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) 2003-2008 |
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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_NETWORK_SIMPLEX_H |
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20 | #define LEMON_NETWORK_SIMPLEX_H |
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21 | |
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22 | /// \ingroup min_cost_flow |
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23 | /// |
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24 | /// \file |
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25 | /// \brief The network simplex algorithm for finding a minimum cost flow. |
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26 | |
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27 | #include <limits> |
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28 | #include <lemon/graph_adaptor.h> |
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29 | #include <lemon/graph_utils.h> |
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30 | #include <lemon/smart_graph.h> |
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31 | |
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32 | /// \brief The pivot rule used in the algorithm. |
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33 | //#define FIRST_ELIGIBLE_PIVOT |
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34 | //#define BEST_ELIGIBLE_PIVOT |
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35 | #define EDGE_BLOCK_PIVOT |
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36 | //#define CANDIDATE_LIST_PIVOT |
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37 | //#define SORTED_LIST_PIVOT |
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38 | |
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39 | //#define _DEBUG_ITER_ |
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40 | |
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41 | |
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42 | // State constant for edges at their lower bounds. |
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43 | #define LOWER 1 |
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44 | // State constant for edges in the spanning tree. |
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45 | #define TREE 0 |
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46 | // State constant for edges at their upper bounds. |
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47 | #define UPPER -1 |
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48 | |
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49 | #ifdef EDGE_BLOCK_PIVOT |
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50 | #include <cmath> |
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51 | #define MIN_BLOCK_SIZE 10 |
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52 | #endif |
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53 | |
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54 | #ifdef CANDIDATE_LIST_PIVOT |
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55 | #include <vector> |
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56 | #define LIST_LENGTH_DIV 50 |
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57 | #define MINOR_LIMIT_DIV 200 |
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58 | #endif |
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59 | |
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60 | #ifdef SORTED_LIST_PIVOT |
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61 | #include <vector> |
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62 | #include <algorithm> |
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63 | #define LIST_LENGTH_DIV 100 |
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64 | #define LOWER_DIV 4 |
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65 | #endif |
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66 | |
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67 | namespace lemon { |
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68 | |
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69 | /// \addtogroup min_cost_flow |
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70 | /// @{ |
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71 | |
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72 | /// \brief Implementation of the network simplex algorithm for |
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73 | /// finding a minimum cost flow. |
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74 | /// |
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75 | /// \ref NetworkSimplex implements the network simplex algorithm for |
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76 | /// finding a minimum cost flow. |
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77 | /// |
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78 | /// \param Graph The directed graph type the algorithm runs on. |
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79 | /// \param LowerMap The type of the lower bound map. |
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80 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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81 | /// \param CostMap The type of the cost (length) map. |
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82 | /// \param SupplyMap The type of the supply map. |
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83 | /// |
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84 | /// \warning |
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85 | /// - Edge capacities and costs should be non-negative integers. |
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86 | /// However \c CostMap::Value should be signed type. |
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87 | /// - Supply values should be signed integers. |
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88 | /// - \c LowerMap::Value must be convertible to |
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89 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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90 | /// convertible to \c SupplyMap::Value. |
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91 | /// |
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92 | /// \author Peter Kovacs |
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93 | |
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94 | template < typename Graph, |
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95 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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96 | typename CapacityMap = LowerMap, |
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97 | typename CostMap = typename Graph::template EdgeMap<int>, |
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98 | typename SupplyMap = typename Graph::template NodeMap |
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99 | <typename CapacityMap::Value> > |
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100 | class NetworkSimplex |
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101 | { |
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102 | typedef typename LowerMap::Value Lower; |
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103 | typedef typename CapacityMap::Value Capacity; |
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104 | typedef typename CostMap::Value Cost; |
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105 | typedef typename SupplyMap::Value Supply; |
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106 | |
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107 | typedef SmartGraph SGraph; |
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108 | GRAPH_TYPEDEFS(typename SGraph); |
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109 | |
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110 | typedef typename SGraph::template EdgeMap<Lower> SLowerMap; |
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111 | typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap; |
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112 | typedef typename SGraph::template EdgeMap<Cost> SCostMap; |
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113 | typedef typename SGraph::template NodeMap<Supply> SSupplyMap; |
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114 | typedef typename SGraph::template NodeMap<Cost> SPotentialMap; |
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115 | |
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116 | typedef typename SGraph::template NodeMap<int> IntNodeMap; |
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117 | typedef typename SGraph::template NodeMap<bool> BoolNodeMap; |
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118 | typedef typename SGraph::template NodeMap<Node> NodeNodeMap; |
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119 | typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap; |
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120 | typedef typename SGraph::template EdgeMap<int> IntEdgeMap; |
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121 | |
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122 | typedef typename Graph::template NodeMap<Node> NodeRefMap; |
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123 | typedef typename Graph::template EdgeMap<Edge> EdgeRefMap; |
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124 | |
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125 | public: |
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126 | |
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127 | /// The type of the flow map. |
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128 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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129 | /// The type of the potential map. |
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130 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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131 | |
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132 | protected: |
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133 | |
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134 | /// Map adaptor class for handling reduced edge costs. |
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135 | class ReducedCostMap : public MapBase<Edge, Cost> |
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136 | { |
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137 | private: |
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138 | |
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139 | const SGraph &gr; |
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140 | const SCostMap &cost_map; |
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141 | const SPotentialMap &pot_map; |
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142 | |
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143 | public: |
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144 | |
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145 | ReducedCostMap( const SGraph &_gr, |
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146 | const SCostMap &_cm, |
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147 | const SPotentialMap &_pm ) : |
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148 | gr(_gr), cost_map(_cm), pot_map(_pm) {} |
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149 | |
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150 | Cost operator[](const Edge &e) const { |
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151 | return cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)]; |
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152 | } |
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153 | |
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154 | }; //class ReducedCostMap |
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155 | |
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156 | protected: |
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157 | |
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158 | /// The directed graph the algorithm runs on. |
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159 | SGraph graph; |
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160 | /// The original graph. |
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161 | const Graph &graph_ref; |
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162 | /// The original lower bound map. |
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163 | const LowerMap *lower; |
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164 | /// The capacity map. |
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165 | SCapacityMap capacity; |
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166 | /// The cost map. |
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167 | SCostMap cost; |
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168 | /// The supply map. |
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169 | SSupplyMap supply; |
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170 | /// The reduced cost map. |
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171 | ReducedCostMap red_cost; |
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172 | bool valid_supply; |
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173 | |
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174 | /// The edge map of the current flow. |
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175 | SCapacityMap flow; |
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176 | /// The potential node map. |
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177 | SPotentialMap potential; |
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178 | FlowMap flow_result; |
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179 | PotentialMap potential_result; |
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180 | |
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181 | /// Node reference for the original graph. |
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182 | NodeRefMap node_ref; |
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183 | /// Edge reference for the original graph. |
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184 | EdgeRefMap edge_ref; |
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185 | |
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186 | /// The \c depth node map of the spanning tree structure. |
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187 | IntNodeMap depth; |
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188 | /// The \c parent node map of the spanning tree structure. |
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189 | NodeNodeMap parent; |
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190 | /// The \c pred_edge node map of the spanning tree structure. |
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191 | EdgeNodeMap pred_edge; |
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192 | /// The \c thread node map of the spanning tree structure. |
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193 | NodeNodeMap thread; |
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194 | /// The \c forward node map of the spanning tree structure. |
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195 | BoolNodeMap forward; |
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196 | /// The state edge map. |
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197 | IntEdgeMap state; |
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198 | /// The root node of the starting spanning tree. |
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199 | Node root; |
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200 | |
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201 | // The entering edge of the current pivot iteration. |
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202 | Edge in_edge; |
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203 | // Temporary nodes used in the current pivot iteration. |
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204 | Node join, u_in, v_in, u_out, v_out; |
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205 | Node right, first, second, last; |
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206 | Node stem, par_stem, new_stem; |
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207 | // The maximum augment amount along the found cycle in the current |
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208 | // pivot iteration. |
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209 | Capacity delta; |
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210 | |
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211 | #ifdef EDGE_BLOCK_PIVOT |
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212 | /// The size of blocks for the "Edge Block" pivot rule. |
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213 | int block_size; |
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214 | #endif |
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215 | #ifdef CANDIDATE_LIST_PIVOT |
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216 | /// \brief The list of candidate edges for the "Candidate List" |
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217 | /// pivot rule. |
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218 | std::vector<Edge> candidates; |
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219 | /// \brief The maximum length of the edge list for the |
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220 | /// "Candidate List" pivot rule. |
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221 | int list_length; |
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222 | /// \brief The maximum number of minor iterations between two major |
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223 | /// itarations. |
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224 | int minor_limit; |
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225 | /// \brief The number of minor iterations. |
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226 | int minor_count; |
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227 | #endif |
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228 | #ifdef SORTED_LIST_PIVOT |
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229 | /// \brief The list of candidate edges for the "Sorted List" |
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230 | /// pivot rule. |
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231 | std::vector<Edge> candidates; |
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232 | /// \brief The maximum length of the edge list for the |
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233 | /// "Sorted List" pivot rule. |
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234 | int list_length; |
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235 | int list_index; |
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236 | #endif |
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237 | |
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238 | public : |
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239 | |
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240 | /// \brief General constructor of the class (with lower bounds). |
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241 | /// |
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242 | /// General constructor of the class (with lower bounds). |
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243 | /// |
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244 | /// \param _graph The directed graph the algorithm runs on. |
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245 | /// \param _lower The lower bounds of the edges. |
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246 | /// \param _capacity The capacities (upper bounds) of the edges. |
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247 | /// \param _cost The cost (length) values of the edges. |
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248 | /// \param _supply The supply values of the nodes (signed). |
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249 | NetworkSimplex( const Graph &_graph, |
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250 | const LowerMap &_lower, |
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251 | const CapacityMap &_capacity, |
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252 | const CostMap &_cost, |
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253 | const SupplyMap &_supply ) : |
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254 | graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph), |
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255 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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256 | potential_result(_graph), depth(graph), parent(graph), |
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257 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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258 | node_ref(graph_ref), edge_ref(graph_ref), |
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259 | red_cost(graph, cost, potential) |
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260 | { |
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261 | // Checking the sum of supply values |
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262 | Supply sum = 0; |
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263 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
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264 | sum += _supply[n]; |
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265 | if (!(valid_supply = sum == 0)) return; |
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266 | |
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267 | // Copying graph_ref to graph |
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268 | graph.reserveNode(countNodes(graph_ref) + 1); |
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269 | graph.reserveEdge(countEdges(graph_ref) + countNodes(graph_ref)); |
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270 | copyGraph(graph, graph_ref) |
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271 | .edgeMap(cost, _cost) |
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272 | .nodeRef(node_ref) |
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273 | .edgeRef(edge_ref) |
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274 | .run(); |
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275 | |
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276 | // Removing non-zero lower bounds |
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277 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) { |
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278 | capacity[edge_ref[e]] = _capacity[e] - _lower[e]; |
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279 | } |
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280 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) { |
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281 | Supply s = _supply[n]; |
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282 | for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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283 | s += _lower[e]; |
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284 | for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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285 | s -= _lower[e]; |
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286 | supply[node_ref[n]] = s; |
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287 | } |
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288 | } |
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289 | |
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290 | /// \brief General constructor of the class (without lower bounds). |
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291 | /// |
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292 | /// General constructor of the class (without lower bounds). |
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293 | /// |
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294 | /// \param _graph The directed graph the algorithm runs on. |
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295 | /// \param _capacity The capacities (upper bounds) of the edges. |
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296 | /// \param _cost The cost (length) values of the edges. |
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297 | /// \param _supply The supply values of the nodes (signed). |
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298 | NetworkSimplex( const Graph &_graph, |
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299 | const CapacityMap &_capacity, |
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300 | const CostMap &_cost, |
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301 | const SupplyMap &_supply ) : |
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302 | graph_ref(_graph), lower(NULL), capacity(graph), cost(graph), |
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303 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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304 | potential_result(_graph), depth(graph), parent(graph), |
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305 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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306 | node_ref(graph_ref), edge_ref(graph_ref), |
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307 | red_cost(graph, cost, potential) |
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308 | { |
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309 | // Checking the sum of supply values |
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310 | Supply sum = 0; |
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311 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
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312 | sum += _supply[n]; |
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313 | if (!(valid_supply = sum == 0)) return; |
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314 | |
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315 | // Copying graph_ref to graph |
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316 | copyGraph(graph, graph_ref) |
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317 | .edgeMap(capacity, _capacity) |
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318 | .edgeMap(cost, _cost) |
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319 | .nodeMap(supply, _supply) |
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320 | .nodeRef(node_ref) |
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321 | .edgeRef(edge_ref) |
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322 | .run(); |
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323 | } |
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324 | |
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325 | /// \brief Simple constructor of the class (with lower bounds). |
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326 | /// |
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327 | /// Simple constructor of the class (with lower bounds). |
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328 | /// |
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329 | /// \param _graph The directed graph the algorithm runs on. |
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330 | /// \param _lower The lower bounds of the edges. |
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331 | /// \param _capacity The capacities (upper bounds) of the edges. |
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332 | /// \param _cost The cost (length) values of the edges. |
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333 | /// \param _s The source node. |
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334 | /// \param _t The target node. |
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335 | /// \param _flow_value The required amount of flow from node \c _s |
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336 | /// to node \c _t (i.e. the supply of \c _s and the demand of \c _t). |
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337 | NetworkSimplex( const Graph &_graph, |
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338 | const LowerMap &_lower, |
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339 | const CapacityMap &_capacity, |
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340 | const CostMap &_cost, |
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341 | typename Graph::Node _s, |
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342 | typename Graph::Node _t, |
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343 | typename SupplyMap::Value _flow_value ) : |
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344 | graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph), |
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345 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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346 | potential_result(_graph), depth(graph), parent(graph), |
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347 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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348 | node_ref(graph_ref), edge_ref(graph_ref), |
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349 | red_cost(graph, cost, potential) |
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350 | { |
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351 | // Copying graph_ref to graph |
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352 | copyGraph(graph, graph_ref) |
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353 | .edgeMap(cost, _cost) |
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354 | .nodeRef(node_ref) |
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355 | .edgeRef(edge_ref) |
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356 | .run(); |
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357 | |
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358 | // Removing non-zero lower bounds |
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359 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) { |
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360 | capacity[edge_ref[e]] = _capacity[e] - _lower[e]; |
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361 | } |
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362 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) { |
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363 | Supply s = 0; |
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364 | if (n == _s) s = _flow_value; |
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365 | if (n == _t) s = -_flow_value; |
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366 | for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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367 | s += _lower[e]; |
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368 | for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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369 | s -= _lower[e]; |
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370 | supply[node_ref[n]] = s; |
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371 | } |
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372 | valid_supply = true; |
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373 | } |
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374 | |
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375 | /// \brief Simple constructor of the class (without lower bounds). |
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376 | /// |
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377 | /// Simple constructor of the class (without lower bounds). |
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378 | /// |
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379 | /// \param _graph The directed graph the algorithm runs on. |
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380 | /// \param _capacity The capacities (upper bounds) of the edges. |
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381 | /// \param _cost The cost (length) values of the edges. |
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382 | /// \param _s The source node. |
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383 | /// \param _t The target node. |
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384 | /// \param _flow_value The required amount of flow from node \c _s |
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385 | /// to node \c _t (i.e. the supply of \c _s and the demand of \c _t). |
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386 | NetworkSimplex( const Graph &_graph, |
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387 | const CapacityMap &_capacity, |
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388 | const CostMap &_cost, |
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389 | typename Graph::Node _s, |
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390 | typename Graph::Node _t, |
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391 | typename SupplyMap::Value _flow_value ) : |
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392 | graph_ref(_graph), lower(NULL), capacity(graph), cost(graph), |
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393 | supply(graph, 0), flow(graph), flow_result(_graph), potential(graph), |
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394 | potential_result(_graph), depth(graph), parent(graph), |
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395 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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396 | node_ref(graph_ref), edge_ref(graph_ref), |
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397 | red_cost(graph, cost, potential) |
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398 | { |
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399 | // Copying graph_ref to graph |
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400 | copyGraph(graph, graph_ref) |
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401 | .edgeMap(capacity, _capacity) |
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402 | .edgeMap(cost, _cost) |
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403 | .nodeRef(node_ref) |
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404 | .edgeRef(edge_ref) |
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405 | .run(); |
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406 | supply[node_ref[_s]] = _flow_value; |
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407 | supply[node_ref[_t]] = -_flow_value; |
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408 | valid_supply = true; |
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409 | } |
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410 | |
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411 | /// \brief Runs the algorithm. |
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412 | /// |
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413 | /// Runs the algorithm. |
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414 | /// |
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415 | /// \return \c true if a feasible flow can be found. |
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416 | bool run() { |
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417 | return init() && start(); |
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418 | } |
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419 | |
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420 | /// \brief Returns a const reference to the flow map. |
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421 | /// |
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422 | /// Returns a const reference to the flow map. |
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423 | /// |
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424 | /// \pre \ref run() must be called before using this function. |
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425 | const FlowMap& flowMap() const { |
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426 | return flow_result; |
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427 | } |
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428 | |
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429 | /// \brief Returns a const reference to the potential map (the dual |
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430 | /// solution). |
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431 | /// |
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432 | /// Returns a const reference to the potential map (the dual |
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433 | /// solution). |
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434 | /// |
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435 | /// \pre \ref run() must be called before using this function. |
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436 | const PotentialMap& potentialMap() const { |
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437 | return potential_result; |
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438 | } |
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439 | |
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440 | /// \brief Returns the total cost of the found flow. |
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441 | /// |
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442 | /// Returns the total cost of the found flow. The complexity of the |
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443 | /// function is \f$ O(e) \f$. |
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444 | /// |
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445 | /// \pre \ref run() must be called before using this function. |
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446 | Cost totalCost() const { |
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447 | Cost c = 0; |
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448 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
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449 | c += flow_result[e] * cost[edge_ref[e]]; |
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450 | return c; |
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451 | } |
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452 | |
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453 | protected: |
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454 | |
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455 | /// \brief Extends the underlaying graph and initializes all the |
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456 | /// node and edge maps. |
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457 | bool init() { |
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458 | if (!valid_supply) return false; |
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459 | |
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460 | // Initializing state and flow maps |
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461 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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462 | flow[e] = 0; |
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463 | state[e] = LOWER; |
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464 | } |
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465 | |
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466 | // Adding an artificial root node to the graph |
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467 | root = graph.addNode(); |
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468 | parent[root] = INVALID; |
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469 | pred_edge[root] = INVALID; |
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470 | depth[root] = 0; |
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471 | supply[root] = 0; |
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472 | potential[root] = 0; |
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473 | |
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474 | // Adding artificial edges to the graph and initializing the node |
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475 | // maps of the spanning tree data structure |
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476 | Supply sum = 0; |
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477 | Node last = root; |
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478 | Edge e; |
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479 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
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480 | for (NodeIt u(graph); u != INVALID; ++u) { |
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481 | if (u == root) continue; |
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482 | thread[last] = u; |
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483 | last = u; |
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484 | parent[u] = root; |
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485 | depth[u] = 1; |
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486 | sum += supply[u]; |
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487 | if (supply[u] >= 0) { |
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488 | e = graph.addEdge(u, root); |
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489 | flow[e] = supply[u]; |
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490 | forward[u] = true; |
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491 | potential[u] = max_cost; |
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492 | } else { |
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493 | e = graph.addEdge(root, u); |
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494 | flow[e] = -supply[u]; |
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495 | forward[u] = false; |
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496 | potential[u] = -max_cost; |
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497 | } |
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498 | cost[e] = max_cost; |
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499 | capacity[e] = std::numeric_limits<Capacity>::max(); |
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500 | state[e] = TREE; |
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501 | pred_edge[u] = e; |
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502 | } |
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503 | thread[last] = root; |
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504 | |
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505 | #ifdef EDGE_BLOCK_PIVOT |
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506 | // Initializing block_size for the edge block pivot rule |
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507 | int edge_num = countEdges(graph); |
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508 | block_size = 2 * int(sqrt(countEdges(graph))); |
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509 | if (block_size < MIN_BLOCK_SIZE) block_size = MIN_BLOCK_SIZE; |
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510 | #endif |
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511 | #ifdef CANDIDATE_LIST_PIVOT |
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512 | int edge_num = countEdges(graph); |
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513 | minor_count = 0; |
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514 | list_length = edge_num / LIST_LENGTH_DIV; |
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515 | minor_limit = edge_num / MINOR_LIMIT_DIV; |
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516 | #endif |
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517 | #ifdef SORTED_LIST_PIVOT |
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518 | int edge_num = countEdges(graph); |
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519 | list_index = 0; |
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520 | list_length = edge_num / LIST_LENGTH_DIV; |
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521 | #endif |
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522 | |
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523 | return sum == 0; |
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524 | } |
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525 | |
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526 | #ifdef FIRST_ELIGIBLE_PIVOT |
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527 | /// \brief Finds entering edge according to the "First Eligible" |
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528 | /// pivot rule. |
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529 | bool findEnteringEdge(EdgeIt &next_edge) { |
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530 | for (EdgeIt e = next_edge; e != INVALID; ++e) { |
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531 | if (state[e] * red_cost[e] < 0) { |
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532 | in_edge = e; |
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533 | next_edge = ++e; |
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534 | return true; |
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535 | } |
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536 | } |
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537 | for (EdgeIt e(graph); e != next_edge; ++e) { |
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538 | if (state[e] * red_cost[e] < 0) { |
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539 | in_edge = e; |
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540 | next_edge = ++e; |
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541 | return true; |
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542 | } |
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543 | } |
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544 | return false; |
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545 | } |
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546 | #endif |
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547 | |
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548 | #ifdef BEST_ELIGIBLE_PIVOT |
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549 | /// \brief Finds entering edge according to the "Best Eligible" |
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550 | /// pivot rule. |
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551 | bool findEnteringEdge() { |
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552 | Cost min = 0; |
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553 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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554 | if (state[e] * red_cost[e] < min) { |
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555 | min = state[e] * red_cost[e]; |
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556 | in_edge = e; |
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557 | } |
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558 | } |
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559 | return min < 0; |
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560 | } |
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561 | #endif |
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562 | |
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563 | #ifdef EDGE_BLOCK_PIVOT |
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564 | /// \brief Finds entering edge according to the "Edge Block" |
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565 | /// pivot rule. |
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566 | bool findEnteringEdge(EdgeIt &next_edge) { |
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567 | // Performing edge block selection |
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568 | Cost curr, min = 0; |
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569 | EdgeIt min_edge(graph); |
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570 | int cnt = 0; |
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571 | for (EdgeIt e = next_edge; e != INVALID; ++e) { |
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572 | if ((curr = state[e] * red_cost[e]) < min) { |
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573 | min = curr; |
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574 | min_edge = e; |
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575 | } |
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576 | if (++cnt == block_size) { |
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577 | if (min < 0) break; |
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578 | cnt = 0; |
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579 | } |
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580 | } |
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581 | if (!(min < 0)) { |
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582 | for (EdgeIt e(graph); e != next_edge; ++e) { |
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583 | if ((curr = state[e] * red_cost[e]) < min) { |
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584 | min = curr; |
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585 | min_edge = e; |
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586 | } |
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587 | if (++cnt == block_size) { |
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588 | if (min < 0) break; |
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589 | cnt = 0; |
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590 | } |
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591 | } |
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592 | } |
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593 | in_edge = min_edge; |
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594 | if ((next_edge = ++min_edge) == INVALID) |
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595 | next_edge = EdgeIt(graph); |
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596 | return min < 0; |
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597 | } |
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598 | #endif |
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599 | |
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600 | #ifdef CANDIDATE_LIST_PIVOT |
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601 | /// \brief Finds entering edge according to the "Candidate List" |
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602 | /// pivot rule. |
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603 | bool findEnteringEdge() { |
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604 | typedef typename std::vector<Edge>::iterator ListIt; |
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605 | |
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606 | if (minor_count >= minor_limit || candidates.size() == 0) { |
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607 | // Major iteration |
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608 | candidates.clear(); |
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609 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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610 | if (state[e] * red_cost[e] < 0) { |
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611 | candidates.push_back(e); |
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612 | if (candidates.size() == list_length) break; |
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613 | } |
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614 | } |
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615 | if (candidates.size() == 0) return false; |
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616 | } |
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617 | |
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618 | // Minor iteration |
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619 | ++minor_count; |
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620 | Cost min = 0; |
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621 | Edge e; |
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622 | for (int i = 0; i < candidates.size(); ++i) { |
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623 | e = candidates[i]; |
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624 | if (state[e] * red_cost[e] < min) { |
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625 | min = state[e] * red_cost[e]; |
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626 | in_edge = e; |
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627 | } |
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628 | } |
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629 | return true; |
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630 | } |
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631 | #endif |
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632 | |
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633 | #ifdef SORTED_LIST_PIVOT |
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634 | /// \brief Functor class to compare edges during sort of the |
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635 | /// candidate list. |
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636 | class SortFunc |
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637 | { |
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638 | private: |
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639 | const IntEdgeMap &st; |
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640 | const ReducedCostMap &rc; |
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641 | public: |
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642 | SortFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) : |
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643 | st(_st), rc(_rc) {} |
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644 | bool operator()(const Edge &e1, const Edge &e2) { |
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645 | return st[e1] * rc[e1] < st[e2] * rc[e2]; |
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646 | } |
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647 | }; |
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648 | |
---|
649 | /// \brief Finds entering edge according to the "Sorted List" |
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650 | /// pivot rule. |
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651 | bool findEnteringEdge() { |
---|
652 | static SortFunc sort_func(state, red_cost); |
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653 | |
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654 | // Minor iteration |
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655 | while (list_index < candidates.size()) { |
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656 | in_edge = candidates[list_index++]; |
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657 | if (state[in_edge] * red_cost[in_edge] < 0) return true; |
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658 | } |
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659 | |
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660 | // Major iteration |
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661 | candidates.clear(); |
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662 | Cost curr, min = 0; |
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663 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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664 | if ((curr = state[e] * red_cost[e]) < min / LOWER_DIV) { |
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665 | candidates.push_back(e); |
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666 | if (curr < min) min = curr; |
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667 | if (candidates.size() == list_length) break; |
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668 | } |
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669 | } |
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670 | if (candidates.size() == 0) return false; |
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671 | sort(candidates.begin(), candidates.end(), sort_func); |
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672 | in_edge = candidates[0]; |
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673 | list_index = 1; |
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674 | return true; |
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675 | } |
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676 | #endif |
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677 | |
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678 | /// \brief Finds the join node. |
---|
679 | Node findJoinNode() { |
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680 | // Finding the join node |
---|
681 | Node u = graph.source(in_edge); |
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682 | Node v = graph.target(in_edge); |
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683 | while (u != v) { |
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684 | if (depth[u] == depth[v]) { |
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685 | u = parent[u]; |
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686 | v = parent[v]; |
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687 | } |
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688 | else if (depth[u] > depth[v]) u = parent[u]; |
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689 | else v = parent[v]; |
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690 | } |
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691 | return u; |
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692 | } |
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693 | |
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694 | /// \brief Finds the leaving edge of the cycle. Returns \c true if |
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695 | /// the leaving edge is not the same as the entering edge. |
---|
696 | bool findLeavingEdge() { |
---|
697 | // Initializing first and second nodes according to the direction |
---|
698 | // of the cycle |
---|
699 | if (state[in_edge] == LOWER) { |
---|
700 | first = graph.source(in_edge); |
---|
701 | second = graph.target(in_edge); |
---|
702 | } else { |
---|
703 | first = graph.target(in_edge); |
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704 | second = graph.source(in_edge); |
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705 | } |
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706 | delta = capacity[in_edge]; |
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707 | bool result = false; |
---|
708 | Capacity d; |
---|
709 | Edge e; |
---|
710 | |
---|
711 | // Searching the cycle along the path form the first node to the |
---|
712 | // root node |
---|
713 | for (Node u = first; u != join; u = parent[u]) { |
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714 | e = pred_edge[u]; |
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715 | d = forward[u] ? flow[e] : capacity[e] - flow[e]; |
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716 | if (d < delta) { |
---|
717 | delta = d; |
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718 | u_out = u; |
---|
719 | u_in = first; |
---|
720 | v_in = second; |
---|
721 | result = true; |
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722 | } |
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723 | } |
---|
724 | // Searching the cycle along the path form the second node to the |
---|
725 | // root node |
---|
726 | for (Node u = second; u != join; u = parent[u]) { |
---|
727 | e = pred_edge[u]; |
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728 | d = forward[u] ? capacity[e] - flow[e] : flow[e]; |
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729 | if (d <= delta) { |
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730 | delta = d; |
---|
731 | u_out = u; |
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732 | u_in = second; |
---|
733 | v_in = first; |
---|
734 | result = true; |
---|
735 | } |
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736 | } |
---|
737 | return result; |
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738 | } |
---|
739 | |
---|
740 | /// \brief Changes \c flow and \c state edge maps. |
---|
741 | void changeFlows(bool change) { |
---|
742 | // Augmenting along the cycle |
---|
743 | if (delta > 0) { |
---|
744 | Capacity val = state[in_edge] * delta; |
---|
745 | flow[in_edge] += val; |
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746 | for (Node u = graph.source(in_edge); u != join; u = parent[u]) { |
---|
747 | flow[pred_edge[u]] += forward[u] ? -val : val; |
---|
748 | } |
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749 | for (Node u = graph.target(in_edge); u != join; u = parent[u]) { |
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750 | flow[pred_edge[u]] += forward[u] ? val : -val; |
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751 | } |
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752 | } |
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753 | // Updating the state of the entering and leaving edges |
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754 | if (change) { |
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755 | state[in_edge] = TREE; |
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756 | state[pred_edge[u_out]] = |
---|
757 | (flow[pred_edge[u_out]] == 0) ? LOWER : UPPER; |
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758 | } else { |
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759 | state[in_edge] = -state[in_edge]; |
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760 | } |
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761 | } |
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762 | |
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763 | /// \brief Updates \c thread and \c parent node maps. |
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764 | void updateThreadParent() { |
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765 | Node u; |
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766 | v_out = parent[u_out]; |
---|
767 | |
---|
768 | // Handling the case when join and v_out coincide |
---|
769 | bool par_first = false; |
---|
770 | if (join == v_out) { |
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771 | for (u = join; u != u_in && u != v_in; u = thread[u]) ; |
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772 | if (u == v_in) { |
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773 | par_first = true; |
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774 | while (thread[u] != u_out) u = thread[u]; |
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775 | first = u; |
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776 | } |
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777 | } |
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778 | |
---|
779 | // Finding the last successor of u_in (u) and the node after it |
---|
780 | // (right) according to the thread index |
---|
781 | for (u = u_in; depth[thread[u]] > depth[u_in]; u = thread[u]) ; |
---|
782 | right = thread[u]; |
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783 | if (thread[v_in] == u_out) { |
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784 | for (last = u; depth[last] > depth[u_out]; last = thread[last]) ; |
---|
785 | if (last == u_out) last = thread[last]; |
---|
786 | } |
---|
787 | else last = thread[v_in]; |
---|
788 | |
---|
789 | // Updating stem nodes |
---|
790 | thread[v_in] = stem = u_in; |
---|
791 | par_stem = v_in; |
---|
792 | while (stem != u_out) { |
---|
793 | thread[u] = new_stem = parent[stem]; |
---|
794 | |
---|
795 | // Finding the node just before the stem node (u) according to |
---|
796 | // the original thread index |
---|
797 | for (u = new_stem; thread[u] != stem; u = thread[u]) ; |
---|
798 | thread[u] = right; |
---|
799 | |
---|
800 | // Changing the parent node of stem and shifting stem and |
---|
801 | // par_stem nodes |
---|
802 | parent[stem] = par_stem; |
---|
803 | par_stem = stem; |
---|
804 | stem = new_stem; |
---|
805 | |
---|
806 | // Finding the last successor of stem (u) and the node after it |
---|
807 | // (right) according to the thread index |
---|
808 | for (u = stem; depth[thread[u]] > depth[stem]; u = thread[u]) ; |
---|
809 | right = thread[u]; |
---|
810 | } |
---|
811 | parent[u_out] = par_stem; |
---|
812 | thread[u] = last; |
---|
813 | |
---|
814 | if (join == v_out && par_first) { |
---|
815 | if (first != v_in) thread[first] = right; |
---|
816 | } else { |
---|
817 | for (u = v_out; thread[u] != u_out; u = thread[u]) ; |
---|
818 | thread[u] = right; |
---|
819 | } |
---|
820 | } |
---|
821 | |
---|
822 | /// \brief Updates \c pred_edge and \c forward node maps. |
---|
823 | void updatePredEdge() { |
---|
824 | Node u = u_out, v; |
---|
825 | while (u != u_in) { |
---|
826 | v = parent[u]; |
---|
827 | pred_edge[u] = pred_edge[v]; |
---|
828 | forward[u] = !forward[v]; |
---|
829 | u = v; |
---|
830 | } |
---|
831 | pred_edge[u_in] = in_edge; |
---|
832 | forward[u_in] = (u_in == graph.source(in_edge)); |
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833 | } |
---|
834 | |
---|
835 | /// \brief Updates \c depth and \c potential node maps. |
---|
836 | void updateDepthPotential() { |
---|
837 | depth[u_in] = depth[v_in] + 1; |
---|
838 | potential[u_in] = forward[u_in] ? |
---|
839 | potential[v_in] + cost[pred_edge[u_in]] : |
---|
840 | potential[v_in] - cost[pred_edge[u_in]]; |
---|
841 | |
---|
842 | Node u = thread[u_in], v; |
---|
843 | while (true) { |
---|
844 | v = parent[u]; |
---|
845 | if (v == INVALID) break; |
---|
846 | depth[u] = depth[v] + 1; |
---|
847 | potential[u] = forward[u] ? |
---|
848 | potential[v] + cost[pred_edge[u]] : |
---|
849 | potential[v] - cost[pred_edge[u]]; |
---|
850 | if (depth[u] <= depth[v_in]) break; |
---|
851 | u = thread[u]; |
---|
852 | } |
---|
853 | } |
---|
854 | |
---|
855 | /// \brief Executes the algorithm. |
---|
856 | bool start() { |
---|
857 | // Processing pivots |
---|
858 | #ifdef _DEBUG_ITER_ |
---|
859 | int iter_num = 0; |
---|
860 | #endif |
---|
861 | #if defined(FIRST_ELIGIBLE_PIVOT) || defined(EDGE_BLOCK_PIVOT) |
---|
862 | EdgeIt next_edge(graph); |
---|
863 | while (findEnteringEdge(next_edge)) |
---|
864 | #else |
---|
865 | while (findEnteringEdge()) |
---|
866 | #endif |
---|
867 | { |
---|
868 | join = findJoinNode(); |
---|
869 | bool change = findLeavingEdge(); |
---|
870 | changeFlows(change); |
---|
871 | if (change) { |
---|
872 | updateThreadParent(); |
---|
873 | updatePredEdge(); |
---|
874 | updateDepthPotential(); |
---|
875 | } |
---|
876 | #ifdef _DEBUG_ITER_ |
---|
877 | ++iter_num; |
---|
878 | #endif |
---|
879 | } |
---|
880 | |
---|
881 | #ifdef _DEBUG_ITER_ |
---|
882 | std::cout << "Network Simplex algorithm finished. " << iter_num |
---|
883 | << " pivot iterations performed." << std::endl; |
---|
884 | #endif |
---|
885 | |
---|
886 | // Checking if the flow amount equals zero on all the |
---|
887 | // artificial edges |
---|
888 | for (InEdgeIt e(graph, root); e != INVALID; ++e) |
---|
889 | if (flow[e] > 0) return false; |
---|
890 | for (OutEdgeIt e(graph, root); e != INVALID; ++e) |
---|
891 | if (flow[e] > 0) return false; |
---|
892 | |
---|
893 | // Copying flow values to flow_result |
---|
894 | if (lower) { |
---|
895 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
---|
896 | flow_result[e] = (*lower)[e] + flow[edge_ref[e]]; |
---|
897 | } else { |
---|
898 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
---|
899 | flow_result[e] = flow[edge_ref[e]]; |
---|
900 | } |
---|
901 | // Copying potential values to potential_result |
---|
902 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
---|
903 | potential_result[n] = potential[node_ref[n]]; |
---|
904 | |
---|
905 | return true; |
---|
906 | } |
---|
907 | |
---|
908 | }; //class NetworkSimplex |
---|
909 | |
---|
910 | ///@} |
---|
911 | |
---|
912 | } //namespace lemon |
---|
913 | |
---|
914 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|