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_MIN_COST_MAX_FLOW_H |
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20 | #define LEMON_MIN_COST_MAX_FLOW_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 An efficient algorithm for finding a minimum cost maximum flow. |
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26 | |
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27 | #include <lemon/preflow.h> |
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28 | #include <lemon/network_simplex.h> |
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29 | #include <lemon/maps.h> |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | /// \addtogroup min_cost_flow |
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34 | /// @{ |
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35 | |
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36 | /// \brief An efficient algorithm for finding a minimum cost |
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37 | /// maximum flow. |
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38 | /// |
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39 | /// \ref MinCostMaxFlow implements an efficient algorithm for |
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40 | /// finding a maximum flow having minimal total cost from a given |
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41 | /// source node to a given target node in a directed graph. |
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42 | /// |
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43 | /// \ref MinCostMaxFlow uses \ref Preflow for finding the maximum |
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44 | /// flow value and \ref NetworkSimplex for finding a minimum cost |
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45 | /// flow of that value. |
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46 | /// According to our benchmark tests \ref Preflow is generally the |
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47 | /// most efficient algorithm for the maximum flow problem and |
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48 | /// \ref NetworkSimplex is the most efficient for the minimum cost |
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49 | /// flow problem in LEMON. |
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50 | /// |
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51 | /// \tparam Graph The directed graph type the algorithm runs on. |
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52 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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53 | /// \tparam CostMap The type of the cost (length) map. |
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54 | /// |
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55 | /// \warning |
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56 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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57 | /// However \c CostMap::Value must be signed type. |
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58 | /// - \c CapacityMap::Value must be convertible to \c CostMap::Value. |
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59 | /// |
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60 | /// \author Peter Kovacs |
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61 | |
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62 | template < typename Graph, |
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63 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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64 | typename CostMap = typename Graph::template EdgeMap<int> > |
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65 | class MinCostMaxFlow |
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66 | { |
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67 | typedef typename Graph::Node Node; |
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68 | typedef typename Graph::Edge Edge; |
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69 | |
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70 | typedef typename CapacityMap::Value Capacity; |
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71 | typedef typename CostMap::Value Cost; |
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72 | typedef typename Graph::template NodeMap<Cost> SupplyMap; |
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73 | |
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74 | typedef Preflow<Graph, CapacityMap> MaxFlowImpl; |
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75 | typedef NetworkSimplex< Graph, CapacityMap, CapacityMap, |
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76 | CostMap, SupplyMap > MinCostFlowImpl; |
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77 | |
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78 | public: |
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79 | |
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80 | /// The type of the flow map. |
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81 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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82 | /// The type of the potential map. |
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83 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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84 | |
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85 | private: |
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86 | |
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87 | // The directed graph the algorithm runs on |
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88 | const Graph &_graph; |
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89 | // The modified capacity map |
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90 | const CapacityMap &_capacity; |
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91 | // The cost map |
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92 | const CostMap &_cost; |
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93 | |
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94 | // Edge map of the found flow |
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95 | FlowMap _flow; |
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96 | // Node map of the found potentials |
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97 | PotentialMap _potential; |
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98 | |
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99 | // The source node |
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100 | Node _source; |
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101 | // The target node |
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102 | Node _target; |
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103 | |
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104 | public: |
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105 | |
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106 | /// \brief The constructor of the class. |
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107 | /// |
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108 | /// The constructor of the class. |
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109 | /// |
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110 | /// \param _graph The directed graph the algorithm runs on. |
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111 | /// \param _capacity The capacities (upper bounds) of the edges. |
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112 | /// \param _cost The cost (length) values of the edges. |
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113 | /// \param _s The source node. |
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114 | /// \param _t The target node. |
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115 | MinCostMaxFlow( const Graph &graph, |
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116 | const CapacityMap &capacity, |
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117 | const CostMap &cost, |
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118 | Node s, Node t ) : |
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119 | _graph(graph), _capacity(capacity), _cost(cost), _flow(graph), |
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120 | _potential(graph), _source(s), _target(t) |
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121 | {} |
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122 | |
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123 | /// \brief Runs the algorithm. |
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124 | /// |
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125 | /// Runs the algorithm. |
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126 | void run() { |
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127 | MaxFlowImpl preflow(_graph, _capacity, _source, _target); |
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128 | preflow.flowMap(_flow).runMinCut(); |
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129 | MinCostFlowImpl mcf( _graph, _capacity, _cost, |
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130 | _source, _target, preflow.flowValue() ); |
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131 | mcf.run(); |
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132 | _flow = mcf.flowMap(); |
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133 | _potential = mcf.potentialMap(); |
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134 | } |
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135 | |
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136 | /// \brief Returns a const reference to the edge map storing the |
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137 | /// found flow. |
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138 | /// |
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139 | /// Returns a const reference to the edge map storing the found flow. |
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140 | /// |
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141 | /// \pre \ref run() must be called before using this function. |
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142 | const FlowMap& flowMap() const { |
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143 | return _flow_result; |
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144 | } |
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145 | |
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146 | /// \brief Returns a const reference to the node map storing the |
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147 | /// found potentials (the dual solution). |
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148 | /// |
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149 | /// Returns a const reference to the node map storing the found |
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150 | /// potentials (the dual solution). |
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151 | /// |
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152 | /// \pre \ref run() must be called before using this function. |
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153 | const PotentialMap& potentialMap() const { |
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154 | return _potential_result; |
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155 | } |
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156 | |
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157 | /// \brief Returns the total cost of the found flow. |
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158 | /// |
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159 | /// Returns the total cost of the found flow. The complexity of the |
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160 | /// function is \f$ O(e) \f$. |
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161 | /// |
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162 | /// \pre \ref run() must be called before using this function. |
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163 | Cost totalCost() const { |
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164 | Cost c = 0; |
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165 | for (typename Graph::EdgeIt e(graph); e != INVALID; ++e) |
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166 | c += _flow[e] * _cost[e]; |
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167 | return c; |
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168 | } |
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169 | |
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170 | }; //class MinCostMaxFlow |
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171 | |
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172 | ///@} |
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173 | |
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174 | } //namespace lemon |
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175 | |
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176 | #endif //LEMON_MIN_COST_MAX_FLOW_H |
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