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 | #include <algorithm> |
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30 | |
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31 | #include <lemon/graph_utils.h> |
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32 | #include <lemon/math.h> |
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33 | |
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34 | namespace lemon { |
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35 | |
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36 | /// \addtogroup min_cost_flow |
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37 | /// @{ |
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38 | |
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39 | /// \brief Implementation of the primal network simplex algorithm |
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40 | /// for finding a minimum cost flow. |
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41 | /// |
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42 | /// \ref NetworkSimplex implements the primal network simplex algorithm |
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43 | /// for finding a minimum cost flow. |
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44 | /// |
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45 | /// \tparam Graph The directed graph type the algorithm runs on. |
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46 | /// \tparam LowerMap The type of the lower bound map. |
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47 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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48 | /// \tparam CostMap The type of the cost (length) map. |
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49 | /// \tparam SupplyMap The type of the supply map. |
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50 | /// |
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51 | /// \warning |
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52 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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53 | /// - Supply values should be \e signed \e integers. |
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54 | /// - The value types of the maps should be convertible to each other. |
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55 | /// - \c CostMap::Value must be signed type. |
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56 | /// |
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57 | /// \note \ref NetworkSimplex provides five different pivot rule |
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58 | /// implementations that significantly affect the efficiency of the |
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59 | /// algorithm. |
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60 | /// By default "Block Search" pivot rule is used, which proved to be |
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61 | /// by far the most efficient according to our benchmark tests. |
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62 | /// However another pivot rule can be selected using \ref run() |
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63 | /// function with the proper parameter. |
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64 | /// |
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65 | /// \author Peter Kovacs |
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66 | template < typename Graph, |
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67 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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68 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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69 | typename CostMap = typename Graph::template EdgeMap<int>, |
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70 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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71 | class NetworkSimplex |
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72 | { |
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73 | GRAPH_TYPEDEFS(typename Graph); |
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74 | |
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75 | typedef typename CapacityMap::Value Capacity; |
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76 | typedef typename CostMap::Value Cost; |
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77 | typedef typename SupplyMap::Value Supply; |
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78 | |
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79 | typedef std::vector<Edge> EdgeVector; |
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80 | typedef std::vector<Node> NodeVector; |
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81 | typedef std::vector<int> IntVector; |
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82 | typedef std::vector<bool> BoolVector; |
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83 | typedef std::vector<Capacity> CapacityVector; |
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84 | typedef std::vector<Cost> CostVector; |
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85 | typedef std::vector<Supply> SupplyVector; |
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86 | |
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87 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
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88 | |
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89 | public: |
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90 | |
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91 | /// The type of the flow map. |
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92 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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93 | /// The type of the potential map. |
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94 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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95 | |
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96 | public: |
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97 | |
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98 | /// Enum type to select the pivot rule used by \ref run(). |
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99 | enum PivotRuleEnum { |
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100 | FIRST_ELIGIBLE_PIVOT, |
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101 | BEST_ELIGIBLE_PIVOT, |
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102 | BLOCK_SEARCH_PIVOT, |
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103 | CANDIDATE_LIST_PIVOT, |
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104 | ALTERING_LIST_PIVOT |
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105 | }; |
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106 | |
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107 | private: |
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108 | |
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109 | /// \brief Implementation of the "First Eligible" pivot rule for the |
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110 | /// \ref NetworkSimplex "network simplex" algorithm. |
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111 | /// |
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112 | /// This class implements the "First Eligible" pivot rule |
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113 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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114 | /// |
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115 | /// For more information see \ref NetworkSimplex::run(). |
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116 | class FirstEligiblePivotRule |
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117 | { |
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118 | private: |
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119 | |
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120 | // References to the NetworkSimplex class |
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121 | const EdgeVector &_edge; |
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122 | const IntVector &_source; |
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123 | const IntVector &_target; |
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124 | const CostVector &_cost; |
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125 | const IntVector &_state; |
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126 | const CostVector &_pi; |
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127 | int &_in_edge; |
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128 | int _edge_num; |
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129 | |
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130 | // Pivot rule data |
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131 | int _next_edge; |
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132 | |
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133 | public: |
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134 | |
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135 | /// Constructor |
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136 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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137 | _edge(ns._edge), _source(ns._source), _target(ns._target), |
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138 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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139 | _in_edge(ns._in_edge), _edge_num(ns._edge_num), _next_edge(0) |
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140 | {} |
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141 | |
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142 | /// Find next entering edge |
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143 | bool findEnteringEdge() { |
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144 | Cost c; |
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145 | for (int e = _next_edge; e < _edge_num; ++e) { |
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146 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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147 | if (c < 0) { |
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148 | _in_edge = e; |
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149 | _next_edge = e + 1; |
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150 | return true; |
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151 | } |
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152 | } |
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153 | for (int e = 0; e < _next_edge; ++e) { |
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154 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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155 | if (c < 0) { |
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156 | _in_edge = e; |
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157 | _next_edge = e + 1; |
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158 | return true; |
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159 | } |
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160 | } |
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161 | return false; |
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162 | } |
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163 | |
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164 | }; //class FirstEligiblePivotRule |
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165 | |
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166 | |
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167 | /// \brief Implementation of the "Best Eligible" pivot rule for the |
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168 | /// \ref NetworkSimplex "network simplex" algorithm. |
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169 | /// |
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170 | /// This class implements the "Best Eligible" pivot rule |
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171 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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172 | /// |
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173 | /// For more information see \ref NetworkSimplex::run(). |
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174 | class BestEligiblePivotRule |
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175 | { |
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176 | private: |
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177 | |
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178 | // References to the NetworkSimplex class |
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179 | const EdgeVector &_edge; |
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180 | const IntVector &_source; |
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181 | const IntVector &_target; |
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182 | const CostVector &_cost; |
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183 | const IntVector &_state; |
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184 | const CostVector &_pi; |
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185 | int &_in_edge; |
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186 | int _edge_num; |
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187 | |
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188 | public: |
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189 | |
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190 | /// Constructor |
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191 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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192 | _edge(ns._edge), _source(ns._source), _target(ns._target), |
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193 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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194 | _in_edge(ns._in_edge), _edge_num(ns._edge_num) |
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195 | {} |
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196 | |
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197 | /// Find next entering edge |
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198 | bool findEnteringEdge() { |
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199 | Cost c, min = 0; |
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200 | for (int e = 0; e < _edge_num; ++e) { |
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201 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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202 | if (c < min) { |
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203 | min = c; |
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204 | _in_edge = e; |
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205 | } |
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206 | } |
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207 | return min < 0; |
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208 | } |
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209 | |
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210 | }; //class BestEligiblePivotRule |
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211 | |
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212 | |
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213 | /// \brief Implementation of the "Block Search" pivot rule for the |
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214 | /// \ref NetworkSimplex "network simplex" algorithm. |
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215 | /// |
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216 | /// This class implements the "Block Search" pivot rule |
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217 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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218 | /// |
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219 | /// For more information see \ref NetworkSimplex::run(). |
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220 | class BlockSearchPivotRule |
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221 | { |
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222 | private: |
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223 | |
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224 | // References to the NetworkSimplex class |
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225 | const EdgeVector &_edge; |
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226 | const IntVector &_source; |
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227 | const IntVector &_target; |
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228 | const CostVector &_cost; |
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229 | const IntVector &_state; |
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230 | const CostVector &_pi; |
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231 | int &_in_edge; |
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232 | int _edge_num; |
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233 | |
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234 | // Pivot rule data |
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235 | int _block_size; |
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236 | int _next_edge; |
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237 | |
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238 | public: |
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239 | |
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240 | /// Constructor |
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241 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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242 | _edge(ns._edge), _source(ns._source), _target(ns._target), |
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243 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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244 | _in_edge(ns._in_edge), _edge_num(ns._edge_num + ns._node_num), _next_edge(0) |
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245 | { |
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246 | // The main parameters of the pivot rule |
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247 | const double BLOCK_SIZE_FACTOR = 2.0; |
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248 | const int MIN_BLOCK_SIZE = 10; |
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249 | |
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250 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edge_num)), |
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251 | MIN_BLOCK_SIZE ); |
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252 | } |
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253 | |
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254 | /// Find next entering edge |
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255 | bool findEnteringEdge() { |
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256 | Cost c, min = 0; |
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257 | int cnt = _block_size; |
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258 | int e, min_edge = _next_edge; |
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259 | for (e = _next_edge; e < _edge_num; ++e) { |
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260 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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261 | if (c < min) { |
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262 | min = c; |
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263 | min_edge = e; |
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264 | } |
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265 | if (--cnt == 0) { |
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266 | if (min < 0) break; |
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267 | cnt = _block_size; |
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268 | } |
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269 | } |
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270 | if (min == 0 || cnt > 0) { |
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271 | for (e = 0; e < _next_edge; ++e) { |
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272 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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273 | if (c < min) { |
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274 | min = c; |
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275 | min_edge = e; |
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276 | } |
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277 | if (--cnt == 0) { |
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278 | if (min < 0) break; |
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279 | cnt = _block_size; |
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280 | } |
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281 | } |
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282 | } |
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283 | if (min >= 0) return false; |
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284 | _in_edge = min_edge; |
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285 | _next_edge = e; |
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286 | return true; |
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287 | } |
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288 | |
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289 | }; //class BlockSearchPivotRule |
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290 | |
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291 | |
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292 | /// \brief Implementation of the "Candidate List" pivot rule for the |
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293 | /// \ref NetworkSimplex "network simplex" algorithm. |
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294 | /// |
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295 | /// This class implements the "Candidate List" pivot rule |
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296 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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297 | /// |
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298 | /// For more information see \ref NetworkSimplex::run(). |
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299 | class CandidateListPivotRule |
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300 | { |
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301 | private: |
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302 | |
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303 | // References to the NetworkSimplex class |
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304 | const EdgeVector &_edge; |
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305 | const IntVector &_source; |
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306 | const IntVector &_target; |
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307 | const CostVector &_cost; |
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308 | const IntVector &_state; |
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309 | const CostVector &_pi; |
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310 | int &_in_edge; |
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311 | int _edge_num; |
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312 | |
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313 | // Pivot rule data |
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314 | IntVector _candidates; |
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315 | int _list_length, _minor_limit; |
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316 | int _curr_length, _minor_count; |
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317 | int _next_edge; |
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318 | |
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319 | public: |
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320 | |
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321 | /// Constructor |
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322 | CandidateListPivotRule(NetworkSimplex &ns) : |
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323 | _edge(ns._edge), _source(ns._source), _target(ns._target), |
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324 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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325 | _in_edge(ns._in_edge), _edge_num(ns._edge_num), _next_edge(0) |
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326 | { |
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327 | // The main parameters of the pivot rule |
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328 | const double LIST_LENGTH_FACTOR = 1.0; |
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329 | const int MIN_LIST_LENGTH = 10; |
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330 | const double MINOR_LIMIT_FACTOR = 0.1; |
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331 | const int MIN_MINOR_LIMIT = 3; |
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332 | |
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333 | _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_edge_num)), |
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334 | MIN_LIST_LENGTH ); |
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335 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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336 | MIN_MINOR_LIMIT ); |
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337 | _curr_length = _minor_count = 0; |
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338 | _candidates.resize(_list_length); |
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339 | } |
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340 | |
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341 | /// Find next entering edge |
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342 | bool findEnteringEdge() { |
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343 | Cost min, c; |
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344 | int e, min_edge = _next_edge; |
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345 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
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346 | // Minor iteration: select the best eligible edge from the |
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347 | // current candidate list |
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348 | ++_minor_count; |
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349 | min = 0; |
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350 | for (int i = 0; i < _curr_length; ++i) { |
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351 | e = _candidates[i]; |
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352 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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353 | if (c < min) { |
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354 | min = c; |
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355 | min_edge = e; |
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356 | } |
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357 | if (c >= 0) { |
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358 | _candidates[i--] = _candidates[--_curr_length]; |
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359 | } |
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360 | } |
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361 | if (min < 0) { |
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362 | _in_edge = min_edge; |
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363 | return true; |
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364 | } |
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365 | } |
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366 | |
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367 | // Major iteration: build a new candidate list |
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368 | min = 0; |
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369 | _curr_length = 0; |
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370 | for (e = _next_edge; e < _edge_num; ++e) { |
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371 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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372 | if (c < 0) { |
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373 | _candidates[_curr_length++] = e; |
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374 | if (c < min) { |
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375 | min = c; |
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376 | min_edge = e; |
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377 | } |
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378 | if (_curr_length == _list_length) break; |
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379 | } |
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380 | } |
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381 | if (_curr_length < _list_length) { |
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382 | for (e = 0; e < _next_edge; ++e) { |
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383 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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384 | if (c < 0) { |
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385 | _candidates[_curr_length++] = e; |
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386 | if (c < min) { |
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387 | min = c; |
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388 | min_edge = e; |
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389 | } |
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390 | if (_curr_length == _list_length) break; |
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391 | } |
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392 | } |
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393 | } |
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394 | if (_curr_length == 0) return false; |
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395 | _minor_count = 1; |
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396 | _in_edge = min_edge; |
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397 | _next_edge = e; |
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398 | return true; |
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399 | } |
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400 | |
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401 | }; //class CandidateListPivotRule |
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402 | |
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403 | |
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404 | /// \brief Implementation of the "Altering Candidate List" pivot rule |
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405 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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406 | /// |
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407 | /// This class implements the "Altering Candidate List" pivot rule |
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408 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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409 | /// |
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410 | /// For more information see \ref NetworkSimplex::run(). |
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411 | class AlteringListPivotRule |
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412 | { |
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413 | private: |
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414 | |
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415 | // References to the NetworkSimplex class |
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416 | const EdgeVector &_edge; |
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417 | const IntVector &_source; |
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418 | const IntVector &_target; |
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419 | const CostVector &_cost; |
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420 | const IntVector &_state; |
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421 | const CostVector &_pi; |
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422 | int &_in_edge; |
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423 | int _edge_num; |
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424 | |
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425 | int _block_size, _head_length, _curr_length; |
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426 | int _next_edge; |
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427 | IntVector _candidates; |
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428 | CostVector _cand_cost; |
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429 | |
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430 | // Functor class to compare edges during sort of the candidate list |
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431 | class SortFunc |
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432 | { |
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433 | private: |
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434 | const CostVector &_map; |
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435 | public: |
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436 | SortFunc(const CostVector &map) : _map(map) {} |
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437 | bool operator()(int left, int right) { |
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438 | return _map[left] > _map[right]; |
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439 | } |
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440 | }; |
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441 | |
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442 | SortFunc _sort_func; |
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443 | |
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444 | public: |
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445 | |
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446 | /// Constructor |
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447 | AlteringListPivotRule(NetworkSimplex &ns) : |
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448 | _edge(ns._edge), _source(ns._source), _target(ns._target), |
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449 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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450 | _in_edge(ns._in_edge), _edge_num(ns._edge_num), |
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451 | _next_edge(0), _cand_cost(ns._edge_num),_sort_func(_cand_cost) |
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452 | { |
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453 | // The main parameters of the pivot rule |
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454 | const double BLOCK_SIZE_FACTOR = 1.5; |
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455 | const int MIN_BLOCK_SIZE = 10; |
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456 | const double HEAD_LENGTH_FACTOR = 0.1; |
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457 | const int MIN_HEAD_LENGTH = 3; |
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458 | |
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459 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edge_num)), |
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460 | MIN_BLOCK_SIZE ); |
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461 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
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462 | MIN_HEAD_LENGTH ); |
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463 | _candidates.resize(_head_length + _block_size); |
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464 | _curr_length = 0; |
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465 | } |
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466 | |
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467 | /// Find next entering edge |
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468 | bool findEnteringEdge() { |
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469 | // Check the current candidate list |
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470 | int e; |
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471 | for (int i = 0; i < _curr_length; ++i) { |
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472 | e = _candidates[i]; |
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473 | _cand_cost[e] = _state[e] * |
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474 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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475 | if (_cand_cost[e] >= 0) { |
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476 | _candidates[i--] = _candidates[--_curr_length]; |
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477 | } |
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478 | } |
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479 | |
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480 | // Extend the list |
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481 | int cnt = _block_size; |
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482 | int last_edge = 0; |
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483 | int limit = _head_length; |
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484 | |
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485 | for (int e = _next_edge; e < _edge_num; ++e) { |
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486 | _cand_cost[e] = _state[e] * |
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487 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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488 | if (_cand_cost[e] < 0) { |
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489 | _candidates[_curr_length++] = e; |
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490 | last_edge = e; |
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491 | } |
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492 | if (--cnt == 0) { |
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493 | if (_curr_length > limit) break; |
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494 | limit = 0; |
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495 | cnt = _block_size; |
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496 | } |
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497 | } |
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498 | if (_curr_length <= limit) { |
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499 | for (int e = 0; e < _next_edge; ++e) { |
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500 | _cand_cost[e] = _state[e] * |
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501 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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502 | if (_cand_cost[e] < 0) { |
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503 | _candidates[_curr_length++] = e; |
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504 | last_edge = e; |
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505 | } |
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506 | if (--cnt == 0) { |
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507 | if (_curr_length > limit) break; |
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508 | limit = 0; |
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509 | cnt = _block_size; |
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510 | } |
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511 | } |
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512 | } |
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513 | if (_curr_length == 0) return false; |
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514 | _next_edge = last_edge + 1; |
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515 | |
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516 | // Make heap of the candidate list (approximating a partial sort) |
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517 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
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518 | _sort_func ); |
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519 | |
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520 | // Pop the first element of the heap |
---|
521 | _in_edge = _candidates[0]; |
---|
522 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
523 | _sort_func ); |
---|
524 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
525 | return true; |
---|
526 | } |
---|
527 | |
---|
528 | }; //class AlteringListPivotRule |
---|
529 | |
---|
530 | private: |
---|
531 | |
---|
532 | // State constants for edges |
---|
533 | enum EdgeStateEnum { |
---|
534 | STATE_UPPER = -1, |
---|
535 | STATE_TREE = 0, |
---|
536 | STATE_LOWER = 1 |
---|
537 | }; |
---|
538 | |
---|
539 | private: |
---|
540 | |
---|
541 | // The original graph |
---|
542 | const Graph &_orig_graph; |
---|
543 | // The original lower bound map |
---|
544 | const LowerMap *_orig_lower; |
---|
545 | // The original capacity map |
---|
546 | const CapacityMap &_orig_cap; |
---|
547 | // The original cost map |
---|
548 | const CostMap &_orig_cost; |
---|
549 | // The original supply map |
---|
550 | const SupplyMap *_orig_supply; |
---|
551 | // The source node (if no supply map was given) |
---|
552 | Node _orig_source; |
---|
553 | // The target node (if no supply map was given) |
---|
554 | Node _orig_target; |
---|
555 | // The flow value (if no supply map was given) |
---|
556 | Capacity _orig_flow_value; |
---|
557 | |
---|
558 | // The flow result map |
---|
559 | FlowMap *_flow_result; |
---|
560 | // The potential result map |
---|
561 | PotentialMap *_potential_result; |
---|
562 | // Indicate if the flow result map is local |
---|
563 | bool _local_flow; |
---|
564 | // Indicate if the potential result map is local |
---|
565 | bool _local_potential; |
---|
566 | |
---|
567 | // The edge references |
---|
568 | EdgeVector _edge; |
---|
569 | // The node references |
---|
570 | NodeVector _node; |
---|
571 | // The node ids |
---|
572 | IntNodeMap _node_id; |
---|
573 | // The source nodes of the edges |
---|
574 | IntVector _source; |
---|
575 | // The target nodess of the edges |
---|
576 | IntVector _target; |
---|
577 | |
---|
578 | // The (modified) capacity vector |
---|
579 | CapacityVector _cap; |
---|
580 | // The cost vector |
---|
581 | CostVector _cost; |
---|
582 | // The (modified) supply vector |
---|
583 | CostVector _supply; |
---|
584 | // The current flow vector |
---|
585 | CapacityVector _flow; |
---|
586 | // The current potential vector |
---|
587 | CostVector _pi; |
---|
588 | |
---|
589 | // The number of nodes in the original graph |
---|
590 | int _node_num; |
---|
591 | // The number of edges in the original graph |
---|
592 | int _edge_num; |
---|
593 | |
---|
594 | // The parent vector of the spanning tree structure |
---|
595 | IntVector _parent; |
---|
596 | // The pred_edge vector of the spanning tree structure |
---|
597 | IntVector _pred; |
---|
598 | // The thread vector of the spanning tree structure |
---|
599 | IntVector _thread; |
---|
600 | |
---|
601 | IntVector _rev_thread; |
---|
602 | IntVector _succ_num; |
---|
603 | IntVector _last_succ; |
---|
604 | |
---|
605 | IntVector _dirty_revs; |
---|
606 | |
---|
607 | // The forward vector of the spanning tree structure |
---|
608 | BoolVector _forward; |
---|
609 | // The state vector |
---|
610 | IntVector _state; |
---|
611 | // The root node |
---|
612 | int _root; |
---|
613 | |
---|
614 | // The entering edge of the current pivot iteration |
---|
615 | int _in_edge; |
---|
616 | |
---|
617 | // Temporary nodes used in the current pivot iteration |
---|
618 | int join, u_in, v_in, u_out, v_out; |
---|
619 | int right, first, second, last; |
---|
620 | int stem, par_stem, new_stem; |
---|
621 | |
---|
622 | // The maximum augment amount along the found cycle in the current |
---|
623 | // pivot iteration |
---|
624 | Capacity delta; |
---|
625 | |
---|
626 | public: |
---|
627 | |
---|
628 | /// \brief General constructor (with lower bounds). |
---|
629 | /// |
---|
630 | /// General constructor (with lower bounds). |
---|
631 | /// |
---|
632 | /// \param graph The directed graph the algorithm runs on. |
---|
633 | /// \param lower The lower bounds of the edges. |
---|
634 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
635 | /// \param cost The cost (length) values of the edges. |
---|
636 | /// \param supply The supply values of the nodes (signed). |
---|
637 | NetworkSimplex( const Graph &graph, |
---|
638 | const LowerMap &lower, |
---|
639 | const CapacityMap &capacity, |
---|
640 | const CostMap &cost, |
---|
641 | const SupplyMap &supply ) : |
---|
642 | _orig_graph(graph), _orig_lower(&lower), _orig_cap(capacity), |
---|
643 | _orig_cost(cost), _orig_supply(&supply), |
---|
644 | _flow_result(NULL), _potential_result(NULL), |
---|
645 | _local_flow(false), _local_potential(false), |
---|
646 | _node_id(graph) |
---|
647 | {} |
---|
648 | |
---|
649 | /// \brief General constructor (without lower bounds). |
---|
650 | /// |
---|
651 | /// General constructor (without lower bounds). |
---|
652 | /// |
---|
653 | /// \param graph The directed graph the algorithm runs on. |
---|
654 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
655 | /// \param cost The cost (length) values of the edges. |
---|
656 | /// \param supply The supply values of the nodes (signed). |
---|
657 | NetworkSimplex( const Graph &graph, |
---|
658 | const CapacityMap &capacity, |
---|
659 | const CostMap &cost, |
---|
660 | const SupplyMap &supply ) : |
---|
661 | _orig_graph(graph), _orig_lower(NULL), _orig_cap(capacity), |
---|
662 | _orig_cost(cost), _orig_supply(&supply), |
---|
663 | _flow_result(NULL), _potential_result(NULL), |
---|
664 | _local_flow(false), _local_potential(false), |
---|
665 | _node_id(graph) |
---|
666 | {} |
---|
667 | |
---|
668 | /// \brief Simple constructor (with lower bounds). |
---|
669 | /// |
---|
670 | /// Simple constructor (with lower bounds). |
---|
671 | /// |
---|
672 | /// \param graph The directed graph the algorithm runs on. |
---|
673 | /// \param lower The lower bounds of the edges. |
---|
674 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
675 | /// \param cost The cost (length) values of the edges. |
---|
676 | /// \param s The source node. |
---|
677 | /// \param t The target node. |
---|
678 | /// \param flow_value The required amount of flow from node \c s |
---|
679 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
680 | NetworkSimplex( const Graph &graph, |
---|
681 | const LowerMap &lower, |
---|
682 | const CapacityMap &capacity, |
---|
683 | const CostMap &cost, |
---|
684 | Node s, Node t, |
---|
685 | Capacity flow_value ) : |
---|
686 | _orig_graph(graph), _orig_lower(&lower), _orig_cap(capacity), |
---|
687 | _orig_cost(cost), _orig_supply(NULL), |
---|
688 | _orig_source(s), _orig_target(t), _orig_flow_value(flow_value), |
---|
689 | _flow_result(NULL), _potential_result(NULL), |
---|
690 | _local_flow(false), _local_potential(false), |
---|
691 | _node_id(graph) |
---|
692 | {} |
---|
693 | |
---|
694 | /// \brief Simple constructor (without lower bounds). |
---|
695 | /// |
---|
696 | /// Simple constructor (without lower bounds). |
---|
697 | /// |
---|
698 | /// \param graph The directed graph the algorithm runs on. |
---|
699 | /// \param capacity The capacities (upper bounds) of the edges. |
---|
700 | /// \param cost The cost (length) values of the edges. |
---|
701 | /// \param s The source node. |
---|
702 | /// \param t The target node. |
---|
703 | /// \param flow_value The required amount of flow from node \c s |
---|
704 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
705 | NetworkSimplex( const Graph &graph, |
---|
706 | const CapacityMap &capacity, |
---|
707 | const CostMap &cost, |
---|
708 | Node s, Node t, |
---|
709 | Capacity flow_value ) : |
---|
710 | _orig_graph(graph), _orig_lower(NULL), _orig_cap(capacity), |
---|
711 | _orig_cost(cost), _orig_supply(NULL), |
---|
712 | _orig_source(s), _orig_target(t), _orig_flow_value(flow_value), |
---|
713 | _flow_result(NULL), _potential_result(NULL), |
---|
714 | _local_flow(false), _local_potential(false), |
---|
715 | _node_id(graph) |
---|
716 | {} |
---|
717 | |
---|
718 | /// Destructor. |
---|
719 | ~NetworkSimplex() { |
---|
720 | if (_local_flow) delete _flow_result; |
---|
721 | if (_local_potential) delete _potential_result; |
---|
722 | } |
---|
723 | |
---|
724 | /// \brief Set the flow map. |
---|
725 | /// |
---|
726 | /// Set the flow map. |
---|
727 | /// |
---|
728 | /// \return \c (*this) |
---|
729 | NetworkSimplex& flowMap(FlowMap &map) { |
---|
730 | if (_local_flow) { |
---|
731 | delete _flow_result; |
---|
732 | _local_flow = false; |
---|
733 | } |
---|
734 | _flow_result = ↦ |
---|
735 | return *this; |
---|
736 | } |
---|
737 | |
---|
738 | /// \brief Set the potential map. |
---|
739 | /// |
---|
740 | /// Set the potential map. |
---|
741 | /// |
---|
742 | /// \return \c (*this) |
---|
743 | NetworkSimplex& potentialMap(PotentialMap &map) { |
---|
744 | if (_local_potential) { |
---|
745 | delete _potential_result; |
---|
746 | _local_potential = false; |
---|
747 | } |
---|
748 | _potential_result = ↦ |
---|
749 | return *this; |
---|
750 | } |
---|
751 | |
---|
752 | /// \name Execution control |
---|
753 | |
---|
754 | /// @{ |
---|
755 | |
---|
756 | /// \brief Runs the algorithm. |
---|
757 | /// |
---|
758 | /// Runs the algorithm. |
---|
759 | /// |
---|
760 | /// \param pivot_rule The pivot rule that is used during the |
---|
761 | /// algorithm. |
---|
762 | /// |
---|
763 | /// The available pivot rules: |
---|
764 | /// |
---|
765 | /// - FIRST_ELIGIBLE_PIVOT The next eligible edge is selected in |
---|
766 | /// a wraparound fashion in every iteration |
---|
767 | /// (\ref FirstEligiblePivotRule). |
---|
768 | /// |
---|
769 | /// - BEST_ELIGIBLE_PIVOT The best eligible edge is selected in |
---|
770 | /// every iteration (\ref BestEligiblePivotRule). |
---|
771 | /// |
---|
772 | /// - BLOCK_SEARCH_PIVOT A specified number of edges are examined in |
---|
773 | /// every iteration in a wraparound fashion and the best eligible |
---|
774 | /// edge is selected from this block (\ref BlockSearchPivotRule). |
---|
775 | /// |
---|
776 | /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is |
---|
777 | /// built from eligible edges in a wraparound fashion and in the |
---|
778 | /// following minor iterations the best eligible edge is selected |
---|
779 | /// from this list (\ref CandidateListPivotRule). |
---|
780 | /// |
---|
781 | /// - ALTERING_LIST_PIVOT It is a modified version of the |
---|
782 | /// "Candidate List" pivot rule. It keeps only the several best |
---|
783 | /// eligible edges from the former candidate list and extends this |
---|
784 | /// list in every iteration (\ref AlteringListPivotRule). |
---|
785 | /// |
---|
786 | /// According to our comprehensive benchmark tests the "Block Search" |
---|
787 | /// pivot rule proved to be the fastest and the most robust on |
---|
788 | /// various test inputs. Thus it is the default option. |
---|
789 | /// |
---|
790 | /// \return \c true if a feasible flow can be found. |
---|
791 | bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) { |
---|
792 | return init() && start(pivot_rule); |
---|
793 | } |
---|
794 | |
---|
795 | /// @} |
---|
796 | |
---|
797 | /// \name Query Functions |
---|
798 | /// The results of the algorithm can be obtained using these |
---|
799 | /// functions.\n |
---|
800 | /// \ref lemon::NetworkSimplex::run() "run()" must be called before |
---|
801 | /// using them. |
---|
802 | |
---|
803 | /// @{ |
---|
804 | |
---|
805 | /// \brief Return a const reference to the edge map storing the |
---|
806 | /// found flow. |
---|
807 | /// |
---|
808 | /// Return a const reference to the edge map storing the found flow. |
---|
809 | /// |
---|
810 | /// \pre \ref run() must be called before using this function. |
---|
811 | const FlowMap& flowMap() const { |
---|
812 | return *_flow_result; |
---|
813 | } |
---|
814 | |
---|
815 | /// \brief Return a const reference to the node map storing the |
---|
816 | /// found potentials (the dual solution). |
---|
817 | /// |
---|
818 | /// Return a const reference to the node map storing the found |
---|
819 | /// potentials (the dual solution). |
---|
820 | /// |
---|
821 | /// \pre \ref run() must be called before using this function. |
---|
822 | const PotentialMap& potentialMap() const { |
---|
823 | return *_potential_result; |
---|
824 | } |
---|
825 | |
---|
826 | /// \brief Return the flow on the given edge. |
---|
827 | /// |
---|
828 | /// Return the flow on the given edge. |
---|
829 | /// |
---|
830 | /// \pre \ref run() must be called before using this function. |
---|
831 | Capacity flow(const typename Graph::Edge& edge) const { |
---|
832 | return (*_flow_result)[edge]; |
---|
833 | } |
---|
834 | |
---|
835 | /// \brief Return the potential of the given node. |
---|
836 | /// |
---|
837 | /// Return the potential of the given node. |
---|
838 | /// |
---|
839 | /// \pre \ref run() must be called before using this function. |
---|
840 | Cost potential(const typename Graph::Node& node) const { |
---|
841 | return (*_potential_result)[node]; |
---|
842 | } |
---|
843 | |
---|
844 | /// \brief Return the total cost of the found flow. |
---|
845 | /// |
---|
846 | /// Return the total cost of the found flow. The complexity of the |
---|
847 | /// function is \f$ O(e) \f$. |
---|
848 | /// |
---|
849 | /// \pre \ref run() must be called before using this function. |
---|
850 | Cost totalCost() const { |
---|
851 | Cost c = 0; |
---|
852 | for (EdgeIt e(_orig_graph); e != INVALID; ++e) |
---|
853 | c += (*_flow_result)[e] * _orig_cost[e]; |
---|
854 | return c; |
---|
855 | } |
---|
856 | |
---|
857 | /// @} |
---|
858 | |
---|
859 | private: |
---|
860 | |
---|
861 | // Initialize internal data structures |
---|
862 | bool init() { |
---|
863 | // Initialize result maps |
---|
864 | if (!_flow_result) { |
---|
865 | _flow_result = new FlowMap(_orig_graph); |
---|
866 | _local_flow = true; |
---|
867 | } |
---|
868 | if (!_potential_result) { |
---|
869 | _potential_result = new PotentialMap(_orig_graph); |
---|
870 | _local_potential = true; |
---|
871 | } |
---|
872 | |
---|
873 | // Initialize vectors |
---|
874 | _node_num = countNodes(_orig_graph); |
---|
875 | _edge_num = countEdges(_orig_graph); |
---|
876 | int all_node_num = _node_num + 1; |
---|
877 | int all_edge_num = _edge_num + _node_num; |
---|
878 | |
---|
879 | _edge.resize(_edge_num); |
---|
880 | _node.reserve(_node_num); |
---|
881 | _source.resize(all_edge_num); |
---|
882 | _target.resize(all_edge_num); |
---|
883 | |
---|
884 | _cap.resize(all_edge_num); |
---|
885 | _cost.resize(all_edge_num); |
---|
886 | _supply.resize(all_node_num); |
---|
887 | _flow.resize(all_edge_num, 0); |
---|
888 | _pi.resize(all_node_num, 0); |
---|
889 | |
---|
890 | _parent.resize(all_node_num); |
---|
891 | _pred.resize(all_node_num); |
---|
892 | _forward.resize(all_node_num); |
---|
893 | _thread.resize(all_node_num); |
---|
894 | _rev_thread.resize(all_node_num); |
---|
895 | _succ_num.resize(all_node_num); |
---|
896 | _last_succ.resize(all_node_num); |
---|
897 | _state.resize(all_edge_num, STATE_LOWER); |
---|
898 | |
---|
899 | // Initialize node related data |
---|
900 | bool valid_supply = true; |
---|
901 | if (_orig_supply) { |
---|
902 | Supply sum = 0; |
---|
903 | int i = 0; |
---|
904 | for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) { |
---|
905 | _node.push_back(n); |
---|
906 | _node_id[n] = i; |
---|
907 | _supply[i] = (*_orig_supply)[n]; |
---|
908 | sum += _supply[i]; |
---|
909 | } |
---|
910 | valid_supply = (sum == 0); |
---|
911 | } else { |
---|
912 | int i = 0; |
---|
913 | for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) { |
---|
914 | _node.push_back(n); |
---|
915 | _node_id[n] = i; |
---|
916 | _supply[i] = 0; |
---|
917 | } |
---|
918 | _supply[_node_id[_orig_source]] = _orig_flow_value; |
---|
919 | _supply[_node_id[_orig_target]] = -_orig_flow_value; |
---|
920 | } |
---|
921 | if (!valid_supply) return false; |
---|
922 | |
---|
923 | // Set data for the artificial root node |
---|
924 | _root = _node_num; |
---|
925 | _parent[_root] = -1; |
---|
926 | _pred[_root] = -1; |
---|
927 | _thread[_root] = 0; |
---|
928 | _rev_thread[0] = _root; |
---|
929 | _succ_num[_root] = all_node_num; |
---|
930 | _last_succ[_root] = _root - 1; |
---|
931 | _supply[_root] = 0; |
---|
932 | _pi[_root] = 0; |
---|
933 | |
---|
934 | // Store the edges in a mixed order |
---|
935 | int k = std::max(int(sqrt(_edge_num)), 10); |
---|
936 | int i = 0; |
---|
937 | for (EdgeIt e(_orig_graph); e != INVALID; ++e) { |
---|
938 | _edge[i] = e; |
---|
939 | if ((i += k) >= _edge_num) i = (i % k) + 1; |
---|
940 | } |
---|
941 | |
---|
942 | // Initialize edge maps |
---|
943 | for (int i = 0; i != _edge_num; ++i) { |
---|
944 | Edge e = _edge[i]; |
---|
945 | _source[i] = _node_id[_orig_graph.source(e)]; |
---|
946 | _target[i] = _node_id[_orig_graph.target(e)]; |
---|
947 | _cost[i] = _orig_cost[e]; |
---|
948 | _cap[i] = _orig_cap[e]; |
---|
949 | } |
---|
950 | |
---|
951 | // Remove non-zero lower bounds |
---|
952 | if (_orig_lower) { |
---|
953 | for (int i = 0; i != _edge_num; ++i) { |
---|
954 | Capacity c = (*_orig_lower)[_edge[i]]; |
---|
955 | if (c != 0) { |
---|
956 | _cap[i] -= c; |
---|
957 | _supply[_source[i]] -= c; |
---|
958 | _supply[_target[i]] += c; |
---|
959 | } |
---|
960 | } |
---|
961 | } |
---|
962 | |
---|
963 | // Add artificial edges and initialize the spanning tree data structure |
---|
964 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
---|
965 | Capacity max_cap = std::numeric_limits<Capacity>::max(); |
---|
966 | for (int u = 0, e = _edge_num; u != _node_num; ++u, ++e) { |
---|
967 | _parent[u] = _root; |
---|
968 | _pred[u] = e; |
---|
969 | _thread[u] = u + 1; |
---|
970 | _rev_thread[u + 1] = u; |
---|
971 | _succ_num[u] = 1; |
---|
972 | _last_succ[u] = u; |
---|
973 | _cap[e] = max_cap; |
---|
974 | _state[e] = STATE_TREE; |
---|
975 | if (_supply[u] >= 0) { |
---|
976 | _forward[u] = true; |
---|
977 | _pi[u] = 0; |
---|
978 | _source[e] = u; |
---|
979 | _target[e] = _root; |
---|
980 | _flow[e] = _supply[u]; |
---|
981 | _cost[e] = 0; |
---|
982 | } |
---|
983 | else { |
---|
984 | _forward[u] = false; |
---|
985 | _pi[u] = max_cost; |
---|
986 | _source[e] = _root; |
---|
987 | _target[e] = u; |
---|
988 | _flow[e] = -_supply[u]; |
---|
989 | _cost[e] = max_cost; |
---|
990 | } |
---|
991 | } |
---|
992 | |
---|
993 | return true; |
---|
994 | } |
---|
995 | |
---|
996 | // Find the join node |
---|
997 | void findJoinNode() { |
---|
998 | int u = _source[_in_edge]; |
---|
999 | int v = _target[_in_edge]; |
---|
1000 | while (u != v) { |
---|
1001 | if (_succ_num[u] < _succ_num[v]) { |
---|
1002 | u = _parent[u]; |
---|
1003 | } else { |
---|
1004 | v = _parent[v]; |
---|
1005 | } |
---|
1006 | } |
---|
1007 | join = u; |
---|
1008 | } |
---|
1009 | |
---|
1010 | // Find the leaving edge of the cycle and returns true if the |
---|
1011 | // leaving edge is not the same as the entering edge |
---|
1012 | bool findLeavingEdge() { |
---|
1013 | // Initialize first and second nodes according to the direction |
---|
1014 | // of the cycle |
---|
1015 | if (_state[_in_edge] == STATE_LOWER) { |
---|
1016 | first = _source[_in_edge]; |
---|
1017 | second = _target[_in_edge]; |
---|
1018 | } else { |
---|
1019 | first = _target[_in_edge]; |
---|
1020 | second = _source[_in_edge]; |
---|
1021 | } |
---|
1022 | delta = _cap[_in_edge]; |
---|
1023 | int result = 0; |
---|
1024 | Capacity d; |
---|
1025 | int e; |
---|
1026 | |
---|
1027 | // Search the cycle along the path form the first node to the root |
---|
1028 | for (int u = first; u != join; u = _parent[u]) { |
---|
1029 | e = _pred[u]; |
---|
1030 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
1031 | if (d < delta) { |
---|
1032 | delta = d; |
---|
1033 | u_out = u; |
---|
1034 | result = 1; |
---|
1035 | } |
---|
1036 | } |
---|
1037 | // Search the cycle along the path form the second node to the root |
---|
1038 | for (int u = second; u != join; u = _parent[u]) { |
---|
1039 | e = _pred[u]; |
---|
1040 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
1041 | if (d <= delta) { |
---|
1042 | delta = d; |
---|
1043 | u_out = u; |
---|
1044 | result = 2; |
---|
1045 | } |
---|
1046 | } |
---|
1047 | |
---|
1048 | if (result == 1) { |
---|
1049 | u_in = first; |
---|
1050 | v_in = second; |
---|
1051 | } else { |
---|
1052 | u_in = second; |
---|
1053 | v_in = first; |
---|
1054 | } |
---|
1055 | return result != 0; |
---|
1056 | } |
---|
1057 | |
---|
1058 | // Change _flow and _state vectors |
---|
1059 | void changeFlow(bool change) { |
---|
1060 | // Augment along the cycle |
---|
1061 | if (delta > 0) { |
---|
1062 | Capacity val = _state[_in_edge] * delta; |
---|
1063 | _flow[_in_edge] += val; |
---|
1064 | for (int u = _source[_in_edge]; u != join; u = _parent[u]) { |
---|
1065 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
1066 | } |
---|
1067 | for (int u = _target[_in_edge]; u != join; u = _parent[u]) { |
---|
1068 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
1069 | } |
---|
1070 | } |
---|
1071 | // Update the state of the entering and leaving edges |
---|
1072 | if (change) { |
---|
1073 | _state[_in_edge] = STATE_TREE; |
---|
1074 | _state[_pred[u_out]] = |
---|
1075 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
1076 | } else { |
---|
1077 | _state[_in_edge] = -_state[_in_edge]; |
---|
1078 | } |
---|
1079 | } |
---|
1080 | |
---|
1081 | // Update the tree structure |
---|
1082 | void updateTreeStructure() { |
---|
1083 | int u, w; |
---|
1084 | int old_rev_thread = _rev_thread[u_out]; |
---|
1085 | int old_succ_num = _succ_num[u_out]; |
---|
1086 | int old_last_succ = _last_succ[u_out]; |
---|
1087 | v_out = _parent[u_out]; |
---|
1088 | |
---|
1089 | u = _last_succ[u_in]; // the last successor of u_in |
---|
1090 | right = _thread[u]; // the node after it |
---|
1091 | |
---|
1092 | // Handle the case when old_rev_thread equals to v_in |
---|
1093 | // (it also means that join and v_out coincide) |
---|
1094 | if (old_rev_thread == v_in) { |
---|
1095 | last = _thread[_last_succ[u_out]]; |
---|
1096 | } else { |
---|
1097 | last = _thread[v_in]; |
---|
1098 | } |
---|
1099 | |
---|
1100 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
1101 | // between u_in and u_out, whose parent have to be changed) |
---|
1102 | _thread[v_in] = stem = u_in; |
---|
1103 | _dirty_revs.clear(); |
---|
1104 | _dirty_revs.push_back(v_in); |
---|
1105 | par_stem = v_in; |
---|
1106 | while (stem != u_out) { |
---|
1107 | // Insert the next stem node into the thread list |
---|
1108 | new_stem = _parent[stem]; |
---|
1109 | _thread[u] = new_stem; |
---|
1110 | _dirty_revs.push_back(u); |
---|
1111 | |
---|
1112 | // Remove the subtree of stem from the thread list |
---|
1113 | w = _rev_thread[stem]; |
---|
1114 | _thread[w] = right; |
---|
1115 | _rev_thread[right] = w; |
---|
1116 | |
---|
1117 | // Change the parent node and shift stem nodes |
---|
1118 | _parent[stem] = par_stem; |
---|
1119 | par_stem = stem; |
---|
1120 | stem = new_stem; |
---|
1121 | |
---|
1122 | // Update u and right nodes |
---|
1123 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
1124 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
1125 | right = _thread[u]; |
---|
1126 | } |
---|
1127 | _parent[u_out] = par_stem; |
---|
1128 | _last_succ[u_out] = u; |
---|
1129 | _thread[u] = last; |
---|
1130 | _rev_thread[last] = u; |
---|
1131 | |
---|
1132 | // Remove the subtree of u_out from the thread list except for |
---|
1133 | // the case when old_rev_thread equals to v_in |
---|
1134 | // (it also means that join and v_out coincide) |
---|
1135 | if (old_rev_thread != v_in) { |
---|
1136 | _thread[old_rev_thread] = right; |
---|
1137 | _rev_thread[right] = old_rev_thread; |
---|
1138 | } |
---|
1139 | |
---|
1140 | // Update _rev_thread using the new _thread values |
---|
1141 | for (int i = 0; i < int(_dirty_revs.size()); ++i) { |
---|
1142 | u = _dirty_revs[i]; |
---|
1143 | _rev_thread[_thread[u]] = u; |
---|
1144 | } |
---|
1145 | |
---|
1146 | // Update _last_succ for the stem nodes from u_out to u_in |
---|
1147 | for (u = u_out; u != u_in; u = _parent[u]) { |
---|
1148 | _last_succ[_parent[u]] = _last_succ[u]; |
---|
1149 | } |
---|
1150 | |
---|
1151 | // Set limits for updating _last_succ form v_in and v_out |
---|
1152 | // towards the root |
---|
1153 | int up_limit_in = -1; |
---|
1154 | int up_limit_out = -1; |
---|
1155 | if (_last_succ[join] == v_in) { |
---|
1156 | up_limit_out = join; |
---|
1157 | } else { |
---|
1158 | up_limit_in = join; |
---|
1159 | } |
---|
1160 | |
---|
1161 | // Update _last_succ from v_in towards the root |
---|
1162 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
1163 | u = _parent[u]) { |
---|
1164 | _last_succ[u] = _last_succ[u_out]; |
---|
1165 | } |
---|
1166 | // Update _last_succ from v_out towards the root |
---|
1167 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
1168 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
1169 | u = _parent[u]) { |
---|
1170 | _last_succ[u] = old_rev_thread; |
---|
1171 | } |
---|
1172 | } else { |
---|
1173 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
1174 | u = _parent[u]) { |
---|
1175 | _last_succ[u] = _last_succ[u_out]; |
---|
1176 | } |
---|
1177 | } |
---|
1178 | |
---|
1179 | // Update _pred and _forward for the stem nodes from u_out to u_in |
---|
1180 | u = u_out; |
---|
1181 | while (u != u_in) { |
---|
1182 | w = _parent[u]; |
---|
1183 | _pred[u] = _pred[w]; |
---|
1184 | _forward[u] = !_forward[w]; |
---|
1185 | u = w; |
---|
1186 | } |
---|
1187 | _pred[u_in] = _in_edge; |
---|
1188 | _forward[u_in] = (u_in == _source[_in_edge]); |
---|
1189 | |
---|
1190 | // Update _succ_num from v_in to join |
---|
1191 | for (u = v_in; u != join; u = _parent[u]) { |
---|
1192 | _succ_num[u] += old_succ_num; |
---|
1193 | } |
---|
1194 | // Update _succ_num from v_out to join |
---|
1195 | for (u = v_out; u != join; u = _parent[u]) { |
---|
1196 | _succ_num[u] -= old_succ_num; |
---|
1197 | } |
---|
1198 | // Update _succ_num for the stem nodes from u_out to u_in |
---|
1199 | int tmp = 0; |
---|
1200 | u = u_out; |
---|
1201 | while (u != u_in) { |
---|
1202 | w = _parent[u]; |
---|
1203 | tmp = _succ_num[u] - _succ_num[w] + tmp; |
---|
1204 | _succ_num[u] = tmp; |
---|
1205 | u = w; |
---|
1206 | } |
---|
1207 | _succ_num[u_in] = old_succ_num; |
---|
1208 | } |
---|
1209 | |
---|
1210 | // Update potentials |
---|
1211 | void updatePotential() { |
---|
1212 | Cost sigma = _forward[u_in] ? |
---|
1213 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
1214 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
1215 | // Update in the lower subtree (which has been moved) |
---|
1216 | int end = _thread[_last_succ[u_in]]; |
---|
1217 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
1218 | _pi[u] += sigma; |
---|
1219 | } |
---|
1220 | } |
---|
1221 | |
---|
1222 | // Execute the algorithm |
---|
1223 | bool start(PivotRuleEnum pivot_rule) { |
---|
1224 | // Select the pivot rule implementation |
---|
1225 | switch (pivot_rule) { |
---|
1226 | case FIRST_ELIGIBLE_PIVOT: |
---|
1227 | return start<FirstEligiblePivotRule>(); |
---|
1228 | case BEST_ELIGIBLE_PIVOT: |
---|
1229 | return start<BestEligiblePivotRule>(); |
---|
1230 | case BLOCK_SEARCH_PIVOT: |
---|
1231 | return start<BlockSearchPivotRule>(); |
---|
1232 | case CANDIDATE_LIST_PIVOT: |
---|
1233 | return start<CandidateListPivotRule>(); |
---|
1234 | case ALTERING_LIST_PIVOT: |
---|
1235 | return start<AlteringListPivotRule>(); |
---|
1236 | } |
---|
1237 | return false; |
---|
1238 | } |
---|
1239 | |
---|
1240 | template<class PivotRuleImplementation> |
---|
1241 | bool start() { |
---|
1242 | PivotRuleImplementation pivot(*this); |
---|
1243 | |
---|
1244 | // Execute the network simplex algorithm |
---|
1245 | while (pivot.findEnteringEdge()) { |
---|
1246 | findJoinNode(); |
---|
1247 | bool change = findLeavingEdge(); |
---|
1248 | changeFlow(change); |
---|
1249 | if (change) { |
---|
1250 | updateTreeStructure(); |
---|
1251 | updatePotential(); |
---|
1252 | } |
---|
1253 | } |
---|
1254 | |
---|
1255 | // Check if the flow amount equals zero on all the artificial edges |
---|
1256 | for (int e = _edge_num; e != _edge_num + _node_num; ++e) { |
---|
1257 | if (_flow[e] > 0) return false; |
---|
1258 | } |
---|
1259 | |
---|
1260 | // Copy flow values to _flow_result |
---|
1261 | if (_orig_lower) { |
---|
1262 | for (int i = 0; i != _edge_num; ++i) { |
---|
1263 | Edge e = _edge[i]; |
---|
1264 | (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i]; |
---|
1265 | } |
---|
1266 | } else { |
---|
1267 | for (int i = 0; i != _edge_num; ++i) { |
---|
1268 | (*_flow_result)[_edge[i]] = _flow[i]; |
---|
1269 | } |
---|
1270 | } |
---|
1271 | // Copy potential values to _potential_result |
---|
1272 | for (int i = 0; i != _node_num; ++i) { |
---|
1273 | (*_potential_result)[_node[i]] = _pi[i]; |
---|
1274 | } |
---|
1275 | |
---|
1276 | return true; |
---|
1277 | } |
---|
1278 | |
---|
1279 | }; //class NetworkSimplex |
---|
1280 | |
---|
1281 | ///@} |
---|
1282 | |
---|
1283 | } //namespace lemon |
---|
1284 | |
---|
1285 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|