1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2009 |
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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/math.h> |
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32 | |
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33 | namespace lemon { |
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34 | |
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35 | /// \addtogroup min_cost_flow |
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36 | /// @{ |
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37 | |
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38 | /// \brief Implementation of the primal network simplex algorithm |
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39 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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40 | /// |
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41 | /// \ref NetworkSimplex implements the primal network simplex algorithm |
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42 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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43 | /// |
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44 | /// \tparam Digraph The digraph type the algorithm runs on. |
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45 | /// \tparam LowerMap The type of the lower bound map. |
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46 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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47 | /// \tparam CostMap The type of the cost (length) map. |
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48 | /// \tparam SupplyMap The type of the supply map. |
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49 | /// |
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50 | /// \warning |
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51 | /// - Arc capacities and costs should be \e non-negative \e integers. |
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52 | /// - Supply values should be \e signed \e integers. |
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53 | /// - The value types of the maps should be convertible to each other. |
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54 | /// - \c CostMap::Value must be signed type. |
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55 | /// |
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56 | /// \note \ref NetworkSimplex provides five different pivot rule |
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57 | /// implementations that significantly affect the efficiency of the |
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58 | /// algorithm. |
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59 | /// By default "Block Search" pivot rule is used, which proved to be |
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60 | /// by far the most efficient according to our benchmark tests. |
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61 | /// However another pivot rule can be selected using \ref run() |
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62 | /// function with the proper parameter. |
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63 | #ifdef DOXYGEN |
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64 | template < typename Digraph, |
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65 | typename LowerMap, |
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66 | typename CapacityMap, |
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67 | typename CostMap, |
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68 | typename SupplyMap > |
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69 | |
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70 | #else |
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71 | template < typename Digraph, |
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72 | typename LowerMap = typename Digraph::template ArcMap<int>, |
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73 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
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74 | typename CostMap = typename Digraph::template ArcMap<int>, |
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75 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
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76 | #endif |
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77 | class NetworkSimplex |
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78 | { |
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79 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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80 | |
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81 | typedef typename CapacityMap::Value Capacity; |
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82 | typedef typename CostMap::Value Cost; |
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83 | typedef typename SupplyMap::Value Supply; |
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84 | |
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85 | typedef std::vector<Arc> ArcVector; |
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86 | typedef std::vector<Node> NodeVector; |
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87 | typedef std::vector<int> IntVector; |
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88 | typedef std::vector<bool> BoolVector; |
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89 | typedef std::vector<Capacity> CapacityVector; |
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90 | typedef std::vector<Cost> CostVector; |
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91 | typedef std::vector<Supply> SupplyVector; |
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92 | |
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93 | public: |
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94 | |
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95 | /// The type of the flow map |
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96 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
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97 | /// The type of the potential map |
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98 | typedef typename Digraph::template NodeMap<Cost> PotentialMap; |
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99 | |
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100 | public: |
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101 | |
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102 | /// Enum type for selecting the pivot rule used by \ref run() |
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103 | enum PivotRuleEnum { |
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104 | FIRST_ELIGIBLE_PIVOT, |
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105 | BEST_ELIGIBLE_PIVOT, |
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106 | BLOCK_SEARCH_PIVOT, |
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107 | CANDIDATE_LIST_PIVOT, |
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108 | ALTERING_LIST_PIVOT |
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109 | }; |
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110 | |
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111 | private: |
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112 | |
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113 | // State constants for arcs |
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114 | enum ArcStateEnum { |
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115 | STATE_UPPER = -1, |
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116 | STATE_TREE = 0, |
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117 | STATE_LOWER = 1 |
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118 | }; |
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119 | |
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120 | private: |
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121 | |
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122 | // References for the original data |
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123 | const Digraph &_orig_graph; |
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124 | const LowerMap *_orig_lower; |
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125 | const CapacityMap &_orig_cap; |
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126 | const CostMap &_orig_cost; |
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127 | const SupplyMap *_orig_supply; |
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128 | Node _orig_source; |
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129 | Node _orig_target; |
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130 | Capacity _orig_flow_value; |
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131 | |
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132 | // Result maps |
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133 | FlowMap *_flow_result; |
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134 | PotentialMap *_potential_result; |
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135 | bool _local_flow; |
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136 | bool _local_potential; |
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137 | |
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138 | // Data structures for storing the graph |
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139 | ArcVector _arc; |
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140 | NodeVector _node; |
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141 | IntNodeMap _node_id; |
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142 | IntVector _source; |
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143 | IntVector _target; |
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144 | |
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145 | // The number of nodes and arcs in the original graph |
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146 | int _node_num; |
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147 | int _arc_num; |
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148 | |
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149 | // Node and arc maps |
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150 | CapacityVector _cap; |
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151 | CostVector _cost; |
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152 | CostVector _supply; |
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153 | CapacityVector _flow; |
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154 | CostVector _pi; |
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155 | |
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156 | // Node and arc maps for the spanning tree structure |
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157 | IntVector _depth; |
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158 | IntVector _parent; |
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159 | IntVector _pred; |
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160 | IntVector _thread; |
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161 | BoolVector _forward; |
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162 | IntVector _state; |
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163 | |
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164 | // The root node |
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165 | int _root; |
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166 | |
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167 | // The entering arc in the current pivot iteration |
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168 | int _in_arc; |
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169 | |
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170 | // Temporary data used in the current pivot iteration |
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171 | int join, u_in, v_in, u_out, v_out; |
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172 | int right, first, second, last; |
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173 | int stem, par_stem, new_stem; |
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174 | Capacity delta; |
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175 | |
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176 | private: |
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177 | |
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178 | /// \brief Implementation of the "First Eligible" pivot rule for the |
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179 | /// \ref NetworkSimplex "network simplex" algorithm. |
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180 | /// |
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181 | /// This class implements the "First Eligible" pivot rule |
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182 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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183 | /// |
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184 | /// For more information see \ref NetworkSimplex::run(). |
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185 | class FirstEligiblePivotRule |
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186 | { |
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187 | private: |
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188 | |
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189 | // References to the NetworkSimplex class |
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190 | const ArcVector &_arc; |
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191 | const IntVector &_source; |
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192 | const IntVector &_target; |
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193 | const CostVector &_cost; |
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194 | const IntVector &_state; |
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195 | const CostVector &_pi; |
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196 | int &_in_arc; |
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197 | int _arc_num; |
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198 | |
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199 | // Pivot rule data |
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200 | int _next_arc; |
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201 | |
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202 | public: |
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203 | |
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204 | /// Constructor |
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205 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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206 | _arc(ns._arc), _source(ns._source), _target(ns._target), |
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207 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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208 | _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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209 | {} |
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210 | |
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211 | /// Find next entering arc |
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212 | bool findEnteringArc() { |
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213 | Cost c; |
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214 | for (int e = _next_arc; e < _arc_num; ++e) { |
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215 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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216 | if (c < 0) { |
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217 | _in_arc = e; |
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218 | _next_arc = e + 1; |
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219 | return true; |
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220 | } |
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221 | } |
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222 | for (int e = 0; e < _next_arc; ++e) { |
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223 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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224 | if (c < 0) { |
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225 | _in_arc = e; |
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226 | _next_arc = e + 1; |
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227 | return true; |
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228 | } |
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229 | } |
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230 | return false; |
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231 | } |
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232 | |
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233 | }; //class FirstEligiblePivotRule |
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234 | |
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235 | |
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236 | /// \brief Implementation of the "Best Eligible" pivot rule for the |
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237 | /// \ref NetworkSimplex "network simplex" algorithm. |
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238 | /// |
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239 | /// This class implements the "Best Eligible" pivot rule |
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240 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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241 | /// |
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242 | /// For more information see \ref NetworkSimplex::run(). |
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243 | class BestEligiblePivotRule |
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244 | { |
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245 | private: |
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246 | |
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247 | // References to the NetworkSimplex class |
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248 | const ArcVector &_arc; |
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249 | const IntVector &_source; |
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250 | const IntVector &_target; |
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251 | const CostVector &_cost; |
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252 | const IntVector &_state; |
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253 | const CostVector &_pi; |
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254 | int &_in_arc; |
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255 | int _arc_num; |
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256 | |
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257 | public: |
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258 | |
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259 | /// Constructor |
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260 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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261 | _arc(ns._arc), _source(ns._source), _target(ns._target), |
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262 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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263 | _in_arc(ns._in_arc), _arc_num(ns._arc_num) |
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264 | {} |
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265 | |
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266 | /// Find next entering arc |
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267 | bool findEnteringArc() { |
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268 | Cost c, min = 0; |
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269 | for (int e = 0; e < _arc_num; ++e) { |
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270 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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271 | if (c < min) { |
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272 | min = c; |
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273 | _in_arc = e; |
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274 | } |
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275 | } |
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276 | return min < 0; |
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277 | } |
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278 | |
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279 | }; //class BestEligiblePivotRule |
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280 | |
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281 | |
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282 | /// \brief Implementation of the "Block Search" pivot rule for the |
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283 | /// \ref NetworkSimplex "network simplex" algorithm. |
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284 | /// |
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285 | /// This class implements the "Block Search" pivot rule |
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286 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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287 | /// |
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288 | /// For more information see \ref NetworkSimplex::run(). |
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289 | class BlockSearchPivotRule |
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290 | { |
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291 | private: |
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292 | |
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293 | // References to the NetworkSimplex class |
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294 | const ArcVector &_arc; |
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295 | const IntVector &_source; |
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296 | const IntVector &_target; |
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297 | const CostVector &_cost; |
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298 | const IntVector &_state; |
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299 | const CostVector &_pi; |
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300 | int &_in_arc; |
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301 | int _arc_num; |
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302 | |
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303 | // Pivot rule data |
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304 | int _block_size; |
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305 | int _next_arc; |
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306 | |
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307 | public: |
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308 | |
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309 | /// Constructor |
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310 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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311 | _arc(ns._arc), _source(ns._source), _target(ns._target), |
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312 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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313 | _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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314 | { |
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315 | // The main parameters of the pivot rule |
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316 | const double BLOCK_SIZE_FACTOR = 2.0; |
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317 | const int MIN_BLOCK_SIZE = 10; |
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318 | |
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319 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
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320 | MIN_BLOCK_SIZE ); |
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321 | } |
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322 | |
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323 | /// Find next entering arc |
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324 | bool findEnteringArc() { |
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325 | Cost c, min = 0; |
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326 | int cnt = _block_size; |
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327 | int e, min_arc = _next_arc; |
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328 | for (e = _next_arc; e < _arc_num; ++e) { |
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329 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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330 | if (c < min) { |
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331 | min = c; |
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332 | min_arc = e; |
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333 | } |
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334 | if (--cnt == 0) { |
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335 | if (min < 0) break; |
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336 | cnt = _block_size; |
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337 | } |
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338 | } |
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339 | if (min == 0 || cnt > 0) { |
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340 | for (e = 0; e < _next_arc; ++e) { |
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341 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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342 | if (c < min) { |
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343 | min = c; |
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344 | min_arc = e; |
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345 | } |
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346 | if (--cnt == 0) { |
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347 | if (min < 0) break; |
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348 | cnt = _block_size; |
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349 | } |
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350 | } |
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351 | } |
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352 | if (min >= 0) return false; |
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353 | _in_arc = min_arc; |
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354 | _next_arc = e; |
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355 | return true; |
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356 | } |
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357 | |
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358 | }; //class BlockSearchPivotRule |
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359 | |
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360 | |
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361 | /// \brief Implementation of the "Candidate List" pivot rule for the |
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362 | /// \ref NetworkSimplex "network simplex" algorithm. |
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363 | /// |
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364 | /// This class implements the "Candidate List" pivot rule |
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365 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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366 | /// |
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367 | /// For more information see \ref NetworkSimplex::run(). |
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368 | class CandidateListPivotRule |
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369 | { |
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370 | private: |
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371 | |
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372 | // References to the NetworkSimplex class |
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373 | const ArcVector &_arc; |
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374 | const IntVector &_source; |
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375 | const IntVector &_target; |
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376 | const CostVector &_cost; |
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377 | const IntVector &_state; |
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378 | const CostVector &_pi; |
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379 | int &_in_arc; |
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380 | int _arc_num; |
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381 | |
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382 | // Pivot rule data |
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383 | IntVector _candidates; |
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384 | int _list_length, _minor_limit; |
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385 | int _curr_length, _minor_count; |
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386 | int _next_arc; |
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387 | |
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388 | public: |
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389 | |
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390 | /// Constructor |
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391 | CandidateListPivotRule(NetworkSimplex &ns) : |
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392 | _arc(ns._arc), _source(ns._source), _target(ns._target), |
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393 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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394 | _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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395 | { |
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396 | // The main parameters of the pivot rule |
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397 | const double LIST_LENGTH_FACTOR = 1.0; |
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398 | const int MIN_LIST_LENGTH = 10; |
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399 | const double MINOR_LIMIT_FACTOR = 0.1; |
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400 | const int MIN_MINOR_LIMIT = 3; |
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401 | |
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402 | _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)), |
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403 | MIN_LIST_LENGTH ); |
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404 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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405 | MIN_MINOR_LIMIT ); |
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406 | _curr_length = _minor_count = 0; |
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407 | _candidates.resize(_list_length); |
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408 | } |
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409 | |
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410 | /// Find next entering arc |
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411 | bool findEnteringArc() { |
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412 | Cost min, c; |
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413 | int e, min_arc = _next_arc; |
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414 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
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415 | // Minor iteration: select the best eligible arc from the |
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416 | // current candidate list |
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417 | ++_minor_count; |
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418 | min = 0; |
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419 | for (int i = 0; i < _curr_length; ++i) { |
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420 | e = _candidates[i]; |
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421 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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422 | if (c < min) { |
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423 | min = c; |
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424 | min_arc = e; |
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425 | } |
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426 | if (c >= 0) { |
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427 | _candidates[i--] = _candidates[--_curr_length]; |
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428 | } |
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429 | } |
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430 | if (min < 0) { |
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431 | _in_arc = min_arc; |
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432 | return true; |
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433 | } |
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434 | } |
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435 | |
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436 | // Major iteration: build a new candidate list |
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437 | min = 0; |
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438 | _curr_length = 0; |
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439 | for (e = _next_arc; e < _arc_num; ++e) { |
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440 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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441 | if (c < 0) { |
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442 | _candidates[_curr_length++] = e; |
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443 | if (c < min) { |
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444 | min = c; |
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445 | min_arc = e; |
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446 | } |
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447 | if (_curr_length == _list_length) break; |
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448 | } |
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449 | } |
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450 | if (_curr_length < _list_length) { |
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451 | for (e = 0; e < _next_arc; ++e) { |
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452 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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453 | if (c < 0) { |
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454 | _candidates[_curr_length++] = e; |
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455 | if (c < min) { |
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456 | min = c; |
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457 | min_arc = e; |
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458 | } |
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459 | if (_curr_length == _list_length) break; |
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460 | } |
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461 | } |
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462 | } |
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463 | if (_curr_length == 0) return false; |
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464 | _minor_count = 1; |
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465 | _in_arc = min_arc; |
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466 | _next_arc = e; |
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467 | return true; |
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468 | } |
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469 | |
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470 | }; //class CandidateListPivotRule |
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471 | |
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472 | |
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473 | /// \brief Implementation of the "Altering Candidate List" pivot rule |
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474 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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475 | /// |
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476 | /// This class implements the "Altering Candidate List" pivot rule |
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477 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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478 | /// |
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479 | /// For more information see \ref NetworkSimplex::run(). |
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480 | class AlteringListPivotRule |
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481 | { |
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482 | private: |
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483 | |
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484 | // References to the NetworkSimplex class |
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485 | const ArcVector &_arc; |
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486 | const IntVector &_source; |
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487 | const IntVector &_target; |
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488 | const CostVector &_cost; |
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489 | const IntVector &_state; |
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490 | const CostVector &_pi; |
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491 | int &_in_arc; |
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492 | int _arc_num; |
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493 | |
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494 | // Pivot rule data |
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495 | int _block_size, _head_length, _curr_length; |
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496 | int _next_arc; |
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497 | IntVector _candidates; |
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498 | CostVector _cand_cost; |
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499 | |
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500 | // Functor class to compare arcs during sort of the candidate list |
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501 | class SortFunc |
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502 | { |
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503 | private: |
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504 | const CostVector &_map; |
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505 | public: |
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506 | SortFunc(const CostVector &map) : _map(map) {} |
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507 | bool operator()(int left, int right) { |
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508 | return _map[left] > _map[right]; |
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509 | } |
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510 | }; |
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511 | |
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512 | SortFunc _sort_func; |
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513 | |
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514 | public: |
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515 | |
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516 | /// Constructor |
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517 | AlteringListPivotRule(NetworkSimplex &ns) : |
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518 | _arc(ns._arc), _source(ns._source), _target(ns._target), |
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519 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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520 | _in_arc(ns._in_arc), _arc_num(ns._arc_num), |
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521 | _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) |
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522 | { |
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523 | // The main parameters of the pivot rule |
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524 | const double BLOCK_SIZE_FACTOR = 1.5; |
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525 | const int MIN_BLOCK_SIZE = 10; |
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526 | const double HEAD_LENGTH_FACTOR = 0.1; |
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527 | const int MIN_HEAD_LENGTH = 3; |
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528 | |
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529 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
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530 | MIN_BLOCK_SIZE ); |
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531 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
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532 | MIN_HEAD_LENGTH ); |
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533 | _candidates.resize(_head_length + _block_size); |
---|
534 | _curr_length = 0; |
---|
535 | } |
---|
536 | |
---|
537 | /// Find next entering arc |
---|
538 | bool findEnteringArc() { |
---|
539 | // Check the current candidate list |
---|
540 | int e; |
---|
541 | for (int i = 0; i < _curr_length; ++i) { |
---|
542 | e = _candidates[i]; |
---|
543 | _cand_cost[e] = _state[e] * |
---|
544 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
545 | if (_cand_cost[e] >= 0) { |
---|
546 | _candidates[i--] = _candidates[--_curr_length]; |
---|
547 | } |
---|
548 | } |
---|
549 | |
---|
550 | // Extend the list |
---|
551 | int cnt = _block_size; |
---|
552 | int last_edge = 0; |
---|
553 | int limit = _head_length; |
---|
554 | |
---|
555 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
556 | _cand_cost[e] = _state[e] * |
---|
557 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
558 | if (_cand_cost[e] < 0) { |
---|
559 | _candidates[_curr_length++] = e; |
---|
560 | last_edge = e; |
---|
561 | } |
---|
562 | if (--cnt == 0) { |
---|
563 | if (_curr_length > limit) break; |
---|
564 | limit = 0; |
---|
565 | cnt = _block_size; |
---|
566 | } |
---|
567 | } |
---|
568 | if (_curr_length <= limit) { |
---|
569 | for (int e = 0; e < _next_arc; ++e) { |
---|
570 | _cand_cost[e] = _state[e] * |
---|
571 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
572 | if (_cand_cost[e] < 0) { |
---|
573 | _candidates[_curr_length++] = e; |
---|
574 | last_edge = e; |
---|
575 | } |
---|
576 | if (--cnt == 0) { |
---|
577 | if (_curr_length > limit) break; |
---|
578 | limit = 0; |
---|
579 | cnt = _block_size; |
---|
580 | } |
---|
581 | } |
---|
582 | } |
---|
583 | if (_curr_length == 0) return false; |
---|
584 | _next_arc = last_edge + 1; |
---|
585 | |
---|
586 | // Make heap of the candidate list (approximating a partial sort) |
---|
587 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
588 | _sort_func ); |
---|
589 | |
---|
590 | // Pop the first element of the heap |
---|
591 | _in_arc = _candidates[0]; |
---|
592 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
593 | _sort_func ); |
---|
594 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
595 | return true; |
---|
596 | } |
---|
597 | |
---|
598 | }; //class AlteringListPivotRule |
---|
599 | |
---|
600 | public: |
---|
601 | |
---|
602 | /// \brief General constructor (with lower bounds). |
---|
603 | /// |
---|
604 | /// General constructor (with lower bounds). |
---|
605 | /// |
---|
606 | /// \param digraph The digraph the algorithm runs on. |
---|
607 | /// \param lower The lower bounds of the arcs. |
---|
608 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
609 | /// \param cost The cost (length) values of the arcs. |
---|
610 | /// \param supply The supply values of the nodes (signed). |
---|
611 | NetworkSimplex( const Digraph &digraph, |
---|
612 | const LowerMap &lower, |
---|
613 | const CapacityMap &capacity, |
---|
614 | const CostMap &cost, |
---|
615 | const SupplyMap &supply ) : |
---|
616 | _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity), |
---|
617 | _orig_cost(cost), _orig_supply(&supply), |
---|
618 | _flow_result(NULL), _potential_result(NULL), |
---|
619 | _local_flow(false), _local_potential(false), |
---|
620 | _node_id(digraph) |
---|
621 | {} |
---|
622 | |
---|
623 | /// \brief General constructor (without lower bounds). |
---|
624 | /// |
---|
625 | /// General constructor (without lower bounds). |
---|
626 | /// |
---|
627 | /// \param digraph The digraph the algorithm runs on. |
---|
628 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
629 | /// \param cost The cost (length) values of the arcs. |
---|
630 | /// \param supply The supply values of the nodes (signed). |
---|
631 | NetworkSimplex( const Digraph &digraph, |
---|
632 | const CapacityMap &capacity, |
---|
633 | const CostMap &cost, |
---|
634 | const SupplyMap &supply ) : |
---|
635 | _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity), |
---|
636 | _orig_cost(cost), _orig_supply(&supply), |
---|
637 | _flow_result(NULL), _potential_result(NULL), |
---|
638 | _local_flow(false), _local_potential(false), |
---|
639 | _node_id(digraph) |
---|
640 | {} |
---|
641 | |
---|
642 | /// \brief Simple constructor (with lower bounds). |
---|
643 | /// |
---|
644 | /// Simple constructor (with lower bounds). |
---|
645 | /// |
---|
646 | /// \param digraph The digraph the algorithm runs on. |
---|
647 | /// \param lower The lower bounds of the arcs. |
---|
648 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
649 | /// \param cost The cost (length) values of the arcs. |
---|
650 | /// \param s The source node. |
---|
651 | /// \param t The target node. |
---|
652 | /// \param flow_value The required amount of flow from node \c s |
---|
653 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
654 | NetworkSimplex( const Digraph &digraph, |
---|
655 | const LowerMap &lower, |
---|
656 | const CapacityMap &capacity, |
---|
657 | const CostMap &cost, |
---|
658 | Node s, Node t, |
---|
659 | Capacity flow_value ) : |
---|
660 | _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity), |
---|
661 | _orig_cost(cost), _orig_supply(NULL), |
---|
662 | _orig_source(s), _orig_target(t), _orig_flow_value(flow_value), |
---|
663 | _flow_result(NULL), _potential_result(NULL), |
---|
664 | _local_flow(false), _local_potential(false), |
---|
665 | _node_id(digraph) |
---|
666 | {} |
---|
667 | |
---|
668 | /// \brief Simple constructor (without lower bounds). |
---|
669 | /// |
---|
670 | /// Simple constructor (without lower bounds). |
---|
671 | /// |
---|
672 | /// \param digraph The digraph the algorithm runs on. |
---|
673 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
674 | /// \param cost The cost (length) values of the arcs. |
---|
675 | /// \param s The source node. |
---|
676 | /// \param t The target node. |
---|
677 | /// \param flow_value The required amount of flow from node \c s |
---|
678 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
679 | NetworkSimplex( const Digraph &digraph, |
---|
680 | const CapacityMap &capacity, |
---|
681 | const CostMap &cost, |
---|
682 | Node s, Node t, |
---|
683 | Capacity flow_value ) : |
---|
684 | _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity), |
---|
685 | _orig_cost(cost), _orig_supply(NULL), |
---|
686 | _orig_source(s), _orig_target(t), _orig_flow_value(flow_value), |
---|
687 | _flow_result(NULL), _potential_result(NULL), |
---|
688 | _local_flow(false), _local_potential(false), |
---|
689 | _node_id(digraph) |
---|
690 | {} |
---|
691 | |
---|
692 | /// Destructor. |
---|
693 | ~NetworkSimplex() { |
---|
694 | if (_local_flow) delete _flow_result; |
---|
695 | if (_local_potential) delete _potential_result; |
---|
696 | } |
---|
697 | |
---|
698 | /// \brief Set the flow map. |
---|
699 | /// |
---|
700 | /// This function sets the flow map. |
---|
701 | /// |
---|
702 | /// \return <tt>(*this)</tt> |
---|
703 | NetworkSimplex& flowMap(FlowMap &map) { |
---|
704 | if (_local_flow) { |
---|
705 | delete _flow_result; |
---|
706 | _local_flow = false; |
---|
707 | } |
---|
708 | _flow_result = ↦ |
---|
709 | return *this; |
---|
710 | } |
---|
711 | |
---|
712 | /// \brief Set the potential map. |
---|
713 | /// |
---|
714 | /// This function sets the potential map. |
---|
715 | /// |
---|
716 | /// \return <tt>(*this)</tt> |
---|
717 | NetworkSimplex& potentialMap(PotentialMap &map) { |
---|
718 | if (_local_potential) { |
---|
719 | delete _potential_result; |
---|
720 | _local_potential = false; |
---|
721 | } |
---|
722 | _potential_result = ↦ |
---|
723 | return *this; |
---|
724 | } |
---|
725 | |
---|
726 | /// \name Execution control |
---|
727 | /// The algorithm can be executed using the |
---|
728 | /// \ref lemon::NetworkSimplex::run() "run()" function. |
---|
729 | /// @{ |
---|
730 | |
---|
731 | /// \brief Run the algorithm. |
---|
732 | /// |
---|
733 | /// This function runs the algorithm. |
---|
734 | /// |
---|
735 | /// \param pivot_rule The pivot rule that is used during the |
---|
736 | /// algorithm. |
---|
737 | /// |
---|
738 | /// The available pivot rules: |
---|
739 | /// |
---|
740 | /// - FIRST_ELIGIBLE_PIVOT The next eligible arc is selected in |
---|
741 | /// a wraparound fashion in every iteration |
---|
742 | /// (\ref FirstEligiblePivotRule). |
---|
743 | /// |
---|
744 | /// - BEST_ELIGIBLE_PIVOT The best eligible arc is selected in |
---|
745 | /// every iteration (\ref BestEligiblePivotRule). |
---|
746 | /// |
---|
747 | /// - BLOCK_SEARCH_PIVOT A specified number of arcs are examined in |
---|
748 | /// every iteration in a wraparound fashion and the best eligible |
---|
749 | /// arc is selected from this block (\ref BlockSearchPivotRule). |
---|
750 | /// |
---|
751 | /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is |
---|
752 | /// built from eligible arcs in a wraparound fashion and in the |
---|
753 | /// following minor iterations the best eligible arc is selected |
---|
754 | /// from this list (\ref CandidateListPivotRule). |
---|
755 | /// |
---|
756 | /// - ALTERING_LIST_PIVOT It is a modified version of the |
---|
757 | /// "Candidate List" pivot rule. It keeps only the several best |
---|
758 | /// eligible arcs from the former candidate list and extends this |
---|
759 | /// list in every iteration (\ref AlteringListPivotRule). |
---|
760 | /// |
---|
761 | /// According to our comprehensive benchmark tests the "Block Search" |
---|
762 | /// pivot rule proved to be the fastest and the most robust on |
---|
763 | /// various test inputs. Thus it is the default option. |
---|
764 | /// |
---|
765 | /// \return \c true if a feasible flow can be found. |
---|
766 | bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) { |
---|
767 | return init() && start(pivot_rule); |
---|
768 | } |
---|
769 | |
---|
770 | /// @} |
---|
771 | |
---|
772 | /// \name Query Functions |
---|
773 | /// The results of the algorithm can be obtained using these |
---|
774 | /// functions.\n |
---|
775 | /// \ref lemon::NetworkSimplex::run() "run()" must be called before |
---|
776 | /// using them. |
---|
777 | /// @{ |
---|
778 | |
---|
779 | /// \brief Return a const reference to the flow map. |
---|
780 | /// |
---|
781 | /// This function returns a const reference to an arc map storing |
---|
782 | /// the found flow. |
---|
783 | /// |
---|
784 | /// \pre \ref run() must be called before using this function. |
---|
785 | const FlowMap& flowMap() const { |
---|
786 | return *_flow_result; |
---|
787 | } |
---|
788 | |
---|
789 | /// \brief Return a const reference to the potential map |
---|
790 | /// (the dual solution). |
---|
791 | /// |
---|
792 | /// This function returns a const reference to a node map storing |
---|
793 | /// the found potentials (the dual solution). |
---|
794 | /// |
---|
795 | /// \pre \ref run() must be called before using this function. |
---|
796 | const PotentialMap& potentialMap() const { |
---|
797 | return *_potential_result; |
---|
798 | } |
---|
799 | |
---|
800 | /// \brief Return the flow on the given arc. |
---|
801 | /// |
---|
802 | /// This function returns the flow on the given arc. |
---|
803 | /// |
---|
804 | /// \pre \ref run() must be called before using this function. |
---|
805 | Capacity flow(const Arc& arc) const { |
---|
806 | return (*_flow_result)[arc]; |
---|
807 | } |
---|
808 | |
---|
809 | /// \brief Return the potential of the given node. |
---|
810 | /// |
---|
811 | /// This function returns the potential of the given node. |
---|
812 | /// |
---|
813 | /// \pre \ref run() must be called before using this function. |
---|
814 | Cost potential(const Node& node) const { |
---|
815 | return (*_potential_result)[node]; |
---|
816 | } |
---|
817 | |
---|
818 | /// \brief Return the total cost of the found flow. |
---|
819 | /// |
---|
820 | /// This function returns the total cost of the found flow. |
---|
821 | /// The complexity of the function is \f$ O(e) \f$. |
---|
822 | /// |
---|
823 | /// \pre \ref run() must be called before using this function. |
---|
824 | Cost totalCost() const { |
---|
825 | Cost c = 0; |
---|
826 | for (ArcIt e(_orig_graph); e != INVALID; ++e) |
---|
827 | c += (*_flow_result)[e] * _orig_cost[e]; |
---|
828 | return c; |
---|
829 | } |
---|
830 | |
---|
831 | /// @} |
---|
832 | |
---|
833 | private: |
---|
834 | |
---|
835 | // Initialize internal data structures |
---|
836 | bool init() { |
---|
837 | // Initialize result maps |
---|
838 | if (!_flow_result) { |
---|
839 | _flow_result = new FlowMap(_orig_graph); |
---|
840 | _local_flow = true; |
---|
841 | } |
---|
842 | if (!_potential_result) { |
---|
843 | _potential_result = new PotentialMap(_orig_graph); |
---|
844 | _local_potential = true; |
---|
845 | } |
---|
846 | |
---|
847 | // Initialize vectors |
---|
848 | _node_num = countNodes(_orig_graph); |
---|
849 | _arc_num = countArcs(_orig_graph); |
---|
850 | int all_node_num = _node_num + 1; |
---|
851 | int all_edge_num = _arc_num + _node_num; |
---|
852 | |
---|
853 | _arc.resize(_arc_num); |
---|
854 | _node.reserve(_node_num); |
---|
855 | _source.resize(all_edge_num); |
---|
856 | _target.resize(all_edge_num); |
---|
857 | |
---|
858 | _cap.resize(all_edge_num); |
---|
859 | _cost.resize(all_edge_num); |
---|
860 | _supply.resize(all_node_num); |
---|
861 | _flow.resize(all_edge_num, 0); |
---|
862 | _pi.resize(all_node_num, 0); |
---|
863 | |
---|
864 | _depth.resize(all_node_num); |
---|
865 | _parent.resize(all_node_num); |
---|
866 | _pred.resize(all_node_num); |
---|
867 | _thread.resize(all_node_num); |
---|
868 | _forward.resize(all_node_num); |
---|
869 | _state.resize(all_edge_num, STATE_LOWER); |
---|
870 | |
---|
871 | // Initialize node related data |
---|
872 | bool valid_supply = true; |
---|
873 | if (_orig_supply) { |
---|
874 | Supply sum = 0; |
---|
875 | int i = 0; |
---|
876 | for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) { |
---|
877 | _node.push_back(n); |
---|
878 | _node_id[n] = i; |
---|
879 | _supply[i] = (*_orig_supply)[n]; |
---|
880 | sum += _supply[i]; |
---|
881 | } |
---|
882 | valid_supply = (sum == 0); |
---|
883 | } else { |
---|
884 | int i = 0; |
---|
885 | for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) { |
---|
886 | _node.push_back(n); |
---|
887 | _node_id[n] = i; |
---|
888 | _supply[i] = 0; |
---|
889 | } |
---|
890 | _supply[_node_id[_orig_source]] = _orig_flow_value; |
---|
891 | _supply[_node_id[_orig_target]] = -_orig_flow_value; |
---|
892 | } |
---|
893 | if (!valid_supply) return false; |
---|
894 | |
---|
895 | // Set data for the artificial root node |
---|
896 | _root = _node_num; |
---|
897 | _depth[_root] = 0; |
---|
898 | _parent[_root] = -1; |
---|
899 | _pred[_root] = -1; |
---|
900 | _thread[_root] = 0; |
---|
901 | _supply[_root] = 0; |
---|
902 | _pi[_root] = 0; |
---|
903 | |
---|
904 | // Store the arcs in a mixed order |
---|
905 | int k = std::max(int(sqrt(_arc_num)), 10); |
---|
906 | int i = 0; |
---|
907 | for (ArcIt e(_orig_graph); e != INVALID; ++e) { |
---|
908 | _arc[i] = e; |
---|
909 | if ((i += k) >= _arc_num) i = (i % k) + 1; |
---|
910 | } |
---|
911 | |
---|
912 | // Initialize arc maps |
---|
913 | for (int i = 0; i != _arc_num; ++i) { |
---|
914 | Arc e = _arc[i]; |
---|
915 | _source[i] = _node_id[_orig_graph.source(e)]; |
---|
916 | _target[i] = _node_id[_orig_graph.target(e)]; |
---|
917 | _cost[i] = _orig_cost[e]; |
---|
918 | _cap[i] = _orig_cap[e]; |
---|
919 | } |
---|
920 | |
---|
921 | // Remove non-zero lower bounds |
---|
922 | if (_orig_lower) { |
---|
923 | for (int i = 0; i != _arc_num; ++i) { |
---|
924 | Capacity c = (*_orig_lower)[_arc[i]]; |
---|
925 | if (c != 0) { |
---|
926 | _cap[i] -= c; |
---|
927 | _supply[_source[i]] -= c; |
---|
928 | _supply[_target[i]] += c; |
---|
929 | } |
---|
930 | } |
---|
931 | } |
---|
932 | |
---|
933 | // Add artificial arcs and initialize the spanning tree data structure |
---|
934 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
---|
935 | Capacity max_cap = std::numeric_limits<Capacity>::max(); |
---|
936 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
937 | _thread[u] = u + 1; |
---|
938 | _depth[u] = 1; |
---|
939 | _parent[u] = _root; |
---|
940 | _pred[u] = e; |
---|
941 | if (_supply[u] >= 0) { |
---|
942 | _flow[e] = _supply[u]; |
---|
943 | _forward[u] = true; |
---|
944 | _pi[u] = -max_cost; |
---|
945 | } else { |
---|
946 | _flow[e] = -_supply[u]; |
---|
947 | _forward[u] = false; |
---|
948 | _pi[u] = max_cost; |
---|
949 | } |
---|
950 | _cost[e] = max_cost; |
---|
951 | _cap[e] = max_cap; |
---|
952 | _state[e] = STATE_TREE; |
---|
953 | } |
---|
954 | |
---|
955 | return true; |
---|
956 | } |
---|
957 | |
---|
958 | // Find the join node |
---|
959 | void findJoinNode() { |
---|
960 | int u = _source[_in_arc]; |
---|
961 | int v = _target[_in_arc]; |
---|
962 | while (_depth[u] > _depth[v]) u = _parent[u]; |
---|
963 | while (_depth[v] > _depth[u]) v = _parent[v]; |
---|
964 | while (u != v) { |
---|
965 | u = _parent[u]; |
---|
966 | v = _parent[v]; |
---|
967 | } |
---|
968 | join = u; |
---|
969 | } |
---|
970 | |
---|
971 | // Find the leaving arc of the cycle and returns true if the |
---|
972 | // leaving arc is not the same as the entering arc |
---|
973 | bool findLeavingArc() { |
---|
974 | // Initialize first and second nodes according to the direction |
---|
975 | // of the cycle |
---|
976 | if (_state[_in_arc] == STATE_LOWER) { |
---|
977 | first = _source[_in_arc]; |
---|
978 | second = _target[_in_arc]; |
---|
979 | } else { |
---|
980 | first = _target[_in_arc]; |
---|
981 | second = _source[_in_arc]; |
---|
982 | } |
---|
983 | delta = _cap[_in_arc]; |
---|
984 | int result = 0; |
---|
985 | Capacity d; |
---|
986 | int e; |
---|
987 | |
---|
988 | // Search the cycle along the path form the first node to the root |
---|
989 | for (int u = first; u != join; u = _parent[u]) { |
---|
990 | e = _pred[u]; |
---|
991 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
992 | if (d < delta) { |
---|
993 | delta = d; |
---|
994 | u_out = u; |
---|
995 | result = 1; |
---|
996 | } |
---|
997 | } |
---|
998 | // Search the cycle along the path form the second node to the root |
---|
999 | for (int u = second; u != join; u = _parent[u]) { |
---|
1000 | e = _pred[u]; |
---|
1001 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
1002 | if (d <= delta) { |
---|
1003 | delta = d; |
---|
1004 | u_out = u; |
---|
1005 | result = 2; |
---|
1006 | } |
---|
1007 | } |
---|
1008 | |
---|
1009 | if (result == 1) { |
---|
1010 | u_in = first; |
---|
1011 | v_in = second; |
---|
1012 | } else { |
---|
1013 | u_in = second; |
---|
1014 | v_in = first; |
---|
1015 | } |
---|
1016 | return result != 0; |
---|
1017 | } |
---|
1018 | |
---|
1019 | // Change _flow and _state vectors |
---|
1020 | void changeFlow(bool change) { |
---|
1021 | // Augment along the cycle |
---|
1022 | if (delta > 0) { |
---|
1023 | Capacity val = _state[_in_arc] * delta; |
---|
1024 | _flow[_in_arc] += val; |
---|
1025 | for (int u = _source[_in_arc]; u != join; u = _parent[u]) { |
---|
1026 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
1027 | } |
---|
1028 | for (int u = _target[_in_arc]; u != join; u = _parent[u]) { |
---|
1029 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
1030 | } |
---|
1031 | } |
---|
1032 | // Update the state of the entering and leaving arcs |
---|
1033 | if (change) { |
---|
1034 | _state[_in_arc] = STATE_TREE; |
---|
1035 | _state[_pred[u_out]] = |
---|
1036 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
1037 | } else { |
---|
1038 | _state[_in_arc] = -_state[_in_arc]; |
---|
1039 | } |
---|
1040 | } |
---|
1041 | |
---|
1042 | // Update _thread and _parent vectors |
---|
1043 | void updateThreadParent() { |
---|
1044 | int u; |
---|
1045 | v_out = _parent[u_out]; |
---|
1046 | |
---|
1047 | // Handle the case when join and v_out coincide |
---|
1048 | bool par_first = false; |
---|
1049 | if (join == v_out) { |
---|
1050 | for (u = join; u != u_in && u != v_in; u = _thread[u]) ; |
---|
1051 | if (u == v_in) { |
---|
1052 | par_first = true; |
---|
1053 | while (_thread[u] != u_out) u = _thread[u]; |
---|
1054 | first = u; |
---|
1055 | } |
---|
1056 | } |
---|
1057 | |
---|
1058 | // Find the last successor of u_in (u) and the node after it (right) |
---|
1059 | // according to the thread index |
---|
1060 | for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ; |
---|
1061 | right = _thread[u]; |
---|
1062 | if (_thread[v_in] == u_out) { |
---|
1063 | for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ; |
---|
1064 | if (last == u_out) last = _thread[last]; |
---|
1065 | } |
---|
1066 | else last = _thread[v_in]; |
---|
1067 | |
---|
1068 | // Update stem nodes |
---|
1069 | _thread[v_in] = stem = u_in; |
---|
1070 | par_stem = v_in; |
---|
1071 | while (stem != u_out) { |
---|
1072 | _thread[u] = new_stem = _parent[stem]; |
---|
1073 | |
---|
1074 | // Find the node just before the stem node (u) according to |
---|
1075 | // the original thread index |
---|
1076 | for (u = new_stem; _thread[u] != stem; u = _thread[u]) ; |
---|
1077 | _thread[u] = right; |
---|
1078 | |
---|
1079 | // Change the parent node of stem and shift stem and par_stem nodes |
---|
1080 | _parent[stem] = par_stem; |
---|
1081 | par_stem = stem; |
---|
1082 | stem = new_stem; |
---|
1083 | |
---|
1084 | // Find the last successor of stem (u) and the node after it (right) |
---|
1085 | // according to the thread index |
---|
1086 | for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ; |
---|
1087 | right = _thread[u]; |
---|
1088 | } |
---|
1089 | _parent[u_out] = par_stem; |
---|
1090 | _thread[u] = last; |
---|
1091 | |
---|
1092 | if (join == v_out && par_first) { |
---|
1093 | if (first != v_in) _thread[first] = right; |
---|
1094 | } else { |
---|
1095 | for (u = v_out; _thread[u] != u_out; u = _thread[u]) ; |
---|
1096 | _thread[u] = right; |
---|
1097 | } |
---|
1098 | } |
---|
1099 | |
---|
1100 | // Update _pred and _forward vectors |
---|
1101 | void updatePredArc() { |
---|
1102 | int u = u_out, v; |
---|
1103 | while (u != u_in) { |
---|
1104 | v = _parent[u]; |
---|
1105 | _pred[u] = _pred[v]; |
---|
1106 | _forward[u] = !_forward[v]; |
---|
1107 | u = v; |
---|
1108 | } |
---|
1109 | _pred[u_in] = _in_arc; |
---|
1110 | _forward[u_in] = (u_in == _source[_in_arc]); |
---|
1111 | } |
---|
1112 | |
---|
1113 | // Update _depth and _potential vectors |
---|
1114 | void updateDepthPotential() { |
---|
1115 | _depth[u_in] = _depth[v_in] + 1; |
---|
1116 | Cost sigma = _forward[u_in] ? |
---|
1117 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
1118 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
1119 | _pi[u_in] += sigma; |
---|
1120 | for(int u = _thread[u_in]; _parent[u] != -1; u = _thread[u]) { |
---|
1121 | _depth[u] = _depth[_parent[u]] + 1; |
---|
1122 | if (_depth[u] <= _depth[u_in]) break; |
---|
1123 | _pi[u] += sigma; |
---|
1124 | } |
---|
1125 | } |
---|
1126 | |
---|
1127 | // Execute the algorithm |
---|
1128 | bool start(PivotRuleEnum pivot_rule) { |
---|
1129 | // Select the pivot rule implementation |
---|
1130 | switch (pivot_rule) { |
---|
1131 | case FIRST_ELIGIBLE_PIVOT: |
---|
1132 | return start<FirstEligiblePivotRule>(); |
---|
1133 | case BEST_ELIGIBLE_PIVOT: |
---|
1134 | return start<BestEligiblePivotRule>(); |
---|
1135 | case BLOCK_SEARCH_PIVOT: |
---|
1136 | return start<BlockSearchPivotRule>(); |
---|
1137 | case CANDIDATE_LIST_PIVOT: |
---|
1138 | return start<CandidateListPivotRule>(); |
---|
1139 | case ALTERING_LIST_PIVOT: |
---|
1140 | return start<AlteringListPivotRule>(); |
---|
1141 | } |
---|
1142 | return false; |
---|
1143 | } |
---|
1144 | |
---|
1145 | template<class PivotRuleImplementation> |
---|
1146 | bool start() { |
---|
1147 | PivotRuleImplementation pivot(*this); |
---|
1148 | |
---|
1149 | // Execute the network simplex algorithm |
---|
1150 | while (pivot.findEnteringArc()) { |
---|
1151 | findJoinNode(); |
---|
1152 | bool change = findLeavingArc(); |
---|
1153 | changeFlow(change); |
---|
1154 | if (change) { |
---|
1155 | updateThreadParent(); |
---|
1156 | updatePredArc(); |
---|
1157 | updateDepthPotential(); |
---|
1158 | } |
---|
1159 | } |
---|
1160 | |
---|
1161 | // Check if the flow amount equals zero on all the artificial arcs |
---|
1162 | for (int e = _arc_num; e != _arc_num + _node_num; ++e) { |
---|
1163 | if (_flow[e] > 0) return false; |
---|
1164 | } |
---|
1165 | |
---|
1166 | // Copy flow values to _flow_result |
---|
1167 | if (_orig_lower) { |
---|
1168 | for (int i = 0; i != _arc_num; ++i) { |
---|
1169 | Arc e = _arc[i]; |
---|
1170 | (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i]; |
---|
1171 | } |
---|
1172 | } else { |
---|
1173 | for (int i = 0; i != _arc_num; ++i) { |
---|
1174 | (*_flow_result)[_arc[i]] = _flow[i]; |
---|
1175 | } |
---|
1176 | } |
---|
1177 | // Copy potential values to _potential_result |
---|
1178 | for (int i = 0; i != _node_num; ++i) { |
---|
1179 | (*_potential_result)[_node[i]] = _pi[i]; |
---|
1180 | } |
---|
1181 | |
---|
1182 | return true; |
---|
1183 | } |
---|
1184 | |
---|
1185 | }; //class NetworkSimplex |
---|
1186 | |
---|
1187 | ///@} |
---|
1188 | |
---|
1189 | } //namespace lemon |
---|
1190 | |
---|
1191 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|