1 | // -*- c++ -*- |
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2 | #ifndef HUGO_MINCOSTFLOW_H |
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3 | #define HUGO_MINCOSTFLOW_H |
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4 | |
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5 | ///\ingroup galgs |
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6 | ///\file |
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7 | ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost |
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8 | |
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9 | |
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10 | #include <hugo/dijkstra.h> |
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11 | #include <hugo/graph_wrapper.h> |
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12 | #include <hugo/maps.h> |
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13 | #include <vector> |
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14 | #include <for_each_macros.h> |
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15 | |
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16 | namespace hugo { |
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17 | |
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18 | /// \addtogroup galgs |
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19 | /// @{ |
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20 | |
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21 | ///\brief Implementation of an algorithm for finding a flow of value \c k |
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22 | ///(for small values of \c k) having minimal total cost between 2 nodes |
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23 | /// |
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24 | /// |
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25 | /// The class \ref hugo::MinCostFlow "MinCostFlow" implements |
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26 | /// an algorithm for solving the following general minimum cost flow problem> |
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27 | /// |
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28 | /// |
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29 | /// |
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30 | /// \warning It is assumed here that the problem has a feasible solution |
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31 | /// |
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32 | /// The range of the length (weight) function is nonnegative reals but |
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33 | /// the range of capacity function is the set of nonnegative integers. |
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34 | /// It is not a polinomial time algorithm for counting the minimum cost |
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35 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
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36 | /// where \c M is the value of the maximal flow. |
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37 | /// |
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38 | ///\author Attila Bernath |
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39 | template <typename Graph, typename LengthMap, typename SupplyDemandMap> |
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40 | class MinCostFlow { |
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41 | |
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42 | typedef typename LengthMap::ValueType Length; |
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43 | |
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44 | |
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45 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
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46 | |
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47 | typedef typename Graph::Node Node; |
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48 | typedef typename Graph::NodeIt NodeIt; |
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49 | typedef typename Graph::Edge Edge; |
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50 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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51 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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52 | |
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53 | // typedef ConstMap<Edge,int> ConstMap; |
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54 | |
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55 | typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType; |
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56 | typedef typename ResGraphType::Edge ResGraphEdge; |
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57 | |
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58 | class ModLengthMap { |
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59 | //typedef typename ResGraphType::template NodeMap<Length> NodeMap; |
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60 | typedef typename Graph::template NodeMap<Length> NodeMap; |
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61 | const ResGraphType& G; |
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62 | // const EdgeIntMap& rev; |
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63 | const LengthMap &ol; |
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64 | const NodeMap &pot; |
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65 | public : |
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66 | typedef typename LengthMap::KeyType KeyType; |
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67 | typedef typename LengthMap::ValueType ValueType; |
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68 | |
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69 | ValueType operator[](typename ResGraphType::Edge e) const { |
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70 | if (G.forward(e)) |
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71 | return ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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72 | else |
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73 | return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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74 | } |
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75 | |
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76 | ModLengthMap(const ResGraphType& _G, |
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77 | const LengthMap &o, const NodeMap &p) : |
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78 | G(_G), /*rev(_rev),*/ ol(o), pot(p){}; |
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79 | };//ModLengthMap |
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80 | |
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81 | |
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82 | protected: |
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83 | |
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84 | //Input |
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85 | const Graph& G; |
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86 | const LengthMap& length; |
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87 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
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88 | |
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89 | |
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90 | //auxiliary variables |
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91 | |
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92 | //To store the flow |
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93 | EdgeIntMap flow; |
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94 | //To store the potentila (dual variables) |
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95 | typename Graph::template NodeMap<Length> potential; |
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96 | //To store excess-deficit values |
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97 | SupplyDemandMap excess_deficit; |
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98 | |
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99 | |
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100 | Length total_length; |
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101 | |
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102 | |
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103 | public : |
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104 | |
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105 | |
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106 | MinCostFlow(Graph& _G, LengthMap& _length, SupplyDemandMap& _supply_demand) : G(_G), |
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107 | length(_length), supply_demand(_supply_demand), flow(_G), potential(_G){ } |
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108 | |
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109 | |
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110 | ///Runs the algorithm. |
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111 | |
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112 | ///Runs the algorithm. |
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113 | |
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114 | ///\todo May be it does make sense to be able to start with a nonzero |
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115 | /// feasible primal-dual solution pair as well. |
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116 | int run() { |
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117 | |
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118 | //Resetting variables from previous runs |
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119 | //total_length = 0; |
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120 | |
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121 | typedef typename Graph::template NodeMap<int> HeapMap; |
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122 | typedef Heap<Node, SupplyDemand, typename Graph::template NodeMap<int>, |
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123 | std::greater<SupplyDemand> > HeapType; |
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124 | |
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125 | //A heap for the excess nodes |
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126 | HeapMap excess_nodes_map(G,-1); |
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127 | HeapType excess_nodes(excess_nodes_map); |
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128 | |
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129 | //A heap for the deficit nodes |
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130 | HeapMap deficit_nodes_map(G,-1); |
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131 | HeapType deficit_nodes(deficit_nodes_map); |
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132 | |
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133 | |
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134 | FOR_EACH_LOC(typename Graph::EdgeIt, e, G){ |
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135 | flow.set(e,0); |
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136 | } |
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137 | |
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138 | //Initial value for delta |
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139 | SupplyDemand delta = 0; |
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140 | |
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141 | FOR_EACH_LOC(typename Graph::NodeIt, n, G){ |
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142 | excess_deficit.set(n,supply_demand[n]); |
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143 | //A supply node |
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144 | if (excess_deficit[n] > 0){ |
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145 | excess_nodes.push(n,excess_deficit[n]); |
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146 | } |
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147 | //A demand node |
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148 | if (excess_deficit[n] < 0){ |
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149 | deficit_nodes.push(n, - excess_deficit[n]); |
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150 | } |
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151 | //Finding out starting value of delta |
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152 | if (delta < abs(excess_deficit[n])){ |
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153 | delta = abs(excess_deficit[n]); |
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154 | } |
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155 | //Initialize the copy of the Dijkstra potential to zero |
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156 | potential.set(n,0); |
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157 | } |
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158 | |
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159 | //It'll be allright as an initial value, though this value |
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160 | //can be the maximum deficit here |
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161 | SupplyDemand max_excess = delta; |
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162 | |
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163 | //We need a residual graph which is uncapacitated |
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164 | ResGraphType res_graph(G, flow); |
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165 | |
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166 | |
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167 | |
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168 | ModLengthMap mod_length(res_graph, length, potential); |
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169 | |
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170 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
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171 | |
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172 | |
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173 | while (max_excess > 0){ |
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174 | |
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175 | |
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176 | //Merge and stuff |
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177 | |
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178 | Node s = excess_nodes.top(); |
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179 | SupplyDemand max_excess = excess_nodes[s]; |
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180 | Node t = deficit_nodes.top(); |
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181 | if (max_excess < dificit_nodes[t]){ |
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182 | max_excess = dificit_nodes[t]; |
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183 | } |
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184 | |
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185 | |
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186 | while(max_excess > ){ |
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187 | |
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188 | |
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189 | //s es t valasztasa |
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190 | |
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191 | //Dijkstra part |
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192 | dijkstra.run(s); |
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193 | |
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194 | /*We know from theory that t can be reached |
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195 | if (!dijkstra.reached(t)){ |
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196 | //There are no k paths from s to t |
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197 | break; |
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198 | }; |
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199 | */ |
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200 | |
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201 | //We have to change the potential |
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202 | FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){ |
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203 | potential[n] += dijkstra.distMap()[n]; |
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204 | } |
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205 | |
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206 | |
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207 | //Augmenting on the sortest path |
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208 | Node n=t; |
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209 | ResGraphEdge e; |
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210 | while (n!=s){ |
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211 | e = dijkstra.pred(n); |
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212 | n = dijkstra.predNode(n); |
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213 | res_graph.augment(e,delta); |
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214 | /* |
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215 | //Let's update the total length |
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216 | if (res_graph.forward(e)) |
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217 | total_length += length[e]; |
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218 | else |
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219 | total_length -= length[e]; |
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220 | */ |
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221 | } |
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222 | |
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223 | //Update the excess_nodes heap |
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224 | if (delta >= excess_nodes[s]){ |
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225 | if (delta > excess_nodes[s]) |
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226 | deficit_nodes.push(s,delta - excess_nodes[s]); |
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227 | excess_nodes.pop(); |
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228 | |
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229 | } |
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230 | else{ |
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231 | excess_nodes[s] -= delta; |
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232 | } |
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233 | //Update the deficit_nodes heap |
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234 | if (delta >= deficit_nodes[t]){ |
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235 | if (delta > deficit_nodes[t]) |
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236 | excess_nodes.push(t,delta - deficit_nodes[t]); |
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237 | deficit_nodes.pop(); |
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238 | |
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239 | } |
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240 | else{ |
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241 | deficit_nodes[t] -= delta; |
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242 | } |
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243 | //Dijkstra part ends here |
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244 | } |
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245 | |
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246 | /* |
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247 | * End of the delta scaling phase |
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248 | */ |
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249 | |
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250 | //Whatever this means |
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251 | delta = delta / 2; |
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252 | |
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253 | /*This is not necessary here |
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254 | //Update the max_excess |
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255 | max_excess = 0; |
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256 | FOR_EACH_LOC(typename Graph::NodeIt, n, G){ |
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257 | if (max_excess < excess_deficit[n]){ |
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258 | max_excess = excess_deficit[n]; |
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259 | } |
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260 | } |
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261 | */ |
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262 | //Reset delta if still too big |
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263 | if (8*number_of_nodes*max_excess <= delta){ |
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264 | delta = max_excess; |
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265 | |
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266 | } |
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267 | |
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268 | }//while(max_excess > 0) |
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269 | |
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270 | |
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271 | return i; |
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272 | } |
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273 | |
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274 | |
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275 | |
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276 | |
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277 | ///This function gives back the total length of the found paths. |
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278 | ///Assumes that \c run() has been run and nothing changed since then. |
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279 | Length totalLength(){ |
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280 | return total_length; |
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281 | } |
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282 | |
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283 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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284 | ///be called before using this function. |
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285 | const EdgeIntMap &getFlow() const { return flow;} |
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286 | |
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287 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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288 | /// \pre \ref run() must be called before using this function. |
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289 | const EdgeIntMap &getPotential() const { return potential;} |
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290 | |
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291 | ///This function checks, whether the given solution is optimal |
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292 | ///Running after a \c run() should return with true |
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293 | ///In this "state of the art" this only check optimality, doesn't bother with feasibility |
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294 | /// |
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295 | ///\todo Is this OK here? |
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296 | bool checkComplementarySlackness(){ |
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297 | Length mod_pot; |
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298 | Length fl_e; |
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299 | FOR_EACH_LOC(typename Graph::EdgeIt, e, G){ |
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300 | //C^{\Pi}_{i,j} |
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301 | mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)]; |
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302 | fl_e = flow[e]; |
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303 | // std::cout << fl_e << std::endl; |
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304 | if (0<fl_e && fl_e<capacity[e]){ |
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305 | if (mod_pot != 0) |
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306 | return false; |
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307 | } |
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308 | else{ |
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309 | if (mod_pot > 0 && fl_e != 0) |
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310 | return false; |
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311 | if (mod_pot < 0 && fl_e != capacity[e]) |
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312 | return false; |
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313 | } |
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314 | } |
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315 | return true; |
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316 | } |
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317 | |
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318 | |
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319 | }; //class MinCostFlow |
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320 | |
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321 | ///@} |
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322 | |
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323 | } //namespace hugo |
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324 | |
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325 | #endif //HUGO_MINCOSTFLOW_H |
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