1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_COST_SCALING_H |
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20 | #define LEMON_COST_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 Cost scaling algorithm for finding a minimum cost flow. |
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26 | |
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27 | #include <deque> |
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28 | #include <lemon/graph_adaptor.h> |
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29 | #include <lemon/graph_utils.h> |
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30 | #include <lemon/maps.h> |
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31 | #include <lemon/math.h> |
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32 | |
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33 | #include <lemon/circulation.h> |
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34 | #include <lemon/bellman_ford.h> |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | /// \addtogroup min_cost_flow |
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39 | /// @{ |
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40 | |
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41 | /// \brief Implementation of the cost scaling algorithm for finding a |
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42 | /// minimum cost flow. |
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43 | /// |
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44 | /// \ref CostScaling implements the cost scaling algorithm performing |
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45 | /// generalized push-relabel operations for finding a minimum cost |
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46 | /// flow. |
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47 | /// |
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48 | /// \tparam Graph The directed graph type the algorithm runs on. |
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49 | /// \tparam LowerMap The type of the lower bound map. |
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50 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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51 | /// \tparam CostMap The type of the cost (length) map. |
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52 | /// \tparam SupplyMap The type of the supply map. |
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53 | /// |
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54 | /// \warning |
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55 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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56 | /// - Supply values should be \e signed \e integers. |
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57 | /// - The value types of the maps should be convertible to each other. |
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58 | /// - \c CostMap::Value must be signed type. |
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59 | /// |
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60 | /// \note Edge costs are multiplied with the number of nodes during |
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61 | /// the algorithm so overflow problems may arise more easily than with |
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62 | /// other minimum cost flow algorithms. |
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63 | /// If it is available, <tt>long long int</tt> type is used instead of |
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64 | /// <tt>long int</tt> in the inside computations. |
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65 | /// |
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66 | /// \author Peter Kovacs |
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67 | template < typename Graph, |
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68 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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69 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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70 | typename CostMap = typename Graph::template EdgeMap<int>, |
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71 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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72 | class CostScaling |
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73 | { |
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74 | GRAPH_TYPEDEFS(typename Graph); |
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75 | |
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76 | typedef typename CapacityMap::Value Capacity; |
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77 | typedef typename CostMap::Value Cost; |
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78 | typedef typename SupplyMap::Value Supply; |
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79 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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80 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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81 | |
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82 | typedef ResGraphAdaptor< const Graph, Capacity, |
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83 | CapacityEdgeMap, CapacityEdgeMap > ResGraph; |
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84 | typedef typename ResGraph::Edge ResEdge; |
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85 | |
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86 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
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87 | typedef long long int LCost; |
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88 | #else |
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89 | typedef long int LCost; |
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90 | #endif |
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91 | typedef typename Graph::template EdgeMap<LCost> LargeCostMap; |
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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 Graph::template EdgeMap<Capacity> FlowMap; |
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97 | /// The type of the potential map. |
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98 | typedef typename Graph::template NodeMap<LCost> PotentialMap; |
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99 | |
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100 | private: |
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101 | |
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102 | /// \brief Map adaptor class for handling residual edge costs. |
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103 | /// |
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104 | /// Map adaptor class for handling residual edge costs. |
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105 | template <typename Map> |
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106 | class ResidualCostMap : public MapBase<ResEdge, typename Map::Value> |
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107 | { |
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108 | private: |
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109 | |
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110 | const Map &_cost_map; |
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111 | |
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112 | public: |
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113 | |
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114 | ///\e |
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115 | ResidualCostMap(const Map &cost_map) : |
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116 | _cost_map(cost_map) {} |
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117 | |
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118 | ///\e |
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119 | typename Map::Value operator[](const ResEdge &e) const { |
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120 | return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
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121 | } |
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122 | |
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123 | }; //class ResidualCostMap |
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124 | |
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125 | /// \brief Map adaptor class for handling reduced edge costs. |
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126 | /// |
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127 | /// Map adaptor class for handling reduced edge costs. |
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128 | class ReducedCostMap : public MapBase<Edge, LCost> |
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129 | { |
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130 | private: |
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131 | |
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132 | const Graph &_gr; |
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133 | const LargeCostMap &_cost_map; |
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134 | const PotentialMap &_pot_map; |
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135 | |
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136 | public: |
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137 | |
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138 | ///\e |
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139 | ReducedCostMap( const Graph &gr, |
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140 | const LargeCostMap &cost_map, |
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141 | const PotentialMap &pot_map ) : |
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142 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
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143 | |
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144 | ///\e |
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145 | LCost operator[](const Edge &e) const { |
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146 | return _cost_map[e] + _pot_map[_gr.source(e)] |
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147 | - _pot_map[_gr.target(e)]; |
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148 | } |
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149 | |
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150 | }; //class ReducedCostMap |
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151 | |
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152 | private: |
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153 | |
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154 | // Scaling factor |
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155 | static const int ALPHA = 4; |
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156 | |
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157 | // Paramters for heuristics |
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158 | static const int BF_HEURISTIC_EPSILON_BOUND = 5000; |
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159 | static const int BF_HEURISTIC_BOUND_FACTOR = 3; |
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160 | |
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161 | private: |
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162 | |
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163 | // The directed graph the algorithm runs on |
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164 | const Graph &_graph; |
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165 | // The original lower bound map |
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166 | const LowerMap *_lower; |
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167 | // The modified capacity map |
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168 | CapacityEdgeMap _capacity; |
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169 | // The original cost map |
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170 | const CostMap &_orig_cost; |
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171 | // The scaled cost map |
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172 | LargeCostMap _cost; |
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173 | // The modified supply map |
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174 | SupplyNodeMap _supply; |
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175 | bool _valid_supply; |
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176 | |
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177 | // Edge map of the current flow |
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178 | FlowMap *_flow; |
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179 | bool _local_flow; |
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180 | // Node map of the current potentials |
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181 | PotentialMap *_potential; |
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182 | bool _local_potential; |
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183 | |
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184 | // The residual cost map |
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185 | ResidualCostMap<LargeCostMap> _res_cost; |
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186 | // The residual graph |
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187 | ResGraph *_res_graph; |
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188 | // The reduced cost map |
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189 | ReducedCostMap *_red_cost; |
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190 | // The excess map |
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191 | SupplyNodeMap _excess; |
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192 | // The epsilon parameter used for cost scaling |
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193 | LCost _epsilon; |
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194 | |
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195 | public: |
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196 | |
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197 | /// \brief General constructor (with lower bounds). |
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198 | /// |
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199 | /// General constructor (with lower bounds). |
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200 | /// |
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201 | /// \param graph The directed graph the algorithm runs on. |
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202 | /// \param lower The lower bounds of the edges. |
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203 | /// \param capacity The capacities (upper bounds) of the edges. |
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204 | /// \param cost The cost (length) values of the edges. |
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205 | /// \param supply The supply values of the nodes (signed). |
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206 | CostScaling( const Graph &graph, |
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207 | const LowerMap &lower, |
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208 | const CapacityMap &capacity, |
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209 | const CostMap &cost, |
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210 | const SupplyMap &supply ) : |
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211 | _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost), |
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212 | _cost(graph), _supply(graph), _flow(NULL), _local_flow(false), |
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213 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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214 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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215 | { |
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216 | // Removing non-zero lower bounds |
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217 | _capacity = subMap(capacity, lower); |
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218 | Supply sum = 0; |
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219 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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220 | Supply s = supply[n]; |
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221 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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222 | s += lower[e]; |
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223 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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224 | s -= lower[e]; |
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225 | _supply[n] = s; |
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226 | sum += s; |
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227 | } |
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228 | _valid_supply = sum == 0; |
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229 | } |
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230 | |
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231 | /// \brief General constructor (without lower bounds). |
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232 | /// |
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233 | /// General constructor (without lower bounds). |
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234 | /// |
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235 | /// \param graph The directed graph the algorithm runs on. |
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236 | /// \param capacity The capacities (upper bounds) of the edges. |
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237 | /// \param cost The cost (length) values of the edges. |
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238 | /// \param supply The supply values of the nodes (signed). |
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239 | CostScaling( const Graph &graph, |
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240 | const CapacityMap &capacity, |
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241 | const CostMap &cost, |
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242 | const SupplyMap &supply ) : |
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243 | _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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244 | _cost(graph), _supply(supply), _flow(NULL), _local_flow(false), |
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245 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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246 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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247 | { |
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248 | // Checking the sum of supply values |
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249 | Supply sum = 0; |
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250 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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251 | _valid_supply = sum == 0; |
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252 | } |
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253 | |
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254 | /// \brief Simple constructor (with lower bounds). |
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255 | /// |
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256 | /// Simple constructor (with lower bounds). |
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257 | /// |
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258 | /// \param graph The directed graph the algorithm runs on. |
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259 | /// \param lower The lower bounds of the edges. |
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260 | /// \param capacity The capacities (upper bounds) of the edges. |
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261 | /// \param cost The cost (length) values of the edges. |
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262 | /// \param s The source node. |
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263 | /// \param t The target node. |
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264 | /// \param flow_value The required amount of flow from node \c s |
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265 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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266 | CostScaling( const Graph &graph, |
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267 | const LowerMap &lower, |
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268 | const CapacityMap &capacity, |
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269 | const CostMap &cost, |
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270 | Node s, Node t, |
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271 | Supply flow_value ) : |
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272 | _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost), |
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273 | _cost(graph), _supply(graph), _flow(NULL), _local_flow(false), |
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274 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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275 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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276 | { |
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277 | // Removing nonzero lower bounds |
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278 | _capacity = subMap(capacity, lower); |
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279 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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280 | Supply sum = 0; |
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281 | if (n == s) sum = flow_value; |
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282 | if (n == t) sum = -flow_value; |
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283 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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284 | sum += lower[e]; |
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285 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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286 | sum -= lower[e]; |
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287 | _supply[n] = sum; |
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288 | } |
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289 | _valid_supply = true; |
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290 | } |
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291 | |
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292 | /// \brief Simple constructor (without lower bounds). |
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293 | /// |
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294 | /// Simple constructor (without lower bounds). |
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295 | /// |
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296 | /// \param graph The directed graph the algorithm runs on. |
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297 | /// \param capacity The capacities (upper bounds) of the edges. |
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298 | /// \param cost The cost (length) values of the edges. |
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299 | /// \param s The source node. |
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300 | /// \param t The target node. |
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301 | /// \param flow_value The required amount of flow from node \c s |
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302 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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303 | CostScaling( const Graph &graph, |
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304 | const CapacityMap &capacity, |
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305 | const CostMap &cost, |
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306 | Node s, Node t, |
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307 | Supply flow_value ) : |
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308 | _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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309 | _cost(graph), _supply(graph, 0), _flow(NULL), _local_flow(false), |
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310 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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311 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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312 | { |
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313 | _supply[s] = flow_value; |
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314 | _supply[t] = -flow_value; |
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315 | _valid_supply = true; |
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316 | } |
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317 | |
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318 | /// Destructor. |
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319 | ~CostScaling() { |
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320 | if (_local_flow) delete _flow; |
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321 | if (_local_potential) delete _potential; |
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322 | delete _res_graph; |
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323 | delete _red_cost; |
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324 | } |
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325 | |
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326 | /// \brief Set the flow map. |
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327 | /// |
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328 | /// Set the flow map. |
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329 | /// |
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330 | /// \return \c (*this) |
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331 | CostScaling& flowMap(FlowMap &map) { |
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332 | if (_local_flow) { |
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333 | delete _flow; |
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334 | _local_flow = false; |
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335 | } |
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336 | _flow = ↦ |
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337 | return *this; |
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338 | } |
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339 | |
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340 | /// \brief Set the potential map. |
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341 | /// |
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342 | /// Set the potential map. |
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343 | /// |
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344 | /// \return \c (*this) |
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345 | CostScaling& potentialMap(PotentialMap &map) { |
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346 | if (_local_potential) { |
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347 | delete _potential; |
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348 | _local_potential = false; |
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349 | } |
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350 | _potential = ↦ |
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351 | return *this; |
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352 | } |
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353 | |
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354 | /// \name Execution control |
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355 | |
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356 | /// @{ |
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357 | |
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358 | /// \brief Run the algorithm. |
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359 | /// |
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360 | /// Run the algorithm. |
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361 | /// |
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362 | /// \return \c true if a feasible flow can be found. |
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363 | bool run() { |
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364 | return init() && start(); |
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365 | } |
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366 | |
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367 | /// @} |
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368 | |
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369 | /// \name Query Functions |
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370 | /// The result of the algorithm can be obtained using these |
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371 | /// functions.\n |
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372 | /// \ref lemon::CostScaling::run() "run()" must be called before |
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373 | /// using them. |
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374 | |
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375 | /// @{ |
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376 | |
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377 | /// \brief Return a const reference to the edge map storing the |
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378 | /// found flow. |
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379 | /// |
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380 | /// Return a const reference to the edge map storing the found flow. |
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381 | /// |
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382 | /// \pre \ref run() must be called before using this function. |
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383 | const FlowMap& flowMap() const { |
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384 | return *_flow; |
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385 | } |
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386 | |
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387 | /// \brief Return a const reference to the node map storing the |
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388 | /// found potentials (the dual solution). |
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389 | /// |
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390 | /// Return a const reference to the node map storing the found |
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391 | /// potentials (the dual solution). |
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392 | /// |
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393 | /// \pre \ref run() must be called before using this function. |
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394 | const PotentialMap& potentialMap() const { |
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395 | return *_potential; |
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396 | } |
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397 | |
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398 | /// \brief Return the flow on the given edge. |
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399 | /// |
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400 | /// Return the flow on the given edge. |
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401 | /// |
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402 | /// \pre \ref run() must be called before using this function. |
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403 | Capacity flow(const Edge& edge) const { |
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404 | return (*_flow)[edge]; |
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405 | } |
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406 | |
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407 | /// \brief Return the potential of the given node. |
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408 | /// |
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409 | /// Return the potential of the given node. |
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410 | /// |
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411 | /// \pre \ref run() must be called before using this function. |
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412 | Cost potential(const Node& node) const { |
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413 | return (*_potential)[node]; |
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414 | } |
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415 | |
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416 | /// \brief Return the total cost of the found flow. |
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417 | /// |
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418 | /// Return the total cost of the found flow. The complexity of the |
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419 | /// function is \f$ O(e) \f$. |
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420 | /// |
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421 | /// \pre \ref run() must be called before using this function. |
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422 | Cost totalCost() const { |
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423 | Cost c = 0; |
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424 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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425 | c += (*_flow)[e] * _orig_cost[e]; |
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426 | return c; |
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427 | } |
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428 | |
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429 | /// @} |
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430 | |
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431 | private: |
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432 | |
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433 | /// Initialize the algorithm. |
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434 | bool init() { |
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435 | if (!_valid_supply) return false; |
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436 | |
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437 | // Initializing flow and potential maps |
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438 | if (!_flow) { |
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439 | _flow = new FlowMap(_graph); |
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440 | _local_flow = true; |
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441 | } |
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442 | if (!_potential) { |
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443 | _potential = new PotentialMap(_graph); |
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444 | _local_potential = true; |
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445 | } |
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446 | |
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447 | _red_cost = new ReducedCostMap(_graph, _cost, *_potential); |
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448 | _res_graph = new ResGraph(_graph, _capacity, *_flow); |
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449 | |
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450 | // Initializing the scaled cost map and the epsilon parameter |
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451 | Cost max_cost = 0; |
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452 | int node_num = countNodes(_graph); |
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453 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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454 | _cost[e] = LCost(_orig_cost[e]) * node_num * ALPHA; |
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455 | if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e]; |
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456 | } |
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457 | _epsilon = max_cost * node_num; |
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458 | |
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459 | // Finding a feasible flow using Circulation |
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460 | Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap, |
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461 | SupplyMap > |
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462 | circulation( _graph, constMap<Edge>(Capacity(0)), _capacity, |
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463 | _supply ); |
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464 | return circulation.flowMap(*_flow).run(); |
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465 | } |
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466 | |
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467 | |
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468 | /// Execute the algorithm. |
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469 | bool start() { |
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470 | std::deque<Node> active_nodes; |
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471 | typename Graph::template NodeMap<bool> hyper(_graph, false); |
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472 | |
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473 | int node_num = countNodes(_graph); |
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474 | for ( ; _epsilon >= 1; _epsilon = _epsilon < ALPHA && _epsilon > 1 ? |
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475 | 1 : _epsilon / ALPHA ) |
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476 | { |
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477 | // Performing price refinement heuristic using Bellman-Ford |
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478 | // algorithm |
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479 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
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480 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
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481 | ShiftCostMap shift_cost(_res_cost, _epsilon); |
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482 | BellmanFord<ResGraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
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483 | bf.init(0); |
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484 | bool done = false; |
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485 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
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486 | for (int i = 0; i < K && !done; ++i) |
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487 | done = bf.processNextWeakRound(); |
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488 | if (done) { |
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489 | for (NodeIt n(_graph); n != INVALID; ++n) |
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490 | (*_potential)[n] = bf.dist(n); |
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491 | continue; |
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492 | } |
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493 | } |
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494 | |
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495 | // Saturating edges not satisfying the optimality condition |
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496 | Capacity delta; |
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497 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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498 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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499 | delta = _capacity[e] - (*_flow)[e]; |
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500 | _excess[_graph.source(e)] -= delta; |
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501 | _excess[_graph.target(e)] += delta; |
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502 | (*_flow)[e] = _capacity[e]; |
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503 | } |
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504 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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505 | _excess[_graph.target(e)] -= (*_flow)[e]; |
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506 | _excess[_graph.source(e)] += (*_flow)[e]; |
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507 | (*_flow)[e] = 0; |
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508 | } |
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509 | } |
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510 | |
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511 | // Finding active nodes (i.e. nodes with positive excess) |
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512 | for (NodeIt n(_graph); n != INVALID; ++n) |
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513 | if (_excess[n] > 0) active_nodes.push_back(n); |
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514 | |
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515 | // Performing push and relabel operations |
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516 | while (active_nodes.size() > 0) { |
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517 | Node n = active_nodes[0], t; |
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518 | bool relabel_enabled = true; |
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519 | |
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520 | // Performing push operations if there are admissible edges |
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521 | if (_excess[n] > 0) { |
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522 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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523 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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524 | delta = _capacity[e] - (*_flow)[e] <= _excess[n] ? |
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525 | _capacity[e] - (*_flow)[e] : _excess[n]; |
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526 | t = _graph.target(e); |
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527 | |
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528 | // Push-look-ahead heuristic |
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529 | Capacity ahead = -_excess[t]; |
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530 | for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) { |
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531 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
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532 | ahead += _capacity[oe] - (*_flow)[oe]; |
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533 | } |
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534 | for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) { |
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535 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
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536 | ahead += (*_flow)[ie]; |
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537 | } |
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538 | if (ahead < 0) ahead = 0; |
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539 | |
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540 | // Pushing flow along the edge |
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541 | if (ahead < delta) { |
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542 | (*_flow)[e] += ahead; |
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543 | _excess[n] -= ahead; |
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544 | _excess[t] += ahead; |
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545 | active_nodes.push_front(t); |
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546 | hyper[t] = true; |
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547 | relabel_enabled = false; |
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548 | break; |
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549 | } else { |
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550 | (*_flow)[e] += delta; |
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551 | _excess[n] -= delta; |
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552 | _excess[t] += delta; |
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553 | if (_excess[t] > 0 && _excess[t] <= delta) |
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554 | active_nodes.push_back(t); |
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555 | } |
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556 | |
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557 | if (_excess[n] == 0) break; |
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558 | } |
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559 | } |
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560 | } |
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561 | |
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562 | if (_excess[n] > 0) { |
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563 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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564 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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565 | delta = (*_flow)[e] <= _excess[n] ? (*_flow)[e] : _excess[n]; |
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566 | t = _graph.source(e); |
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567 | |
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568 | // Push-look-ahead heuristic |
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569 | Capacity ahead = -_excess[t]; |
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570 | for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) { |
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571 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
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572 | ahead += _capacity[oe] - (*_flow)[oe]; |
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573 | } |
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574 | for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) { |
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575 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
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576 | ahead += (*_flow)[ie]; |
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577 | } |
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578 | if (ahead < 0) ahead = 0; |
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579 | |
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580 | // Pushing flow along the edge |
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581 | if (ahead < delta) { |
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582 | (*_flow)[e] -= ahead; |
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583 | _excess[n] -= ahead; |
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584 | _excess[t] += ahead; |
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585 | active_nodes.push_front(t); |
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586 | hyper[t] = true; |
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587 | relabel_enabled = false; |
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588 | break; |
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589 | } else { |
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590 | (*_flow)[e] -= delta; |
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591 | _excess[n] -= delta; |
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592 | _excess[t] += delta; |
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593 | if (_excess[t] > 0 && _excess[t] <= delta) |
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594 | active_nodes.push_back(t); |
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595 | } |
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596 | |
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597 | if (_excess[n] == 0) break; |
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598 | } |
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599 | } |
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600 | } |
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601 | |
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602 | if (relabel_enabled && (_excess[n] > 0 || hyper[n])) { |
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603 | // Performing relabel operation if the node is still active |
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604 | LCost min_red_cost = std::numeric_limits<LCost>::max(); |
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605 | for (OutEdgeIt oe(_graph, n); oe != INVALID; ++oe) { |
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606 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
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607 | (*_red_cost)[oe] < min_red_cost ) |
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608 | min_red_cost = (*_red_cost)[oe]; |
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609 | } |
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610 | for (InEdgeIt ie(_graph, n); ie != INVALID; ++ie) { |
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611 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
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612 | min_red_cost = -(*_red_cost)[ie]; |
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613 | } |
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614 | (*_potential)[n] -= min_red_cost + _epsilon; |
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615 | hyper[n] = false; |
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616 | } |
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617 | |
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618 | // Removing active nodes with non-positive excess |
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619 | while ( active_nodes.size() > 0 && |
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620 | _excess[active_nodes[0]] <= 0 && |
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621 | !hyper[active_nodes[0]] ) { |
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622 | active_nodes.pop_front(); |
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623 | } |
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624 | } |
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625 | } |
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626 | |
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627 | // Computing node potentials for the original costs |
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628 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
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629 | BellmanFord< ResGraph, ResidualCostMap<CostMap> > |
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630 | bf(*_res_graph, res_cost); |
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631 | bf.init(0); bf.start(); |
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632 | for (NodeIt n(_graph); n != INVALID; ++n) |
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633 | (*_potential)[n] = bf.dist(n); |
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634 | |
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635 | // Handling non-zero lower bounds |
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636 | if (_lower) { |
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637 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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638 | (*_flow)[e] += (*_lower)[e]; |
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639 | } |
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640 | return true; |
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641 | } |
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642 | |
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643 | }; //class CostScaling |
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644 | |
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645 | ///@} |
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646 | |
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647 | } //namespace lemon |
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648 | |
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649 | #endif //LEMON_COST_SCALING_H |
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