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 Capacity scaling algorithm for finding a minimum cost flow. |
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26 | |
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27 | #include <vector> |
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28 | #include <lemon/bin_heap.h> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | /// \addtogroup min_cost_flow |
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33 | /// @{ |
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34 | |
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35 | /// \brief Implementation of the capacity scaling algorithm for |
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36 | /// finding a minimum cost flow. |
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37 | /// |
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38 | /// \ref CapacityScaling implements the capacity scaling version |
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39 | /// of the successive shortest path algorithm for finding a minimum |
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40 | /// cost flow. |
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41 | /// |
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42 | /// \tparam Graph The directed graph type the algorithm runs on. |
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43 | /// \tparam LowerMap The type of the lower bound map. |
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44 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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45 | /// \tparam CostMap The type of the cost (length) map. |
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46 | /// \tparam SupplyMap The type of the supply map. |
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47 | /// |
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48 | /// \warning |
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49 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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50 | /// - Supply values should be \e signed \e integers. |
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51 | /// - The value types of the maps should be convertible to each other. |
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52 | /// - \c CostMap::Value must be signed type. |
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53 | /// |
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54 | /// \author Peter Kovacs |
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55 | template < typename Graph, |
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56 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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57 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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58 | typename CostMap = typename Graph::template EdgeMap<int>, |
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59 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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60 | class CapacityScaling |
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61 | { |
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62 | GRAPH_TYPEDEFS(typename Graph); |
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63 | |
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64 | typedef typename CapacityMap::Value Capacity; |
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65 | typedef typename CostMap::Value Cost; |
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66 | typedef typename SupplyMap::Value Supply; |
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67 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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68 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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69 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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70 | |
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71 | public: |
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72 | |
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73 | /// The type of the flow map. |
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74 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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75 | /// The type of the potential map. |
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76 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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77 | |
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78 | private: |
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79 | |
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80 | /// \brief Special implementation of the \ref Dijkstra algorithm |
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81 | /// for finding shortest paths in the residual network. |
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82 | /// |
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83 | /// \ref ResidualDijkstra is a special implementation of the |
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84 | /// \ref Dijkstra algorithm for finding shortest paths in the |
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85 | /// residual network of the graph with respect to the reduced edge |
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86 | /// costs and modifying the node potentials according to the |
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87 | /// distance of the nodes. |
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88 | class ResidualDijkstra |
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89 | { |
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90 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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91 | typedef BinHeap<Cost, HeapCrossRef> Heap; |
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92 | |
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93 | private: |
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94 | |
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95 | // The directed graph the algorithm runs on |
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96 | const Graph &_graph; |
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97 | |
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98 | // The main maps |
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99 | const FlowMap &_flow; |
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100 | const CapacityEdgeMap &_res_cap; |
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101 | const CostMap &_cost; |
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102 | const SupplyNodeMap &_excess; |
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103 | PotentialMap &_potential; |
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104 | |
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105 | // The distance map |
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106 | PotentialMap _dist; |
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107 | // The pred edge map |
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108 | PredMap &_pred; |
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109 | // The processed (i.e. permanently labeled) nodes |
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110 | std::vector<Node> _proc_nodes; |
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111 | |
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112 | public: |
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113 | |
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114 | /// Constructor. |
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115 | ResidualDijkstra( const Graph &graph, |
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116 | const FlowMap &flow, |
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117 | const CapacityEdgeMap &res_cap, |
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118 | const CostMap &cost, |
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119 | const SupplyMap &excess, |
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120 | PotentialMap &potential, |
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121 | PredMap &pred ) : |
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122 | _graph(graph), _flow(flow), _res_cap(res_cap), _cost(cost), |
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123 | _excess(excess), _potential(potential), _dist(graph), |
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124 | _pred(pred) |
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125 | {} |
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126 | |
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127 | /// Run the algorithm from the given source node. |
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128 | Node run(Node s, Capacity delta = 1) { |
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129 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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130 | Heap heap(heap_cross_ref); |
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131 | heap.push(s, 0); |
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132 | _pred[s] = INVALID; |
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133 | _proc_nodes.clear(); |
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134 | |
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135 | // Processing nodes |
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136 | while (!heap.empty() && _excess[heap.top()] > -delta) { |
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137 | Node u = heap.top(), v; |
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138 | Cost d = heap.prio() + _potential[u], nd; |
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139 | _dist[u] = heap.prio(); |
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140 | heap.pop(); |
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141 | _proc_nodes.push_back(u); |
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142 | |
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143 | // Traversing outgoing edges |
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144 | for (OutEdgeIt e(_graph, u); e != INVALID; ++e) { |
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145 | if (_res_cap[e] >= delta) { |
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146 | v = _graph.target(e); |
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147 | switch(heap.state(v)) { |
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148 | case Heap::PRE_HEAP: |
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149 | heap.push(v, d + _cost[e] - _potential[v]); |
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150 | _pred[v] = e; |
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151 | break; |
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152 | case Heap::IN_HEAP: |
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153 | nd = d + _cost[e] - _potential[v]; |
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154 | if (nd < heap[v]) { |
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155 | heap.decrease(v, nd); |
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156 | _pred[v] = e; |
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157 | } |
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158 | break; |
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159 | case Heap::POST_HEAP: |
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160 | break; |
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161 | } |
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162 | } |
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163 | } |
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164 | |
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165 | // Traversing incoming edges |
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166 | for (InEdgeIt e(_graph, u); e != INVALID; ++e) { |
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167 | if (_flow[e] >= delta) { |
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168 | v = _graph.source(e); |
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169 | switch(heap.state(v)) { |
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170 | case Heap::PRE_HEAP: |
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171 | heap.push(v, d - _cost[e] - _potential[v]); |
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172 | _pred[v] = e; |
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173 | break; |
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174 | case Heap::IN_HEAP: |
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175 | nd = d - _cost[e] - _potential[v]; |
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176 | if (nd < heap[v]) { |
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177 | heap.decrease(v, nd); |
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178 | _pred[v] = e; |
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179 | } |
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180 | break; |
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181 | case Heap::POST_HEAP: |
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182 | break; |
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183 | } |
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184 | } |
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185 | } |
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186 | } |
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187 | if (heap.empty()) return INVALID; |
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188 | |
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189 | // Updating potentials of processed nodes |
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190 | Node t = heap.top(); |
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191 | Cost t_dist = heap.prio(); |
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192 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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193 | _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
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194 | |
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195 | return t; |
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196 | } |
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197 | |
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198 | }; //class ResidualDijkstra |
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199 | |
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200 | private: |
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201 | |
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202 | // The directed graph the algorithm runs on |
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203 | const Graph &_graph; |
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204 | // The original lower bound map |
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205 | const LowerMap *_lower; |
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206 | // The modified capacity map |
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207 | CapacityEdgeMap _capacity; |
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208 | // The original cost map |
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209 | const CostMap &_cost; |
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210 | // The modified supply map |
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211 | SupplyNodeMap _supply; |
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212 | bool _valid_supply; |
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213 | |
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214 | // Edge map of the current flow |
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215 | FlowMap *_flow; |
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216 | bool _local_flow; |
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217 | // Node map of the current potentials |
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218 | PotentialMap *_potential; |
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219 | bool _local_potential; |
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220 | |
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221 | // The residual capacity map |
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222 | CapacityEdgeMap _res_cap; |
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223 | // The excess map |
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224 | SupplyNodeMap _excess; |
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225 | // The excess nodes (i.e. nodes with positive excess) |
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226 | std::vector<Node> _excess_nodes; |
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227 | // The deficit nodes (i.e. nodes with negative excess) |
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228 | std::vector<Node> _deficit_nodes; |
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229 | |
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230 | // The delta parameter used for capacity scaling |
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231 | Capacity _delta; |
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232 | // The maximum number of phases |
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233 | int _phase_num; |
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234 | |
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235 | // The pred edge map |
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236 | PredMap _pred; |
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237 | // Implementation of the Dijkstra algorithm for finding augmenting |
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238 | // shortest paths in the residual network |
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239 | ResidualDijkstra *_dijkstra; |
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240 | |
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241 | public: |
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242 | |
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243 | /// \brief General constructor (with lower bounds). |
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244 | /// |
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245 | /// General constructor (with lower bounds). |
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246 | /// |
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247 | /// \param graph The directed graph the algorithm runs on. |
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248 | /// \param lower The lower bounds of the edges. |
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249 | /// \param capacity The capacities (upper bounds) of the edges. |
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250 | /// \param cost The cost (length) values of the edges. |
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251 | /// \param supply The supply values of the nodes (signed). |
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252 | CapacityScaling( const Graph &graph, |
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253 | const LowerMap &lower, |
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254 | const CapacityMap &capacity, |
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255 | const CostMap &cost, |
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256 | const SupplyMap &supply ) : |
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257 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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258 | _supply(graph), _flow(0), _local_flow(false), |
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259 | _potential(0), _local_potential(false), |
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260 | _res_cap(graph), _excess(graph), _pred(graph) |
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261 | { |
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262 | // Removing non-zero lower bounds |
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263 | _capacity = subMap(capacity, lower); |
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264 | _res_cap = _capacity; |
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265 | Supply sum = 0; |
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266 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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267 | Supply s = supply[n]; |
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268 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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269 | s += lower[e]; |
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270 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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271 | s -= lower[e]; |
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272 | _supply[n] = s; |
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273 | sum += s; |
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274 | } |
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275 | _valid_supply = sum == 0; |
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276 | } |
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277 | |
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278 | /// \brief General constructor (without lower bounds). |
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279 | /// |
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280 | /// General constructor (without lower bounds). |
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281 | /// |
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282 | /// \param graph The directed graph the algorithm runs on. |
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283 | /// \param capacity The capacities (upper bounds) of the edges. |
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284 | /// \param cost The cost (length) values of the edges. |
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285 | /// \param supply The supply values of the nodes (signed). |
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286 | CapacityScaling( const Graph &graph, |
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287 | const CapacityMap &capacity, |
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288 | const CostMap &cost, |
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289 | const SupplyMap &supply ) : |
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290 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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291 | _supply(supply), _flow(0), _local_flow(false), |
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292 | _potential(0), _local_potential(false), |
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293 | _res_cap(capacity), _excess(graph), _pred(graph) |
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294 | { |
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295 | // Checking the sum of supply values |
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296 | Supply sum = 0; |
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297 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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298 | _valid_supply = sum == 0; |
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299 | } |
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300 | |
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301 | /// \brief Simple constructor (with lower bounds). |
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302 | /// |
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303 | /// Simple constructor (with lower bounds). |
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304 | /// |
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305 | /// \param graph The directed graph the algorithm runs on. |
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306 | /// \param lower The lower bounds of the edges. |
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307 | /// \param capacity The capacities (upper bounds) of the edges. |
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308 | /// \param cost The cost (length) values of the edges. |
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309 | /// \param s The source node. |
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310 | /// \param t The target node. |
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311 | /// \param flow_value The required amount of flow from node \c s |
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312 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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313 | CapacityScaling( const Graph &graph, |
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314 | const LowerMap &lower, |
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315 | const CapacityMap &capacity, |
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316 | const CostMap &cost, |
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317 | Node s, Node t, |
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318 | Supply flow_value ) : |
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319 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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320 | _supply(graph), _flow(0), _local_flow(false), |
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321 | _potential(0), _local_potential(false), |
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322 | _res_cap(graph), _excess(graph), _pred(graph) |
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323 | { |
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324 | // Removing non-zero lower bounds |
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325 | _capacity = subMap(capacity, lower); |
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326 | _res_cap = _capacity; |
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327 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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328 | Supply sum = 0; |
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329 | if (n == s) sum = flow_value; |
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330 | if (n == t) sum = -flow_value; |
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331 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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332 | sum += lower[e]; |
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333 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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334 | sum -= lower[e]; |
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335 | _supply[n] = sum; |
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336 | } |
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337 | _valid_supply = true; |
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338 | } |
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339 | |
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340 | /// \brief Simple constructor (without lower bounds). |
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341 | /// |
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342 | /// Simple constructor (without lower bounds). |
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343 | /// |
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344 | /// \param graph The directed graph the algorithm runs on. |
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345 | /// \param capacity The capacities (upper bounds) of the edges. |
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346 | /// \param cost The cost (length) values of the edges. |
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347 | /// \param s The source node. |
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348 | /// \param t The target node. |
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349 | /// \param flow_value The required amount of flow from node \c s |
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350 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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351 | CapacityScaling( const Graph &graph, |
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352 | const CapacityMap &capacity, |
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353 | const CostMap &cost, |
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354 | Node s, Node t, |
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355 | Supply flow_value ) : |
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356 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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357 | _supply(graph, 0), _flow(0), _local_flow(false), |
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358 | _potential(0), _local_potential(false), |
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359 | _res_cap(capacity), _excess(graph), _pred(graph) |
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360 | { |
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361 | _supply[s] = flow_value; |
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362 | _supply[t] = -flow_value; |
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363 | _valid_supply = true; |
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364 | } |
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365 | |
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366 | /// Destructor. |
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367 | ~CapacityScaling() { |
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368 | if (_local_flow) delete _flow; |
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369 | if (_local_potential) delete _potential; |
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370 | delete _dijkstra; |
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371 | } |
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372 | |
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373 | /// \brief Set the flow map. |
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374 | /// |
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375 | /// Set the flow map. |
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376 | /// |
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377 | /// \return \c (*this) |
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378 | CapacityScaling& flowMap(FlowMap &map) { |
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379 | if (_local_flow) { |
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380 | delete _flow; |
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381 | _local_flow = false; |
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382 | } |
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383 | _flow = ↦ |
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384 | return *this; |
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385 | } |
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386 | |
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387 | /// \brief Set the potential map. |
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388 | /// |
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389 | /// Set the potential map. |
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390 | /// |
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391 | /// \return \c (*this) |
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392 | CapacityScaling& potentialMap(PotentialMap &map) { |
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393 | if (_local_potential) { |
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394 | delete _potential; |
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395 | _local_potential = false; |
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396 | } |
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397 | _potential = ↦ |
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398 | return *this; |
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399 | } |
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400 | |
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401 | /// \name Execution control |
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402 | |
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403 | /// @{ |
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404 | |
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405 | /// \brief Run the algorithm. |
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406 | /// |
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407 | /// This function runs the algorithm. |
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408 | /// |
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409 | /// \param scaling Enable or disable capacity scaling. |
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410 | /// If the maximum edge capacity and/or the amount of total supply |
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411 | /// is rather small, the algorithm could be slightly faster without |
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412 | /// scaling. |
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413 | /// |
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414 | /// \return \c true if a feasible flow can be found. |
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415 | bool run(bool scaling = true) { |
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416 | return init(scaling) && start(); |
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417 | } |
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418 | |
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419 | /// @} |
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420 | |
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421 | /// \name Query Functions |
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422 | /// The results of the algorithm can be obtained using these |
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423 | /// functions.\n |
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424 | /// \ref lemon::CapacityScaling::run() "run()" must be called before |
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425 | /// using them. |
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426 | |
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427 | /// @{ |
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428 | |
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429 | /// \brief Return a const reference to the edge map storing the |
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430 | /// found flow. |
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431 | /// |
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432 | /// Return a const reference to the edge map storing the found flow. |
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433 | /// |
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434 | /// \pre \ref run() must be called before using this function. |
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435 | const FlowMap& flowMap() const { |
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436 | return *_flow; |
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437 | } |
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438 | |
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439 | /// \brief Return a const reference to the node map storing the |
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440 | /// found potentials (the dual solution). |
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441 | /// |
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442 | /// Return a const reference to the node map storing the found |
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443 | /// potentials (the dual solution). |
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444 | /// |
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445 | /// \pre \ref run() must be called before using this function. |
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446 | const PotentialMap& potentialMap() const { |
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447 | return *_potential; |
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448 | } |
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449 | |
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450 | /// \brief Return the flow on the given edge. |
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451 | /// |
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452 | /// Return the flow on the given edge. |
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453 | /// |
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454 | /// \pre \ref run() must be called before using this function. |
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455 | Capacity flow(const Edge& edge) const { |
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456 | return (*_flow)[edge]; |
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457 | } |
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458 | |
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459 | /// \brief Return the potential of the given node. |
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460 | /// |
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461 | /// Return the potential of the given node. |
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462 | /// |
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463 | /// \pre \ref run() must be called before using this function. |
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464 | Cost potential(const Node& node) const { |
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465 | return (*_potential)[node]; |
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466 | } |
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467 | |
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468 | /// \brief Return the total cost of the found flow. |
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469 | /// |
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470 | /// Return the total cost of the found flow. The complexity of the |
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471 | /// function is \f$ O(e) \f$. |
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472 | /// |
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473 | /// \pre \ref run() must be called before using this function. |
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474 | Cost totalCost() const { |
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475 | Cost c = 0; |
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476 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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477 | c += (*_flow)[e] * _cost[e]; |
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478 | return c; |
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479 | } |
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480 | |
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481 | /// @} |
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482 | |
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483 | private: |
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484 | |
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485 | /// Initialize the algorithm. |
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486 | bool init(bool scaling) { |
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487 | if (!_valid_supply) return false; |
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488 | |
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489 | // Initializing maps |
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490 | if (!_flow) { |
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491 | _flow = new FlowMap(_graph); |
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492 | _local_flow = true; |
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493 | } |
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494 | if (!_potential) { |
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495 | _potential = new PotentialMap(_graph); |
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496 | _local_potential = true; |
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497 | } |
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498 | for (EdgeIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0; |
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499 | for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0; |
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500 | _excess = _supply; |
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501 | |
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502 | _dijkstra = new ResidualDijkstra( _graph, *_flow, _res_cap, _cost, |
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503 | _excess, *_potential, _pred ); |
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504 | |
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505 | // Initializing delta value |
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506 | if (scaling) { |
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507 | // With scaling |
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508 | Supply max_sup = 0, max_dem = 0; |
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509 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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510 | if ( _supply[n] > max_sup) max_sup = _supply[n]; |
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511 | if (-_supply[n] > max_dem) max_dem = -_supply[n]; |
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512 | } |
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513 | Capacity max_cap = 0; |
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514 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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515 | if (_capacity[e] > max_cap) max_cap = _capacity[e]; |
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516 | } |
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517 | max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
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518 | _phase_num = 0; |
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519 | for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) |
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520 | ++_phase_num; |
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521 | } else { |
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522 | // Without scaling |
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523 | _delta = 1; |
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524 | } |
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525 | |
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526 | return true; |
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527 | } |
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528 | |
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529 | bool start() { |
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530 | if (_delta > 1) |
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531 | return startWithScaling(); |
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532 | else |
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533 | return startWithoutScaling(); |
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534 | } |
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535 | |
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536 | /// Execute the capacity scaling algorithm. |
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537 | bool startWithScaling() { |
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538 | // Processing capacity scaling phases |
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539 | Node s, t; |
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540 | int phase_cnt = 0; |
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541 | int factor = 4; |
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542 | while (true) { |
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543 | // Saturating all edges not satisfying the optimality condition |
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544 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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545 | Node u = _graph.source(e), v = _graph.target(e); |
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546 | Cost c = _cost[e] + (*_potential)[u] - (*_potential)[v]; |
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547 | if (c < 0 && _res_cap[e] >= _delta) { |
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548 | _excess[u] -= _res_cap[e]; |
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549 | _excess[v] += _res_cap[e]; |
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550 | (*_flow)[e] = _capacity[e]; |
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551 | _res_cap[e] = 0; |
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552 | } |
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553 | else if (c > 0 && (*_flow)[e] >= _delta) { |
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554 | _excess[u] += (*_flow)[e]; |
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555 | _excess[v] -= (*_flow)[e]; |
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556 | (*_flow)[e] = 0; |
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557 | _res_cap[e] = _capacity[e]; |
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558 | } |
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559 | } |
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560 | |
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561 | // Finding excess nodes and deficit nodes |
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562 | _excess_nodes.clear(); |
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563 | _deficit_nodes.clear(); |
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564 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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565 | if (_excess[n] >= _delta) _excess_nodes.push_back(n); |
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566 | if (_excess[n] <= -_delta) _deficit_nodes.push_back(n); |
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567 | } |
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568 | int next_node = 0, next_def_node = 0; |
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569 | |
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570 | // Finding augmenting shortest paths |
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571 | while (next_node < int(_excess_nodes.size())) { |
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572 | // Checking deficit nodes |
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573 | if (_delta > 1) { |
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574 | bool delta_deficit = false; |
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575 | for ( ; next_def_node < int(_deficit_nodes.size()); |
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576 | ++next_def_node ) { |
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577 | if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { |
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578 | delta_deficit = true; |
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579 | break; |
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580 | } |
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581 | } |
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582 | if (!delta_deficit) break; |
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583 | } |
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584 | |
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585 | // Running Dijkstra |
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586 | s = _excess_nodes[next_node]; |
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587 | if ((t = _dijkstra->run(s, _delta)) == INVALID) { |
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588 | if (_delta > 1) { |
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589 | ++next_node; |
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590 | continue; |
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591 | } |
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592 | return false; |
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593 | } |
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594 | |
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595 | // Augmenting along a shortest path from s to t. |
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596 | Capacity d = std::min(_excess[s], -_excess[t]); |
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597 | Node u = t; |
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598 | Edge e; |
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599 | if (d > _delta) { |
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600 | while ((e = _pred[u]) != INVALID) { |
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601 | Capacity rc; |
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602 | if (u == _graph.target(e)) { |
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603 | rc = _res_cap[e]; |
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604 | u = _graph.source(e); |
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605 | } else { |
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606 | rc = (*_flow)[e]; |
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607 | u = _graph.target(e); |
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608 | } |
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609 | if (rc < d) d = rc; |
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610 | } |
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611 | } |
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612 | u = t; |
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613 | while ((e = _pred[u]) != INVALID) { |
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614 | if (u == _graph.target(e)) { |
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615 | (*_flow)[e] += d; |
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616 | _res_cap[e] -= d; |
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617 | u = _graph.source(e); |
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618 | } else { |
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619 | (*_flow)[e] -= d; |
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620 | _res_cap[e] += d; |
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621 | u = _graph.target(e); |
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622 | } |
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623 | } |
---|
624 | _excess[s] -= d; |
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625 | _excess[t] += d; |
---|
626 | |
---|
627 | if (_excess[s] < _delta) ++next_node; |
---|
628 | } |
---|
629 | |
---|
630 | if (_delta == 1) break; |
---|
631 | if (++phase_cnt > _phase_num / 4) factor = 2; |
---|
632 | _delta = _delta <= factor ? 1 : _delta / factor; |
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633 | } |
---|
634 | |
---|
635 | // Handling non-zero lower bounds |
---|
636 | if (_lower) { |
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637 | for (EdgeIt e(_graph); e != INVALID; ++e) |
---|
638 | (*_flow)[e] += (*_lower)[e]; |
---|
639 | } |
---|
640 | return true; |
---|
641 | } |
---|
642 | |
---|
643 | /// Execute the successive shortest path algorithm. |
---|
644 | bool startWithoutScaling() { |
---|
645 | // Finding excess nodes |
---|
646 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
647 | if (_excess[n] > 0) _excess_nodes.push_back(n); |
---|
648 | if (_excess_nodes.size() == 0) return true; |
---|
649 | int next_node = 0; |
---|
650 | |
---|
651 | // Finding shortest paths |
---|
652 | Node s, t; |
---|
653 | while ( _excess[_excess_nodes[next_node]] > 0 || |
---|
654 | ++next_node < int(_excess_nodes.size()) ) |
---|
655 | { |
---|
656 | // Running Dijkstra |
---|
657 | s = _excess_nodes[next_node]; |
---|
658 | if ((t = _dijkstra->run(s)) == INVALID) return false; |
---|
659 | |
---|
660 | // Augmenting along a shortest path from s to t |
---|
661 | Capacity d = std::min(_excess[s], -_excess[t]); |
---|
662 | Node u = t; |
---|
663 | Edge e; |
---|
664 | if (d > 1) { |
---|
665 | while ((e = _pred[u]) != INVALID) { |
---|
666 | Capacity rc; |
---|
667 | if (u == _graph.target(e)) { |
---|
668 | rc = _res_cap[e]; |
---|
669 | u = _graph.source(e); |
---|
670 | } else { |
---|
671 | rc = (*_flow)[e]; |
---|
672 | u = _graph.target(e); |
---|
673 | } |
---|
674 | if (rc < d) d = rc; |
---|
675 | } |
---|
676 | } |
---|
677 | u = t; |
---|
678 | while ((e = _pred[u]) != INVALID) { |
---|
679 | if (u == _graph.target(e)) { |
---|
680 | (*_flow)[e] += d; |
---|
681 | _res_cap[e] -= d; |
---|
682 | u = _graph.source(e); |
---|
683 | } else { |
---|
684 | (*_flow)[e] -= d; |
---|
685 | _res_cap[e] += d; |
---|
686 | u = _graph.target(e); |
---|
687 | } |
---|
688 | } |
---|
689 | _excess[s] -= d; |
---|
690 | _excess[t] += d; |
---|
691 | } |
---|
692 | |
---|
693 | // Handling non-zero lower bounds |
---|
694 | if (_lower) { |
---|
695 | for (EdgeIt e(_graph); e != INVALID; ++e) |
---|
696 | (*_flow)[e] += (*_lower)[e]; |
---|
697 | } |
---|
698 | return true; |
---|
699 | } |
---|
700 | |
---|
701 | }; //class CapacityScaling |
---|
702 | |
---|
703 | ///@} |
---|
704 | |
---|
705 | } //namespace lemon |
---|
706 | |
---|
707 | #endif //LEMON_CAPACITY_SCALING_H |
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