1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_CAPACITY_SCALING_H |
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20 | #define LEMON_CAPACITY_SCALING_H |
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21 | |
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22 | /// \ingroup min_cost_flow |
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23 | /// |
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24 | /// \file |
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25 | /// \brief The capacity scaling algorithm for finding a minimum cost |
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26 | /// flow. |
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27 | |
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28 | #include <vector> |
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29 | #include <lemon/graph_adaptor.h> |
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30 | #include <lemon/dijkstra.h> |
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31 | |
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32 | #define WITH_SCALING |
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33 | |
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34 | #ifdef WITH_SCALING |
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35 | #define SCALING_FACTOR 2 |
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36 | #endif |
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37 | |
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38 | //#define _DEBUG_ITER_ |
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39 | |
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40 | namespace lemon { |
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41 | |
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42 | /// \addtogroup min_cost_flow |
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43 | /// @{ |
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44 | |
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45 | /// \brief Implementation of the capacity scaling version of the |
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46 | /// successive shortest path algorithm for finding a minimum cost |
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47 | /// flow. |
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48 | /// |
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49 | /// \ref lemon::CapacityScaling "CapacityScaling" implements the |
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50 | /// capacity scaling version of the successive shortest path |
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51 | /// algorithm for finding a minimum cost flow. |
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52 | /// |
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53 | /// \param Graph The directed graph type the algorithm runs on. |
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54 | /// \param LowerMap The type of the lower bound map. |
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55 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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56 | /// \param CostMap The type of the cost (length) map. |
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57 | /// \param SupplyMap The type of the supply map. |
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58 | /// |
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59 | /// \warning |
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60 | /// - Edge capacities and costs should be nonnegative integers. |
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61 | /// However \c CostMap::Value should be signed type. |
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62 | /// - Supply values should be signed integers. |
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63 | /// - \c LowerMap::Value must be convertible to |
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64 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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65 | /// convertible to \c SupplyMap::Value. |
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66 | /// |
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67 | /// \author Peter Kovacs |
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68 | |
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69 | template < typename Graph, |
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70 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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71 | typename CapacityMap = LowerMap, |
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72 | typename CostMap = typename Graph::template EdgeMap<int>, |
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73 | typename SupplyMap = typename Graph::template NodeMap |
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74 | <typename CapacityMap::Value> > |
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75 | class CapacityScaling |
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76 | { |
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77 | typedef typename Graph::Node Node; |
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78 | typedef typename Graph::NodeIt NodeIt; |
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79 | typedef typename Graph::Edge Edge; |
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80 | typedef typename Graph::EdgeIt EdgeIt; |
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81 | typedef typename Graph::InEdgeIt InEdgeIt; |
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82 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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83 | |
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84 | typedef typename LowerMap::Value Lower; |
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85 | typedef typename CapacityMap::Value Capacity; |
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86 | typedef typename CostMap::Value Cost; |
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87 | typedef typename SupplyMap::Value Supply; |
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88 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
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89 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
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90 | |
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91 | typedef ResGraphAdaptor< const Graph, Capacity, |
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92 | CapacityRefMap, CapacityRefMap > ResGraph; |
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93 | typedef typename ResGraph::Node ResNode; |
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94 | typedef typename ResGraph::NodeIt ResNodeIt; |
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95 | typedef typename ResGraph::Edge ResEdge; |
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96 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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97 | |
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98 | public: |
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99 | |
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100 | /// \brief The type of the flow map. |
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101 | typedef CapacityRefMap FlowMap; |
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102 | /// \brief The type of the potential map. |
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103 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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104 | |
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105 | protected: |
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106 | |
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107 | /// \brief Map adaptor class for handling reduced edge costs. |
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108 | class ReducedCostMap : public MapBase<ResEdge, Cost> |
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109 | { |
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110 | private: |
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111 | |
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112 | const ResGraph &gr; |
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113 | const CostMap &cost_map; |
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114 | const PotentialMap &pot_map; |
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115 | |
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116 | public: |
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117 | |
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118 | ReducedCostMap( const ResGraph &_gr, |
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119 | const CostMap &_cost, |
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120 | const PotentialMap &_pot ) : |
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121 | gr(_gr), cost_map(_cost), pot_map(_pot) {} |
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122 | |
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123 | Cost operator[](const ResEdge &e) const { |
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124 | return ResGraph::forward(e) ? |
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125 | cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)] : |
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126 | -cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)]; |
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127 | } |
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128 | |
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129 | }; //class ReducedCostMap |
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130 | |
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131 | /// \brief Map class for the \ref lemon::Dijkstra "Dijkstra" |
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132 | /// algorithm to update node potentials. |
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133 | class PotentialUpdateMap : public MapBase<ResNode, Cost> |
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134 | { |
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135 | private: |
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136 | |
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137 | PotentialMap *pot; |
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138 | typedef std::pair<ResNode, Cost> Pair; |
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139 | std::vector<Pair> data; |
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140 | |
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141 | public: |
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142 | |
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143 | void potentialMap(PotentialMap &_pot) { |
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144 | pot = &_pot; |
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145 | } |
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146 | |
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147 | void init() { |
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148 | data.clear(); |
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149 | } |
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150 | |
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151 | void set(const ResNode &n, const Cost &v) { |
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152 | data.push_back(Pair(n, v)); |
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153 | } |
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154 | |
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155 | void update() { |
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156 | Cost val = data[data.size()-1].second; |
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157 | for (int i = 0; i < data.size()-1; ++i) |
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158 | (*pot)[data[i].first] += val - data[i].second; |
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159 | } |
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160 | |
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161 | }; //class PotentialUpdateMap |
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162 | |
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163 | #ifdef WITH_SCALING |
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164 | /// \brief Map adaptor class for identifing deficit nodes. |
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165 | class DeficitBoolMap : public MapBase<ResNode, bool> |
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166 | { |
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167 | private: |
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168 | |
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169 | const SupplyRefMap &imb; |
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170 | const Capacity δ |
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171 | |
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172 | public: |
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173 | |
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174 | DeficitBoolMap(const SupplyRefMap &_imb, const Capacity &_delta) : |
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175 | imb(_imb), delta(_delta) {} |
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176 | |
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177 | bool operator[](const ResNode &n) const { |
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178 | return imb[n] <= -delta; |
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179 | } |
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180 | |
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181 | }; //class DeficitBoolMap |
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182 | |
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183 | /// \brief Map adaptor class for filtering edges with at least |
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184 | /// \c delta residual capacity. |
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185 | class DeltaFilterMap : public MapBase<ResEdge, bool> |
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186 | { |
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187 | private: |
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188 | |
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189 | const ResGraph &gr; |
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190 | const Capacity δ |
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191 | |
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192 | public: |
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193 | |
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194 | DeltaFilterMap(const ResGraph &_gr, const Capacity &_delta) : |
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195 | gr(_gr), delta(_delta) {} |
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196 | |
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197 | bool operator[](const ResEdge &e) const { |
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198 | return gr.rescap(e) >= delta; |
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199 | } |
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200 | |
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201 | }; //class DeltaFilterMap |
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202 | |
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203 | typedef EdgeSubGraphAdaptor<const ResGraph, const DeltaFilterMap> |
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204 | DeltaResGraph; |
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205 | |
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206 | /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class. |
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207 | class ResDijkstraTraits : |
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208 | public DijkstraDefaultTraits<DeltaResGraph, ReducedCostMap> |
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209 | { |
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210 | public: |
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211 | |
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212 | typedef PotentialUpdateMap DistMap; |
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213 | |
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214 | static DistMap *createDistMap(const DeltaResGraph&) { |
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215 | return new DistMap(); |
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216 | } |
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217 | |
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218 | }; //class ResDijkstraTraits |
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219 | |
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220 | #else //WITHOUT_CAPACITY_SCALING |
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221 | /// \brief Map adaptor class for identifing deficit nodes. |
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222 | class DeficitBoolMap : public MapBase<ResNode, bool> |
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223 | { |
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224 | private: |
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225 | |
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226 | const SupplyRefMap &imb; |
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227 | |
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228 | public: |
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229 | |
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230 | DeficitBoolMap(const SupplyRefMap &_imb) : imb(_imb) {} |
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231 | |
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232 | bool operator[](const ResNode &n) const { |
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233 | return imb[n] < 0; |
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234 | } |
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235 | |
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236 | }; //class DeficitBoolMap |
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237 | |
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238 | /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class. |
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239 | class ResDijkstraTraits : |
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240 | public DijkstraDefaultTraits<ResGraph, ReducedCostMap> |
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241 | { |
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242 | public: |
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243 | |
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244 | typedef PotentialUpdateMap DistMap; |
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245 | |
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246 | static DistMap *createDistMap(const ResGraph&) { |
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247 | return new DistMap(); |
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248 | } |
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249 | |
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250 | }; //class ResDijkstraTraits |
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251 | #endif |
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252 | |
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253 | protected: |
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254 | |
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255 | /// \brief The directed graph the algorithm runs on. |
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256 | const Graph &graph; |
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257 | /// \brief The original lower bound map. |
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258 | const LowerMap *lower; |
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259 | /// \brief The modified capacity map. |
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260 | CapacityRefMap capacity; |
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261 | /// \brief The cost map. |
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262 | const CostMap &cost; |
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263 | /// \brief The modified supply map. |
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264 | SupplyRefMap supply; |
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265 | /// \brief The sum of supply values equals zero. |
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266 | bool valid_supply; |
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267 | |
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268 | /// \brief The edge map of the current flow. |
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269 | FlowMap flow; |
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270 | /// \brief The potential node map. |
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271 | PotentialMap potential; |
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272 | /// \brief The residual graph. |
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273 | ResGraph res_graph; |
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274 | /// \brief The reduced cost map. |
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275 | ReducedCostMap red_cost; |
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276 | |
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277 | /// \brief The imbalance map. |
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278 | SupplyRefMap imbalance; |
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279 | /// \brief The excess nodes. |
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280 | std::vector<ResNode> excess_nodes; |
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281 | /// \brief The index of the next excess node. |
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282 | int next_node; |
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283 | |
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284 | #ifdef WITH_SCALING |
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285 | typedef Dijkstra<DeltaResGraph, ReducedCostMap, ResDijkstraTraits> |
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286 | ResDijkstra; |
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287 | /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding |
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288 | /// shortest paths in the residual graph with respect to the |
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289 | /// reduced edge costs. |
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290 | ResDijkstra dijkstra; |
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291 | |
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292 | /// \brief The delta parameter used for capacity scaling. |
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293 | Capacity delta; |
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294 | /// \brief Edge filter map for filtering edges with at least |
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295 | /// \c delta residual capacity. |
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296 | DeltaFilterMap delta_filter; |
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297 | /// \brief The delta residual graph (i.e. the subgraph of the |
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298 | /// residual graph consisting of edges with at least \c delta |
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299 | /// residual capacity). |
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300 | DeltaResGraph dres_graph; |
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301 | /// \brief Map for identifing deficit nodes. |
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302 | DeficitBoolMap delta_deficit; |
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303 | |
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304 | /// \brief The deficit nodes. |
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305 | std::vector<ResNode> deficit_nodes; |
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306 | |
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307 | #else //WITHOUT_CAPACITY_SCALING |
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308 | typedef Dijkstra<ResGraph, ReducedCostMap, ResDijkstraTraits> |
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309 | ResDijkstra; |
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310 | /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding |
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311 | /// shortest paths in the residual graph with respect to the |
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312 | /// reduced edge costs. |
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313 | ResDijkstra dijkstra; |
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314 | /// \brief Map for identifing deficit nodes. |
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315 | DeficitBoolMap has_deficit; |
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316 | #endif |
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317 | |
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318 | /// \brief Pred map for the \ref lemon::Dijkstra "Dijkstra" class. |
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319 | typename ResDijkstra::PredMap pred; |
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320 | /// \brief Dist map for the \ref lemon::Dijkstra "Dijkstra" class to |
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321 | /// update node potentials. |
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322 | PotentialUpdateMap updater; |
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323 | |
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324 | public : |
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325 | |
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326 | /// \brief General constructor of the class (with lower bounds). |
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327 | /// |
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328 | /// General constructor of the class (with lower bounds). |
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329 | /// |
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330 | /// \param _graph The directed graph the algorithm runs on. |
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331 | /// \param _lower The lower bounds of the edges. |
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332 | /// \param _capacity The capacities (upper bounds) of the edges. |
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333 | /// \param _cost The cost (length) values of the edges. |
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334 | /// \param _supply The supply values of the nodes (signed). |
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335 | CapacityScaling( const Graph &_graph, |
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336 | const LowerMap &_lower, |
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337 | const CapacityMap &_capacity, |
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338 | const CostMap &_cost, |
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339 | const SupplyMap &_supply ) : |
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340 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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341 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
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342 | res_graph(_graph, capacity, flow), |
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343 | red_cost(res_graph, cost, potential), imbalance(_graph), |
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344 | #ifdef WITH_SCALING |
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345 | delta(0), delta_filter(res_graph, delta), |
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346 | dres_graph(res_graph, delta_filter), |
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347 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
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348 | delta_deficit(imbalance, delta) |
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349 | #else //WITHOUT_CAPACITY_SCALING |
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350 | dijkstra(res_graph, red_cost), pred(res_graph), |
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351 | has_deficit(imbalance) |
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352 | #endif |
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353 | { |
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354 | // Removing nonzero lower bounds |
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355 | capacity = subMap(_capacity, _lower); |
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356 | Supply sum = 0; |
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357 | for (NodeIt n(graph); n != INVALID; ++n) { |
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358 | Supply s = _supply[n]; |
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359 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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360 | s += _lower[e]; |
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361 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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362 | s -= _lower[e]; |
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363 | supply[n] = s; |
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364 | sum += s; |
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365 | } |
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366 | valid_supply = sum == 0; |
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367 | } |
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368 | |
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369 | /// \brief General constructor of the class (without lower bounds). |
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370 | /// |
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371 | /// General constructor of the class (without lower bounds). |
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372 | /// |
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373 | /// \param _graph The directed graph the algorithm runs on. |
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374 | /// \param _capacity The capacities (upper bounds) of the edges. |
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375 | /// \param _cost The cost (length) values of the edges. |
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376 | /// \param _supply The supply values of the nodes (signed). |
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377 | CapacityScaling( const Graph &_graph, |
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378 | const CapacityMap &_capacity, |
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379 | const CostMap &_cost, |
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380 | const SupplyMap &_supply ) : |
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381 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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382 | supply(_supply), flow(_graph, 0), potential(_graph, 0), |
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383 | res_graph(_graph, capacity, flow), |
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384 | red_cost(res_graph, cost, potential), imbalance(_graph), |
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385 | #ifdef WITH_SCALING |
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386 | delta(0), delta_filter(res_graph, delta), |
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387 | dres_graph(res_graph, delta_filter), |
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388 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
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389 | delta_deficit(imbalance, delta) |
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390 | #else //WITHOUT_CAPACITY_SCALING |
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391 | dijkstra(res_graph, red_cost), pred(res_graph), |
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392 | has_deficit(imbalance) |
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393 | #endif |
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394 | { |
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395 | // Checking the sum of supply values |
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396 | Supply sum = 0; |
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397 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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398 | valid_supply = sum == 0; |
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399 | } |
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400 | |
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401 | /// \brief Simple constructor of the class (with lower bounds). |
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402 | /// |
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403 | /// Simple constructor of the class (with lower bounds). |
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404 | /// |
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405 | /// \param _graph The directed graph the algorithm runs on. |
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406 | /// \param _lower The lower bounds of the edges. |
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407 | /// \param _capacity The capacities (upper bounds) of the edges. |
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408 | /// \param _cost The cost (length) values of the edges. |
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409 | /// \param _s The source node. |
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410 | /// \param _t The target node. |
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411 | /// \param _flow_value The required amount of flow from node \c _s |
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412 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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413 | /// \c _t). |
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414 | CapacityScaling( const Graph &_graph, |
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415 | const LowerMap &_lower, |
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416 | const CapacityMap &_capacity, |
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417 | const CostMap &_cost, |
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418 | Node _s, Node _t, |
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419 | Supply _flow_value ) : |
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420 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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421 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
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422 | res_graph(_graph, capacity, flow), |
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423 | red_cost(res_graph, cost, potential), imbalance(_graph), |
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424 | #ifdef WITH_SCALING |
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425 | delta(0), delta_filter(res_graph, delta), |
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426 | dres_graph(res_graph, delta_filter), |
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427 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
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428 | delta_deficit(imbalance, delta) |
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429 | #else //WITHOUT_CAPACITY_SCALING |
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430 | dijkstra(res_graph, red_cost), pred(res_graph), |
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431 | has_deficit(imbalance) |
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432 | #endif |
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433 | { |
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434 | // Removing nonzero lower bounds |
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435 | capacity = subMap(_capacity, _lower); |
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436 | for (NodeIt n(graph); n != INVALID; ++n) { |
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437 | Supply s = 0; |
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438 | if (n == _s) s = _flow_value; |
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439 | if (n == _t) s = -_flow_value; |
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440 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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441 | s += _lower[e]; |
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442 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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443 | s -= _lower[e]; |
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444 | supply[n] = s; |
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445 | } |
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446 | valid_supply = true; |
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447 | } |
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448 | |
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449 | /// \brief Simple constructor of the class (without lower bounds). |
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450 | /// |
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451 | /// Simple constructor of the class (without lower bounds). |
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452 | /// |
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453 | /// \param _graph The directed graph the algorithm runs on. |
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454 | /// \param _capacity The capacities (upper bounds) of the edges. |
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455 | /// \param _cost The cost (length) values of the edges. |
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456 | /// \param _s The source node. |
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457 | /// \param _t The target node. |
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458 | /// \param _flow_value The required amount of flow from node \c _s |
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459 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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460 | /// \c _t). |
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461 | CapacityScaling( const Graph &_graph, |
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462 | const CapacityMap &_capacity, |
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463 | const CostMap &_cost, |
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464 | Node _s, Node _t, |
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465 | Supply _flow_value ) : |
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466 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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467 | supply(_graph, 0), flow(_graph, 0), potential(_graph, 0), |
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468 | res_graph(_graph, capacity, flow), |
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469 | red_cost(res_graph, cost, potential), imbalance(_graph), |
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470 | #ifdef WITH_SCALING |
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471 | delta(0), delta_filter(res_graph, delta), |
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472 | dres_graph(res_graph, delta_filter), |
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473 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
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474 | delta_deficit(imbalance, delta) |
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475 | #else //WITHOUT_CAPACITY_SCALING |
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476 | dijkstra(res_graph, red_cost), pred(res_graph), |
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477 | has_deficit(imbalance) |
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478 | #endif |
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479 | { |
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480 | supply[_s] = _flow_value; |
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481 | supply[_t] = -_flow_value; |
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482 | valid_supply = true; |
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483 | } |
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484 | |
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485 | /// \brief Returns a const reference to the flow map. |
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486 | /// |
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487 | /// Returns a const reference to the flow map. |
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488 | /// |
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489 | /// \pre \ref run() must be called before using this function. |
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490 | const FlowMap& flowMap() const { |
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491 | return flow; |
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492 | } |
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493 | |
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494 | /// \brief Returns a const reference to the potential map (the dual |
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495 | /// solution). |
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496 | /// |
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497 | /// Returns a const reference to the potential map (the dual |
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498 | /// solution). |
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499 | /// |
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500 | /// \pre \ref run() must be called before using this function. |
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501 | const PotentialMap& potentialMap() const { |
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502 | return potential; |
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503 | } |
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504 | |
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505 | /// \brief Returns the total cost of the found flow. |
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506 | /// |
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507 | /// Returns the total cost of the found flow. The complexity of the |
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508 | /// function is \f$ O(e) \f$. |
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509 | /// |
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510 | /// \pre \ref run() must be called before using this function. |
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511 | Cost totalCost() const { |
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512 | Cost c = 0; |
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513 | for (EdgeIt e(graph); e != INVALID; ++e) |
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514 | c += flow[e] * cost[e]; |
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515 | return c; |
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516 | } |
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517 | |
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518 | /// \brief Runs the algorithm. |
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519 | /// |
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520 | /// Runs the algorithm. |
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521 | /// |
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522 | /// \return \c true if a feasible flow can be found. |
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523 | bool run() { |
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524 | return init() && start(); |
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525 | } |
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526 | |
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527 | protected: |
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528 | |
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529 | /// \brief Initializes the algorithm. |
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530 | bool init() { |
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531 | if (!valid_supply) return false; |
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532 | imbalance = supply; |
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533 | |
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534 | // Initalizing Dijkstra class |
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535 | updater.potentialMap(potential); |
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536 | dijkstra.distMap(updater).predMap(pred); |
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537 | |
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538 | #ifdef WITH_SCALING |
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539 | // Initilaizing delta value |
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540 | Supply max_sup = 0, max_dem = 0; |
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541 | for (NodeIt n(graph); n != INVALID; ++n) { |
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542 | if (supply[n] > max_sup) max_sup = supply[n]; |
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543 | if (supply[n] < -max_dem) max_dem = -supply[n]; |
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544 | } |
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545 | if (max_dem < max_sup) max_sup = max_dem; |
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546 | for ( delta = 1; SCALING_FACTOR * delta < max_sup; |
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547 | delta *= SCALING_FACTOR ) ; |
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548 | #endif |
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549 | return true; |
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550 | } |
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551 | |
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552 | #ifdef WITH_SCALING |
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553 | /// \brief Executes the capacity scaling version of the successive |
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554 | /// shortest path algorithm. |
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555 | bool start() { |
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556 | typedef typename DeltaResGraph::EdgeIt DeltaResEdgeIt; |
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557 | typedef typename DeltaResGraph::Edge DeltaResEdge; |
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558 | #ifdef _DEBUG_ITER_ |
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559 | int dijk_num = 0; |
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560 | #endif |
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561 | |
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562 | // Processing capacity scaling phases |
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563 | ResNode s, t; |
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564 | for ( ; delta >= 1; delta = delta < SCALING_FACTOR && delta > 1 ? |
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565 | 1 : delta / SCALING_FACTOR ) |
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566 | { |
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567 | // Saturating edges not satisfying the optimality condition |
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568 | Capacity r; |
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569 | for (DeltaResEdgeIt e(dres_graph); e != INVALID; ++e) { |
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570 | if (red_cost[e] < 0) { |
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571 | res_graph.augment(e, r = res_graph.rescap(e)); |
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572 | imbalance[dres_graph.source(e)] -= r; |
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573 | imbalance[dres_graph.target(e)] += r; |
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574 | } |
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575 | } |
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576 | |
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577 | // Finding excess nodes |
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578 | excess_nodes.clear(); |
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579 | deficit_nodes.clear(); |
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580 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
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581 | if (imbalance[n] >= delta) excess_nodes.push_back(n); |
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582 | if (imbalance[n] <= -delta) deficit_nodes.push_back(n); |
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583 | } |
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584 | next_node = 0; |
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585 | |
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586 | // Finding shortest paths |
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587 | while (next_node < excess_nodes.size()) { |
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588 | // Checking deficit nodes |
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589 | if (delta > 1) { |
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590 | bool delta_def = false; |
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591 | for (int i = 0; i < deficit_nodes.size(); ++i) { |
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592 | if (imbalance[deficit_nodes[i]] <= -delta) { |
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593 | delta_def = true; |
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594 | break; |
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595 | } |
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596 | } |
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597 | if (!delta_def) break; |
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598 | } |
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599 | |
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600 | // Running Dijkstra |
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601 | s = excess_nodes[next_node]; |
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602 | updater.init(); |
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603 | dijkstra.init(); |
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604 | dijkstra.addSource(s); |
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605 | #ifdef _DEBUG_ITER_ |
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606 | ++dijk_num; |
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607 | #endif |
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608 | if ((t = dijkstra.start(delta_deficit)) == INVALID) { |
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609 | if (delta > 1) { |
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610 | ++next_node; |
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611 | continue; |
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612 | } |
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613 | return false; |
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614 | } |
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615 | |
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616 | // Updating node potentials |
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617 | updater.update(); |
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618 | |
---|
619 | // Augment along a shortest path from s to t |
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620 | Capacity d = imbalance[s] < -imbalance[t] ? |
---|
621 | imbalance[s] : -imbalance[t]; |
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622 | ResNode u = t; |
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623 | ResEdge e; |
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624 | if (d > delta) { |
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625 | while ((e = pred[u]) != INVALID) { |
---|
626 | if (res_graph.rescap(e) < d) d = res_graph.rescap(e); |
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627 | u = dres_graph.source(e); |
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628 | } |
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629 | } |
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630 | u = t; |
---|
631 | while ((e = pred[u]) != INVALID) { |
---|
632 | res_graph.augment(e, d); |
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633 | u = dres_graph.source(e); |
---|
634 | } |
---|
635 | imbalance[s] -= d; |
---|
636 | imbalance[t] += d; |
---|
637 | if (imbalance[s] < delta) ++next_node; |
---|
638 | } |
---|
639 | } |
---|
640 | #ifdef _DEBUG_ITER_ |
---|
641 | std::cout << "Capacity Scaling algorithm finished with running Dijkstra algorithm " |
---|
642 | << dijk_num << " times." << std::endl; |
---|
643 | #endif |
---|
644 | |
---|
645 | // Handling nonzero lower bounds |
---|
646 | if (lower) { |
---|
647 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
648 | flow[e] += (*lower)[e]; |
---|
649 | } |
---|
650 | return true; |
---|
651 | } |
---|
652 | |
---|
653 | #else //WITHOUT_CAPACITY_SCALING |
---|
654 | /// \brief Executes the successive shortest path algorithm without |
---|
655 | /// capacity scaling. |
---|
656 | bool start() { |
---|
657 | // Finding excess nodes |
---|
658 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
---|
659 | if (imbalance[n] > 0) excess_nodes.push_back(n); |
---|
660 | } |
---|
661 | if (excess_nodes.size() == 0) return true; |
---|
662 | next_node = 0; |
---|
663 | |
---|
664 | // Finding shortest paths |
---|
665 | ResNode s, t; |
---|
666 | while ( imbalance[excess_nodes[next_node]] > 0 || |
---|
667 | ++next_node < excess_nodes.size() ) |
---|
668 | { |
---|
669 | // Running Dijkstra |
---|
670 | s = excess_nodes[next_node]; |
---|
671 | updater.init(); |
---|
672 | dijkstra.init(); |
---|
673 | dijkstra.addSource(s); |
---|
674 | if ((t = dijkstra.start(has_deficit)) == INVALID) |
---|
675 | return false; |
---|
676 | |
---|
677 | // Updating node potentials |
---|
678 | updater.update(); |
---|
679 | |
---|
680 | // Augmenting along a shortest path from s to t |
---|
681 | Capacity delta = imbalance[s] < -imbalance[t] ? |
---|
682 | imbalance[s] : -imbalance[t]; |
---|
683 | ResNode u = t; |
---|
684 | ResEdge e; |
---|
685 | while ((e = pred[u]) != INVALID) { |
---|
686 | if (res_graph.rescap(e) < delta) delta = res_graph.rescap(e); |
---|
687 | u = res_graph.source(e); |
---|
688 | } |
---|
689 | u = t; |
---|
690 | while ((e = pred[u]) != INVALID) { |
---|
691 | res_graph.augment(e, delta); |
---|
692 | u = res_graph.source(e); |
---|
693 | } |
---|
694 | imbalance[s] -= delta; |
---|
695 | imbalance[t] += delta; |
---|
696 | } |
---|
697 | |
---|
698 | // Handling nonzero lower bounds |
---|
699 | if (lower) { |
---|
700 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
701 | flow[e] += (*lower)[e]; |
---|
702 | } |
---|
703 | return true; |
---|
704 | } |
---|
705 | #endif |
---|
706 | |
---|
707 | }; //class CapacityScaling |
---|
708 | |
---|
709 | ///@} |
---|
710 | |
---|
711 | } //namespace lemon |
---|
712 | |
---|
713 | #endif //LEMON_CAPACITY_SCALING_H |
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