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 Network simplex algorithm for finding a minimum cost flow. |
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26 | |
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27 | #include <vector> |
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28 | #include <limits> |
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29 | |
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30 | #include <lemon/graph_adaptor.h> |
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31 | #include <lemon/graph_utils.h> |
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32 | #include <lemon/smart_graph.h> |
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33 | #include <lemon/math.h> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \addtogroup min_cost_flow |
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38 | /// @{ |
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39 | |
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40 | /// \brief Implementation of the primal network simplex algorithm |
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41 | /// for finding a minimum cost flow. |
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42 | /// |
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43 | /// \ref NetworkSimplex implements the primal network simplex algorithm |
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44 | /// for finding a minimum cost flow. |
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45 | /// |
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46 | /// \tparam Graph The directed graph type the algorithm runs on. |
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47 | /// \tparam LowerMap The type of the lower bound map. |
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48 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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49 | /// \tparam CostMap The type of the cost (length) map. |
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50 | /// \tparam SupplyMap The type of the supply map. |
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51 | /// |
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52 | /// \warning |
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53 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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54 | /// - Supply values should be \e signed \e integers. |
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55 | /// - The value types of the maps should be convertible to each other. |
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56 | /// - \c CostMap::Value must be signed type. |
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57 | /// |
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58 | /// \note \ref NetworkSimplex provides five different pivot rule |
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59 | /// implementations that significantly affect the efficiency of the |
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60 | /// algorithm. |
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61 | /// By default "Block Search" pivot rule is used, which proved to be |
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62 | /// by far the most efficient according to our benchmark tests. |
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63 | /// However another pivot rule can be selected using \ref run() |
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64 | /// function with the proper parameter. |
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65 | /// |
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66 | /// \author Peter Kovacs |
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67 | template < typename Graph, |
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68 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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69 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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70 | typename CostMap = typename Graph::template EdgeMap<int>, |
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71 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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72 | class NetworkSimplex |
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73 | { |
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74 | typedef typename CapacityMap::Value Capacity; |
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75 | typedef typename CostMap::Value Cost; |
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76 | typedef typename SupplyMap::Value Supply; |
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77 | |
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78 | typedef SmartGraph SGraph; |
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79 | GRAPH_TYPEDEFS(typename SGraph); |
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80 | |
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81 | typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap; |
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82 | typedef typename SGraph::template EdgeMap<Cost> SCostMap; |
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83 | typedef typename SGraph::template NodeMap<Supply> SSupplyMap; |
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84 | typedef typename SGraph::template NodeMap<Cost> SPotentialMap; |
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85 | |
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86 | typedef typename SGraph::template NodeMap<int> IntNodeMap; |
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87 | typedef typename SGraph::template NodeMap<bool> BoolNodeMap; |
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88 | typedef typename SGraph::template NodeMap<Node> NodeNodeMap; |
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89 | typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap; |
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90 | typedef typename SGraph::template EdgeMap<int> IntEdgeMap; |
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91 | typedef typename SGraph::template EdgeMap<bool> BoolEdgeMap; |
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92 | |
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93 | typedef typename Graph::template NodeMap<Node> NodeRefMap; |
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94 | typedef typename Graph::template EdgeMap<Edge> EdgeRefMap; |
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95 | |
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96 | typedef std::vector<Edge> EdgeVector; |
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97 | |
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98 | public: |
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99 | |
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100 | /// The type of the flow map. |
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101 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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102 | /// The type of the potential map. |
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103 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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104 | |
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105 | public: |
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106 | |
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107 | /// Enum type to select the pivot rule used by \ref run(). |
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108 | enum PivotRuleEnum { |
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109 | FIRST_ELIGIBLE_PIVOT, |
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110 | BEST_ELIGIBLE_PIVOT, |
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111 | BLOCK_SEARCH_PIVOT, |
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112 | CANDIDATE_LIST_PIVOT, |
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113 | ALTERING_LIST_PIVOT |
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114 | }; |
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115 | |
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116 | private: |
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117 | |
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118 | /// \brief Map adaptor class for handling reduced edge costs. |
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119 | /// |
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120 | /// Map adaptor class for handling reduced edge costs. |
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121 | class ReducedCostMap : public MapBase<Edge, Cost> |
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122 | { |
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123 | private: |
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124 | |
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125 | const SGraph &_gr; |
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126 | const SCostMap &_cost_map; |
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127 | const SPotentialMap &_pot_map; |
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128 | |
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129 | public: |
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130 | |
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131 | ///\e |
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132 | ReducedCostMap( const SGraph &gr, |
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133 | const SCostMap &cost_map, |
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134 | const SPotentialMap &pot_map ) : |
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135 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
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136 | |
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137 | ///\e |
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138 | Cost operator[](const Edge &e) const { |
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139 | return _cost_map[e] + _pot_map[_gr.source(e)] |
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140 | - _pot_map[_gr.target(e)]; |
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141 | } |
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142 | |
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143 | }; //class ReducedCostMap |
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144 | |
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145 | private: |
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146 | |
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147 | /// \brief Implementation of the "First Eligible" pivot rule for the |
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148 | /// \ref NetworkSimplex "network simplex" algorithm. |
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149 | /// |
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150 | /// This class implements the "First Eligible" pivot rule |
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151 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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152 | /// |
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153 | /// For more information see \ref NetworkSimplex::run(). |
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154 | class FirstEligiblePivotRule |
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155 | { |
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156 | private: |
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157 | |
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158 | // References to the NetworkSimplex class |
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159 | NetworkSimplex &_ns; |
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160 | EdgeVector &_edges; |
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161 | |
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162 | int _next_edge; |
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163 | |
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164 | public: |
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165 | |
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166 | /// Constructor |
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167 | FirstEligiblePivotRule(NetworkSimplex &ns, EdgeVector &edges) : |
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168 | _ns(ns), _edges(edges), _next_edge(0) {} |
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169 | |
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170 | /// Find next entering edge |
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171 | inline bool findEnteringEdge() { |
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172 | Edge e; |
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173 | for (int i = _next_edge; i < int(_edges.size()); ++i) { |
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174 | e = _edges[i]; |
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175 | if (_ns._state[e] * _ns._red_cost[e] < 0) { |
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176 | _ns._in_edge = e; |
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177 | _next_edge = i + 1; |
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178 | return true; |
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179 | } |
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180 | } |
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181 | for (int i = 0; i < _next_edge; ++i) { |
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182 | e = _edges[i]; |
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183 | if (_ns._state[e] * _ns._red_cost[e] < 0) { |
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184 | _ns._in_edge = e; |
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185 | _next_edge = i + 1; |
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186 | return true; |
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187 | } |
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188 | } |
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189 | return false; |
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190 | } |
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191 | }; //class FirstEligiblePivotRule |
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192 | |
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193 | /// \brief Implementation of the "Best Eligible" pivot rule for the |
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194 | /// \ref NetworkSimplex "network simplex" algorithm. |
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195 | /// |
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196 | /// This class implements the "Best Eligible" pivot rule |
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197 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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198 | /// |
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199 | /// For more information see \ref NetworkSimplex::run(). |
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200 | class BestEligiblePivotRule |
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201 | { |
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202 | private: |
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203 | |
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204 | // References to the NetworkSimplex class |
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205 | NetworkSimplex &_ns; |
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206 | EdgeVector &_edges; |
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207 | |
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208 | public: |
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209 | |
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210 | /// Constructor |
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211 | BestEligiblePivotRule(NetworkSimplex &ns, EdgeVector &edges) : |
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212 | _ns(ns), _edges(edges) {} |
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213 | |
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214 | /// Find next entering edge |
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215 | inline bool findEnteringEdge() { |
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216 | Cost min = 0; |
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217 | Edge e; |
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218 | for (int i = 0; i < int(_edges.size()); ++i) { |
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219 | e = _edges[i]; |
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220 | if (_ns._state[e] * _ns._red_cost[e] < min) { |
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221 | min = _ns._state[e] * _ns._red_cost[e]; |
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222 | _ns._in_edge = e; |
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223 | } |
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224 | } |
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225 | return min < 0; |
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226 | } |
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227 | }; //class BestEligiblePivotRule |
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228 | |
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229 | /// \brief Implementation of the "Block Search" pivot rule for the |
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230 | /// \ref NetworkSimplex "network simplex" algorithm. |
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231 | /// |
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232 | /// This class implements the "Block Search" pivot rule |
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233 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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234 | /// |
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235 | /// For more information see \ref NetworkSimplex::run(). |
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236 | class BlockSearchPivotRule |
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237 | { |
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238 | private: |
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239 | |
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240 | // References to the NetworkSimplex class |
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241 | NetworkSimplex &_ns; |
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242 | EdgeVector &_edges; |
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243 | |
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244 | int _block_size; |
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245 | int _next_edge, _min_edge; |
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246 | |
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247 | public: |
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248 | |
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249 | /// Constructor |
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250 | BlockSearchPivotRule(NetworkSimplex &ns, EdgeVector &edges) : |
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251 | _ns(ns), _edges(edges), _next_edge(0), _min_edge(0) |
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252 | { |
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253 | // The main parameters of the pivot rule |
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254 | const double BLOCK_SIZE_FACTOR = 2.0; |
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255 | const int MIN_BLOCK_SIZE = 10; |
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256 | |
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257 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edges.size())), |
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258 | MIN_BLOCK_SIZE ); |
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259 | } |
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260 | |
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261 | /// Find next entering edge |
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262 | inline bool findEnteringEdge() { |
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263 | Cost curr, min = 0; |
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264 | Edge e; |
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265 | int cnt = _block_size; |
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266 | int i; |
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267 | for (i = _next_edge; i < int(_edges.size()); ++i) { |
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268 | e = _edges[i]; |
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269 | if ((curr = _ns._state[e] * _ns._red_cost[e]) < min) { |
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270 | min = curr; |
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271 | _min_edge = i; |
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272 | } |
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273 | if (--cnt == 0) { |
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274 | if (min < 0) break; |
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275 | cnt = _block_size; |
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276 | } |
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277 | } |
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278 | if (min == 0 || cnt > 0) { |
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279 | for (i = 0; i < _next_edge; ++i) { |
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280 | e = _edges[i]; |
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281 | if ((curr = _ns._state[e] * _ns._red_cost[e]) < min) { |
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282 | min = curr; |
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283 | _min_edge = i; |
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284 | } |
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285 | if (--cnt == 0) { |
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286 | if (min < 0) break; |
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287 | cnt = _block_size; |
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288 | } |
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289 | } |
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290 | } |
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291 | if (min >= 0) return false; |
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292 | _ns._in_edge = _edges[_min_edge]; |
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293 | _next_edge = i; |
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294 | return true; |
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295 | } |
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296 | }; //class BlockSearchPivotRule |
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297 | |
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298 | /// \brief Implementation of the "Candidate List" pivot rule for the |
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299 | /// \ref NetworkSimplex "network simplex" algorithm. |
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300 | /// |
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301 | /// This class implements the "Candidate List" pivot rule |
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302 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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303 | /// |
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304 | /// For more information see \ref NetworkSimplex::run(). |
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305 | class CandidateListPivotRule |
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306 | { |
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307 | private: |
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308 | |
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309 | // References to the NetworkSimplex class |
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310 | NetworkSimplex &_ns; |
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311 | EdgeVector &_edges; |
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312 | |
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313 | EdgeVector _candidates; |
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314 | int _list_length, _minor_limit; |
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315 | int _curr_length, _minor_count; |
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316 | int _next_edge, _min_edge; |
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317 | |
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318 | public: |
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319 | |
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320 | /// Constructor |
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321 | CandidateListPivotRule(NetworkSimplex &ns, EdgeVector &edges) : |
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322 | _ns(ns), _edges(edges), _next_edge(0), _min_edge(0) |
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323 | { |
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324 | // The main parameters of the pivot rule |
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325 | const double LIST_LENGTH_FACTOR = 1.0; |
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326 | const int MIN_LIST_LENGTH = 10; |
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327 | const double MINOR_LIMIT_FACTOR = 0.1; |
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328 | const int MIN_MINOR_LIMIT = 3; |
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329 | |
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330 | _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_edges.size())), |
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331 | MIN_LIST_LENGTH ); |
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332 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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333 | MIN_MINOR_LIMIT ); |
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334 | _curr_length = _minor_count = 0; |
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335 | _candidates.resize(_list_length); |
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336 | } |
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337 | |
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338 | /// Find next entering edge |
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339 | inline bool findEnteringEdge() { |
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340 | Cost min, curr; |
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341 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
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342 | // Minor iteration: selecting the best eligible edge from |
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343 | // the current candidate list |
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344 | ++_minor_count; |
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345 | Edge e; |
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346 | min = 0; |
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347 | for (int i = 0; i < _curr_length; ++i) { |
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348 | e = _candidates[i]; |
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349 | curr = _ns._state[e] * _ns._red_cost[e]; |
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350 | if (curr < min) { |
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351 | min = curr; |
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352 | _ns._in_edge = e; |
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353 | } |
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354 | if (curr >= 0) { |
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355 | _candidates[i--] = _candidates[--_curr_length]; |
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356 | } |
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357 | } |
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358 | if (min < 0) return true; |
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359 | } |
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360 | |
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361 | // Major iteration: building a new candidate list |
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362 | Edge e; |
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363 | min = 0; |
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364 | _curr_length = 0; |
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365 | int i; |
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366 | for (i = _next_edge; i < int(_edges.size()); ++i) { |
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367 | e = _edges[i]; |
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368 | if ((curr = _ns._state[e] * _ns._red_cost[e]) < 0) { |
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369 | _candidates[_curr_length++] = e; |
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370 | if (curr < min) { |
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371 | min = curr; |
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372 | _min_edge = i; |
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373 | } |
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374 | if (_curr_length == _list_length) break; |
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375 | } |
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376 | } |
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377 | if (_curr_length < _list_length) { |
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378 | for (i = 0; i < _next_edge; ++i) { |
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379 | e = _edges[i]; |
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380 | if ((curr = _ns._state[e] * _ns._red_cost[e]) < 0) { |
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381 | _candidates[_curr_length++] = e; |
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382 | if (curr < min) { |
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383 | min = curr; |
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384 | _min_edge = i; |
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385 | } |
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386 | if (_curr_length == _list_length) break; |
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387 | } |
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388 | } |
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389 | } |
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390 | if (_curr_length == 0) return false; |
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391 | _minor_count = 1; |
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392 | _ns._in_edge = _edges[_min_edge]; |
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393 | _next_edge = i; |
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394 | return true; |
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395 | } |
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396 | }; //class CandidateListPivotRule |
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397 | |
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398 | /// \brief Implementation of the "Altering Candidate List" pivot rule |
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399 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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400 | /// |
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401 | /// This class implements the "Altering Candidate List" pivot rule |
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402 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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403 | /// |
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404 | /// For more information see \ref NetworkSimplex::run(). |
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405 | class AlteringListPivotRule |
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406 | { |
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407 | private: |
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408 | |
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409 | // References to the NetworkSimplex class |
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410 | NetworkSimplex &_ns; |
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411 | EdgeVector &_edges; |
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412 | |
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413 | EdgeVector _candidates; |
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414 | SCostMap _cand_cost; |
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415 | int _block_size, _head_length, _curr_length; |
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416 | int _next_edge; |
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417 | |
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418 | // Functor class to compare edges during sort of the candidate list |
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419 | class SortFunc |
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420 | { |
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421 | private: |
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422 | const SCostMap &_map; |
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423 | public: |
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424 | SortFunc(const SCostMap &map) : _map(map) {} |
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425 | bool operator()(const Edge &e1, const Edge &e2) { |
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426 | return _map[e1] < _map[e2]; |
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427 | } |
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428 | }; |
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429 | |
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430 | SortFunc _sort_func; |
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431 | |
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432 | public: |
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433 | |
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434 | /// Constructor |
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435 | AlteringListPivotRule(NetworkSimplex &ns, EdgeVector &edges) : |
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436 | _ns(ns), _edges(edges), _cand_cost(_ns._graph), |
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437 | _next_edge(0), _sort_func(_cand_cost) |
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438 | { |
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439 | // The main parameters of the pivot rule |
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440 | const double BLOCK_SIZE_FACTOR = 1.0; |
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441 | const int MIN_BLOCK_SIZE = 10; |
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442 | const double HEAD_LENGTH_FACTOR = 0.1; |
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443 | const int MIN_HEAD_LENGTH = 5; |
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444 | |
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445 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edges.size())), |
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446 | MIN_BLOCK_SIZE ); |
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447 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
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448 | MIN_HEAD_LENGTH ); |
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449 | _candidates.resize(_head_length + _block_size); |
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450 | _curr_length = 0; |
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451 | } |
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452 | |
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453 | /// Find next entering edge |
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454 | inline bool findEnteringEdge() { |
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455 | // Checking the current candidate list |
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456 | Edge e; |
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457 | for (int idx = 0; idx < _curr_length; ++idx) { |
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458 | e = _candidates[idx]; |
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459 | if ((_cand_cost[e] = _ns._state[e] * _ns._red_cost[e]) >= 0) { |
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460 | _candidates[idx--] = _candidates[--_curr_length]; |
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461 | } |
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462 | } |
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463 | |
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464 | // Extending the list |
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465 | int cnt = _block_size; |
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466 | int last_edge = 0; |
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467 | int limit = _head_length; |
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468 | for (int i = _next_edge; i < int(_edges.size()); ++i) { |
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469 | e = _edges[i]; |
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470 | if ((_cand_cost[e] = _ns._state[e] * _ns._red_cost[e]) < 0) { |
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471 | _candidates[_curr_length++] = e; |
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472 | last_edge = i; |
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473 | } |
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474 | if (--cnt == 0) { |
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475 | if (_curr_length > limit) break; |
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476 | limit = 0; |
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477 | cnt = _block_size; |
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478 | } |
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479 | } |
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480 | if (_curr_length <= limit) { |
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481 | for (int i = 0; i < _next_edge; ++i) { |
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482 | e = _edges[i]; |
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483 | if ((_cand_cost[e] = _ns._state[e] * _ns._red_cost[e]) < 0) { |
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484 | _candidates[_curr_length++] = e; |
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485 | last_edge = i; |
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486 | } |
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487 | if (--cnt == 0) { |
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488 | if (_curr_length > limit) break; |
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489 | limit = 0; |
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490 | cnt = _block_size; |
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491 | } |
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492 | } |
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493 | } |
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494 | if (_curr_length == 0) return false; |
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495 | _next_edge = last_edge + 1; |
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496 | |
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497 | // Sorting the list partially |
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498 | EdgeVector::iterator sort_end = _candidates.begin(); |
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499 | EdgeVector::iterator vector_end = _candidates.begin(); |
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500 | for (int idx = 0; idx < _curr_length; ++idx) { |
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501 | ++vector_end; |
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502 | if (idx <= _head_length) ++sort_end; |
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503 | } |
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504 | partial_sort(_candidates.begin(), sort_end, vector_end, _sort_func); |
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505 | |
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506 | _ns._in_edge = _candidates[0]; |
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507 | if (_curr_length > _head_length) { |
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508 | _candidates[0] = _candidates[_head_length - 1]; |
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509 | _curr_length = _head_length - 1; |
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510 | } else { |
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511 | _candidates[0] = _candidates[_curr_length - 1]; |
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512 | --_curr_length; |
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513 | } |
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514 | |
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515 | return true; |
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516 | } |
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517 | }; //class AlteringListPivotRule |
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518 | |
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519 | private: |
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520 | |
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521 | // State constants for edges |
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522 | enum EdgeStateEnum { |
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523 | STATE_UPPER = -1, |
---|
524 | STATE_TREE = 0, |
---|
525 | STATE_LOWER = 1 |
---|
526 | }; |
---|
527 | |
---|
528 | private: |
---|
529 | |
---|
530 | // The directed graph the algorithm runs on |
---|
531 | SGraph _graph; |
---|
532 | // The original graph |
---|
533 | const Graph &_graph_ref; |
---|
534 | // The original lower bound map |
---|
535 | const LowerMap *_lower; |
---|
536 | // The capacity map |
---|
537 | SCapacityMap _capacity; |
---|
538 | // The cost map |
---|
539 | SCostMap _cost; |
---|
540 | // The supply map |
---|
541 | SSupplyMap _supply; |
---|
542 | bool _valid_supply; |
---|
543 | |
---|
544 | // Edge map of the current flow |
---|
545 | SCapacityMap _flow; |
---|
546 | // Node map of the current potentials |
---|
547 | SPotentialMap _potential; |
---|
548 | |
---|
549 | // The depth node map of the spanning tree structure |
---|
550 | IntNodeMap _depth; |
---|
551 | // The parent node map of the spanning tree structure |
---|
552 | NodeNodeMap _parent; |
---|
553 | // The pred_edge node map of the spanning tree structure |
---|
554 | EdgeNodeMap _pred_edge; |
---|
555 | // The thread node map of the spanning tree structure |
---|
556 | NodeNodeMap _thread; |
---|
557 | // The forward node map of the spanning tree structure |
---|
558 | BoolNodeMap _forward; |
---|
559 | // The state edge map |
---|
560 | IntEdgeMap _state; |
---|
561 | // The root node of the starting spanning tree |
---|
562 | Node _root; |
---|
563 | |
---|
564 | // The reduced cost map |
---|
565 | ReducedCostMap _red_cost; |
---|
566 | |
---|
567 | // The non-artifical edges |
---|
568 | EdgeVector _edges; |
---|
569 | |
---|
570 | // Members for handling the original graph |
---|
571 | FlowMap *_flow_result; |
---|
572 | PotentialMap *_potential_result; |
---|
573 | bool _local_flow; |
---|
574 | bool _local_potential; |
---|
575 | NodeRefMap _node_ref; |
---|
576 | EdgeRefMap _edge_ref; |
---|
577 | |
---|
578 | // The entering edge of the current pivot iteration. |
---|
579 | Edge _in_edge; |
---|
580 | |
---|
581 | // Temporary nodes used in the current pivot iteration. |
---|
582 | Node join, u_in, v_in, u_out, v_out; |
---|
583 | Node right, first, second, last; |
---|
584 | Node stem, par_stem, new_stem; |
---|
585 | // The maximum augment amount along the found cycle in the current |
---|
586 | // pivot iteration. |
---|
587 | Capacity delta; |
---|
588 | |
---|
589 | public : |
---|
590 | |
---|
591 | /// \brief General constructor (with lower bounds). |
---|
592 | /// |
---|
593 | /// General constructor (with lower bounds). |
---|
594 | /// |
---|
595 | /// \param graph The directed graph the algorithm runs on. |
---|
596 | /// \param lower The lower bounds of the edges. |
---|
597 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
598 | /// \param cost The cost (length) values of the edges. |
---|
599 | /// \param supply The supply values of the nodes (signed). |
---|
600 | NetworkSimplex( const Graph &graph, |
---|
601 | const LowerMap &lower, |
---|
602 | const CapacityMap &capacity, |
---|
603 | const CostMap &cost, |
---|
604 | const SupplyMap &supply ) : |
---|
605 | _graph(), _graph_ref(graph), _lower(&lower), _capacity(_graph), |
---|
606 | _cost(_graph), _supply(_graph), _flow(_graph), |
---|
607 | _potential(_graph), _depth(_graph), _parent(_graph), |
---|
608 | _pred_edge(_graph), _thread(_graph), _forward(_graph), |
---|
609 | _state(_graph), _red_cost(_graph, _cost, _potential), |
---|
610 | _flow_result(NULL), _potential_result(NULL), |
---|
611 | _local_flow(false), _local_potential(false), |
---|
612 | _node_ref(graph), _edge_ref(graph) |
---|
613 | { |
---|
614 | // Check the sum of supply values |
---|
615 | Supply sum = 0; |
---|
616 | for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n) |
---|
617 | sum += supply[n]; |
---|
618 | if (!(_valid_supply = sum == 0)) return; |
---|
619 | |
---|
620 | // Copy _graph_ref to _graph |
---|
621 | _graph.reserveNode(countNodes(_graph_ref) + 1); |
---|
622 | _graph.reserveEdge(countEdges(_graph_ref) + countNodes(_graph_ref)); |
---|
623 | copyGraph(_graph, _graph_ref) |
---|
624 | .edgeMap(_capacity, capacity) |
---|
625 | .edgeMap(_cost, cost) |
---|
626 | .nodeMap(_supply, supply) |
---|
627 | .nodeRef(_node_ref) |
---|
628 | .edgeRef(_edge_ref) |
---|
629 | .run(); |
---|
630 | |
---|
631 | // Remove non-zero lower bounds |
---|
632 | for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) { |
---|
633 | if (lower[e] != 0) { |
---|
634 | _capacity[_edge_ref[e]] = capacity[e] - lower[e]; |
---|
635 | _supply[_node_ref[_graph_ref.source(e)]] -= lower[e]; |
---|
636 | _supply[_node_ref[_graph_ref.target(e)]] += lower[e]; |
---|
637 | } |
---|
638 | } |
---|
639 | } |
---|
640 | |
---|
641 | /// \brief General constructor (without lower bounds). |
---|
642 | /// |
---|
643 | /// General constructor (without lower bounds). |
---|
644 | /// |
---|
645 | /// \param graph The directed graph the algorithm runs on. |
---|
646 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
647 | /// \param cost The cost (length) values of the edges. |
---|
648 | /// \param supply The supply values of the nodes (signed). |
---|
649 | NetworkSimplex( const Graph &graph, |
---|
650 | const CapacityMap &capacity, |
---|
651 | const CostMap &cost, |
---|
652 | const SupplyMap &supply ) : |
---|
653 | _graph(), _graph_ref(graph), _lower(NULL), _capacity(_graph), |
---|
654 | _cost(_graph), _supply(_graph), _flow(_graph), |
---|
655 | _potential(_graph), _depth(_graph), _parent(_graph), |
---|
656 | _pred_edge(_graph), _thread(_graph), _forward(_graph), |
---|
657 | _state(_graph), _red_cost(_graph, _cost, _potential), |
---|
658 | _flow_result(NULL), _potential_result(NULL), |
---|
659 | _local_flow(false), _local_potential(false), |
---|
660 | _node_ref(graph), _edge_ref(graph) |
---|
661 | { |
---|
662 | // Check the sum of supply values |
---|
663 | Supply sum = 0; |
---|
664 | for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n) |
---|
665 | sum += supply[n]; |
---|
666 | if (!(_valid_supply = sum == 0)) return; |
---|
667 | |
---|
668 | // Copy _graph_ref to _graph |
---|
669 | _graph.reserveNode(countNodes(_graph_ref) + 1); |
---|
670 | _graph.reserveEdge(countEdges(_graph_ref) + countNodes(_graph_ref)); |
---|
671 | copyGraph(_graph, _graph_ref) |
---|
672 | .edgeMap(_capacity, capacity) |
---|
673 | .edgeMap(_cost, cost) |
---|
674 | .nodeMap(_supply, supply) |
---|
675 | .nodeRef(_node_ref) |
---|
676 | .edgeRef(_edge_ref) |
---|
677 | .run(); |
---|
678 | } |
---|
679 | |
---|
680 | /// \brief Simple constructor (with lower bounds). |
---|
681 | /// |
---|
682 | /// Simple constructor (with lower bounds). |
---|
683 | /// |
---|
684 | /// \param graph The directed graph the algorithm runs on. |
---|
685 | /// \param lower The lower bounds of the edges. |
---|
686 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
687 | /// \param cost The cost (length) values of the edges. |
---|
688 | /// \param s The source node. |
---|
689 | /// \param t The target node. |
---|
690 | /// \param flow_value The required amount of flow from node \c s |
---|
691 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
692 | NetworkSimplex( const Graph &graph, |
---|
693 | const LowerMap &lower, |
---|
694 | const CapacityMap &capacity, |
---|
695 | const CostMap &cost, |
---|
696 | typename Graph::Node s, |
---|
697 | typename Graph::Node t, |
---|
698 | typename SupplyMap::Value flow_value ) : |
---|
699 | _graph(), _graph_ref(graph), _lower(&lower), _capacity(_graph), |
---|
700 | _cost(_graph), _supply(_graph, 0), _flow(_graph), |
---|
701 | _potential(_graph), _depth(_graph), _parent(_graph), |
---|
702 | _pred_edge(_graph), _thread(_graph), _forward(_graph), |
---|
703 | _state(_graph), _red_cost(_graph, _cost, _potential), |
---|
704 | _flow_result(NULL), _potential_result(NULL), |
---|
705 | _local_flow(false), _local_potential(false), |
---|
706 | _node_ref(graph), _edge_ref(graph) |
---|
707 | { |
---|
708 | // Copy _graph_ref to graph |
---|
709 | _graph.reserveNode(countNodes(_graph_ref) + 1); |
---|
710 | _graph.reserveEdge(countEdges(_graph_ref) + countNodes(_graph_ref)); |
---|
711 | copyGraph(_graph, _graph_ref) |
---|
712 | .edgeMap(_capacity, capacity) |
---|
713 | .edgeMap(_cost, cost) |
---|
714 | .nodeRef(_node_ref) |
---|
715 | .edgeRef(_edge_ref) |
---|
716 | .run(); |
---|
717 | |
---|
718 | // Remove non-zero lower bounds |
---|
719 | _supply[_node_ref[s]] = flow_value; |
---|
720 | _supply[_node_ref[t]] = -flow_value; |
---|
721 | for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) { |
---|
722 | if (lower[e] != 0) { |
---|
723 | _capacity[_edge_ref[e]] = capacity[e] - lower[e]; |
---|
724 | _supply[_node_ref[_graph_ref.source(e)]] -= lower[e]; |
---|
725 | _supply[_node_ref[_graph_ref.target(e)]] += lower[e]; |
---|
726 | } |
---|
727 | } |
---|
728 | _valid_supply = true; |
---|
729 | } |
---|
730 | |
---|
731 | /// \brief Simple constructor (without lower bounds). |
---|
732 | /// |
---|
733 | /// Simple constructor (without lower bounds). |
---|
734 | /// |
---|
735 | /// \param graph The directed graph the algorithm runs on. |
---|
736 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
737 | /// \param cost The cost (length) values of the edges. |
---|
738 | /// \param s The source node. |
---|
739 | /// \param t The target node. |
---|
740 | /// \param flow_value The required amount of flow from node \c s |
---|
741 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
742 | NetworkSimplex( const Graph &graph, |
---|
743 | const CapacityMap &capacity, |
---|
744 | const CostMap &cost, |
---|
745 | typename Graph::Node s, |
---|
746 | typename Graph::Node t, |
---|
747 | typename SupplyMap::Value flow_value ) : |
---|
748 | _graph(), _graph_ref(graph), _lower(NULL), _capacity(_graph), |
---|
749 | _cost(_graph), _supply(_graph, 0), _flow(_graph), |
---|
750 | _potential(_graph), _depth(_graph), _parent(_graph), |
---|
751 | _pred_edge(_graph), _thread(_graph), _forward(_graph), |
---|
752 | _state(_graph), _red_cost(_graph, _cost, _potential), |
---|
753 | _flow_result(NULL), _potential_result(NULL), |
---|
754 | _local_flow(false), _local_potential(false), |
---|
755 | _node_ref(graph), _edge_ref(graph) |
---|
756 | { |
---|
757 | // Copy _graph_ref to graph |
---|
758 | _graph.reserveNode(countNodes(_graph_ref) + 1); |
---|
759 | _graph.reserveEdge(countEdges(_graph_ref) + countNodes(_graph_ref)); |
---|
760 | copyGraph(_graph, _graph_ref) |
---|
761 | .edgeMap(_capacity, capacity) |
---|
762 | .edgeMap(_cost, cost) |
---|
763 | .nodeRef(_node_ref) |
---|
764 | .edgeRef(_edge_ref) |
---|
765 | .run(); |
---|
766 | _supply[_node_ref[s]] = flow_value; |
---|
767 | _supply[_node_ref[t]] = -flow_value; |
---|
768 | _valid_supply = true; |
---|
769 | } |
---|
770 | |
---|
771 | /// Destructor. |
---|
772 | ~NetworkSimplex() { |
---|
773 | if (_local_flow) delete _flow_result; |
---|
774 | if (_local_potential) delete _potential_result; |
---|
775 | } |
---|
776 | |
---|
777 | /// \brief Set the flow map. |
---|
778 | /// |
---|
779 | /// Set the flow map. |
---|
780 | /// |
---|
781 | /// \return \c (*this) |
---|
782 | NetworkSimplex& flowMap(FlowMap &map) { |
---|
783 | if (_local_flow) { |
---|
784 | delete _flow_result; |
---|
785 | _local_flow = false; |
---|
786 | } |
---|
787 | _flow_result = ↦ |
---|
788 | return *this; |
---|
789 | } |
---|
790 | |
---|
791 | /// \brief Set the potential map. |
---|
792 | /// |
---|
793 | /// Set the potential map. |
---|
794 | /// |
---|
795 | /// \return \c (*this) |
---|
796 | NetworkSimplex& potentialMap(PotentialMap &map) { |
---|
797 | if (_local_potential) { |
---|
798 | delete _potential_result; |
---|
799 | _local_potential = false; |
---|
800 | } |
---|
801 | _potential_result = ↦ |
---|
802 | return *this; |
---|
803 | } |
---|
804 | |
---|
805 | /// \name Execution control |
---|
806 | |
---|
807 | /// @{ |
---|
808 | |
---|
809 | /// \brief Runs the algorithm. |
---|
810 | /// |
---|
811 | /// Runs the algorithm. |
---|
812 | /// |
---|
813 | /// \param pivot_rule The pivot rule that is used during the |
---|
814 | /// algorithm. |
---|
815 | /// |
---|
816 | /// The available pivot rules: |
---|
817 | /// |
---|
818 | /// - FIRST_ELIGIBLE_PIVOT The next eligible edge is selected in |
---|
819 | /// a wraparound fashion in every iteration |
---|
820 | /// (\ref FirstEligiblePivotRule). |
---|
821 | /// |
---|
822 | /// - BEST_ELIGIBLE_PIVOT The best eligible edge is selected in |
---|
823 | /// every iteration (\ref BestEligiblePivotRule). |
---|
824 | /// |
---|
825 | /// - BLOCK_SEARCH_PIVOT A specified number of edges are examined in |
---|
826 | /// every iteration in a wraparound fashion and the best eligible |
---|
827 | /// edge is selected from this block (\ref BlockSearchPivotRule). |
---|
828 | /// |
---|
829 | /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is |
---|
830 | /// built from eligible edges in a wraparound fashion and in the |
---|
831 | /// following minor iterations the best eligible edge is selected |
---|
832 | /// from this list (\ref CandidateListPivotRule). |
---|
833 | /// |
---|
834 | /// - ALTERING_LIST_PIVOT It is a modified version of the |
---|
835 | /// "Candidate List" pivot rule. It keeps only the several best |
---|
836 | /// eligible edges from the former candidate list and extends this |
---|
837 | /// list in every iteration (\ref AlteringListPivotRule). |
---|
838 | /// |
---|
839 | /// According to our comprehensive benchmark tests the "Block Search" |
---|
840 | /// pivot rule proved to be by far the fastest and the most robust |
---|
841 | /// on various test inputs. Thus it is the default option. |
---|
842 | /// |
---|
843 | /// \return \c true if a feasible flow can be found. |
---|
844 | bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) { |
---|
845 | return init() && start(pivot_rule); |
---|
846 | } |
---|
847 | |
---|
848 | /// @} |
---|
849 | |
---|
850 | /// \name Query Functions |
---|
851 | /// The results of the algorithm can be obtained using these |
---|
852 | /// functions.\n |
---|
853 | /// \ref lemon::NetworkSimplex::run() "run()" must be called before |
---|
854 | /// using them. |
---|
855 | |
---|
856 | /// @{ |
---|
857 | |
---|
858 | /// \brief Return a const reference to the edge map storing the |
---|
859 | /// found flow. |
---|
860 | /// |
---|
861 | /// Return a const reference to the edge map storing the found flow. |
---|
862 | /// |
---|
863 | /// \pre \ref run() must be called before using this function. |
---|
864 | const FlowMap& flowMap() const { |
---|
865 | return *_flow_result; |
---|
866 | } |
---|
867 | |
---|
868 | /// \brief Return a const reference to the node map storing the |
---|
869 | /// found potentials (the dual solution). |
---|
870 | /// |
---|
871 | /// Return a const reference to the node map storing the found |
---|
872 | /// potentials (the dual solution). |
---|
873 | /// |
---|
874 | /// \pre \ref run() must be called before using this function. |
---|
875 | const PotentialMap& potentialMap() const { |
---|
876 | return *_potential_result; |
---|
877 | } |
---|
878 | |
---|
879 | /// \brief Return the flow on the given edge. |
---|
880 | /// |
---|
881 | /// Return the flow on the given edge. |
---|
882 | /// |
---|
883 | /// \pre \ref run() must be called before using this function. |
---|
884 | Capacity flow(const typename Graph::Edge& edge) const { |
---|
885 | return (*_flow_result)[edge]; |
---|
886 | } |
---|
887 | |
---|
888 | /// \brief Return the potential of the given node. |
---|
889 | /// |
---|
890 | /// Return the potential of the given node. |
---|
891 | /// |
---|
892 | /// \pre \ref run() must be called before using this function. |
---|
893 | Cost potential(const typename Graph::Node& node) const { |
---|
894 | return (*_potential_result)[node]; |
---|
895 | } |
---|
896 | |
---|
897 | /// \brief Return the total cost of the found flow. |
---|
898 | /// |
---|
899 | /// Return the total cost of the found flow. The complexity of the |
---|
900 | /// function is \f$ O(e) \f$. |
---|
901 | /// |
---|
902 | /// \pre \ref run() must be called before using this function. |
---|
903 | Cost totalCost() const { |
---|
904 | Cost c = 0; |
---|
905 | for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) |
---|
906 | c += (*_flow_result)[e] * _cost[_edge_ref[e]]; |
---|
907 | return c; |
---|
908 | } |
---|
909 | |
---|
910 | /// @} |
---|
911 | |
---|
912 | private: |
---|
913 | |
---|
914 | /// \brief Extend the underlying graph and initialize all the |
---|
915 | /// node and edge maps. |
---|
916 | bool init() { |
---|
917 | if (!_valid_supply) return false; |
---|
918 | |
---|
919 | // Initializing result maps |
---|
920 | if (!_flow_result) { |
---|
921 | _flow_result = new FlowMap(_graph_ref); |
---|
922 | _local_flow = true; |
---|
923 | } |
---|
924 | if (!_potential_result) { |
---|
925 | _potential_result = new PotentialMap(_graph_ref); |
---|
926 | _local_potential = true; |
---|
927 | } |
---|
928 | |
---|
929 | // Initializing the edge vector and the edge maps |
---|
930 | _edges.reserve(countEdges(_graph)); |
---|
931 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
932 | _edges.push_back(e); |
---|
933 | _flow[e] = 0; |
---|
934 | _state[e] = STATE_LOWER; |
---|
935 | } |
---|
936 | |
---|
937 | // Adding an artificial root node to the graph |
---|
938 | _root = _graph.addNode(); |
---|
939 | _parent[_root] = INVALID; |
---|
940 | _pred_edge[_root] = INVALID; |
---|
941 | _depth[_root] = 0; |
---|
942 | _supply[_root] = 0; |
---|
943 | _potential[_root] = 0; |
---|
944 | |
---|
945 | // Adding artificial edges to the graph and initializing the node |
---|
946 | // maps of the spanning tree data structure |
---|
947 | Node last = _root; |
---|
948 | Edge e; |
---|
949 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
---|
950 | for (NodeIt u(_graph); u != INVALID; ++u) { |
---|
951 | if (u == _root) continue; |
---|
952 | _thread[last] = u; |
---|
953 | last = u; |
---|
954 | _parent[u] = _root; |
---|
955 | _depth[u] = 1; |
---|
956 | if (_supply[u] >= 0) { |
---|
957 | e = _graph.addEdge(u, _root); |
---|
958 | _flow[e] = _supply[u]; |
---|
959 | _forward[u] = true; |
---|
960 | _potential[u] = -max_cost; |
---|
961 | } else { |
---|
962 | e = _graph.addEdge(_root, u); |
---|
963 | _flow[e] = -_supply[u]; |
---|
964 | _forward[u] = false; |
---|
965 | _potential[u] = max_cost; |
---|
966 | } |
---|
967 | _cost[e] = max_cost; |
---|
968 | _capacity[e] = std::numeric_limits<Capacity>::max(); |
---|
969 | _state[e] = STATE_TREE; |
---|
970 | _pred_edge[u] = e; |
---|
971 | } |
---|
972 | _thread[last] = _root; |
---|
973 | |
---|
974 | return true; |
---|
975 | } |
---|
976 | |
---|
977 | /// Find the join node. |
---|
978 | inline Node findJoinNode() { |
---|
979 | Node u = _graph.source(_in_edge); |
---|
980 | Node v = _graph.target(_in_edge); |
---|
981 | while (u != v) { |
---|
982 | if (_depth[u] == _depth[v]) { |
---|
983 | u = _parent[u]; |
---|
984 | v = _parent[v]; |
---|
985 | } |
---|
986 | else if (_depth[u] > _depth[v]) u = _parent[u]; |
---|
987 | else v = _parent[v]; |
---|
988 | } |
---|
989 | return u; |
---|
990 | } |
---|
991 | |
---|
992 | /// \brief Find the leaving edge of the cycle. |
---|
993 | /// \return \c true if the leaving edge is not the same as the |
---|
994 | /// entering edge. |
---|
995 | inline bool findLeavingEdge() { |
---|
996 | // Initializing first and second nodes according to the direction |
---|
997 | // of the cycle |
---|
998 | if (_state[_in_edge] == STATE_LOWER) { |
---|
999 | first = _graph.source(_in_edge); |
---|
1000 | second = _graph.target(_in_edge); |
---|
1001 | } else { |
---|
1002 | first = _graph.target(_in_edge); |
---|
1003 | second = _graph.source(_in_edge); |
---|
1004 | } |
---|
1005 | delta = _capacity[_in_edge]; |
---|
1006 | bool result = false; |
---|
1007 | Capacity d; |
---|
1008 | Edge e; |
---|
1009 | |
---|
1010 | // Searching the cycle along the path form the first node to the |
---|
1011 | // root node |
---|
1012 | for (Node u = first; u != join; u = _parent[u]) { |
---|
1013 | e = _pred_edge[u]; |
---|
1014 | d = _forward[u] ? _flow[e] : _capacity[e] - _flow[e]; |
---|
1015 | if (d < delta) { |
---|
1016 | delta = d; |
---|
1017 | u_out = u; |
---|
1018 | u_in = first; |
---|
1019 | v_in = second; |
---|
1020 | result = true; |
---|
1021 | } |
---|
1022 | } |
---|
1023 | // Searching the cycle along the path form the second node to the |
---|
1024 | // root node |
---|
1025 | for (Node u = second; u != join; u = _parent[u]) { |
---|
1026 | e = _pred_edge[u]; |
---|
1027 | d = _forward[u] ? _capacity[e] - _flow[e] : _flow[e]; |
---|
1028 | if (d <= delta) { |
---|
1029 | delta = d; |
---|
1030 | u_out = u; |
---|
1031 | u_in = second; |
---|
1032 | v_in = first; |
---|
1033 | result = true; |
---|
1034 | } |
---|
1035 | } |
---|
1036 | return result; |
---|
1037 | } |
---|
1038 | |
---|
1039 | /// Change \c flow and \c state edge maps. |
---|
1040 | inline void changeFlows(bool change) { |
---|
1041 | // Augmenting along the cycle |
---|
1042 | if (delta > 0) { |
---|
1043 | Capacity val = _state[_in_edge] * delta; |
---|
1044 | _flow[_in_edge] += val; |
---|
1045 | for (Node u = _graph.source(_in_edge); u != join; u = _parent[u]) { |
---|
1046 | _flow[_pred_edge[u]] += _forward[u] ? -val : val; |
---|
1047 | } |
---|
1048 | for (Node u = _graph.target(_in_edge); u != join; u = _parent[u]) { |
---|
1049 | _flow[_pred_edge[u]] += _forward[u] ? val : -val; |
---|
1050 | } |
---|
1051 | } |
---|
1052 | // Updating the state of the entering and leaving edges |
---|
1053 | if (change) { |
---|
1054 | _state[_in_edge] = STATE_TREE; |
---|
1055 | _state[_pred_edge[u_out]] = |
---|
1056 | (_flow[_pred_edge[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
1057 | } else { |
---|
1058 | _state[_in_edge] = -_state[_in_edge]; |
---|
1059 | } |
---|
1060 | } |
---|
1061 | |
---|
1062 | /// Update \c thread and \c parent node maps. |
---|
1063 | inline void updateThreadParent() { |
---|
1064 | Node u; |
---|
1065 | v_out = _parent[u_out]; |
---|
1066 | |
---|
1067 | // Handling the case when join and v_out coincide |
---|
1068 | bool par_first = false; |
---|
1069 | if (join == v_out) { |
---|
1070 | for (u = join; u != u_in && u != v_in; u = _thread[u]) ; |
---|
1071 | if (u == v_in) { |
---|
1072 | par_first = true; |
---|
1073 | while (_thread[u] != u_out) u = _thread[u]; |
---|
1074 | first = u; |
---|
1075 | } |
---|
1076 | } |
---|
1077 | |
---|
1078 | // Finding the last successor of u_in (u) and the node after it |
---|
1079 | // (right) according to the thread index |
---|
1080 | for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ; |
---|
1081 | right = _thread[u]; |
---|
1082 | if (_thread[v_in] == u_out) { |
---|
1083 | for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ; |
---|
1084 | if (last == u_out) last = _thread[last]; |
---|
1085 | } |
---|
1086 | else last = _thread[v_in]; |
---|
1087 | |
---|
1088 | // Updating stem nodes |
---|
1089 | _thread[v_in] = stem = u_in; |
---|
1090 | par_stem = v_in; |
---|
1091 | while (stem != u_out) { |
---|
1092 | _thread[u] = new_stem = _parent[stem]; |
---|
1093 | |
---|
1094 | // Finding the node just before the stem node (u) according to |
---|
1095 | // the original thread index |
---|
1096 | for (u = new_stem; _thread[u] != stem; u = _thread[u]) ; |
---|
1097 | _thread[u] = right; |
---|
1098 | |
---|
1099 | // Changing the parent node of stem and shifting stem and |
---|
1100 | // par_stem nodes |
---|
1101 | _parent[stem] = par_stem; |
---|
1102 | par_stem = stem; |
---|
1103 | stem = new_stem; |
---|
1104 | |
---|
1105 | // Finding the last successor of stem (u) and the node after it |
---|
1106 | // (right) according to the thread index |
---|
1107 | for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ; |
---|
1108 | right = _thread[u]; |
---|
1109 | } |
---|
1110 | _parent[u_out] = par_stem; |
---|
1111 | _thread[u] = last; |
---|
1112 | |
---|
1113 | if (join == v_out && par_first) { |
---|
1114 | if (first != v_in) _thread[first] = right; |
---|
1115 | } else { |
---|
1116 | for (u = v_out; _thread[u] != u_out; u = _thread[u]) ; |
---|
1117 | _thread[u] = right; |
---|
1118 | } |
---|
1119 | } |
---|
1120 | |
---|
1121 | /// Update \c pred_edge and \c forward node maps. |
---|
1122 | inline void updatePredEdge() { |
---|
1123 | Node u = u_out, v; |
---|
1124 | while (u != u_in) { |
---|
1125 | v = _parent[u]; |
---|
1126 | _pred_edge[u] = _pred_edge[v]; |
---|
1127 | _forward[u] = !_forward[v]; |
---|
1128 | u = v; |
---|
1129 | } |
---|
1130 | _pred_edge[u_in] = _in_edge; |
---|
1131 | _forward[u_in] = (u_in == _graph.source(_in_edge)); |
---|
1132 | } |
---|
1133 | |
---|
1134 | /// Update \c depth and \c potential node maps. |
---|
1135 | inline void updateDepthPotential() { |
---|
1136 | _depth[u_in] = _depth[v_in] + 1; |
---|
1137 | Cost sigma = _forward[u_in] ? |
---|
1138 | _potential[v_in] - _potential[u_in] - _cost[_pred_edge[u_in]] : |
---|
1139 | _potential[v_in] - _potential[u_in] + _cost[_pred_edge[u_in]]; |
---|
1140 | _potential[u_in] += sigma; |
---|
1141 | for(Node u = _thread[u_in]; _parent[u] != INVALID; u = _thread[u]) { |
---|
1142 | _depth[u] = _depth[_parent[u]] + 1; |
---|
1143 | if (_depth[u] <= _depth[u_in]) break; |
---|
1144 | _potential[u] += sigma; |
---|
1145 | } |
---|
1146 | } |
---|
1147 | |
---|
1148 | /// Execute the algorithm. |
---|
1149 | bool start(PivotRuleEnum pivot_rule) { |
---|
1150 | // Selecting the pivot rule implementation |
---|
1151 | switch (pivot_rule) { |
---|
1152 | case FIRST_ELIGIBLE_PIVOT: |
---|
1153 | return start<FirstEligiblePivotRule>(); |
---|
1154 | case BEST_ELIGIBLE_PIVOT: |
---|
1155 | return start<BestEligiblePivotRule>(); |
---|
1156 | case BLOCK_SEARCH_PIVOT: |
---|
1157 | return start<BlockSearchPivotRule>(); |
---|
1158 | case CANDIDATE_LIST_PIVOT: |
---|
1159 | return start<CandidateListPivotRule>(); |
---|
1160 | case ALTERING_LIST_PIVOT: |
---|
1161 | return start<AlteringListPivotRule>(); |
---|
1162 | } |
---|
1163 | return false; |
---|
1164 | } |
---|
1165 | |
---|
1166 | template<class PivotRuleImplementation> |
---|
1167 | bool start() { |
---|
1168 | PivotRuleImplementation pivot(*this, _edges); |
---|
1169 | |
---|
1170 | // Executing the network simplex algorithm |
---|
1171 | while (pivot.findEnteringEdge()) { |
---|
1172 | join = findJoinNode(); |
---|
1173 | bool change = findLeavingEdge(); |
---|
1174 | changeFlows(change); |
---|
1175 | if (change) { |
---|
1176 | updateThreadParent(); |
---|
1177 | updatePredEdge(); |
---|
1178 | updateDepthPotential(); |
---|
1179 | } |
---|
1180 | } |
---|
1181 | |
---|
1182 | // Checking if the flow amount equals zero on all the artificial |
---|
1183 | // edges |
---|
1184 | for (InEdgeIt e(_graph, _root); e != INVALID; ++e) |
---|
1185 | if (_flow[e] > 0) return false; |
---|
1186 | for (OutEdgeIt e(_graph, _root); e != INVALID; ++e) |
---|
1187 | if (_flow[e] > 0) return false; |
---|
1188 | |
---|
1189 | // Copying flow values to _flow_result |
---|
1190 | if (_lower) { |
---|
1191 | for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) |
---|
1192 | (*_flow_result)[e] = (*_lower)[e] + _flow[_edge_ref[e]]; |
---|
1193 | } else { |
---|
1194 | for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) |
---|
1195 | (*_flow_result)[e] = _flow[_edge_ref[e]]; |
---|
1196 | } |
---|
1197 | // Copying potential values to _potential_result |
---|
1198 | for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n) |
---|
1199 | (*_potential_result)[n] = _potential[_node_ref[n]]; |
---|
1200 | |
---|
1201 | return true; |
---|
1202 | } |
---|
1203 | |
---|
1204 | }; //class NetworkSimplex |
---|
1205 | |
---|
1206 | ///@} |
---|
1207 | |
---|
1208 | } //namespace lemon |
---|
1209 | |
---|
1210 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|