Edge>::iterator it = |
---|
905 | (*_node_data)[vi].heap_index.find(tree); |
---|
906 | |
---|
907 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
908 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
909 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
910 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
911 | it->second = e; |
---|
912 | } |
---|
913 | } else { |
---|
914 | (*_node_data)[vi].heap.push(e, rw); |
---|
915 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
916 | } |
---|
917 | |
---|
918 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
919 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
920 | |
---|
921 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
922 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
923 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
924 | (*_blossom_data)[vb].offset); |
---|
925 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
926 | (*_blossom_data)[vb].offset){ |
---|
927 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
928 | (*_blossom_data)[vb].offset); |
---|
929 | } |
---|
930 | } |
---|
931 | } |
---|
932 | } |
---|
933 | } |
---|
934 | } |
---|
935 | (*_blossom_data)[blossom].offset = 0; |
---|
936 | } |
---|
937 | |
---|
938 | void matchedToOdd(int blossom) { |
---|
939 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
940 | _delta2->erase(blossom); |
---|
941 | } |
---|
942 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
943 | if (!_blossom_set->trivial(blossom)) { |
---|
944 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
945 | (*_blossom_data)[blossom].offset); |
---|
946 | } |
---|
947 | } |
---|
948 | |
---|
949 | void evenToMatched(int blossom, int tree) { |
---|
950 | if (!_blossom_set->trivial(blossom)) { |
---|
951 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
952 | } |
---|
953 | |
---|
954 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
955 | n != INVALID; ++n) { |
---|
956 | int ni = (*_node_index)[n]; |
---|
957 | (*_node_data)[ni].pot -= _delta_sum; |
---|
958 | |
---|
959 | _delta1->erase(n); |
---|
960 | |
---|
961 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
962 | Node v = _ugraph.source(e); |
---|
963 | int vb = _blossom_set->find(v); |
---|
964 | int vi = (*_node_index)[v]; |
---|
965 | |
---|
966 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
967 | dualScale * _weight[e]; |
---|
968 | |
---|
969 | if (vb == blossom) { |
---|
970 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
971 | _delta3->erase(e); |
---|
972 | } |
---|
973 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
974 | |
---|
975 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
976 | _delta3->erase(e); |
---|
977 | } |
---|
978 | |
---|
979 | int vt = _tree_set->find(vb); |
---|
980 | |
---|
981 | if (vt != tree) { |
---|
982 | |
---|
983 | Edge r = _ugraph.oppositeEdge(e); |
---|
984 | |
---|
985 | typename std::map<int, Edge>::iterator it = |
---|
986 | (*_node_data)[ni].heap_index.find(vt); |
---|
987 | |
---|
988 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
989 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
990 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
991 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
992 | it->second = r; |
---|
993 | } |
---|
994 | } else { |
---|
995 | (*_node_data)[ni].heap.push(r, rw); |
---|
996 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
997 | } |
---|
998 | |
---|
999 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
1000 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
1001 | |
---|
1002 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
1003 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
1004 | (*_blossom_data)[blossom].offset); |
---|
1005 | } else if ((*_delta2)[blossom] > |
---|
1006 | _blossom_set->classPrio(blossom) - |
---|
1007 | (*_blossom_data)[blossom].offset){ |
---|
1008 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
1009 | (*_blossom_data)[blossom].offset); |
---|
1010 | } |
---|
1011 | } |
---|
1012 | } |
---|
1013 | |
---|
1014 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
1015 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1016 | _delta3->erase(e); |
---|
1017 | } |
---|
1018 | } else { |
---|
1019 | |
---|
1020 | typename std::map<int, Edge>::iterator it = |
---|
1021 | (*_node_data)[vi].heap_index.find(tree); |
---|
1022 | |
---|
1023 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
1024 | (*_node_data)[vi].heap.erase(it->second); |
---|
1025 | (*_node_data)[vi].heap_index.erase(it); |
---|
1026 | if ((*_node_data)[vi].heap.empty()) { |
---|
1027 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
1028 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
1029 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
1030 | } |
---|
1031 | |
---|
1032 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
1033 | if (_blossom_set->classPrio(vb) == |
---|
1034 | std::numeric_limits<Value>::max()) { |
---|
1035 | _delta2->erase(vb); |
---|
1036 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
1037 | (*_blossom_data)[vb].offset) { |
---|
1038 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
1039 | (*_blossom_data)[vb].offset); |
---|
1040 | } |
---|
1041 | } |
---|
1042 | } |
---|
1043 | } |
---|
1044 | } |
---|
1045 | } |
---|
1046 | } |
---|
1047 | |
---|
1048 | void oddToMatched(int blossom) { |
---|
1049 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
1050 | |
---|
1051 | if (_blossom_set->classPrio(blossom) != |
---|
1052 | std::numeric_limits<Value>::max()) { |
---|
1053 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
1054 | (*_blossom_data)[blossom].offset); |
---|
1055 | } |
---|
1056 | |
---|
1057 | if (!_blossom_set->trivial(blossom)) { |
---|
1058 | _delta4->erase(blossom); |
---|
1059 | } |
---|
1060 | } |
---|
1061 | |
---|
1062 | void oddToEven(int blossom, int tree) { |
---|
1063 | if (!_blossom_set->trivial(blossom)) { |
---|
1064 | _delta4->erase(blossom); |
---|
1065 | (*_blossom_data)[blossom].pot -= |
---|
1066 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
1067 | } |
---|
1068 | |
---|
1069 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
1070 | n != INVALID; ++n) { |
---|
1071 | int ni = (*_node_index)[n]; |
---|
1072 | |
---|
1073 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
1074 | |
---|
1075 | (*_node_data)[ni].heap.clear(); |
---|
1076 | (*_node_data)[ni].heap_index.clear(); |
---|
1077 | (*_node_data)[ni].pot += |
---|
1078 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
1079 | |
---|
1080 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
1081 | |
---|
1082 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
1083 | Node v = _ugraph.source(e); |
---|
1084 | int vb = _blossom_set->find(v); |
---|
1085 | int vi = (*_node_index)[v]; |
---|
1086 | |
---|
1087 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
1088 | dualScale * _weight[e]; |
---|
1089 | |
---|
1090 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
1091 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
1092 | _delta3->push(e, rw / 2); |
---|
1093 | } |
---|
1094 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
1095 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
1096 | _delta3->push(e, rw); |
---|
1097 | } |
---|
1098 | } else { |
---|
1099 | |
---|
1100 | typename std::map<int, Edge>::iterator it = |
---|
1101 | (*_node_data)[vi].heap_index.find(tree); |
---|
1102 | |
---|
1103 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
1104 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
1105 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
1106 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
1107 | it->second = e; |
---|
1108 | } |
---|
1109 | } else { |
---|
1110 | (*_node_data)[vi].heap.push(e, rw); |
---|
1111 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
1112 | } |
---|
1113 | |
---|
1114 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
1115 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
1116 | |
---|
1117 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
1118 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
1119 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
1120 | (*_blossom_data)[vb].offset); |
---|
1121 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
1122 | (*_blossom_data)[vb].offset) { |
---|
1123 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
1124 | (*_blossom_data)[vb].offset); |
---|
1125 | } |
---|
1126 | } |
---|
1127 | } |
---|
1128 | } |
---|
1129 | } |
---|
1130 | } |
---|
1131 | (*_blossom_data)[blossom].offset = 0; |
---|
1132 | } |
---|
1133 | |
---|
1134 | |
---|
1135 | void matchedToUnmatched(int blossom) { |
---|
1136 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
1137 | _delta2->erase(blossom); |
---|
1138 | } |
---|
1139 | |
---|
1140 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
1141 | n != INVALID; ++n) { |
---|
1142 | int ni = (*_node_index)[n]; |
---|
1143 | |
---|
1144 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
1145 | |
---|
1146 | (*_node_data)[ni].heap.clear(); |
---|
1147 | (*_node_data)[ni].heap_index.clear(); |
---|
1148 | |
---|
1149 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
1150 | Node v = _ugraph.target(e); |
---|
1151 | int vb = _blossom_set->find(v); |
---|
1152 | int vi = (*_node_index)[v]; |
---|
1153 | |
---|
1154 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
1155 | dualScale * _weight[e]; |
---|
1156 | |
---|
1157 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
1158 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
1159 | _delta3->push(e, rw); |
---|
1160 | } |
---|
1161 | } |
---|
1162 | } |
---|
1163 | } |
---|
1164 | } |
---|
1165 | |
---|
1166 | void unmatchedToMatched(int blossom) { |
---|
1167 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
1168 | n != INVALID; ++n) { |
---|
1169 | int ni = (*_node_index)[n]; |
---|
1170 | |
---|
1171 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
1172 | Node v = _ugraph.source(e); |
---|
1173 | int vb = _blossom_set->find(v); |
---|
1174 | int vi = (*_node_index)[v]; |
---|
1175 | |
---|
1176 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
1177 | dualScale * _weight[e]; |
---|
1178 | |
---|
1179 | if (vb == blossom) { |
---|
1180 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1181 | _delta3->erase(e); |
---|
1182 | } |
---|
1183 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
1184 | |
---|
1185 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1186 | _delta3->erase(e); |
---|
1187 | } |
---|
1188 | |
---|
1189 | int vt = _tree_set->find(vb); |
---|
1190 | |
---|
1191 | Edge r = _ugraph.oppositeEdge(e); |
---|
1192 | |
---|
1193 | typename std::map<int, Edge>::iterator it = |
---|
1194 | (*_node_data)[ni].heap_index.find(vt); |
---|
1195 | |
---|
1196 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
1197 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
1198 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
1199 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
1200 | it->second = r; |
---|
1201 | } |
---|
1202 | } else { |
---|
1203 | (*_node_data)[ni].heap.push(r, rw); |
---|
1204 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
1205 | } |
---|
1206 | |
---|
1207 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
1208 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
1209 | |
---|
1210 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
1211 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
1212 | (*_blossom_data)[blossom].offset); |
---|
1213 | } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)- |
---|
1214 | (*_blossom_data)[blossom].offset){ |
---|
1215 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
1216 | (*_blossom_data)[blossom].offset); |
---|
1217 | } |
---|
1218 | } |
---|
1219 | |
---|
1220 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
1221 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1222 | _delta3->erase(e); |
---|
1223 | } |
---|
1224 | } |
---|
1225 | } |
---|
1226 | } |
---|
1227 | } |
---|
1228 | |
---|
1229 | void alternatePath(int even, int tree) { |
---|
1230 | int odd; |
---|
1231 | |
---|
1232 | evenToMatched(even, tree); |
---|
1233 | (*_blossom_data)[even].status = MATCHED; |
---|
1234 | |
---|
1235 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
1236 | odd = _blossom_set->find(_ugraph.target((*_blossom_data)[even].pred)); |
---|
1237 | (*_blossom_data)[odd].status = MATCHED; |
---|
1238 | oddToMatched(odd); |
---|
1239 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
1240 | |
---|
1241 | even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred)); |
---|
1242 | (*_blossom_data)[even].status = MATCHED; |
---|
1243 | evenToMatched(even, tree); |
---|
1244 | (*_blossom_data)[even].next = |
---|
1245 | _ugraph.oppositeEdge((*_blossom_data)[odd].pred); |
---|
1246 | } |
---|
1247 | |
---|
1248 | } |
---|
1249 | |
---|
1250 | void destroyTree(int tree) { |
---|
1251 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
1252 | if ((*_blossom_data)[b].status == EVEN) { |
---|
1253 | (*_blossom_data)[b].status = MATCHED; |
---|
1254 | evenToMatched(b, tree); |
---|
1255 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
1256 | (*_blossom_data)[b].status = MATCHED; |
---|
1257 | oddToMatched(b); |
---|
1258 | } |
---|
1259 | } |
---|
1260 | _tree_set->eraseClass(tree); |
---|
1261 | } |
---|
1262 | |
---|
1263 | |
---|
1264 | void unmatchNode(const Node& node) { |
---|
1265 | int blossom = _blossom_set->find(node); |
---|
1266 | int tree = _tree_set->find(blossom); |
---|
1267 | |
---|
1268 | alternatePath(blossom, tree); |
---|
1269 | destroyTree(tree); |
---|
1270 | |
---|
1271 | (*_blossom_data)[blossom].status = UNMATCHED; |
---|
1272 | (*_blossom_data)[blossom].base = node; |
---|
1273 | matchedToUnmatched(blossom); |
---|
1274 | } |
---|
1275 | |
---|
1276 | |
---|
1277 | void augmentOnEdge(const UEdge& edge) { |
---|
1278 | |
---|
1279 | int left = _blossom_set->find(_ugraph.source(edge)); |
---|
1280 | int right = _blossom_set->find(_ugraph.target(edge)); |
---|
1281 | |
---|
1282 | if ((*_blossom_data)[left].status == EVEN) { |
---|
1283 | int left_tree = _tree_set->find(left); |
---|
1284 | alternatePath(left, left_tree); |
---|
1285 | destroyTree(left_tree); |
---|
1286 | } else { |
---|
1287 | (*_blossom_data)[left].status = MATCHED; |
---|
1288 | unmatchedToMatched(left); |
---|
1289 | } |
---|
1290 | |
---|
1291 | if ((*_blossom_data)[right].status == EVEN) { |
---|
1292 | int right_tree = _tree_set->find(right); |
---|
1293 | alternatePath(right, right_tree); |
---|
1294 | destroyTree(right_tree); |
---|
1295 | } else { |
---|
1296 | (*_blossom_data)[right].status = MATCHED; |
---|
1297 | unmatchedToMatched(right); |
---|
1298 | } |
---|
1299 | |
---|
1300 | (*_blossom_data)[left].next = _ugraph.direct(edge, true); |
---|
1301 | (*_blossom_data)[right].next = _ugraph.direct(edge, false); |
---|
1302 | } |
---|
1303 | |
---|
1304 | void extendOnEdge(const Edge& edge) { |
---|
1305 | int base = _blossom_set->find(_ugraph.target(edge)); |
---|
1306 | int tree = _tree_set->find(base); |
---|
1307 | |
---|
1308 | int odd = _blossom_set->find(_ugraph.source(edge)); |
---|
1309 | _tree_set->insert(odd, tree); |
---|
1310 | (*_blossom_data)[odd].status = ODD; |
---|
1311 | matchedToOdd(odd); |
---|
1312 | (*_blossom_data)[odd].pred = edge; |
---|
1313 | |
---|
1314 | int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next)); |
---|
1315 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
1316 | _tree_set->insert(even, tree); |
---|
1317 | (*_blossom_data)[even].status = EVEN; |
---|
1318 | matchedToEven(even, tree); |
---|
1319 | } |
---|
1320 | |
---|
1321 | void shrinkOnEdge(const UEdge& uedge, int tree) { |
---|
1322 | int nca = -1; |
---|
1323 | std::vector<int> left_path, right_path; |
---|
1324 | |
---|
1325 | { |
---|
1326 | std::set<int> left_set, right_set; |
---|
1327 | int left = _blossom_set->find(_ugraph.source(uedge)); |
---|
1328 | left_path.push_back(left); |
---|
1329 | left_set.insert(left); |
---|
1330 | |
---|
1331 | int right = _blossom_set->find(_ugraph.target(uedge)); |
---|
1332 | right_path.push_back(right); |
---|
1333 | right_set.insert(right); |
---|
1334 | |
---|
1335 | while (true) { |
---|
1336 | |
---|
1337 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
1338 | |
---|
1339 | left = |
---|
1340 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
1341 | left_path.push_back(left); |
---|
1342 | left = |
---|
1343 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
1344 | left_path.push_back(left); |
---|
1345 | |
---|
1346 | left_set.insert(left); |
---|
1347 | |
---|
1348 | if (right_set.find(left) != right_set.end()) { |
---|
1349 | nca = left; |
---|
1350 | break; |
---|
1351 | } |
---|
1352 | |
---|
1353 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
1354 | |
---|
1355 | right = |
---|
1356 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
1357 | right_path.push_back(right); |
---|
1358 | right = |
---|
1359 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
1360 | right_path.push_back(right); |
---|
1361 | |
---|
1362 | right_set.insert(right); |
---|
1363 | |
---|
1364 | if (left_set.find(right) != left_set.end()) { |
---|
1365 | nca = right; |
---|
1366 | break; |
---|
1367 | } |
---|
1368 | |
---|
1369 | } |
---|
1370 | |
---|
1371 | if (nca == -1) { |
---|
1372 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
1373 | nca = right; |
---|
1374 | while (left_set.find(nca) == left_set.end()) { |
---|
1375 | nca = |
---|
1376 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
1377 | right_path.push_back(nca); |
---|
1378 | nca = |
---|
1379 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
1380 | right_path.push_back(nca); |
---|
1381 | } |
---|
1382 | } else { |
---|
1383 | nca = left; |
---|
1384 | while (right_set.find(nca) == right_set.end()) { |
---|
1385 | nca = |
---|
1386 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
1387 | left_path.push_back(nca); |
---|
1388 | nca = |
---|
1389 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
1390 | left_path.push_back(nca); |
---|
1391 | } |
---|
1392 | } |
---|
1393 | } |
---|
1394 | } |
---|
1395 | |
---|
1396 | std::vector<int> subblossoms; |
---|
1397 | Edge prev; |
---|
1398 | |
---|
1399 | prev = _ugraph.direct(uedge, true); |
---|
1400 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
1401 | subblossoms.push_back(left_path[i]); |
---|
1402 | (*_blossom_data)[left_path[i]].next = prev; |
---|
1403 | _tree_set->erase(left_path[i]); |
---|
1404 | |
---|
1405 | subblossoms.push_back(left_path[i + 1]); |
---|
1406 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
1407 | oddToEven(left_path[i + 1], tree); |
---|
1408 | _tree_set->erase(left_path[i + 1]); |
---|
1409 | prev = _ugraph.oppositeEdge((*_blossom_data)[left_path[i + 1]].pred); |
---|
1410 | } |
---|
1411 | |
---|
1412 | int k = 0; |
---|
1413 | while (right_path[k] != nca) ++k; |
---|
1414 | |
---|
1415 | subblossoms.push_back(nca); |
---|
1416 | (*_blossom_data)[nca].next = prev; |
---|
1417 | |
---|
1418 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
1419 | subblossoms.push_back(right_path[i + 1]); |
---|
1420 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
1421 | oddToEven(right_path[i + 1], tree); |
---|
1422 | _tree_set->erase(right_path[i + 1]); |
---|
1423 | |
---|
1424 | (*_blossom_data)[right_path[i + 1]].next = |
---|
1425 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
1426 | |
---|
1427 | subblossoms.push_back(right_path[i]); |
---|
1428 | _tree_set->erase(right_path[i]); |
---|
1429 | } |
---|
1430 | |
---|
1431 | int surface = |
---|
1432 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
1433 | |
---|
1434 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
1435 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
1436 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
1437 | } |
---|
1438 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
1439 | } |
---|
1440 | |
---|
1441 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
1442 | (*_blossom_data)[surface].offset = 0; |
---|
1443 | (*_blossom_data)[surface].status = EVEN; |
---|
1444 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
1445 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
1446 | |
---|
1447 | _tree_set->insert(surface, tree); |
---|
1448 | _tree_set->erase(nca); |
---|
1449 | } |
---|
1450 | |
---|
1451 | void splitBlossom(int blossom) { |
---|
1452 | Edge next = (*_blossom_data)[blossom].next; |
---|
1453 | Edge pred = (*_blossom_data)[blossom].pred; |
---|
1454 | |
---|
1455 | int tree = _tree_set->find(blossom); |
---|
1456 | |
---|
1457 | (*_blossom_data)[blossom].status = MATCHED; |
---|
1458 | oddToMatched(blossom); |
---|
1459 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
1460 | _delta2->erase(blossom); |
---|
1461 | } |
---|
1462 | |
---|
1463 | std::vector<int> subblossoms; |
---|
1464 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
1465 | |
---|
1466 | Value offset = (*_blossom_data)[blossom].offset; |
---|
1467 | int b = _blossom_set->find(_ugraph.source(pred)); |
---|
1468 | int d = _blossom_set->find(_ugraph.source(next)); |
---|
1469 | |
---|
1470 | int ib, id; |
---|
1471 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
1472 | if (subblossoms[i] == b) ib = i; |
---|
1473 | if (subblossoms[i] == d) id = i; |
---|
1474 | |
---|
1475 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
1476 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
1477 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
1478 | } |
---|
1479 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
1480 | std::numeric_limits<Value>::max()) { |
---|
1481 | _delta2->push(subblossoms[i], |
---|
1482 | _blossom_set->classPrio(subblossoms[i]) - |
---|
1483 | (*_blossom_data)[subblossoms[i]].offset); |
---|
1484 | } |
---|
1485 | } |
---|
1486 | |
---|
1487 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
1488 | for (int i = (id + 1) % subblossoms.size(); |
---|
1489 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
1490 | int sb = subblossoms[i]; |
---|
1491 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1492 | (*_blossom_data)[sb].next = |
---|
1493 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
1494 | } |
---|
1495 | |
---|
1496 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
1497 | int sb = subblossoms[i]; |
---|
1498 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1499 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
1500 | |
---|
1501 | (*_blossom_data)[sb].status = ODD; |
---|
1502 | matchedToOdd(sb); |
---|
1503 | _tree_set->insert(sb, tree); |
---|
1504 | (*_blossom_data)[sb].pred = pred; |
---|
1505 | (*_blossom_data)[sb].next = |
---|
1506 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
1507 | |
---|
1508 | pred = (*_blossom_data)[ub].next; |
---|
1509 | |
---|
1510 | (*_blossom_data)[tb].status = EVEN; |
---|
1511 | matchedToEven(tb, tree); |
---|
1512 | _tree_set->insert(tb, tree); |
---|
1513 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
1514 | } |
---|
1515 | |
---|
1516 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
1517 | matchedToOdd(subblossoms[id]); |
---|
1518 | _tree_set->insert(subblossoms[id], tree); |
---|
1519 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
1520 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
1521 | |
---|
1522 | } else { |
---|
1523 | |
---|
1524 | for (int i = (ib + 1) % subblossoms.size(); |
---|
1525 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
1526 | int sb = subblossoms[i]; |
---|
1527 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1528 | (*_blossom_data)[sb].next = |
---|
1529 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
1530 | } |
---|
1531 | |
---|
1532 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
1533 | int sb = subblossoms[i]; |
---|
1534 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1535 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
1536 | |
---|
1537 | (*_blossom_data)[sb].status = ODD; |
---|
1538 | matchedToOdd(sb); |
---|
1539 | _tree_set->insert(sb, tree); |
---|
1540 | (*_blossom_data)[sb].next = next; |
---|
1541 | (*_blossom_data)[sb].pred = |
---|
1542 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
1543 | |
---|
1544 | (*_blossom_data)[tb].status = EVEN; |
---|
1545 | matchedToEven(tb, tree); |
---|
1546 | _tree_set->insert(tb, tree); |
---|
1547 | (*_blossom_data)[tb].pred = |
---|
1548 | (*_blossom_data)[tb].next = |
---|
1549 | _ugraph.oppositeEdge((*_blossom_data)[ub].next); |
---|
1550 | next = (*_blossom_data)[ub].next; |
---|
1551 | } |
---|
1552 | |
---|
1553 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
1554 | matchedToOdd(subblossoms[ib]); |
---|
1555 | _tree_set->insert(subblossoms[ib], tree); |
---|
1556 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
1557 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
1558 | } |
---|
1559 | _tree_set->erase(blossom); |
---|
1560 | } |
---|
1561 | |
---|
1562 | void extractBlossom(int blossom, const Node& base, const Edge& matching) { |
---|
1563 | if (_blossom_set->trivial(blossom)) { |
---|
1564 | int bi = (*_node_index)[base]; |
---|
1565 | Value pot = (*_node_data)[bi].pot; |
---|
1566 | |
---|
1567 | _matching->set(base, matching); |
---|
1568 | _blossom_node_list.push_back(base); |
---|
1569 | _node_potential->set(base, pot); |
---|
1570 | } else { |
---|
1571 | |
---|
1572 | Value pot = (*_blossom_data)[blossom].pot; |
---|
1573 | int bn = _blossom_node_list.size(); |
---|
1574 | |
---|
1575 | std::vector<int> subblossoms; |
---|
1576 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
1577 | int b = _blossom_set->find(base); |
---|
1578 | int ib = -1; |
---|
1579 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
1580 | if (subblossoms[i] == b) { ib = i; break; } |
---|
1581 | } |
---|
1582 | |
---|
1583 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
1584 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
1585 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
1586 | |
---|
1587 | Edge m = (*_blossom_data)[tb].next; |
---|
1588 | extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m)); |
---|
1589 | extractBlossom(tb, _ugraph.source(m), m); |
---|
1590 | } |
---|
1591 | extractBlossom(subblossoms[ib], base, matching); |
---|
1592 | |
---|
1593 | int en = _blossom_node_list.size(); |
---|
1594 | |
---|
1595 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
1596 | } |
---|
1597 | } |
---|
1598 | |
---|
1599 | void extractMatching() { |
---|
1600 | std::vector<int> blossoms; |
---|
1601 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
1602 | blossoms.push_back(c); |
---|
1603 | } |
---|
1604 | |
---|
1605 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
1606 | if ((*_blossom_data)[blossoms[i]].status == MATCHED) { |
---|
1607 | |
---|
1608 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
1609 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
1610 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
1611 | n != INVALID; ++n) { |
---|
1612 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
1613 | } |
---|
1614 | |
---|
1615 | Edge matching = (*_blossom_data)[blossoms[i]].next; |
---|
1616 | Node base = _ugraph.source(matching); |
---|
1617 | extractBlossom(blossoms[i], base, matching); |
---|
1618 | } else { |
---|
1619 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
1620 | extractBlossom(blossoms[i], base, INVALID); |
---|
1621 | } |
---|
1622 | } |
---|
1623 | } |
---|
1624 | |
---|
1625 | public: |
---|
1626 | |
---|
1627 | /// \brief Constructor |
---|
1628 | /// |
---|
1629 | /// Constructor. |
---|
1630 | MaxWeightedMatching(const UGraph& ugraph, const WeightMap& weight) |
---|
1631 | : _ugraph(ugraph), _weight(weight), _matching(0), |
---|
1632 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
1633 | _node_num(0), _blossom_num(0), |
---|
1634 | |
---|
1635 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
1636 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
1637 | _tree_set_index(0), _tree_set(0), |
---|
1638 | |
---|
1639 | _delta1_index(0), _delta1(0), |
---|
1640 | _delta2_index(0), _delta2(0), |
---|
1641 | _delta3_index(0), _delta3(0), |
---|
1642 | _delta4_index(0), _delta4(0), |
---|
1643 | |
---|
1644 | _delta_sum() {} |
---|
1645 | |
---|
1646 | ~MaxWeightedMatching() { |
---|
1647 | destroyStructures(); |
---|
1648 | } |
---|
1649 | |
---|
1650 | /// \name Execution control |
---|
1651 | /// The simplest way to execute the algorithm is to use the member |
---|
1652 | /// \c run() member function. |
---|
1653 | |
---|
1654 | ///@{ |
---|
1655 | |
---|
1656 | /// \brief Initialize the algorithm |
---|
1657 | /// |
---|
1658 | /// Initialize the algorithm |
---|
1659 | void init() { |
---|
1660 | createStructures(); |
---|
1661 | |
---|
1662 | for (EdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
1663 | _node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP); |
---|
1664 | } |
---|
1665 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
1666 | _delta1_index->set(n, _delta1->PRE_HEAP); |
---|
1667 | } |
---|
1668 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
1669 | _delta3_index->set(e, _delta3->PRE_HEAP); |
---|
1670 | } |
---|
1671 | for (int i = 0; i < _blossom_num; ++i) { |
---|
1672 | _delta2_index->set(i, _delta2->PRE_HEAP); |
---|
1673 | _delta4_index->set(i, _delta4->PRE_HEAP); |
---|
1674 | } |
---|
1675 | |
---|
1676 | int index = 0; |
---|
1677 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
1678 | Value max = 0; |
---|
1679 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
1680 | if (_ugraph.target(e) == n) continue; |
---|
1681 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
1682 | max = (dualScale * _weight[e]) / 2; |
---|
1683 | } |
---|
1684 | } |
---|
1685 | _node_index->set(n, index); |
---|
1686 | (*_node_data)[index].pot = max; |
---|
1687 | _delta1->push(n, max); |
---|
1688 | int blossom = |
---|
1689 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
1690 | |
---|
1691 | _tree_set->insert(blossom); |
---|
1692 | |
---|
1693 | (*_blossom_data)[blossom].status = EVEN; |
---|
1694 | (*_blossom_data)[blossom].pred = INVALID; |
---|
1695 | (*_blossom_data)[blossom].next = INVALID; |
---|
1696 | (*_blossom_data)[blossom].pot = 0; |
---|
1697 | (*_blossom_data)[blossom].offset = 0; |
---|
1698 | ++index; |
---|
1699 | } |
---|
1700 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
1701 | int si = (*_node_index)[_ugraph.source(e)]; |
---|
1702 | int ti = (*_node_index)[_ugraph.target(e)]; |
---|
1703 | if (_ugraph.source(e) != _ugraph.target(e)) { |
---|
1704 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
1705 | dualScale * _weight[e]) / 2); |
---|
1706 | } |
---|
1707 | } |
---|
1708 | } |
---|
1709 | |
---|
1710 | /// \brief Starts the algorithm |
---|
1711 | /// |
---|
1712 | /// Starts the algorithm |
---|
1713 | void start() { |
---|
1714 | enum OpType { |
---|
1715 | D1, D2, D3, D4 |
---|
1716 | }; |
---|
1717 | |
---|
1718 | int unmatched = _node_num; |
---|
1719 | while (unmatched > 0) { |
---|
1720 | Value d1 = !_delta1->empty() ? |
---|
1721 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
1722 | |
---|
1723 | Value d2 = !_delta2->empty() ? |
---|
1724 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
1725 | |
---|
1726 | Value d3 = !_delta3->empty() ? |
---|
1727 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
1728 | |
---|
1729 | Value d4 = !_delta4->empty() ? |
---|
1730 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
1731 | |
---|
1732 | _delta_sum = d1; OpType ot = D1; |
---|
1733 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
1734 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
1735 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
1736 | |
---|
1737 | |
---|
1738 | switch (ot) { |
---|
1739 | case D1: |
---|
1740 | { |
---|
1741 | Node n = _delta1->top(); |
---|
1742 | unmatchNode(n); |
---|
1743 | --unmatched; |
---|
1744 | } |
---|
1745 | break; |
---|
1746 | case D2: |
---|
1747 | { |
---|
1748 | int blossom = _delta2->top(); |
---|
1749 | Node n = _blossom_set->classTop(blossom); |
---|
1750 | Edge e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
1751 | extendOnEdge(e); |
---|
1752 | } |
---|
1753 | break; |
---|
1754 | case D3: |
---|
1755 | { |
---|
1756 | UEdge e = _delta3->top(); |
---|
1757 | |
---|
1758 | int left_blossom = _blossom_set->find(_ugraph.source(e)); |
---|
1759 | int right_blossom = _blossom_set->find(_ugraph.target(e)); |
---|
1760 | |
---|
1761 | if (left_blossom == right_blossom) { |
---|
1762 | _delta3->pop(); |
---|
1763 | } else { |
---|
1764 | int left_tree; |
---|
1765 | if ((*_blossom_data)[left_blossom].status == EVEN) { |
---|
1766 | left_tree = _tree_set->find(left_blossom); |
---|
1767 | } else { |
---|
1768 | left_tree = -1; |
---|
1769 | ++unmatched; |
---|
1770 | } |
---|
1771 | int right_tree; |
---|
1772 | if ((*_blossom_data)[right_blossom].status == EVEN) { |
---|
1773 | right_tree = _tree_set->find(right_blossom); |
---|
1774 | } else { |
---|
1775 | right_tree = -1; |
---|
1776 | ++unmatched; |
---|
1777 | } |
---|
1778 | |
---|
1779 | if (left_tree == right_tree) { |
---|
1780 | shrinkOnEdge(e, left_tree); |
---|
1781 | } else { |
---|
1782 | augmentOnEdge(e); |
---|
1783 | unmatched -= 2; |
---|
1784 | } |
---|
1785 | } |
---|
1786 | } break; |
---|
1787 | case D4: |
---|
1788 | splitBlossom(_delta4->top()); |
---|
1789 | break; |
---|
1790 | } |
---|
1791 | } |
---|
1792 | extractMatching(); |
---|
1793 | } |
---|
1794 | |
---|
1795 | /// \brief Runs %MaxWeightedMatching algorithm. |
---|
1796 | /// |
---|
1797 | /// This method runs the %MaxWeightedMatching algorithm. |
---|
1798 | /// |
---|
1799 | /// \note mwm.run() is just a shortcut of the following code. |
---|
1800 | /// \code |
---|
1801 | /// mwm.init(); |
---|
1802 | /// mwm.start(); |
---|
1803 | /// \endcode |
---|
1804 | void run() { |
---|
1805 | init(); |
---|
1806 | start(); |
---|
1807 | } |
---|
1808 | |
---|
1809 | /// @} |
---|
1810 | |
---|
1811 | /// \name Primal solution |
---|
1812 | /// Functions for get the primal solution, ie. the matching. |
---|
1813 | |
---|
1814 | /// @{ |
---|
1815 | |
---|
1816 | /// \brief Returns the matching value. |
---|
1817 | /// |
---|
1818 | /// Returns the matching value. |
---|
1819 | Value matchingValue() const { |
---|
1820 | Value sum = 0; |
---|
1821 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
1822 | if ((*_matching)[n] != INVALID) { |
---|
1823 | sum += _weight[(*_matching)[n]]; |
---|
1824 | } |
---|
1825 | } |
---|
1826 | return sum /= 2; |
---|
1827 | } |
---|
1828 | |
---|
1829 | /// \brief Returns true when the edge is in the matching. |
---|
1830 | /// |
---|
1831 | /// Returns true when the edge is in the matching. |
---|
1832 | bool matching(const UEdge& edge) const { |
---|
1833 | return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true); |
---|
1834 | } |
---|
1835 | |
---|
1836 | /// \brief Returns the incident matching edge. |
---|
1837 | /// |
---|
1838 | /// Returns the incident matching edge from given node. If the |
---|
1839 | /// node is not matched then it gives back \c INVALID. |
---|
1840 | Edge matching(const Node& node) const { |
---|
1841 | return (*_matching)[node]; |
---|
1842 | } |
---|
1843 | |
---|
1844 | /// \brief Returns the mate of the node. |
---|
1845 | /// |
---|
1846 | /// Returns the adjancent node in a mathcing edge. If the node is |
---|
1847 | /// not matched then it gives back \c INVALID. |
---|
1848 | Node mate(const Node& node) const { |
---|
1849 | return (*_matching)[node] != INVALID ? |
---|
1850 | _ugraph.target((*_matching)[node]) : INVALID; |
---|
1851 | } |
---|
1852 | |
---|
1853 | /// @} |
---|
1854 | |
---|
1855 | /// \name Dual solution |
---|
1856 | /// Functions for get the dual solution. |
---|
1857 | |
---|
1858 | /// @{ |
---|
1859 | |
---|
1860 | /// \brief Returns the value of the dual solution. |
---|
1861 | /// |
---|
1862 | /// Returns the value of the dual solution. It should be equal to |
---|
1863 | /// the primal value scaled by \ref dualScale "dual scale". |
---|
1864 | Value dualValue() const { |
---|
1865 | Value sum = 0; |
---|
1866 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
1867 | sum += nodeValue(n); |
---|
1868 | } |
---|
1869 | for (int i = 0; i < blossomNum(); ++i) { |
---|
1870 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
1871 | } |
---|
1872 | return sum; |
---|
1873 | } |
---|
1874 | |
---|
1875 | /// \brief Returns the value of the node. |
---|
1876 | /// |
---|
1877 | /// Returns the the value of the node. |
---|
1878 | Value nodeValue(const Node& n) const { |
---|
1879 | return (*_node_potential)[n]; |
---|
1880 | } |
---|
1881 | |
---|
1882 | /// \brief Returns the number of the blossoms in the basis. |
---|
1883 | /// |
---|
1884 | /// Returns the number of the blossoms in the basis. |
---|
1885 | /// \see BlossomIt |
---|
1886 | int blossomNum() const { |
---|
1887 | return _blossom_potential.size(); |
---|
1888 | } |
---|
1889 | |
---|
1890 | |
---|
1891 | /// \brief Returns the number of the nodes in the blossom. |
---|
1892 | /// |
---|
1893 | /// Returns the number of the nodes in the blossom. |
---|
1894 | int blossomSize(int k) const { |
---|
1895 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
1896 | } |
---|
1897 | |
---|
1898 | /// \brief Returns the value of the blossom. |
---|
1899 | /// |
---|
1900 | /// Returns the the value of the blossom. |
---|
1901 | /// \see BlossomIt |
---|
1902 | Value blossomValue(int k) const { |
---|
1903 | return _blossom_potential[k].value; |
---|
1904 | } |
---|
1905 | |
---|
1906 | /// \brief Lemon iterator for get the items of the blossom. |
---|
1907 | /// |
---|
1908 | /// Lemon iterator for get the nodes of the blossom. This class |
---|
1909 | /// provides a common style lemon iterator which gives back a |
---|
1910 | /// subset of the nodes. |
---|
1911 | class BlossomIt { |
---|
1912 | public: |
---|
1913 | |
---|
1914 | /// \brief Constructor. |
---|
1915 | /// |
---|
1916 | /// Constructor for get the nodes of the variable. |
---|
1917 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
1918 | : _algorithm(&algorithm) |
---|
1919 | { |
---|
1920 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
1921 | _last = _algorithm->_blossom_potential[variable].end; |
---|
1922 | } |
---|
1923 | |
---|
1924 | /// \brief Invalid constructor. |
---|
1925 | /// |
---|
1926 | /// Invalid constructor. |
---|
1927 | BlossomIt(Invalid) : _index(-1) {} |
---|
1928 | |
---|
1929 | /// \brief Conversion to node. |
---|
1930 | /// |
---|
1931 | /// Conversion to node. |
---|
1932 | operator Node() const { |
---|
1933 | return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID; |
---|
1934 | } |
---|
1935 | |
---|
1936 | /// \brief Increment operator. |
---|
1937 | /// |
---|
1938 | /// Increment operator. |
---|
1939 | BlossomIt& operator++() { |
---|
1940 | ++_index; |
---|
1941 | if (_index == _last) { |
---|
1942 | _index = -1; |
---|
1943 | } |
---|
1944 | return *this; |
---|
1945 | } |
---|
1946 | |
---|
1947 | bool operator==(const BlossomIt& it) const { |
---|
1948 | return _index == it._index; |
---|
1949 | } |
---|
1950 | bool operator!=(const BlossomIt& it) const { |
---|
1951 | return _index != it._index; |
---|
1952 | } |
---|
1953 | |
---|
1954 | private: |
---|
1955 | const MaxWeightedMatching* _algorithm; |
---|
1956 | int _last; |
---|
1957 | int _index; |
---|
1958 | }; |
---|
1959 | |
---|
1960 | /// @} |
---|
1961 | |
---|
1962 | }; |
---|
1963 | |
---|
1964 | /// \ingroup matching |
---|
1965 | /// |
---|
1966 | /// \brief Weighted perfect matching in general undirected graphs |
---|
1967 | /// |
---|
1968 | /// This class provides an efficient implementation of Edmond's |
---|
1969 | /// maximum weighted perfecr matching algorithm. The implementation |
---|
1970 | /// is based on extensive use of priority queues and provides |
---|
1971 | /// \f$O(nm\log(n))\f$ time complexity. |
---|
1972 | /// |
---|
1973 | /// The maximum weighted matching problem is to find undirected |
---|
1974 | /// edges in the graph with maximum overall weight and no two of |
---|
1975 | /// them shares their endpoints and covers all nodes. The problem |
---|
1976 | /// can be formulated with the next linear program: |
---|
1977 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
1978 | ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f] |
---|
1979 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
1980 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
1981 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
1982 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both endpoints in |
---|
1983 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of |
---|
1984 | /// the nodes. |
---|
1985 | /// |
---|
1986 | /// The algorithm calculates an optimal matching and a proof of the |
---|
1987 | /// optimality. The solution of the dual problem can be used to check |
---|
1988 | /// the result of the algorithm. The dual linear problem is the next: |
---|
1989 | /// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f] |
---|
1990 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
1991 | /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f] |
---|
1992 | /// |
---|
1993 | /// The algorithm can be executed with \c run() or the \c init() and |
---|
1994 | /// then the \c start() member functions. After it the matching can |
---|
1995 | /// be asked with \c matching() or mate() functions. The dual |
---|
1996 | /// solution can be get with \c nodeValue(), \c blossomNum() and \c |
---|
1997 | /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt |
---|
1998 | /// "BlossomIt" nested class which is able to iterate on the nodes |
---|
1999 | /// of a blossom. If the value type is integral then the dual |
---|
2000 | /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4". |
---|
2001 | /// |
---|
2002 | /// \author Balazs Dezso |
---|
2003 | template <typename _UGraph, |
---|
2004 | typename _WeightMap = typename _UGraph::template UEdgeMap<int> > |
---|
2005 | class MaxWeightedPerfectMatching { |
---|
2006 | public: |
---|
2007 | |
---|
2008 | typedef _UGraph UGraph; |
---|
2009 | typedef _WeightMap WeightMap; |
---|
2010 | typedef typename WeightMap::Value Value; |
---|
2011 | |
---|
2012 | /// \brief Scaling factor for dual solution |
---|
2013 | /// |
---|
2014 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
2015 | /// according to the value type. |
---|
2016 | static const int dualScale = |
---|
2017 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
2018 | |
---|
2019 | typedef typename UGraph::template NodeMap<typename UGraph::Edge> |
---|
2020 | MatchingMap; |
---|
2021 | |
---|
2022 | private: |
---|
2023 | |
---|
2024 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
2025 | |
---|
2026 | typedef typename UGraph::template NodeMap<Value> NodePotential; |
---|
2027 | typedef std::vector<Node> BlossomNodeList; |
---|
2028 | |
---|
2029 | struct BlossomVariable { |
---|
2030 | int begin, end; |
---|
2031 | Value value; |
---|
2032 | |
---|
2033 | BlossomVariable(int _begin, int _end, Value _value) |
---|
2034 | : begin(_begin), end(_end), value(_value) {} |
---|
2035 | |
---|
2036 | }; |
---|
2037 | |
---|
2038 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
2039 | |
---|
2040 | const UGraph& _ugraph; |
---|
2041 | const WeightMap& _weight; |
---|
2042 | |
---|
2043 | MatchingMap* _matching; |
---|
2044 | |
---|
2045 | NodePotential* _node_potential; |
---|
2046 | |
---|
2047 | BlossomPotential _blossom_potential; |
---|
2048 | BlossomNodeList _blossom_node_list; |
---|
2049 | |
---|
2050 | int _node_num; |
---|
2051 | int _blossom_num; |
---|
2052 | |
---|
2053 | typedef typename UGraph::template NodeMap<int> NodeIntMap; |
---|
2054 | typedef typename UGraph::template EdgeMap<int> EdgeIntMap; |
---|
2055 | typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap; |
---|
2056 | typedef IntegerMap<int> IntIntMap; |
---|
2057 | |
---|
2058 | enum Status { |
---|
2059 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
2060 | }; |
---|
2061 | |
---|
2062 | typedef HeapUnionFind<Value, NodeIntMap> BlossomSet; |
---|
2063 | struct BlossomData { |
---|
2064 | int tree; |
---|
2065 | Status status; |
---|
2066 | Edge pred, next; |
---|
2067 | Value pot, offset; |
---|
2068 | }; |
---|
2069 | |
---|
2070 | NodeIntMap *_blossom_index; |
---|
2071 | BlossomSet *_blossom_set; |
---|
2072 | IntegerMap<BlossomData>* _blossom_data; |
---|
2073 | |
---|
2074 | NodeIntMap *_node_index; |
---|
2075 | EdgeIntMap *_node_heap_index; |
---|
2076 | |
---|
2077 | struct NodeData { |
---|
2078 | |
---|
2079 | NodeData(EdgeIntMap& node_heap_index) |
---|
2080 | : heap(node_heap_index) {} |
---|
2081 | |
---|
2082 | int blossom; |
---|
2083 | Value pot; |
---|
2084 | BinHeap<Value, EdgeIntMap> heap; |
---|
2085 | std::map<int, Edge> heap_index; |
---|
2086 | |
---|
2087 | int tree; |
---|
2088 | }; |
---|
2089 | |
---|
2090 | IntegerMap<NodeData>* _node_data; |
---|
2091 | |
---|
2092 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
2093 | |
---|
2094 | IntIntMap *_tree_set_index; |
---|
2095 | TreeSet *_tree_set; |
---|
2096 | |
---|
2097 | IntIntMap *_delta2_index; |
---|
2098 | BinHeap<Value, IntIntMap> *_delta2; |
---|
2099 | |
---|
2100 | UEdgeIntMap *_delta3_index; |
---|
2101 | BinHeap<Value, UEdgeIntMap> *_delta3; |
---|
2102 | |
---|
2103 | IntIntMap *_delta4_index; |
---|
2104 | BinHeap<Value, IntIntMap> *_delta4; |
---|
2105 | |
---|
2106 | Value _delta_sum; |
---|
2107 | |
---|
2108 | void createStructures() { |
---|
2109 | _node_num = countNodes(_ugraph); |
---|
2110 | _blossom_num = _node_num * 3 / 2; |
---|
2111 | |
---|
2112 | if (!_matching) { |
---|
2113 | _matching = new MatchingMap(_ugraph); |
---|
2114 | } |
---|
2115 | if (!_node_potential) { |
---|
2116 | _node_potential = new NodePotential(_ugraph); |
---|
2117 | } |
---|
2118 | if (!_blossom_set) { |
---|
2119 | _blossom_index = new NodeIntMap(_ugraph); |
---|
2120 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
2121 | _blossom_data = new IntegerMap<BlossomData>(_blossom_num); |
---|
2122 | } |
---|
2123 | |
---|
2124 | if (!_node_index) { |
---|
2125 | _node_index = new NodeIntMap(_ugraph); |
---|
2126 | _node_heap_index = new EdgeIntMap(_ugraph); |
---|
2127 | _node_data = new IntegerMap<NodeData>(_node_num, |
---|
2128 | NodeData(*_node_heap_index)); |
---|
2129 | } |
---|
2130 | |
---|
2131 | if (!_tree_set) { |
---|
2132 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
2133 | _tree_set = new TreeSet(*_tree_set_index); |
---|
2134 | } |
---|
2135 | if (!_delta2) { |
---|
2136 | _delta2_index = new IntIntMap(_blossom_num); |
---|
2137 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
2138 | } |
---|
2139 | if (!_delta3) { |
---|
2140 | _delta3_index = new UEdgeIntMap(_ugraph); |
---|
2141 | _delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index); |
---|
2142 | } |
---|
2143 | if (!_delta4) { |
---|
2144 | _delta4_index = new IntIntMap(_blossom_num); |
---|
2145 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
2146 | } |
---|
2147 | } |
---|
2148 | |
---|
2149 | void destroyStructures() { |
---|
2150 | _node_num = countNodes(_ugraph); |
---|
2151 | _blossom_num = _node_num * 3 / 2; |
---|
2152 | |
---|
2153 | if (_matching) { |
---|
2154 | delete _matching; |
---|
2155 | } |
---|
2156 | if (_node_potential) { |
---|
2157 | delete _node_potential; |
---|
2158 | } |
---|
2159 | if (_blossom_set) { |
---|
2160 | delete _blossom_index; |
---|
2161 | delete _blossom_set; |
---|
2162 | delete _blossom_data; |
---|
2163 | } |
---|
2164 | |
---|
2165 | if (_node_index) { |
---|
2166 | delete _node_index; |
---|
2167 | delete _node_heap_index; |
---|
2168 | delete _node_data; |
---|
2169 | } |
---|
2170 | |
---|
2171 | if (_tree_set) { |
---|
2172 | delete _tree_set_index; |
---|
2173 | delete _tree_set; |
---|
2174 | } |
---|
2175 | if (_delta2) { |
---|
2176 | delete _delta2_index; |
---|
2177 | delete _delta2; |
---|
2178 | } |
---|
2179 | if (_delta3) { |
---|
2180 | delete _delta3_index; |
---|
2181 | delete _delta3; |
---|
2182 | } |
---|
2183 | if (_delta4) { |
---|
2184 | delete _delta4_index; |
---|
2185 | delete _delta4; |
---|
2186 | } |
---|
2187 | } |
---|
2188 | |
---|
2189 | void matchedToEven(int blossom, int tree) { |
---|
2190 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
2191 | _delta2->erase(blossom); |
---|
2192 | } |
---|
2193 | |
---|
2194 | if (!_blossom_set->trivial(blossom)) { |
---|
2195 | (*_blossom_data)[blossom].pot -= |
---|
2196 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
2197 | } |
---|
2198 | |
---|
2199 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
2200 | n != INVALID; ++n) { |
---|
2201 | |
---|
2202 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
2203 | int ni = (*_node_index)[n]; |
---|
2204 | |
---|
2205 | (*_node_data)[ni].heap.clear(); |
---|
2206 | (*_node_data)[ni].heap_index.clear(); |
---|
2207 | |
---|
2208 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
2209 | |
---|
2210 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2211 | Node v = _ugraph.source(e); |
---|
2212 | int vb = _blossom_set->find(v); |
---|
2213 | int vi = (*_node_index)[v]; |
---|
2214 | |
---|
2215 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
2216 | dualScale * _weight[e]; |
---|
2217 | |
---|
2218 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
2219 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
2220 | _delta3->push(e, rw / 2); |
---|
2221 | } |
---|
2222 | } else { |
---|
2223 | typename std::map<int, Edge>::iterator it = |
---|
2224 | (*_node_data)[vi].heap_index.find(tree); |
---|
2225 | |
---|
2226 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
2227 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
2228 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
2229 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
2230 | it->second = e; |
---|
2231 | } |
---|
2232 | } else { |
---|
2233 | (*_node_data)[vi].heap.push(e, rw); |
---|
2234 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
2235 | } |
---|
2236 | |
---|
2237 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
2238 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
2239 | |
---|
2240 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
2241 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
2242 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
2243 | (*_blossom_data)[vb].offset); |
---|
2244 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
2245 | (*_blossom_data)[vb].offset){ |
---|
2246 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
2247 | (*_blossom_data)[vb].offset); |
---|
2248 | } |
---|
2249 | } |
---|
2250 | } |
---|
2251 | } |
---|
2252 | } |
---|
2253 | } |
---|
2254 | (*_blossom_data)[blossom].offset = 0; |
---|
2255 | } |
---|
2256 | |
---|
2257 | void matchedToOdd(int blossom) { |
---|
2258 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
2259 | _delta2->erase(blossom); |
---|
2260 | } |
---|
2261 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
2262 | if (!_blossom_set->trivial(blossom)) { |
---|
2263 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
2264 | (*_blossom_data)[blossom].offset); |
---|
2265 | } |
---|
2266 | } |
---|
2267 | |
---|
2268 | void evenToMatched(int blossom, int tree) { |
---|
2269 | if (!_blossom_set->trivial(blossom)) { |
---|
2270 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
2271 | } |
---|
2272 | |
---|
2273 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
2274 | n != INVALID; ++n) { |
---|
2275 | int ni = (*_node_index)[n]; |
---|
2276 | (*_node_data)[ni].pot -= _delta_sum; |
---|
2277 | |
---|
2278 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2279 | Node v = _ugraph.source(e); |
---|
2280 | int vb = _blossom_set->find(v); |
---|
2281 | int vi = (*_node_index)[v]; |
---|
2282 | |
---|
2283 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
2284 | dualScale * _weight[e]; |
---|
2285 | |
---|
2286 | if (vb == blossom) { |
---|
2287 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
2288 | _delta3->erase(e); |
---|
2289 | } |
---|
2290 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
2291 | |
---|
2292 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
2293 | _delta3->erase(e); |
---|
2294 | } |
---|
2295 | |
---|
2296 | int vt = _tree_set->find(vb); |
---|
2297 | |
---|
2298 | if (vt != tree) { |
---|
2299 | |
---|
2300 | Edge r = _ugraph.oppositeEdge(e); |
---|
2301 | |
---|
2302 | typename std::map<int, Edge>::iterator it = |
---|
2303 | (*_node_data)[ni].heap_index.find(vt); |
---|
2304 | |
---|
2305 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
2306 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
2307 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
2308 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
2309 | it->second = r; |
---|
2310 | } |
---|
2311 | } else { |
---|
2312 | (*_node_data)[ni].heap.push(r, rw); |
---|
2313 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
2314 | } |
---|
2315 | |
---|
2316 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
2317 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
2318 | |
---|
2319 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
2320 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
2321 | (*_blossom_data)[blossom].offset); |
---|
2322 | } else if ((*_delta2)[blossom] > |
---|
2323 | _blossom_set->classPrio(blossom) - |
---|
2324 | (*_blossom_data)[blossom].offset){ |
---|
2325 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
2326 | (*_blossom_data)[blossom].offset); |
---|
2327 | } |
---|
2328 | } |
---|
2329 | } |
---|
2330 | } else { |
---|
2331 | |
---|
2332 | typename std::map<int, Edge>::iterator it = |
---|
2333 | (*_node_data)[vi].heap_index.find(tree); |
---|
2334 | |
---|
2335 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
2336 | (*_node_data)[vi].heap.erase(it->second); |
---|
2337 | (*_node_data)[vi].heap_index.erase(it); |
---|
2338 | if ((*_node_data)[vi].heap.empty()) { |
---|
2339 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
2340 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
2341 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
2342 | } |
---|
2343 | |
---|
2344 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
2345 | if (_blossom_set->classPrio(vb) == |
---|
2346 | std::numeric_limits<Value>::max()) { |
---|
2347 | _delta2->erase(vb); |
---|
2348 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
2349 | (*_blossom_data)[vb].offset) { |
---|
2350 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
2351 | (*_blossom_data)[vb].offset); |
---|
2352 | } |
---|
2353 | } |
---|
2354 | } |
---|
2355 | } |
---|
2356 | } |
---|
2357 | } |
---|
2358 | } |
---|
2359 | |
---|
2360 | void oddToMatched(int blossom) { |
---|
2361 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
2362 | |
---|
2363 | if (_blossom_set->classPrio(blossom) != |
---|
2364 | std::numeric_limits<Value>::max()) { |
---|
2365 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
2366 | (*_blossom_data)[blossom].offset); |
---|
2367 | } |
---|
2368 | |
---|
2369 | if (!_blossom_set->trivial(blossom)) { |
---|
2370 | _delta4->erase(blossom); |
---|
2371 | } |
---|
2372 | } |
---|
2373 | |
---|
2374 | void oddToEven(int blossom, int tree) { |
---|
2375 | if (!_blossom_set->trivial(blossom)) { |
---|
2376 | _delta4->erase(blossom); |
---|
2377 | (*_blossom_data)[blossom].pot -= |
---|
2378 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
2379 | } |
---|
2380 | |
---|
2381 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
2382 | n != INVALID; ++n) { |
---|
2383 | int ni = (*_node_index)[n]; |
---|
2384 | |
---|
2385 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
2386 | |
---|
2387 | (*_node_data)[ni].heap.clear(); |
---|
2388 | (*_node_data)[ni].heap_index.clear(); |
---|
2389 | (*_node_data)[ni].pot += |
---|
2390 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
2391 | |
---|
2392 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2393 | Node v = _ugraph.source(e); |
---|
2394 | int vb = _blossom_set->find(v); |
---|
2395 | int vi = (*_node_index)[v]; |
---|
2396 | |
---|
2397 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
2398 | dualScale * _weight[e]; |
---|
2399 | |
---|
2400 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
2401 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
2402 | _delta3->push(e, rw / 2); |
---|
2403 | } |
---|
2404 | } else { |
---|
2405 | |
---|
2406 | typename std::map<int, Edge>::iterator it = |
---|
2407 | (*_node_data)[vi].heap_index.find(tree); |
---|
2408 | |
---|
2409 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
2410 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
2411 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
2412 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
2413 | it->second = e; |
---|
2414 | } |
---|
2415 | } else { |
---|
2416 | (*_node_data)[vi].heap.push(e, rw); |
---|
2417 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
2418 | } |
---|
2419 | |
---|
2420 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
2421 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
2422 | |
---|
2423 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
2424 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
2425 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
2426 | (*_blossom_data)[vb].offset); |
---|
2427 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
2428 | (*_blossom_data)[vb].offset) { |
---|
2429 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
2430 | (*_blossom_data)[vb].offset); |
---|
2431 | } |
---|
2432 | } |
---|
2433 | } |
---|
2434 | } |
---|
2435 | } |
---|
2436 | } |
---|
2437 | (*_blossom_data)[blossom].offset = 0; |
---|
2438 | } |
---|
2439 | |
---|
2440 | void alternatePath(int even, int tree) { |
---|
2441 | int odd; |
---|
2442 | |
---|
2443 | evenToMatched(even, tree); |
---|
2444 | (*_blossom_data)[even].status = MATCHED; |
---|
2445 | |
---|
2446 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
2447 | odd = _blossom_set->find(_ugraph.target((*_blossom_data)[even].pred)); |
---|
2448 | (*_blossom_data)[odd].status = MATCHED; |
---|
2449 | oddToMatched(odd); |
---|
2450 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
2451 | |
---|
2452 | even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred)); |
---|
2453 | (*_blossom_data)[even].status = MATCHED; |
---|
2454 | evenToMatched(even, tree); |
---|
2455 | (*_blossom_data)[even].next = |
---|
2456 | _ugraph.oppositeEdge((*_blossom_data)[odd].pred); |
---|
2457 | } |
---|
2458 | |
---|
2459 | } |
---|
2460 | |
---|
2461 | void destroyTree(int tree) { |
---|
2462 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
2463 | if ((*_blossom_data)[b].status == EVEN) { |
---|
2464 | (*_blossom_data)[b].status = MATCHED; |
---|
2465 | evenToMatched(b, tree); |
---|
2466 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
2467 | (*_blossom_data)[b].status = MATCHED; |
---|
2468 | oddToMatched(b); |
---|
2469 | } |
---|
2470 | } |
---|
2471 | _tree_set->eraseClass(tree); |
---|
2472 | } |
---|
2473 | |
---|
2474 | void augmentOnEdge(const UEdge& edge) { |
---|
2475 | |
---|
2476 | int left = _blossom_set->find(_ugraph.source(edge)); |
---|
2477 | int right = _blossom_set->find(_ugraph.target(edge)); |
---|
2478 | |
---|
2479 | int left_tree = _tree_set->find(left); |
---|
2480 | alternatePath(left, left_tree); |
---|
2481 | destroyTree(left_tree); |
---|
2482 | |
---|
2483 | int right_tree = _tree_set->find(right); |
---|
2484 | alternatePath(right, right_tree); |
---|
2485 | destroyTree(right_tree); |
---|
2486 | |
---|
2487 | (*_blossom_data)[left].next = _ugraph.direct(edge, true); |
---|
2488 | (*_blossom_data)[right].next = _ugraph.direct(edge, false); |
---|
2489 | } |
---|
2490 | |
---|
2491 | void extendOnEdge(const Edge& edge) { |
---|
2492 | int base = _blossom_set->find(_ugraph.target(edge)); |
---|
2493 | int tree = _tree_set->find(base); |
---|
2494 | |
---|
2495 | int odd = _blossom_set->find(_ugraph.source(edge)); |
---|
2496 | _tree_set->insert(odd, tree); |
---|
2497 | (*_blossom_data)[odd].status = ODD; |
---|
2498 | matchedToOdd(odd); |
---|
2499 | (*_blossom_data)[odd].pred = edge; |
---|
2500 | |
---|
2501 | int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next)); |
---|
2502 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
2503 | _tree_set->insert(even, tree); |
---|
2504 | (*_blossom_data)[even].status = EVEN; |
---|
2505 | matchedToEven(even, tree); |
---|
2506 | } |
---|
2507 | |
---|
2508 | void shrinkOnEdge(const UEdge& uedge, int tree) { |
---|
2509 | int nca = -1; |
---|
2510 | std::vector<int> left_path, right_path; |
---|
2511 | |
---|
2512 | { |
---|
2513 | std::set<int> left_set, right_set; |
---|
2514 | int left = _blossom_set->find(_ugraph.source(uedge)); |
---|
2515 | left_path.push_back(left); |
---|
2516 | left_set.insert(left); |
---|
2517 | |
---|
2518 | int right = _blossom_set->find(_ugraph.target(uedge)); |
---|
2519 | right_path.push_back(right); |
---|
2520 | right_set.insert(right); |
---|
2521 | |
---|
2522 | while (true) { |
---|
2523 | |
---|
2524 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
2525 | |
---|
2526 | left = |
---|
2527 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
2528 | left_path.push_back(left); |
---|
2529 | left = |
---|
2530 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
2531 | left_path.push_back(left); |
---|
2532 | |
---|
2533 | left_set.insert(left); |
---|
2534 | |
---|
2535 | if (right_set.find(left) != right_set.end()) { |
---|
2536 | nca = left; |
---|
2537 | break; |
---|
2538 | } |
---|
2539 | |
---|
2540 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
2541 | |
---|
2542 | right = |
---|
2543 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
2544 | right_path.push_back(right); |
---|
2545 | right = |
---|
2546 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
2547 | right_path.push_back(right); |
---|
2548 | |
---|
2549 | right_set.insert(right); |
---|
2550 | |
---|
2551 | if (left_set.find(right) != left_set.end()) { |
---|
2552 | nca = right; |
---|
2553 | break; |
---|
2554 | } |
---|
2555 | |
---|
2556 | } |
---|
2557 | |
---|
2558 | if (nca == -1) { |
---|
2559 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
2560 | nca = right; |
---|
2561 | while (left_set.find(nca) == left_set.end()) { |
---|
2562 | nca = |
---|
2563 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
2564 | right_path.push_back(nca); |
---|
2565 | nca = |
---|
2566 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
2567 | right_path.push_back(nca); |
---|
2568 | } |
---|
2569 | } else { |
---|
2570 | nca = left; |
---|
2571 | while (right_set.find(nca) == right_set.end()) { |
---|
2572 | nca = |
---|
2573 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
2574 | left_path.push_back(nca); |
---|
2575 | nca = |
---|
2576 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
2577 | left_path.push_back(nca); |
---|
2578 | } |
---|
2579 | } |
---|
2580 | } |
---|
2581 | } |
---|
2582 | |
---|
2583 | std::vector<int> subblossoms; |
---|
2584 | Edge prev; |
---|
2585 | |
---|
2586 | prev = _ugraph.direct(uedge, true); |
---|
2587 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
2588 | subblossoms.push_back(left_path[i]); |
---|
2589 | (*_blossom_data)[left_path[i]].next = prev; |
---|
2590 | _tree_set->erase(left_path[i]); |
---|
2591 | |
---|
2592 | subblossoms.push_back(left_path[i + 1]); |
---|
2593 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
2594 | oddToEven(left_path[i + 1], tree); |
---|
2595 | _tree_set->erase(left_path[i + 1]); |
---|
2596 | prev = _ugraph.oppositeEdge((*_blossom_data)[left_path[i + 1]].pred); |
---|
2597 | } |
---|
2598 | |
---|
2599 | int k = 0; |
---|
2600 | while (right_path[k] != nca) ++k; |
---|
2601 | |
---|
2602 | subblossoms.push_back(nca); |
---|
2603 | (*_blossom_data)[nca].next = prev; |
---|
2604 | |
---|
2605 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
2606 | subblossoms.push_back(right_path[i + 1]); |
---|
2607 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
2608 | oddToEven(right_path[i + 1], tree); |
---|
2609 | _tree_set->erase(right_path[i + 1]); |
---|
2610 | |
---|
2611 | (*_blossom_data)[right_path[i + 1]].next = |
---|
2612 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
2613 | |
---|
2614 | subblossoms.push_back(right_path[i]); |
---|
2615 | _tree_set->erase(right_path[i]); |
---|
2616 | } |
---|
2617 | |
---|
2618 | int surface = |
---|
2619 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
2620 | |
---|
2621 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
2622 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
2623 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
2624 | } |
---|
2625 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
2626 | } |
---|
2627 | |
---|
2628 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
2629 | (*_blossom_data)[surface].offset = 0; |
---|
2630 | (*_blossom_data)[surface].status = EVEN; |
---|
2631 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
2632 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
2633 | |
---|
2634 | _tree_set->insert(surface, tree); |
---|
2635 | _tree_set->erase(nca); |
---|
2636 | } |
---|
2637 | |
---|
2638 | void splitBlossom(int blossom) { |
---|
2639 | Edge next = (*_blossom_data)[blossom].next; |
---|
2640 | Edge pred = (*_blossom_data)[blossom].pred; |
---|
2641 | |
---|
2642 | int tree = _tree_set->find(blossom); |
---|
2643 | |
---|
2644 | (*_blossom_data)[blossom].status = MATCHED; |
---|
2645 | oddToMatched(blossom); |
---|
2646 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
2647 | _delta2->erase(blossom); |
---|
2648 | } |
---|
2649 | |
---|
2650 | std::vector<int> subblossoms; |
---|
2651 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
2652 | |
---|
2653 | Value offset = (*_blossom_data)[blossom].offset; |
---|
2654 | int b = _blossom_set->find(_ugraph.source(pred)); |
---|
2655 | int d = _blossom_set->find(_ugraph.source(next)); |
---|
2656 | |
---|
2657 | int ib, id; |
---|
2658 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
2659 | if (subblossoms[i] == b) ib = i; |
---|
2660 | if (subblossoms[i] == d) id = i; |
---|
2661 | |
---|
2662 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
2663 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
2664 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
2665 | } |
---|
2666 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
2667 | std::numeric_limits<Value>::max()) { |
---|
2668 | _delta2->push(subblossoms[i], |
---|
2669 | _blossom_set->classPrio(subblossoms[i]) - |
---|
2670 | (*_blossom_data)[subblossoms[i]].offset); |
---|
2671 | } |
---|
2672 | } |
---|
2673 | |
---|
2674 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
2675 | for (int i = (id + 1) % subblossoms.size(); |
---|
2676 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
2677 | int sb = subblossoms[i]; |
---|
2678 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2679 | (*_blossom_data)[sb].next = |
---|
2680 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
2681 | } |
---|
2682 | |
---|
2683 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
2684 | int sb = subblossoms[i]; |
---|
2685 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2686 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
2687 | |
---|
2688 | (*_blossom_data)[sb].status = ODD; |
---|
2689 | matchedToOdd(sb); |
---|
2690 | _tree_set->insert(sb, tree); |
---|
2691 | (*_blossom_data)[sb].pred = pred; |
---|
2692 | (*_blossom_data)[sb].next = |
---|
2693 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
2694 | |
---|
2695 | pred = (*_blossom_data)[ub].next; |
---|
2696 | |
---|
2697 | (*_blossom_data)[tb].status = EVEN; |
---|
2698 | matchedToEven(tb, tree); |
---|
2699 | _tree_set->insert(tb, tree); |
---|
2700 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
2701 | } |
---|
2702 | |
---|
2703 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
2704 | matchedToOdd(subblossoms[id]); |
---|
2705 | _tree_set->insert(subblossoms[id], tree); |
---|
2706 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
2707 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
2708 | |
---|
2709 | } else { |
---|
2710 | |
---|
2711 | for (int i = (ib + 1) % subblossoms.size(); |
---|
2712 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
2713 | int sb = subblossoms[i]; |
---|
2714 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2715 | (*_blossom_data)[sb].next = |
---|
2716 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
2717 | } |
---|
2718 | |
---|
2719 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
2720 | int sb = subblossoms[i]; |
---|
2721 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2722 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
2723 | |
---|
2724 | (*_blossom_data)[sb].status = ODD; |
---|
2725 | matchedToOdd(sb); |
---|
2726 | _tree_set->insert(sb, tree); |
---|
2727 | (*_blossom_data)[sb].next = next; |
---|
2728 | (*_blossom_data)[sb].pred = |
---|
2729 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
2730 | |
---|
2731 | (*_blossom_data)[tb].status = EVEN; |
---|
2732 | matchedToEven(tb, tree); |
---|
2733 | _tree_set->insert(tb, tree); |
---|
2734 | (*_blossom_data)[tb].pred = |
---|
2735 | (*_blossom_data)[tb].next = |
---|
2736 | _ugraph.oppositeEdge((*_blossom_data)[ub].next); |
---|
2737 | next = (*_blossom_data)[ub].next; |
---|
2738 | } |
---|
2739 | |
---|
2740 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
2741 | matchedToOdd(subblossoms[ib]); |
---|
2742 | _tree_set->insert(subblossoms[ib], tree); |
---|
2743 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
2744 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
2745 | } |
---|
2746 | _tree_set->erase(blossom); |
---|
2747 | } |
---|
2748 | |
---|
2749 | void extractBlossom(int blossom, const Node& base, const Edge& matching) { |
---|
2750 | if (_blossom_set->trivial(blossom)) { |
---|
2751 | int bi = (*_node_index)[base]; |
---|
2752 | Value pot = (*_node_data)[bi].pot; |
---|
2753 | |
---|
2754 | _matching->set(base, matching); |
---|
2755 | _blossom_node_list.push_back(base); |
---|
2756 | _node_potential->set(base, pot); |
---|
2757 | } else { |
---|
2758 | |
---|
2759 | Value pot = (*_blossom_data)[blossom].pot; |
---|
2760 | int bn = _blossom_node_list.size(); |
---|
2761 | |
---|
2762 | std::vector<int> subblossoms; |
---|
2763 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
2764 | int b = _blossom_set->find(base); |
---|
2765 | int ib = -1; |
---|
2766 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
2767 | if (subblossoms[i] == b) { ib = i; break; } |
---|
2768 | } |
---|
2769 | |
---|
2770 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
2771 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
2772 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
2773 | |
---|
2774 | Edge m = (*_blossom_data)[tb].next; |
---|
2775 | extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m)); |
---|
2776 | extractBlossom(tb, _ugraph.source(m), m); |
---|
2777 | } |
---|
2778 | extractBlossom(subblossoms[ib], base, matching); |
---|
2779 | |
---|
2780 | int en = _blossom_node_list.size(); |
---|
2781 | |
---|
2782 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
2783 | } |
---|
2784 | } |
---|
2785 | |
---|
2786 | void extractMatching() { |
---|
2787 | std::vector<int> blossoms; |
---|
2788 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
2789 | blossoms.push_back(c); |
---|
2790 | } |
---|
2791 | |
---|
2792 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
2793 | |
---|
2794 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
2795 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
2796 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
2797 | n != INVALID; ++n) { |
---|
2798 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
2799 | } |
---|
2800 | |
---|
2801 | Edge matching = (*_blossom_data)[blossoms[i]].next; |
---|
2802 | Node base = _ugraph.source(matching); |
---|
2803 | extractBlossom(blossoms[i], base, matching); |
---|
2804 | } |
---|
2805 | } |
---|
2806 | |
---|
2807 | public: |
---|
2808 | |
---|
2809 | /// \brief Constructor |
---|
2810 | /// |
---|
2811 | /// Constructor. |
---|
2812 | MaxWeightedPerfectMatching(const UGraph& ugraph, const WeightMap& weight) |
---|
2813 | : _ugraph(ugraph), _weight(weight), _matching(0), |
---|
2814 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
2815 | _node_num(0), _blossom_num(0), |
---|
2816 | |
---|
2817 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
2818 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
2819 | _tree_set_index(0), _tree_set(0), |
---|
2820 | |
---|
2821 | _delta2_index(0), _delta2(0), |
---|
2822 | _delta3_index(0), _delta3(0), |
---|
2823 | _delta4_index(0), _delta4(0), |
---|
2824 | |
---|
2825 | _delta_sum() {} |
---|
2826 | |
---|
2827 | ~MaxWeightedPerfectMatching() { |
---|
2828 | destroyStructures(); |
---|
2829 | } |
---|
2830 | |
---|
2831 | /// \name Execution control |
---|
2832 | /// The simplest way to execute the algorithm is to use the member |
---|
2833 | /// \c run() member function. |
---|
2834 | |
---|
2835 | ///@{ |
---|
2836 | |
---|
2837 | /// \brief Initialize the algorithm |
---|
2838 | /// |
---|
2839 | /// Initialize the algorithm |
---|
2840 | void init() { |
---|
2841 | createStructures(); |
---|
2842 | |
---|
2843 | for (EdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2844 | _node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP); |
---|
2845 | } |
---|
2846 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2847 | _delta3_index->set(e, _delta3->PRE_HEAP); |
---|
2848 | } |
---|
2849 | for (int i = 0; i < _blossom_num; ++i) { |
---|
2850 | _delta2_index->set(i, _delta2->PRE_HEAP); |
---|
2851 | _delta4_index->set(i, _delta4->PRE_HEAP); |
---|
2852 | } |
---|
2853 | |
---|
2854 | int index = 0; |
---|
2855 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
2856 | Value max = std::numeric_limits<Value>::min(); |
---|
2857 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
2858 | if (_ugraph.target(e) == n) continue; |
---|
2859 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
2860 | max = (dualScale * _weight[e]) / 2; |
---|
2861 | } |
---|
2862 | } |
---|
2863 | _node_index->set(n, index); |
---|
2864 | (*_node_data)[index].pot = max; |
---|
2865 | int blossom = |
---|
2866 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
2867 | |
---|
2868 | _tree_set->insert(blossom); |
---|
2869 | |
---|
2870 | (*_blossom_data)[blossom].status = EVEN; |
---|
2871 | (*_blossom_data)[blossom].pred = INVALID; |
---|
2872 | (*_blossom_data)[blossom].next = INVALID; |
---|
2873 | (*_blossom_data)[blossom].pot = 0; |
---|
2874 | (*_blossom_data)[blossom].offset = 0; |
---|
2875 | ++index; |
---|
2876 | } |
---|
2877 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
2878 | int si = (*_node_index)[_ugraph.source(e)]; |
---|
2879 | int ti = (*_node_index)[_ugraph.target(e)]; |
---|
2880 | if (_ugraph.source(e) != _ugraph.target(e)) { |
---|
2881 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
2882 | dualScale * _weight[e]) / 2); |
---|
2883 | } |
---|
2884 | } |
---|
2885 | } |
---|
2886 | |
---|
2887 | /// \brief Starts the algorithm |
---|
2888 | /// |
---|
2889 | /// Starts the algorithm |
---|
2890 | bool start() { |
---|
2891 | enum OpType { |
---|
2892 | D2, D3, D4 |
---|
2893 | }; |
---|
2894 | |
---|
2895 | int unmatched = _node_num; |
---|
2896 | while (unmatched > 0) { |
---|
2897 | Value d2 = !_delta2->empty() ? |
---|
2898 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
2899 | |
---|
2900 | Value d3 = !_delta3->empty() ? |
---|
2901 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
2902 | |
---|
2903 | Value d4 = !_delta4->empty() ? |
---|
2904 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
2905 | |
---|
2906 | _delta_sum = d2; OpType ot = D2; |
---|
2907 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
2908 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
2909 | |
---|
2910 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
2911 | return false; |
---|
2912 | } |
---|
2913 | |
---|
2914 | switch (ot) { |
---|
2915 | case D2: |
---|
2916 | { |
---|
2917 | int blossom = _delta2->top(); |
---|
2918 | Node n = _blossom_set->classTop(blossom); |
---|
2919 | Edge e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
2920 | extendOnEdge(e); |
---|
2921 | } |
---|
2922 | break; |
---|
2923 | case D3: |
---|
2924 | { |
---|
2925 | UEdge e = _delta3->top(); |
---|
2926 | |
---|
2927 | int left_blossom = _blossom_set->find(_ugraph.source(e)); |
---|
2928 | int right_blossom = _blossom_set->find(_ugraph.target(e)); |
---|
2929 | |
---|
2930 | if (left_blossom == right_blossom) { |
---|
2931 | _delta3->pop(); |
---|
2932 | } else { |
---|
2933 | int left_tree = _tree_set->find(left_blossom); |
---|
2934 | int right_tree = _tree_set->find(right_blossom); |
---|
2935 | |
---|
2936 | if (left_tree == right_tree) { |
---|
2937 | shrinkOnEdge(e, left_tree); |
---|
2938 | } else { |
---|
2939 | augmentOnEdge(e); |
---|
2940 | unmatched -= 2; |
---|
2941 | } |
---|
2942 | } |
---|
2943 | } break; |
---|
2944 | case D4: |
---|
2945 | splitBlossom(_delta4->top()); |
---|
2946 | break; |
---|
2947 | } |
---|
2948 | } |
---|
2949 | extractMatching(); |
---|
2950 | return true; |
---|
2951 | } |
---|
2952 | |
---|
2953 | /// \brief Runs %MaxWeightedPerfectMatching algorithm. |
---|
2954 | /// |
---|
2955 | /// This method runs the %MaxWeightedPerfectMatching algorithm. |
---|
2956 | /// |
---|
2957 | /// \note mwm.run() is just a shortcut of the following code. |
---|
2958 | /// \code |
---|
2959 | /// mwm.init(); |
---|
2960 | /// mwm.start(); |
---|
2961 | /// \endcode |
---|
2962 | bool run() { |
---|
2963 | init(); |
---|
2964 | return start(); |
---|
2965 | } |
---|
2966 | |
---|
2967 | /// @} |
---|
2968 | |
---|
2969 | /// \name Primal solution |
---|
2970 | /// Functions for get the primal solution, ie. the matching. |
---|
2971 | |
---|
2972 | /// @{ |
---|
2973 | |
---|
2974 | /// \brief Returns the matching value. |
---|
2975 | /// |
---|
2976 | /// Returns the matching value. |
---|
2977 | Value matchingValue() const { |
---|
2978 | Value sum = 0; |
---|
2979 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
2980 | if ((*_matching)[n] != INVALID) { |
---|
2981 | sum += _weight[(*_matching)[n]]; |
---|
2982 | } |
---|
2983 | } |
---|
2984 | return sum /= 2; |
---|
2985 | } |
---|
2986 | |
---|
2987 | /// \brief Returns true when the edge is in the matching. |
---|
2988 | /// |
---|
2989 | /// Returns true when the edge is in the matching. |
---|
2990 | bool matching(const UEdge& edge) const { |
---|
2991 | return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true); |
---|
2992 | } |
---|
2993 | |
---|
2994 | /// \brief Returns the incident matching edge. |
---|
2995 | /// |
---|
2996 | /// Returns the incident matching edge from given node. |
---|
2997 | Edge matching(const Node& node) const { |
---|
2998 | return (*_matching)[node]; |
---|
2999 | } |
---|
3000 | |
---|
3001 | /// \brief Returns the mate of the node. |
---|
3002 | /// |
---|
3003 | /// Returns the adjancent node in a mathcing edge. |
---|
3004 | Node mate(const Node& node) const { |
---|
3005 | return _ugraph.target((*_matching)[node]); |
---|
3006 | } |
---|
3007 | |
---|
3008 | /// @} |
---|
3009 | |
---|
3010 | /// \name Dual solution |
---|
3011 | /// Functions for get the dual solution. |
---|
3012 | |
---|
3013 | /// @{ |
---|
3014 | |
---|
3015 | /// \brief Returns the value of the dual solution. |
---|
3016 | /// |
---|
3017 | /// Returns the value of the dual solution. It should be equal to |
---|
3018 | /// the primal value scaled by \ref dualScale "dual scale". |
---|
3019 | Value dualValue() const { |
---|
3020 | Value sum = 0; |
---|
3021 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
3022 | sum += nodeValue(n); |
---|
3023 | } |
---|
3024 | for (int i = 0; i < blossomNum(); ++i) { |
---|
3025 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
3026 | } |
---|
3027 | return sum; |
---|
3028 | } |
---|
3029 | |
---|
3030 | /// \brief Returns the value of the node. |
---|
3031 | /// |
---|
3032 | /// Returns the the value of the node. |
---|
3033 | Value nodeValue(const Node& n) const { |
---|
3034 | return (*_node_potential)[n]; |
---|
3035 | } |
---|
3036 | |
---|
3037 | /// \brief Returns the number of the blossoms in the basis. |
---|
3038 | /// |
---|
3039 | /// Returns the number of the blossoms in the basis. |
---|
3040 | /// \see BlossomIt |
---|
3041 | int blossomNum() const { |
---|
3042 | return _blossom_potential.size(); |
---|
3043 | } |
---|
3044 | |
---|
3045 | |
---|
3046 | /// \brief Returns the number of the nodes in the blossom. |
---|
3047 | /// |
---|
3048 | /// Returns the number of the nodes in the blossom. |
---|
3049 | int blossomSize(int k) const { |
---|
3050 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
3051 | } |
---|
3052 | |
---|
3053 | /// \brief Returns the value of the blossom. |
---|
3054 | /// |
---|
3055 | /// Returns the the value of the blossom. |
---|
3056 | /// \see BlossomIt |
---|
3057 | Value blossomValue(int k) const { |
---|
3058 | return _blossom_potential[k].value; |
---|
3059 | } |
---|
3060 | |
---|
3061 | /// \brief Lemon iterator for get the items of the blossom. |
---|
3062 | /// |
---|
3063 | /// Lemon iterator for get the nodes of the blossom. This class |
---|
3064 | /// provides a common style lemon iterator which gives back a |
---|
3065 | /// subset of the nodes. |
---|
3066 | class BlossomIt { |
---|
3067 | public: |
---|
3068 | |
---|
3069 | /// \brief Constructor. |
---|
3070 | /// |
---|
3071 | /// Constructor for get the nodes of the variable. |
---|
3072 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
3073 | : _algorithm(&algorithm) |
---|
3074 | { |
---|
3075 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
3076 | _last = _algorithm->_blossom_potential[variable].end; |
---|
3077 | } |
---|
3078 | |
---|
3079 | /// \brief Invalid constructor. |
---|
3080 | /// |
---|
3081 | /// Invalid constructor. |
---|
3082 | BlossomIt(Invalid) : _index(-1) {} |
---|
3083 | |
---|
3084 | /// \brief Conversion to node. |
---|
3085 | /// |
---|
3086 | /// Conversion to node. |
---|
3087 | operator Node() const { |
---|
3088 | return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID; |
---|
3089 | } |
---|
3090 | |
---|
3091 | /// \brief Increment operator. |
---|
3092 | /// |
---|
3093 | /// Increment operator. |
---|
3094 | BlossomIt& operator++() { |
---|
3095 | ++_index; |
---|
3096 | if (_index == _last) { |
---|
3097 | _index = -1; |
---|
3098 | } |
---|
3099 | return *this; |
---|
3100 | } |
---|
3101 | |
---|
3102 | bool operator==(const BlossomIt& it) const { |
---|
3103 | return _index == it._index; |
---|
3104 | } |
---|
3105 | bool operator!=(const BlossomIt& it) const { |
---|
3106 | return _index != it._index; |
---|
3107 | } |
---|
3108 | |
---|
3109 | private: |
---|
3110 | const MaxWeightedPerfectMatching* _algorithm; |
---|
3111 | int _last; |
---|
3112 | int _index; |
---|
3113 | }; |
---|
3114 | |
---|
3115 | /// @} |
---|
3116 | |
---|
3117 | }; |
---|
3118 | |
---|
3119 | |
---|
3120 | } //END OF NAMESPACE LEMON |
---|
3121 | |
---|
3122 | #endif //LEMON_MAX_MATCHING_H |
---|