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_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 |
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26 | /// flow. |
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27 | |
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28 | #include <limits> |
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29 | #include <lemon/graph_adaptor.h> |
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30 | #include <lemon/graph_utils.h> |
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31 | #include <lemon/smart_graph.h> |
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32 | |
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33 | /// \brief The pivot rule used in the algorithm. |
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34 | //#define FIRST_ELIGIBLE_PIVOT |
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35 | //#define BEST_ELIGIBLE_PIVOT |
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36 | #define EDGE_BLOCK_PIVOT |
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37 | //#define CANDIDATE_LIST_PIVOT |
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38 | //#define SORTED_LIST_PIVOT |
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39 | |
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40 | //#define _DEBUG_ITER_ |
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41 | |
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42 | |
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43 | /// \brief State constant for edges at their lower bounds. |
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44 | #define LOWER 1 |
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45 | /// \brief State constant for edges in the spanning tree. |
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46 | #define TREE 0 |
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47 | /// \brief State constant for edges at their upper bounds. |
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48 | #define UPPER -1 |
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49 | |
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50 | #ifdef EDGE_BLOCK_PIVOT |
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51 | #include <cmath> |
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52 | /// \brief Lower bound for the size of blocks. |
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53 | #define MIN_BLOCK_SIZE 10 |
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54 | #endif |
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55 | |
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56 | #ifdef CANDIDATE_LIST_PIVOT |
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57 | #include <vector> |
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58 | #define LIST_LENGTH_DIV 50 |
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59 | #define MINOR_LIMIT_DIV 200 |
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60 | #endif |
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61 | |
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62 | #ifdef SORTED_LIST_PIVOT |
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63 | #include <vector> |
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64 | #include <algorithm> |
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65 | #define LIST_LENGTH_DIV 100 |
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66 | #define LOWER_DIV 4 |
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67 | #endif |
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68 | |
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69 | namespace lemon { |
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70 | |
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71 | /// \addtogroup min_cost_flow |
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72 | /// @{ |
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73 | |
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74 | /// \brief Implementation of the network simplex algorithm for |
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75 | /// finding a minimum cost flow. |
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76 | /// |
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77 | /// \ref lemon::NetworkSimplex "NetworkSimplex" implements the |
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78 | /// network simplex algorithm for finding a minimum cost flow. |
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79 | /// |
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80 | /// \param Graph The directed graph type the algorithm runs on. |
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81 | /// \param LowerMap The type of the lower bound map. |
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82 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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83 | /// \param CostMap The type of the cost (length) map. |
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84 | /// \param SupplyMap The type of the supply map. |
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85 | /// |
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86 | /// \warning |
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87 | /// - Edge capacities and costs should be nonnegative integers. |
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88 | /// However \c CostMap::Value should be signed type. |
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89 | /// - Supply values should be signed integers. |
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90 | /// - \c LowerMap::Value must be convertible to |
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91 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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92 | /// convertible to \c SupplyMap::Value. |
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93 | /// |
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94 | /// \author Peter Kovacs |
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95 | |
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96 | template < typename Graph, |
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97 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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98 | typename CapacityMap = LowerMap, |
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99 | typename CostMap = typename Graph::template EdgeMap<int>, |
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100 | typename SupplyMap = typename Graph::template NodeMap |
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101 | <typename CapacityMap::Value> > |
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102 | class NetworkSimplex |
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103 | { |
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104 | typedef typename LowerMap::Value Lower; |
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105 | typedef typename CapacityMap::Value Capacity; |
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106 | typedef typename CostMap::Value Cost; |
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107 | typedef typename SupplyMap::Value Supply; |
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108 | |
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109 | typedef SmartGraph SGraph; |
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110 | typedef typename SGraph::Node Node; |
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111 | typedef typename SGraph::NodeIt NodeIt; |
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112 | typedef typename SGraph::Edge Edge; |
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113 | typedef typename SGraph::EdgeIt EdgeIt; |
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114 | typedef typename SGraph::InEdgeIt InEdgeIt; |
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115 | typedef typename SGraph::OutEdgeIt OutEdgeIt; |
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116 | |
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117 | typedef typename SGraph::template EdgeMap<Lower> SLowerMap; |
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118 | typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap; |
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119 | typedef typename SGraph::template EdgeMap<Cost> SCostMap; |
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120 | typedef typename SGraph::template NodeMap<Supply> SSupplyMap; |
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121 | typedef typename SGraph::template NodeMap<Cost> SPotentialMap; |
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122 | |
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123 | typedef typename SGraph::template NodeMap<int> IntNodeMap; |
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124 | typedef typename SGraph::template NodeMap<bool> BoolNodeMap; |
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125 | typedef typename SGraph::template NodeMap<Node> NodeNodeMap; |
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126 | typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap; |
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127 | typedef typename SGraph::template EdgeMap<int> IntEdgeMap; |
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128 | |
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129 | typedef typename Graph::template NodeMap<Node> NodeRefMap; |
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130 | typedef typename Graph::template EdgeMap<Edge> EdgeRefMap; |
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131 | |
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132 | public: |
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133 | |
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134 | /// \brief The type of the flow map. |
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135 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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136 | /// \brief The type of the potential map. |
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137 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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138 | |
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139 | protected: |
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140 | |
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141 | /// \brief Map adaptor class for handling reduced edge costs. |
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142 | class ReducedCostMap : public MapBase<Edge, Cost> |
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143 | { |
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144 | private: |
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145 | |
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146 | const SGraph &gr; |
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147 | const SCostMap &cost_map; |
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148 | const SPotentialMap &pot_map; |
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149 | |
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150 | public: |
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151 | |
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152 | ReducedCostMap( const SGraph &_gr, |
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153 | const SCostMap &_cm, |
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154 | const SPotentialMap &_pm ) : |
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155 | gr(_gr), cost_map(_cm), pot_map(_pm) {} |
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156 | |
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157 | Cost operator[](const Edge &e) const { |
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158 | return cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)]; |
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159 | } |
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160 | |
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161 | }; //class ReducedCostMap |
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162 | |
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163 | protected: |
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164 | |
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165 | /// \brief The directed graph the algorithm runs on. |
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166 | SGraph graph; |
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167 | /// \brief The original graph. |
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168 | const Graph &graph_ref; |
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169 | /// \brief The original lower bound map. |
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170 | const LowerMap *lower; |
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171 | /// \brief The capacity map. |
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172 | SCapacityMap capacity; |
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173 | /// \brief The cost map. |
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174 | SCostMap cost; |
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175 | /// \brief The supply map. |
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176 | SSupplyMap supply; |
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177 | /// \brief The reduced cost map. |
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178 | ReducedCostMap red_cost; |
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179 | /// \brief The sum of supply values equals zero. |
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180 | bool valid_supply; |
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181 | |
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182 | /// \brief The edge map of the current flow. |
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183 | SCapacityMap flow; |
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184 | /// \brief The edge map of the found flow on the original graph. |
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185 | FlowMap flow_result; |
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186 | /// \brief The potential node map. |
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187 | SPotentialMap potential; |
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188 | /// \brief The potential node map on the original graph. |
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189 | PotentialMap potential_result; |
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190 | |
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191 | /// \brief Node reference for the original graph. |
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192 | NodeRefMap node_ref; |
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193 | /// \brief Edge reference for the original graph. |
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194 | EdgeRefMap edge_ref; |
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195 | |
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196 | /// \brief The depth node map of the spanning tree structure. |
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197 | IntNodeMap depth; |
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198 | /// \brief The parent node map of the spanning tree structure. |
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199 | NodeNodeMap parent; |
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200 | /// \brief The pred_edge node map of the spanning tree structure. |
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201 | EdgeNodeMap pred_edge; |
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202 | /// \brief The thread node map of the spanning tree structure. |
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203 | NodeNodeMap thread; |
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204 | /// \brief The forward node map of the spanning tree structure. |
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205 | BoolNodeMap forward; |
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206 | /// \brief The state edge map. |
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207 | IntEdgeMap state; |
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208 | |
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209 | |
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210 | #ifdef EDGE_BLOCK_PIVOT |
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211 | /// \brief The size of blocks for the "Edge Block" pivot rule. |
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212 | int block_size; |
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213 | #endif |
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214 | #ifdef CANDIDATE_LIST_PIVOT |
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215 | /// \brief The list of candidate edges for the "Candidate List" |
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216 | /// pivot rule. |
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217 | std::vector<Edge> candidates; |
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218 | /// \brief The maximum length of the edge list for the |
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219 | /// "Candidate List" pivot rule. |
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220 | int list_length; |
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221 | /// \brief The maximum number of minor iterations between two major |
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222 | /// itarations. |
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223 | int minor_limit; |
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224 | /// \brief The number of minor iterations. |
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225 | int minor_count; |
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226 | #endif |
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227 | #ifdef SORTED_LIST_PIVOT |
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228 | /// \brief The list of candidate edges for the "Sorted List" |
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229 | /// pivot rule. |
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230 | std::vector<Edge> candidates; |
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231 | /// \brief The maximum length of the edge list for the |
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232 | /// "Sorted List" pivot rule. |
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233 | int list_length; |
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234 | int list_index; |
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235 | #endif |
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236 | |
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237 | // Root node of the starting spanning tree. |
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238 | Node root; |
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239 | // The entering edge of the current pivot iteration. |
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240 | Edge in_edge; |
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241 | // Temporary nodes used in the current pivot iteration. |
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242 | Node join, u_in, v_in, u_out, v_out; |
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243 | Node right, first, second, last; |
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244 | Node stem, par_stem, new_stem; |
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245 | // The maximum augment amount along the cycle in the current pivot |
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246 | // iteration. |
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247 | Capacity delta; |
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248 | |
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249 | public : |
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250 | |
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251 | /// \brief General constructor of the class (with lower bounds). |
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252 | /// |
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253 | /// General constructor of the class (with lower bounds). |
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254 | /// |
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255 | /// \param _graph The directed graph the algorithm runs on. |
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256 | /// \param _lower The lower bounds of the edges. |
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257 | /// \param _capacity The capacities (upper bounds) of the edges. |
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258 | /// \param _cost The cost (length) values of the edges. |
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259 | /// \param _supply The supply values of the nodes (signed). |
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260 | NetworkSimplex( const Graph &_graph, |
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261 | const LowerMap &_lower, |
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262 | const CapacityMap &_capacity, |
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263 | const CostMap &_cost, |
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264 | const SupplyMap &_supply ) : |
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265 | graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph), |
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266 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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267 | potential_result(_graph), depth(graph), parent(graph), |
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268 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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269 | node_ref(graph_ref), edge_ref(graph_ref), |
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270 | red_cost(graph, cost, potential) |
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271 | { |
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272 | // Checking the sum of supply values |
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273 | Supply sum = 0; |
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274 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
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275 | sum += _supply[n]; |
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276 | if (!(valid_supply = sum == 0)) return; |
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277 | |
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278 | // Copying graph_ref to graph |
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279 | graph.reserveNode(countNodes(graph_ref) + 1); |
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280 | graph.reserveEdge(countEdges(graph_ref) + countNodes(graph_ref)); |
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281 | copyGraph(graph, graph_ref) |
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282 | .edgeMap(cost, _cost) |
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283 | .nodeRef(node_ref) |
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284 | .edgeRef(edge_ref) |
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285 | .run(); |
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286 | |
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287 | // Removing nonzero lower bounds |
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288 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) { |
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289 | capacity[edge_ref[e]] = _capacity[e] - _lower[e]; |
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290 | } |
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291 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) { |
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292 | Supply s = _supply[n]; |
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293 | for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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294 | s += _lower[e]; |
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295 | for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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296 | s -= _lower[e]; |
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297 | supply[node_ref[n]] = s; |
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298 | } |
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299 | } |
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300 | |
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301 | /// \brief General constructor of the class (without lower bounds). |
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302 | /// |
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303 | /// General constructor of the class (without lower bounds). |
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304 | /// |
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305 | /// \param _graph The directed graph the algorithm runs on. |
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306 | /// \param _capacity The capacities (upper bounds) of the edges. |
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307 | /// \param _cost The cost (length) values of the edges. |
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308 | /// \param _supply The supply values of the nodes (signed). |
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309 | NetworkSimplex( const Graph &_graph, |
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310 | const CapacityMap &_capacity, |
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311 | const CostMap &_cost, |
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312 | const SupplyMap &_supply ) : |
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313 | graph_ref(_graph), lower(NULL), capacity(graph), cost(graph), |
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314 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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315 | potential_result(_graph), depth(graph), parent(graph), |
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316 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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317 | node_ref(graph_ref), edge_ref(graph_ref), |
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318 | red_cost(graph, cost, potential) |
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319 | { |
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320 | // Checking the sum of supply values |
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321 | Supply sum = 0; |
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322 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
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323 | sum += _supply[n]; |
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324 | if (!(valid_supply = sum == 0)) return; |
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325 | |
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326 | // Copying graph_ref to graph |
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327 | copyGraph(graph, graph_ref) |
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328 | .edgeMap(capacity, _capacity) |
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329 | .edgeMap(cost, _cost) |
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330 | .nodeMap(supply, _supply) |
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331 | .nodeRef(node_ref) |
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332 | .edgeRef(edge_ref) |
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333 | .run(); |
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334 | } |
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335 | |
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336 | /// \brief Simple constructor of the class (with lower bounds). |
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337 | /// |
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338 | /// Simple constructor of the class (with lower bounds). |
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339 | /// |
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340 | /// \param _graph The directed graph the algorithm runs on. |
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341 | /// \param _lower The lower bounds of the edges. |
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342 | /// \param _capacity The capacities (upper bounds) of the edges. |
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343 | /// \param _cost The cost (length) values of the edges. |
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344 | /// \param _s The source node. |
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345 | /// \param _t The target node. |
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346 | /// \param _flow_value The required amount of flow from node \c _s |
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347 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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348 | /// \c _t). |
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349 | NetworkSimplex( const Graph &_graph, |
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350 | const LowerMap &_lower, |
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351 | const CapacityMap &_capacity, |
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352 | const CostMap &_cost, |
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353 | typename Graph::Node _s, |
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354 | typename Graph::Node _t, |
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355 | typename SupplyMap::Value _flow_value ) : |
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356 | graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph), |
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357 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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358 | potential_result(_graph), depth(graph), parent(graph), |
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359 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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360 | node_ref(graph_ref), edge_ref(graph_ref), |
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361 | red_cost(graph, cost, potential) |
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362 | { |
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363 | // Copying graph_ref to graph |
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364 | copyGraph(graph, graph_ref) |
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365 | .edgeMap(cost, _cost) |
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366 | .nodeRef(node_ref) |
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367 | .edgeRef(edge_ref) |
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368 | .run(); |
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369 | |
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370 | // Removing nonzero lower bounds |
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371 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) { |
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372 | capacity[edge_ref[e]] = _capacity[e] - _lower[e]; |
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373 | } |
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374 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) { |
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375 | Supply s = 0; |
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376 | if (n == _s) s = _flow_value; |
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377 | if (n == _t) s = -_flow_value; |
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378 | for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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379 | s += _lower[e]; |
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380 | for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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381 | s -= _lower[e]; |
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382 | supply[node_ref[n]] = s; |
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383 | } |
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384 | valid_supply = true; |
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385 | } |
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386 | |
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387 | /// \brief Simple constructor of the class (without lower bounds). |
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388 | /// |
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389 | /// Simple constructor of the class (without lower bounds). |
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390 | /// |
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391 | /// \param _graph The directed graph the algorithm runs on. |
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392 | /// \param _capacity The capacities (upper bounds) of the edges. |
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393 | /// \param _cost The cost (length) values of the edges. |
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394 | /// \param _s The source node. |
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395 | /// \param _t The target node. |
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396 | /// \param _flow_value The required amount of flow from node \c _s |
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397 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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398 | /// \c _t). |
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399 | NetworkSimplex( const Graph &_graph, |
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400 | const CapacityMap &_capacity, |
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401 | const CostMap &_cost, |
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402 | typename Graph::Node _s, |
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403 | typename Graph::Node _t, |
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404 | typename SupplyMap::Value _flow_value ) : |
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405 | graph_ref(_graph), lower(NULL), capacity(graph), cost(graph), |
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406 | supply(graph, 0), flow(graph), flow_result(_graph), potential(graph), |
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407 | potential_result(_graph), depth(graph), parent(graph), |
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408 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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409 | node_ref(graph_ref), edge_ref(graph_ref), |
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410 | red_cost(graph, cost, potential) |
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411 | { |
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412 | // Copying graph_ref to graph |
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413 | copyGraph(graph, graph_ref) |
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414 | .edgeMap(capacity, _capacity) |
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415 | .edgeMap(cost, _cost) |
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416 | .nodeRef(node_ref) |
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417 | .edgeRef(edge_ref) |
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418 | .run(); |
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419 | supply[node_ref[_s]] = _flow_value; |
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420 | supply[node_ref[_t]] = -_flow_value; |
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421 | valid_supply = true; |
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422 | } |
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423 | |
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424 | /// \brief Returns a const reference to the flow map. |
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425 | /// |
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426 | /// Returns a const reference to the flow map. |
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427 | /// |
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428 | /// \pre \ref run() must be called before using this function. |
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429 | const FlowMap& flowMap() const { |
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430 | return flow_result; |
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431 | } |
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432 | |
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433 | /// \brief Returns a const reference to the potential map (the dual |
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434 | /// solution). |
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435 | /// |
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436 | /// Returns a const reference to the potential map (the dual |
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437 | /// solution). |
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438 | /// |
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439 | /// \pre \ref run() must be called before using this function. |
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440 | const PotentialMap& potentialMap() const { |
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441 | return potential_result; |
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442 | } |
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443 | |
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444 | /// \brief Returns the total cost of the found flow. |
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445 | /// |
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446 | /// Returns the total cost of the found flow. The complexity of the |
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447 | /// function is \f$ O(e) \f$. |
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448 | /// |
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449 | /// \pre \ref run() must be called before using this function. |
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450 | Cost totalCost() const { |
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451 | Cost c = 0; |
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452 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
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453 | c += flow_result[e] * cost[edge_ref[e]]; |
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454 | return c; |
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455 | } |
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456 | |
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457 | /// \brief Runs the algorithm. |
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458 | /// |
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459 | /// Runs the algorithm. |
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460 | /// |
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461 | /// \return \c true if a feasible flow can be found. |
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462 | bool run() { |
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463 | return init() && start(); |
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464 | } |
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465 | |
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466 | protected: |
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467 | |
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468 | /// \brief Extends the underlaying graph and initializes all the |
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469 | /// node and edge maps. |
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470 | bool init() { |
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471 | if (!valid_supply) return false; |
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472 | |
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473 | // Initializing state and flow maps |
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474 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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475 | flow[e] = 0; |
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476 | state[e] = LOWER; |
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477 | } |
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478 | |
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479 | // Adding an artificial root node to the graph |
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480 | root = graph.addNode(); |
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481 | parent[root] = INVALID; |
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482 | pred_edge[root] = INVALID; |
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483 | depth[root] = 0; |
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484 | supply[root] = 0; |
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485 | potential[root] = 0; |
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486 | |
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487 | // Adding artificial edges to the graph and initializing the node |
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488 | // maps of the spanning tree data structure |
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489 | Supply sum = 0; |
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490 | Node last = root; |
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491 | Edge e; |
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492 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
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493 | for (NodeIt u(graph); u != INVALID; ++u) { |
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494 | if (u == root) continue; |
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495 | thread[last] = u; |
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496 | last = u; |
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497 | parent[u] = root; |
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498 | depth[u] = 1; |
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499 | sum += supply[u]; |
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500 | if (supply[u] >= 0) { |
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501 | e = graph.addEdge(u, root); |
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502 | flow[e] = supply[u]; |
---|
503 | forward[u] = true; |
---|
504 | potential[u] = max_cost; |
---|
505 | } else { |
---|
506 | e = graph.addEdge(root, u); |
---|
507 | flow[e] = -supply[u]; |
---|
508 | forward[u] = false; |
---|
509 | potential[u] = -max_cost; |
---|
510 | } |
---|
511 | cost[e] = max_cost; |
---|
512 | capacity[e] = std::numeric_limits<Capacity>::max(); |
---|
513 | state[e] = TREE; |
---|
514 | pred_edge[u] = e; |
---|
515 | } |
---|
516 | thread[last] = root; |
---|
517 | |
---|
518 | #ifdef EDGE_BLOCK_PIVOT |
---|
519 | // Initializing block_size for the edge block pivot rule |
---|
520 | int edge_num = countEdges(graph); |
---|
521 | block_size = 2 * int(sqrt(countEdges(graph))); |
---|
522 | if (block_size < MIN_BLOCK_SIZE) block_size = MIN_BLOCK_SIZE; |
---|
523 | // block_size = edge_num >= BLOCK_NUM * MIN_BLOCK_SIZE ? |
---|
524 | // edge_num / BLOCK_NUM : MIN_BLOCK_SIZE; |
---|
525 | #endif |
---|
526 | #ifdef CANDIDATE_LIST_PIVOT |
---|
527 | int edge_num = countEdges(graph); |
---|
528 | minor_count = 0; |
---|
529 | list_length = edge_num / LIST_LENGTH_DIV; |
---|
530 | minor_limit = edge_num / MINOR_LIMIT_DIV; |
---|
531 | #endif |
---|
532 | #ifdef SORTED_LIST_PIVOT |
---|
533 | int edge_num = countEdges(graph); |
---|
534 | list_index = 0; |
---|
535 | list_length = edge_num / LIST_LENGTH_DIV; |
---|
536 | #endif |
---|
537 | |
---|
538 | return sum == 0; |
---|
539 | } |
---|
540 | |
---|
541 | #ifdef FIRST_ELIGIBLE_PIVOT |
---|
542 | /// \brief Finds entering edge according to the "First Eligible" |
---|
543 | /// pivot rule. |
---|
544 | bool findEnteringEdge(EdgeIt &next_edge) { |
---|
545 | for (EdgeIt e = next_edge; e != INVALID; ++e) { |
---|
546 | if (state[e] * red_cost[e] < 0) { |
---|
547 | in_edge = e; |
---|
548 | next_edge = ++e; |
---|
549 | return true; |
---|
550 | } |
---|
551 | } |
---|
552 | for (EdgeIt e(graph); e != next_edge; ++e) { |
---|
553 | if (state[e] * red_cost[e] < 0) { |
---|
554 | in_edge = e; |
---|
555 | next_edge = ++e; |
---|
556 | return true; |
---|
557 | } |
---|
558 | } |
---|
559 | return false; |
---|
560 | } |
---|
561 | #endif |
---|
562 | |
---|
563 | #ifdef BEST_ELIGIBLE_PIVOT |
---|
564 | /// \brief Finds entering edge according to the "Best Eligible" |
---|
565 | /// pivot rule. |
---|
566 | bool findEnteringEdge() { |
---|
567 | Cost min = 0; |
---|
568 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
569 | if (state[e] * red_cost[e] < min) { |
---|
570 | min = state[e] * red_cost[e]; |
---|
571 | in_edge = e; |
---|
572 | } |
---|
573 | } |
---|
574 | return min < 0; |
---|
575 | } |
---|
576 | #endif |
---|
577 | |
---|
578 | #ifdef EDGE_BLOCK_PIVOT |
---|
579 | /// \brief Finds entering edge according to the "Edge Block" |
---|
580 | /// pivot rule. |
---|
581 | bool findEnteringEdge(EdgeIt &next_edge) { |
---|
582 | // Performing edge block selection |
---|
583 | Cost curr, min = 0; |
---|
584 | EdgeIt min_edge(graph); |
---|
585 | int cnt = 0; |
---|
586 | for (EdgeIt e = next_edge; e != INVALID; ++e) { |
---|
587 | if ((curr = state[e] * red_cost[e]) < min) { |
---|
588 | min = curr; |
---|
589 | min_edge = e; |
---|
590 | } |
---|
591 | if (++cnt == block_size) { |
---|
592 | if (min < 0) break; |
---|
593 | cnt = 0; |
---|
594 | } |
---|
595 | } |
---|
596 | if (!(min < 0)) { |
---|
597 | for (EdgeIt e(graph); e != next_edge; ++e) { |
---|
598 | if ((curr = state[e] * red_cost[e]) < min) { |
---|
599 | min = curr; |
---|
600 | min_edge = e; |
---|
601 | } |
---|
602 | if (++cnt == block_size) { |
---|
603 | if (min < 0) break; |
---|
604 | cnt = 0; |
---|
605 | } |
---|
606 | } |
---|
607 | } |
---|
608 | in_edge = min_edge; |
---|
609 | if ((next_edge = ++min_edge) == INVALID) |
---|
610 | next_edge = EdgeIt(graph); |
---|
611 | return min < 0; |
---|
612 | } |
---|
613 | #endif |
---|
614 | |
---|
615 | #ifdef CANDIDATE_LIST_PIVOT |
---|
616 | /// \brief Finds entering edge according to the "Candidate List" |
---|
617 | /// pivot rule. |
---|
618 | bool findEnteringEdge() { |
---|
619 | typedef typename std::vector<Edge>::iterator ListIt; |
---|
620 | |
---|
621 | if (minor_count >= minor_limit || candidates.size() == 0) { |
---|
622 | // Major iteration |
---|
623 | candidates.clear(); |
---|
624 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
625 | if (state[e] * red_cost[e] < 0) { |
---|
626 | candidates.push_back(e); |
---|
627 | if (candidates.size() == list_length) break; |
---|
628 | } |
---|
629 | } |
---|
630 | if (candidates.size() == 0) return false; |
---|
631 | } |
---|
632 | |
---|
633 | // Minor iteration |
---|
634 | ++minor_count; |
---|
635 | Cost min = 0; |
---|
636 | Edge e; |
---|
637 | for (int i = 0; i < candidates.size(); ++i) { |
---|
638 | e = candidates[i]; |
---|
639 | if (state[e] * red_cost[e] < min) { |
---|
640 | min = state[e] * red_cost[e]; |
---|
641 | in_edge = e; |
---|
642 | } |
---|
643 | } |
---|
644 | return true; |
---|
645 | } |
---|
646 | #endif |
---|
647 | |
---|
648 | #ifdef SORTED_LIST_PIVOT |
---|
649 | /// \brief Functor class to compare edges during sort of the |
---|
650 | /// candidate list. |
---|
651 | class SortFunc |
---|
652 | { |
---|
653 | private: |
---|
654 | const IntEdgeMap &st; |
---|
655 | const ReducedCostMap &rc; |
---|
656 | public: |
---|
657 | SortFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) : |
---|
658 | st(_st), rc(_rc) {} |
---|
659 | bool operator()(const Edge &e1, const Edge &e2) { |
---|
660 | return st[e1] * rc[e1] < st[e2] * rc[e2]; |
---|
661 | } |
---|
662 | }; |
---|
663 | |
---|
664 | /// \brief Finds entering edge according to the "Sorted List" |
---|
665 | /// pivot rule. |
---|
666 | bool findEnteringEdge() { |
---|
667 | static SortFunc sort_func(state, red_cost); |
---|
668 | |
---|
669 | // Minor iteration |
---|
670 | while (list_index < candidates.size()) { |
---|
671 | in_edge = candidates[list_index++]; |
---|
672 | if (state[in_edge] * red_cost[in_edge] < 0) return true; |
---|
673 | } |
---|
674 | |
---|
675 | // Major iteration |
---|
676 | candidates.clear(); |
---|
677 | Cost curr, min = 0; |
---|
678 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
679 | if ((curr = state[e] * red_cost[e]) < min / LOWER_DIV) { |
---|
680 | candidates.push_back(e); |
---|
681 | if (curr < min) min = curr; |
---|
682 | if (candidates.size() == list_length) break; |
---|
683 | } |
---|
684 | } |
---|
685 | if (candidates.size() == 0) return false; |
---|
686 | sort(candidates.begin(), candidates.end(), sort_func); |
---|
687 | in_edge = candidates[0]; |
---|
688 | list_index = 1; |
---|
689 | return true; |
---|
690 | } |
---|
691 | #endif |
---|
692 | |
---|
693 | /// \brief Finds the join node. |
---|
694 | Node findJoinNode() { |
---|
695 | // Finding the join node |
---|
696 | Node u = graph.source(in_edge); |
---|
697 | Node v = graph.target(in_edge); |
---|
698 | while (u != v) { |
---|
699 | if (depth[u] == depth[v]) { |
---|
700 | u = parent[u]; |
---|
701 | v = parent[v]; |
---|
702 | } |
---|
703 | else if (depth[u] > depth[v]) u = parent[u]; |
---|
704 | else v = parent[v]; |
---|
705 | } |
---|
706 | return u; |
---|
707 | } |
---|
708 | |
---|
709 | /// \brief Finds the leaving edge of the cycle. Returns \c true if |
---|
710 | /// the leaving edge is not the same as the entering edge. |
---|
711 | bool findLeavingEdge() { |
---|
712 | // Initializing first and second nodes according to the direction |
---|
713 | // of the cycle |
---|
714 | if (state[in_edge] == LOWER) { |
---|
715 | first = graph.source(in_edge); |
---|
716 | second = graph.target(in_edge); |
---|
717 | } else { |
---|
718 | first = graph.target(in_edge); |
---|
719 | second = graph.source(in_edge); |
---|
720 | } |
---|
721 | delta = capacity[in_edge]; |
---|
722 | bool result = false; |
---|
723 | Capacity d; |
---|
724 | Edge e; |
---|
725 | |
---|
726 | // Searching the cycle along the path form the first node to the |
---|
727 | // root node |
---|
728 | for (Node u = first; u != join; u = parent[u]) { |
---|
729 | e = pred_edge[u]; |
---|
730 | d = forward[u] ? flow[e] : capacity[e] - flow[e]; |
---|
731 | if (d < delta) { |
---|
732 | delta = d; |
---|
733 | u_out = u; |
---|
734 | u_in = first; |
---|
735 | v_in = second; |
---|
736 | result = true; |
---|
737 | } |
---|
738 | } |
---|
739 | // Searching the cycle along the path form the second node to the |
---|
740 | // root node |
---|
741 | for (Node u = second; u != join; u = parent[u]) { |
---|
742 | e = pred_edge[u]; |
---|
743 | d = forward[u] ? capacity[e] - flow[e] : flow[e]; |
---|
744 | if (d <= delta) { |
---|
745 | delta = d; |
---|
746 | u_out = u; |
---|
747 | u_in = second; |
---|
748 | v_in = first; |
---|
749 | result = true; |
---|
750 | } |
---|
751 | } |
---|
752 | return result; |
---|
753 | } |
---|
754 | |
---|
755 | /// \brief Changes flow and state edge maps. |
---|
756 | void changeFlows(bool change) { |
---|
757 | // Augmenting along the cycle |
---|
758 | if (delta > 0) { |
---|
759 | Capacity val = state[in_edge] * delta; |
---|
760 | flow[in_edge] += val; |
---|
761 | for (Node u = graph.source(in_edge); u != join; u = parent[u]) { |
---|
762 | flow[pred_edge[u]] += forward[u] ? -val : val; |
---|
763 | } |
---|
764 | for (Node u = graph.target(in_edge); u != join; u = parent[u]) { |
---|
765 | flow[pred_edge[u]] += forward[u] ? val : -val; |
---|
766 | } |
---|
767 | } |
---|
768 | // Updating the state of the entering and leaving edges |
---|
769 | if (change) { |
---|
770 | state[in_edge] = TREE; |
---|
771 | state[pred_edge[u_out]] = |
---|
772 | (flow[pred_edge[u_out]] == 0) ? LOWER : UPPER; |
---|
773 | } else { |
---|
774 | state[in_edge] = -state[in_edge]; |
---|
775 | } |
---|
776 | } |
---|
777 | |
---|
778 | /// \brief Updates thread and parent node maps. |
---|
779 | void updateThreadParent() { |
---|
780 | Node u; |
---|
781 | v_out = parent[u_out]; |
---|
782 | |
---|
783 | // Handling the case when join and v_out coincide |
---|
784 | bool par_first = false; |
---|
785 | if (join == v_out) { |
---|
786 | for (u = join; u != u_in && u != v_in; u = thread[u]) ; |
---|
787 | if (u == v_in) { |
---|
788 | par_first = true; |
---|
789 | while (thread[u] != u_out) u = thread[u]; |
---|
790 | first = u; |
---|
791 | } |
---|
792 | } |
---|
793 | |
---|
794 | // Finding the last successor of u_in (u) and the node after it |
---|
795 | // (right) according to the thread index |
---|
796 | for (u = u_in; depth[thread[u]] > depth[u_in]; u = thread[u]) ; |
---|
797 | right = thread[u]; |
---|
798 | if (thread[v_in] == u_out) { |
---|
799 | for (last = u; depth[last] > depth[u_out]; last = thread[last]) ; |
---|
800 | if (last == u_out) last = thread[last]; |
---|
801 | } |
---|
802 | else last = thread[v_in]; |
---|
803 | |
---|
804 | // Updating stem nodes |
---|
805 | thread[v_in] = stem = u_in; |
---|
806 | par_stem = v_in; |
---|
807 | while (stem != u_out) { |
---|
808 | thread[u] = new_stem = parent[stem]; |
---|
809 | |
---|
810 | // Finding the node just before the stem node (u) according to |
---|
811 | // the original thread index |
---|
812 | for (u = new_stem; thread[u] != stem; u = thread[u]) ; |
---|
813 | thread[u] = right; |
---|
814 | |
---|
815 | // Changing the parent node of stem and shifting stem and |
---|
816 | // par_stem nodes |
---|
817 | parent[stem] = par_stem; |
---|
818 | par_stem = stem; |
---|
819 | stem = new_stem; |
---|
820 | |
---|
821 | // Finding the last successor of stem (u) and the node after it |
---|
822 | // (right) according to the thread index |
---|
823 | for (u = stem; depth[thread[u]] > depth[stem]; u = thread[u]) ; |
---|
824 | right = thread[u]; |
---|
825 | } |
---|
826 | parent[u_out] = par_stem; |
---|
827 | thread[u] = last; |
---|
828 | |
---|
829 | if (join == v_out && par_first) { |
---|
830 | if (first != v_in) thread[first] = right; |
---|
831 | } else { |
---|
832 | for (u = v_out; thread[u] != u_out; u = thread[u]) ; |
---|
833 | thread[u] = right; |
---|
834 | } |
---|
835 | } |
---|
836 | |
---|
837 | /// \brief Updates pred_edge and forward node maps. |
---|
838 | void updatePredEdge() { |
---|
839 | Node u = u_out, v; |
---|
840 | while (u != u_in) { |
---|
841 | v = parent[u]; |
---|
842 | pred_edge[u] = pred_edge[v]; |
---|
843 | forward[u] = !forward[v]; |
---|
844 | u = v; |
---|
845 | } |
---|
846 | pred_edge[u_in] = in_edge; |
---|
847 | forward[u_in] = (u_in == graph.source(in_edge)); |
---|
848 | } |
---|
849 | |
---|
850 | /// \brief Updates depth and potential node maps. |
---|
851 | void updateDepthPotential() { |
---|
852 | depth[u_in] = depth[v_in] + 1; |
---|
853 | potential[u_in] = forward[u_in] ? |
---|
854 | potential[v_in] + cost[pred_edge[u_in]] : |
---|
855 | potential[v_in] - cost[pred_edge[u_in]]; |
---|
856 | |
---|
857 | Node u = thread[u_in], v; |
---|
858 | while (true) { |
---|
859 | v = parent[u]; |
---|
860 | if (v == INVALID) break; |
---|
861 | depth[u] = depth[v] + 1; |
---|
862 | potential[u] = forward[u] ? |
---|
863 | potential[v] + cost[pred_edge[u]] : |
---|
864 | potential[v] - cost[pred_edge[u]]; |
---|
865 | if (depth[u] <= depth[v_in]) break; |
---|
866 | u = thread[u]; |
---|
867 | } |
---|
868 | } |
---|
869 | |
---|
870 | /// \brief Executes the algorithm. |
---|
871 | bool start() { |
---|
872 | // Processing pivots |
---|
873 | #ifdef _DEBUG_ITER_ |
---|
874 | int iter_num = 0; |
---|
875 | #endif |
---|
876 | #if defined(FIRST_ELIGIBLE_PIVOT) || defined(EDGE_BLOCK_PIVOT) |
---|
877 | EdgeIt next_edge(graph); |
---|
878 | while (findEnteringEdge(next_edge)) |
---|
879 | #else |
---|
880 | while (findEnteringEdge()) |
---|
881 | #endif |
---|
882 | { |
---|
883 | join = findJoinNode(); |
---|
884 | bool change = findLeavingEdge(); |
---|
885 | changeFlows(change); |
---|
886 | if (change) { |
---|
887 | updateThreadParent(); |
---|
888 | updatePredEdge(); |
---|
889 | updateDepthPotential(); |
---|
890 | } |
---|
891 | #ifdef _DEBUG_ITER_ |
---|
892 | ++iter_num; |
---|
893 | #endif |
---|
894 | } |
---|
895 | |
---|
896 | #ifdef _DEBUG_ITER_ |
---|
897 | std::cout << "Network Simplex algorithm finished. " << iter_num |
---|
898 | << " pivot iterations performed." << std::endl; |
---|
899 | #endif |
---|
900 | |
---|
901 | // Checking if the flow amount equals zero on all the |
---|
902 | // artificial edges |
---|
903 | for (InEdgeIt e(graph, root); e != INVALID; ++e) |
---|
904 | if (flow[e] > 0) return false; |
---|
905 | for (OutEdgeIt e(graph, root); e != INVALID; ++e) |
---|
906 | if (flow[e] > 0) return false; |
---|
907 | |
---|
908 | // Copying flow values to flow_result |
---|
909 | if (lower) { |
---|
910 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
---|
911 | flow_result[e] = (*lower)[e] + flow[edge_ref[e]]; |
---|
912 | } else { |
---|
913 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
---|
914 | flow_result[e] = flow[edge_ref[e]]; |
---|
915 | } |
---|
916 | // Copying potential values to potential_result |
---|
917 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
---|
918 | potential_result[n] = potential[node_ref[n]]; |
---|
919 | |
---|
920 | return true; |
---|
921 | } |
---|
922 | |
---|
923 | }; //class NetworkSimplex |
---|
924 | |
---|
925 | ///@} |
---|
926 | |
---|
927 | } //namespace lemon |
---|
928 | |
---|
929 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|