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_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 <lemon/graph_adaptor.h> |
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29 | #include <lemon/bin_heap.h> |
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30 | #include <vector> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \addtogroup min_cost_flow |
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35 | /// @{ |
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36 | |
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37 | /// \brief Implementation of the capacity scaling version of the |
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38 | /// successive shortest path algorithm for finding a minimum cost |
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39 | /// flow. |
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40 | /// |
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41 | /// \ref CapacityScaling implements the capacity scaling version |
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42 | /// of the successive shortest path algorithm for finding a minimum |
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43 | /// cost flow. |
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44 | /// |
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45 | /// \param Graph The directed graph type the algorithm runs on. |
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46 | /// \param LowerMap The type of the lower bound map. |
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47 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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48 | /// \param CostMap The type of the cost (length) map. |
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49 | /// \param SupplyMap The type of the supply map. |
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50 | /// |
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51 | /// \warning |
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52 | /// - Edge capacities and costs should be nonnegative integers. |
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53 | /// However \c CostMap::Value should be signed type. |
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54 | /// - Supply values should be signed integers. |
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55 | /// - \c LowerMap::Value must be convertible to |
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56 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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57 | /// convertible to \c SupplyMap::Value. |
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58 | /// |
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59 | /// \author Peter Kovacs |
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60 | |
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61 | template < typename Graph, |
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62 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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63 | typename CapacityMap = LowerMap, |
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64 | typename CostMap = typename Graph::template EdgeMap<int>, |
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65 | typename SupplyMap = typename Graph::template NodeMap |
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66 | <typename CapacityMap::Value> > |
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67 | class CapacityScaling |
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68 | { |
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69 | typedef typename Graph::Node Node; |
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70 | typedef typename Graph::NodeIt NodeIt; |
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71 | typedef typename Graph::Edge Edge; |
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72 | typedef typename Graph::EdgeIt EdgeIt; |
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73 | typedef typename Graph::InEdgeIt InEdgeIt; |
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74 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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75 | |
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76 | typedef typename LowerMap::Value Lower; |
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77 | typedef typename CapacityMap::Value Capacity; |
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78 | typedef typename CostMap::Value Cost; |
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79 | typedef typename SupplyMap::Value Supply; |
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80 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
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81 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
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82 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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83 | |
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84 | public: |
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85 | |
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86 | /// \brief Type to enable or disable capacity scaling. |
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87 | enum ScalingEnum { |
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88 | WITH_SCALING = 0, |
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89 | WITHOUT_SCALING = -1 |
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90 | }; |
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91 | |
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92 | /// \brief The type of the flow map. |
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93 | typedef CapacityRefMap FlowMap; |
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94 | /// \brief The type of the potential map. |
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95 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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96 | |
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97 | protected: |
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98 | |
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99 | /// \brief Special implementation of the \ref Dijkstra algorithm |
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100 | /// for finding shortest paths in the residual network of the graph |
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101 | /// with respect to the reduced edge costs and modifying the |
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102 | /// node potentials according to the distance of the nodes. |
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103 | class ResidualDijkstra |
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104 | { |
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105 | typedef typename Graph::template NodeMap<Cost> CostNodeMap; |
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106 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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107 | |
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108 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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109 | typedef BinHeap<Cost, HeapCrossRef> Heap; |
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110 | |
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111 | protected: |
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112 | |
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113 | /// \brief The directed graph the algorithm runs on. |
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114 | const Graph &graph; |
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115 | |
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116 | /// \brief The flow map. |
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117 | const FlowMap &flow; |
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118 | /// \brief The residual capacity map. |
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119 | const CapacityRefMap &res_cap; |
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120 | /// \brief The cost map. |
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121 | const CostMap &cost; |
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122 | /// \brief The excess map. |
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123 | const SupplyRefMap &excess; |
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124 | |
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125 | /// \brief The potential map. |
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126 | PotentialMap &potential; |
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127 | |
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128 | /// \brief The distance map. |
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129 | CostNodeMap dist; |
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130 | /// \brief The map of predecessors edges. |
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131 | PredMap &pred; |
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132 | /// \brief The processed (i.e. permanently labeled) nodes. |
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133 | std::vector<Node> proc_nodes; |
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134 | |
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135 | public: |
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136 | |
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137 | /// \brief The constructor of the class. |
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138 | ResidualDijkstra( const Graph &_graph, |
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139 | const FlowMap &_flow, |
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140 | const CapacityRefMap &_res_cap, |
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141 | const CostMap &_cost, |
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142 | const SupplyMap &_excess, |
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143 | PotentialMap &_potential, |
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144 | PredMap &_pred ) : |
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145 | graph(_graph), flow(_flow), res_cap(_res_cap), cost(_cost), |
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146 | excess(_excess), potential(_potential), dist(_graph), |
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147 | pred(_pred) |
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148 | {} |
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149 | |
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150 | /// \brief Runs the algorithm from the given source node. |
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151 | Node run(Node s, Capacity delta) { |
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152 | HeapCrossRef heap_cross_ref(graph, Heap::PRE_HEAP); |
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153 | Heap heap(heap_cross_ref); |
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154 | heap.push(s, 0); |
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155 | pred[s] = INVALID; |
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156 | proc_nodes.clear(); |
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157 | |
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158 | // Processing nodes |
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159 | while (!heap.empty() && excess[heap.top()] > -delta) { |
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160 | Node u = heap.top(), v; |
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161 | Cost d = heap.prio() - potential[u], nd; |
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162 | dist[u] = heap.prio(); |
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163 | heap.pop(); |
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164 | proc_nodes.push_back(u); |
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165 | |
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166 | // Traversing outgoing edges |
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167 | for (OutEdgeIt e(graph, u); e != INVALID; ++e) { |
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168 | if (res_cap[e] >= delta) { |
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169 | v = graph.target(e); |
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170 | switch(heap.state(v)) { |
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171 | case Heap::PRE_HEAP: |
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172 | heap.push(v, d + cost[e] + potential[v]); |
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173 | pred[v] = e; |
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174 | break; |
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175 | case Heap::IN_HEAP: |
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176 | nd = d + cost[e] + potential[v]; |
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177 | if (nd < heap[v]) { |
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178 | heap.decrease(v, nd); |
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179 | pred[v] = e; |
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180 | } |
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181 | break; |
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182 | case Heap::POST_HEAP: |
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183 | break; |
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184 | } |
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185 | } |
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186 | } |
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187 | |
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188 | // Traversing incoming edges |
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189 | for (InEdgeIt e(graph, u); e != INVALID; ++e) { |
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190 | if (flow[e] >= delta) { |
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191 | v = graph.source(e); |
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192 | switch(heap.state(v)) { |
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193 | case Heap::PRE_HEAP: |
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194 | heap.push(v, d - cost[e] + potential[v]); |
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195 | pred[v] = e; |
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196 | break; |
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197 | case Heap::IN_HEAP: |
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198 | nd = d - cost[e] + potential[v]; |
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199 | if (nd < heap[v]) { |
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200 | heap.decrease(v, nd); |
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201 | pred[v] = e; |
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202 | } |
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203 | break; |
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204 | case Heap::POST_HEAP: |
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205 | break; |
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206 | } |
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207 | } |
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208 | } |
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209 | } |
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210 | if (heap.empty()) return INVALID; |
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211 | |
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212 | // Updating potentials of processed nodes |
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213 | Node t = heap.top(); |
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214 | Cost dt = heap.prio(); |
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215 | for (int i = 0; i < proc_nodes.size(); ++i) |
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216 | potential[proc_nodes[i]] -= dist[proc_nodes[i]] - dt; |
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217 | |
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218 | return t; |
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219 | } |
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220 | |
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221 | }; //class ResidualDijkstra |
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222 | |
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223 | protected: |
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224 | |
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225 | /// \brief The directed graph the algorithm runs on. |
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226 | const Graph &graph; |
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227 | /// \brief The original lower bound map. |
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228 | const LowerMap *lower; |
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229 | /// \brief The modified capacity map. |
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230 | CapacityRefMap capacity; |
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231 | /// \brief The cost map. |
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232 | const CostMap &cost; |
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233 | /// \brief The modified supply map. |
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234 | SupplyRefMap supply; |
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235 | /// \brief The sum of supply values equals zero. |
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236 | bool valid_supply; |
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237 | |
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238 | /// \brief The edge map of the current flow. |
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239 | FlowMap flow; |
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240 | /// \brief The potential node map. |
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241 | PotentialMap potential; |
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242 | |
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243 | /// \brief The residual capacity map. |
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244 | CapacityRefMap res_cap; |
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245 | /// \brief The excess map. |
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246 | SupplyRefMap excess; |
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247 | /// \brief The excess nodes (i.e. nodes with positive excess). |
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248 | std::vector<Node> excess_nodes; |
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249 | /// \brief The index of the next excess node. |
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250 | int next_node; |
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251 | |
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252 | /// \brief The scaling status (enabled or disabled). |
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253 | ScalingEnum scaling; |
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254 | /// \brief The delta parameter used for capacity scaling. |
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255 | Capacity delta; |
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256 | /// \brief The maximum number of phases. |
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257 | Capacity phase_num; |
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258 | /// \brief The deficit nodes. |
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259 | std::vector<Node> deficit_nodes; |
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260 | |
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261 | /// \brief Implementation of the \ref Dijkstra algorithm for |
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262 | /// finding augmenting shortest paths in the residual network. |
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263 | ResidualDijkstra dijkstra; |
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264 | /// \brief The map of predecessors edges. |
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265 | PredMap pred; |
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266 | |
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267 | public : |
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268 | |
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269 | /// \brief General constructor of the class (with lower bounds). |
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270 | /// |
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271 | /// General constructor of the class (with lower bounds). |
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272 | /// |
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273 | /// \param _graph The directed graph the algorithm runs on. |
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274 | /// \param _lower The lower bounds of the edges. |
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275 | /// \param _capacity The capacities (upper bounds) of the edges. |
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276 | /// \param _cost The cost (length) values of the edges. |
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277 | /// \param _supply The supply values of the nodes (signed). |
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278 | CapacityScaling( const Graph &_graph, |
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279 | const LowerMap &_lower, |
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280 | const CapacityMap &_capacity, |
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281 | const CostMap &_cost, |
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282 | const SupplyMap &_supply ) : |
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283 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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284 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
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285 | res_cap(_graph), excess(_graph), pred(_graph), |
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286 | dijkstra(graph, flow, res_cap, cost, excess, potential, pred) |
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287 | { |
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288 | // Removing nonzero lower bounds |
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289 | capacity = subMap(_capacity, _lower); |
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290 | res_cap = capacity; |
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291 | Supply sum = 0; |
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292 | for (NodeIt n(graph); n != INVALID; ++n) { |
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293 | Supply s = _supply[n]; |
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294 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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295 | s += _lower[e]; |
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296 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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297 | s -= _lower[e]; |
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298 | supply[n] = s; |
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299 | sum += s; |
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300 | } |
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301 | valid_supply = sum == 0; |
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302 | } |
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303 | |
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304 | /// \brief General constructor of the class (without lower bounds). |
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305 | /// |
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306 | /// General constructor of the class (without lower bounds). |
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307 | /// |
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308 | /// \param _graph The directed graph the algorithm runs on. |
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309 | /// \param _capacity The capacities (upper bounds) of the edges. |
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310 | /// \param _cost The cost (length) values of the edges. |
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311 | /// \param _supply The supply values of the nodes (signed). |
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312 | CapacityScaling( const Graph &_graph, |
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313 | const CapacityMap &_capacity, |
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314 | const CostMap &_cost, |
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315 | const SupplyMap &_supply ) : |
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316 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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317 | supply(_supply), flow(_graph, 0), potential(_graph, 0), |
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318 | res_cap(_capacity), excess(_graph), pred(_graph), |
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319 | dijkstra(graph, flow, res_cap, cost, excess, potential) |
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320 | { |
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321 | // Checking the sum of supply values |
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322 | Supply sum = 0; |
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323 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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324 | valid_supply = sum == 0; |
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325 | } |
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326 | |
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327 | /// \brief Simple constructor of the class (with lower bounds). |
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328 | /// |
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329 | /// Simple constructor of the class (with lower bounds). |
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330 | /// |
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331 | /// \param _graph The directed graph the algorithm runs on. |
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332 | /// \param _lower The lower bounds of the edges. |
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333 | /// \param _capacity The capacities (upper bounds) of the edges. |
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334 | /// \param _cost The cost (length) values of the edges. |
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335 | /// \param _s The source node. |
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336 | /// \param _t The target node. |
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337 | /// \param _flow_value The required amount of flow from node \c _s |
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338 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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339 | /// \c _t). |
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340 | CapacityScaling( const Graph &_graph, |
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341 | const LowerMap &_lower, |
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342 | const CapacityMap &_capacity, |
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343 | const CostMap &_cost, |
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344 | Node _s, Node _t, |
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345 | Supply _flow_value ) : |
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346 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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347 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
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348 | res_cap(_graph), excess(_graph), pred(_graph), |
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349 | dijkstra(graph, flow, res_cap, cost, excess, potential) |
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350 | { |
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351 | // Removing nonzero lower bounds |
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352 | capacity = subMap(_capacity, _lower); |
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353 | res_cap = capacity; |
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354 | for (NodeIt n(graph); n != INVALID; ++n) { |
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355 | Supply s = 0; |
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356 | if (n == _s) s = _flow_value; |
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357 | if (n == _t) s = -_flow_value; |
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358 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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359 | s += _lower[e]; |
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360 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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361 | s -= _lower[e]; |
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362 | supply[n] = s; |
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363 | } |
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364 | valid_supply = true; |
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365 | } |
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366 | |
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367 | /// \brief Simple constructor of the class (without lower bounds). |
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368 | /// |
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369 | /// Simple constructor of the class (without lower bounds). |
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370 | /// |
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371 | /// \param _graph The directed graph the algorithm runs on. |
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372 | /// \param _capacity The capacities (upper bounds) of the edges. |
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373 | /// \param _cost The cost (length) values of the edges. |
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374 | /// \param _s The source node. |
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375 | /// \param _t The target node. |
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376 | /// \param _flow_value The required amount of flow from node \c _s |
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377 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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378 | /// \c _t). |
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379 | CapacityScaling( const Graph &_graph, |
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380 | const CapacityMap &_capacity, |
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381 | const CostMap &_cost, |
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382 | Node _s, Node _t, |
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383 | Supply _flow_value ) : |
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384 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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385 | supply(_graph, 0), flow(_graph, 0), potential(_graph, 0), |
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386 | res_cap(_capacity), excess(_graph), pred(_graph), |
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387 | dijkstra(graph, flow, res_cap, cost, excess, potential) |
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388 | { |
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389 | supply[_s] = _flow_value; |
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390 | supply[_t] = -_flow_value; |
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391 | valid_supply = true; |
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392 | } |
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393 | |
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394 | /// \brief Returns a const reference to the flow map. |
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395 | /// |
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396 | /// Returns a const reference to the flow map. |
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397 | /// |
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398 | /// \pre \ref run() must be called before using this function. |
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399 | const FlowMap& flowMap() const { |
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400 | return flow; |
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401 | } |
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402 | |
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403 | /// \brief Returns a const reference to the potential map (the dual |
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404 | /// solution). |
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405 | /// |
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406 | /// Returns a const reference to the potential map (the dual |
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407 | /// solution). |
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408 | /// |
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409 | /// \pre \ref run() must be called before using this function. |
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410 | const PotentialMap& potentialMap() const { |
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411 | return potential; |
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412 | } |
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413 | |
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414 | /// \brief Returns the total cost of the found flow. |
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415 | /// |
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416 | /// Returns the total cost of the found flow. The complexity of the |
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417 | /// function is \f$ O(e) \f$. |
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418 | /// |
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419 | /// \pre \ref run() must be called before using this function. |
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420 | Cost totalCost() const { |
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421 | Cost c = 0; |
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422 | for (EdgeIt e(graph); e != INVALID; ++e) |
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423 | c += flow[e] * cost[e]; |
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424 | return c; |
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425 | } |
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426 | |
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427 | /// \brief Runs the algorithm. |
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428 | /// |
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429 | /// Runs the algorithm. |
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430 | /// |
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431 | /// \param scaling_mode The scaling mode. In case of WITH_SCALING |
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432 | /// capacity scaling is enabled in the algorithm (this is the |
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433 | /// default value) otherwise it is disabled. |
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434 | /// If the maximum edge capacity and/or the amount of total supply |
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435 | /// is small, the algorithm could be faster without scaling. |
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436 | /// |
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437 | /// \return \c true if a feasible flow can be found. |
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438 | bool run(int scaling_mode = WITH_SCALING) { |
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439 | return init(scaling_mode) && start(); |
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440 | } |
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441 | |
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442 | protected: |
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443 | |
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444 | /// \brief Initializes the algorithm. |
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445 | bool init(int scaling_mode) { |
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446 | if (!valid_supply) return false; |
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447 | excess = supply; |
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448 | |
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449 | // Initilaizing delta value |
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450 | if (scaling_mode == WITH_SCALING) { |
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451 | // With scaling |
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452 | Supply max_sup = 0, max_dem = 0; |
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453 | for (NodeIt n(graph); n != INVALID; ++n) { |
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454 | if ( supply[n] > max_sup) max_sup = supply[n]; |
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455 | if (-supply[n] > max_dem) max_dem = -supply[n]; |
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456 | } |
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457 | if (max_dem < max_sup) max_sup = max_dem; |
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458 | phase_num = 0; |
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459 | for (delta = 1; 2 * delta <= max_sup; delta *= 2) |
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460 | ++phase_num; |
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461 | } else { |
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462 | // Without scaling |
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463 | delta = 1; |
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464 | } |
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465 | return true; |
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466 | } |
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467 | |
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468 | /// \brief Executes the algorithm. |
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469 | bool start() { |
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470 | if (delta > 1) |
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471 | return startWithScaling(); |
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472 | else |
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473 | return startWithoutScaling(); |
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474 | } |
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475 | |
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476 | /// \brief Executes the capacity scaling version of the successive |
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477 | /// shortest path algorithm. |
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478 | bool startWithScaling() { |
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479 | // Processing capacity scaling phases |
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480 | Node s, t; |
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481 | int phase_cnt = 0; |
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482 | int factor = 4; |
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483 | while (true) { |
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484 | // Saturating all edges not satisfying the optimality condition |
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485 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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486 | Node u = graph.source(e), v = graph.target(e); |
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487 | Cost c = cost[e] - potential[u] + potential[v]; |
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488 | if (c < 0 && res_cap[e] >= delta) { |
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489 | excess[u] -= res_cap[e]; |
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490 | excess[v] += res_cap[e]; |
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491 | flow[e] = capacity[e]; |
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492 | res_cap[e] = 0; |
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493 | } |
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494 | else if (c > 0 && flow[e] >= delta) { |
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495 | excess[u] += flow[e]; |
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496 | excess[v] -= flow[e]; |
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497 | flow[e] = 0; |
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498 | res_cap[e] = capacity[e]; |
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499 | } |
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500 | } |
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501 | |
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502 | // Finding excess nodes and deficit nodes |
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503 | excess_nodes.clear(); |
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504 | deficit_nodes.clear(); |
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505 | for (NodeIt n(graph); n != INVALID; ++n) { |
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506 | if (excess[n] >= delta) excess_nodes.push_back(n); |
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507 | if (excess[n] <= -delta) deficit_nodes.push_back(n); |
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508 | } |
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509 | next_node = 0; |
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510 | |
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511 | // Finding augmenting shortest paths |
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512 | while (next_node < excess_nodes.size()) { |
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513 | // Checking deficit nodes |
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514 | if (delta > 1) { |
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515 | bool delta_deficit = false; |
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516 | for (int i = 0; i < deficit_nodes.size(); ++i) { |
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517 | if (excess[deficit_nodes[i]] <= -delta) { |
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518 | delta_deficit = true; |
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519 | break; |
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520 | } |
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521 | } |
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522 | if (!delta_deficit) break; |
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523 | } |
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524 | |
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525 | // Running Dijkstra |
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526 | s = excess_nodes[next_node]; |
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527 | if ((t = dijkstra.run(s, delta)) == INVALID) { |
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528 | if (delta > 1) { |
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529 | ++next_node; |
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530 | continue; |
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531 | } |
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532 | return false; |
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533 | } |
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534 | |
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535 | // Augmenting along a shortest path from s to t. |
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536 | Capacity d = excess[s] < -excess[t] ? excess[s] : -excess[t]; |
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537 | Node u = t; |
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538 | Edge e; |
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539 | if (d > delta) { |
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540 | while ((e = pred[u]) != INVALID) { |
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541 | Capacity rc; |
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542 | if (u == graph.target(e)) { |
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543 | rc = res_cap[e]; |
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544 | u = graph.source(e); |
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545 | } else { |
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546 | rc = flow[e]; |
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547 | u = graph.target(e); |
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548 | } |
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549 | if (rc < d) d = rc; |
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550 | } |
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551 | } |
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552 | u = t; |
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553 | while ((e = pred[u]) != INVALID) { |
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554 | if (u == graph.target(e)) { |
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555 | flow[e] += d; |
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556 | res_cap[e] -= d; |
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557 | u = graph.source(e); |
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558 | } else { |
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559 | flow[e] -= d; |
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560 | res_cap[e] += d; |
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561 | u = graph.target(e); |
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562 | } |
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563 | } |
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564 | excess[s] -= d; |
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565 | excess[t] += d; |
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566 | |
---|
567 | if (excess[s] < delta) ++next_node; |
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568 | } |
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569 | |
---|
570 | if (delta == 1) break; |
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571 | if (++phase_cnt > phase_num / 4) factor = 2; |
---|
572 | delta = delta <= factor ? 1 : delta / factor; |
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573 | } |
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574 | |
---|
575 | // Handling nonzero lower bounds |
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576 | if (lower) { |
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577 | for (EdgeIt e(graph); e != INVALID; ++e) |
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578 | flow[e] += (*lower)[e]; |
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579 | } |
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580 | return true; |
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581 | } |
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582 | |
---|
583 | /// \brief Executes the successive shortest path algorithm without |
---|
584 | /// capacity scaling. |
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585 | bool startWithoutScaling() { |
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586 | // Finding excess nodes |
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587 | for (NodeIt n(graph); n != INVALID; ++n) { |
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588 | if (excess[n] > 0) excess_nodes.push_back(n); |
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589 | } |
---|
590 | if (excess_nodes.size() == 0) return true; |
---|
591 | next_node = 0; |
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592 | |
---|
593 | // Finding shortest paths |
---|
594 | Node s, t; |
---|
595 | while ( excess[excess_nodes[next_node]] > 0 || |
---|
596 | ++next_node < excess_nodes.size() ) |
---|
597 | { |
---|
598 | // Running Dijkstra |
---|
599 | s = excess_nodes[next_node]; |
---|
600 | if ((t = dijkstra.run(s, 1)) == INVALID) |
---|
601 | return false; |
---|
602 | |
---|
603 | // Augmenting along a shortest path from s to t |
---|
604 | Capacity d = excess[s] < -excess[t] ? excess[s] : -excess[t]; |
---|
605 | Node u = t; |
---|
606 | Edge e; |
---|
607 | while ((e = pred[u]) != INVALID) { |
---|
608 | Capacity rc; |
---|
609 | if (u == graph.target(e)) { |
---|
610 | rc = res_cap[e]; |
---|
611 | u = graph.source(e); |
---|
612 | } else { |
---|
613 | rc = flow[e]; |
---|
614 | u = graph.target(e); |
---|
615 | } |
---|
616 | if (rc < d) d = rc; |
---|
617 | } |
---|
618 | u = t; |
---|
619 | while ((e = pred[u]) != INVALID) { |
---|
620 | if (u == graph.target(e)) { |
---|
621 | flow[e] += d; |
---|
622 | res_cap[e] -= d; |
---|
623 | u = graph.source(e); |
---|
624 | } else { |
---|
625 | flow[e] -= d; |
---|
626 | res_cap[e] += d; |
---|
627 | u = graph.target(e); |
---|
628 | } |
---|
629 | } |
---|
630 | excess[s] -= d; |
---|
631 | excess[t] += d; |
---|
632 | } |
---|
633 | |
---|
634 | // Handling nonzero lower bounds |
---|
635 | if (lower) { |
---|
636 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
637 | flow[e] += (*lower)[e]; |
---|
638 | } |
---|
639 | return true; |
---|
640 | } |
---|
641 | |
---|
642 | }; //class CapacityScaling |
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643 | |
---|
644 | ///@} |
---|
645 | |
---|
646 | } //namespace lemon |
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647 | |
---|
648 | #endif //LEMON_CAPACITY_SCALING_H |
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