1 | // -*- c++ -*- |
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2 | #ifndef HUGO_MINCOSTFLOWS_H |
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3 | #define HUGO_MINCOSTFLOWS_H |
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4 | |
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5 | ///\ingroup flowalgs |
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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 | |
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15 | namespace hugo { |
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16 | |
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17 | /// \addtogroup flowalgs |
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18 | /// @{ |
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19 | |
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20 | ///\brief Implementation of an algorithm for finding a flow of value \c k |
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21 | ///(for small values of \c k) having minimal total cost between 2 nodes |
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22 | /// |
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23 | /// |
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24 | /// The class \ref hugo::MinCostFlows "MinCostFlows" implements |
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25 | /// an algorithm for finding a flow of value \c k |
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26 | ///(for small values of \c k) having minimal total cost |
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27 | /// from a given source node to a given target node in an |
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28 | /// edge-weighted directed graph having nonnegative integer capacities. |
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29 | /// The range of the length (weight) function is nonnegative reals but |
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30 | /// the range of capacity function is the set of nonnegative integers. |
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31 | /// It is not a polinomial time algorithm for counting the minimum cost |
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32 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
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33 | /// where \c M is the value of the maximal flow. |
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34 | /// |
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35 | ///\author Attila Bernath |
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36 | template <typename Graph, typename LengthMap, typename CapacityMap> |
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37 | class MinCostFlows { |
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38 | |
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39 | typedef typename LengthMap::ValueType Length; |
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40 | |
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41 | //Warning: this should be integer type |
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42 | typedef typename CapacityMap::ValueType Capacity; |
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43 | |
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44 | typedef typename Graph::Node Node; |
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45 | typedef typename Graph::NodeIt NodeIt; |
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46 | typedef typename Graph::Edge Edge; |
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47 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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48 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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49 | |
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50 | // typedef ConstMap<Edge,int> ConstMap; |
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51 | |
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52 | typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType; |
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53 | typedef typename ResGraphType::Edge ResGraphEdge; |
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54 | |
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55 | class ModLengthMap { |
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56 | //typedef typename ResGraphType::template NodeMap<Length> NodeMap; |
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57 | typedef typename Graph::template NodeMap<Length> NodeMap; |
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58 | const ResGraphType& G; |
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59 | // const EdgeIntMap& rev; |
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60 | const LengthMap &ol; |
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61 | const NodeMap &pot; |
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62 | public : |
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63 | typedef typename LengthMap::KeyType KeyType; |
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64 | typedef typename LengthMap::ValueType ValueType; |
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65 | |
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66 | ValueType operator[](typename ResGraphType::Edge e) const { |
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67 | if (G.forward(e)) |
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68 | return ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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69 | else |
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70 | return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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71 | } |
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72 | |
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73 | ModLengthMap(const ResGraphType& _G, |
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74 | const LengthMap &o, const NodeMap &p) : |
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75 | G(_G), /*rev(_rev),*/ ol(o), pot(p){}; |
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76 | };//ModLengthMap |
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77 | |
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78 | |
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79 | protected: |
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80 | |
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81 | //Input |
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82 | const Graph& G; |
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83 | const LengthMap& length; |
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84 | const CapacityMap& capacity; |
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85 | |
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86 | |
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87 | //auxiliary variables |
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88 | |
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89 | //To store the flow |
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90 | EdgeIntMap flow; |
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91 | //To store the potential (dual variables) |
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92 | typedef typename Graph::template NodeMap<Length> PotentialMap; |
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93 | PotentialMap potential; |
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94 | |
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95 | |
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96 | Length total_length; |
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97 | |
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98 | |
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99 | public : |
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100 | |
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101 | |
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102 | MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), |
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103 | length(_length), capacity(_cap), flow(_G), potential(_G){ } |
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104 | |
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105 | |
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106 | ///Runs the algorithm. |
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107 | |
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108 | ///Runs the algorithm. |
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109 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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110 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
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111 | ///\todo May be it does make sense to be able to start with a nonzero |
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112 | /// feasible primal-dual solution pair as well. |
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113 | int run(Node s, Node t, int k) { |
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114 | |
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115 | //Resetting variables from previous runs |
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116 | total_length = 0; |
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117 | |
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118 | for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0); |
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119 | |
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120 | //Initialize the potential to zero |
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121 | for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0); |
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122 | |
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123 | |
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124 | //We need a residual graph |
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125 | ResGraphType res_graph(G, capacity, flow); |
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126 | |
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127 | |
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128 | ModLengthMap mod_length(res_graph, length, potential); |
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129 | |
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130 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
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131 | |
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132 | int i; |
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133 | for (i=0; i<k; ++i){ |
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134 | dijkstra.run(s); |
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135 | if (!dijkstra.reached(t)){ |
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136 | //There are no k paths from s to t |
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137 | break; |
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138 | }; |
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139 | |
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140 | //We have to change the potential |
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141 | for(typename ResGraphType::NodeIt n(res_graph); n!=INVALID; ++n) |
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142 | potential[n] += dijkstra.distMap()[n]; |
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143 | |
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144 | |
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145 | //Augmenting on the sortest path |
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146 | Node n=t; |
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147 | ResGraphEdge e; |
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148 | while (n!=s){ |
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149 | e = dijkstra.pred(n); |
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150 | n = dijkstra.predNode(n); |
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151 | res_graph.augment(e,1); |
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152 | //Let's update the total length |
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153 | if (res_graph.forward(e)) |
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154 | total_length += length[e]; |
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155 | else |
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156 | total_length -= length[e]; |
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157 | } |
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158 | |
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159 | |
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160 | } |
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161 | |
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162 | |
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163 | return i; |
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164 | } |
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165 | |
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166 | |
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167 | |
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168 | |
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169 | ///This function gives back the total length of the found paths. |
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170 | ///Assumes that \c run() has been run and nothing changed since then. |
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171 | Length totalLength(){ |
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172 | return total_length; |
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173 | } |
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174 | |
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175 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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176 | ///be called before using this function. |
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177 | const EdgeIntMap &getFlow() const { return flow;} |
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178 | |
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179 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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180 | /// \pre \ref run() must be called before using this function. |
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181 | const PotentialMap &getPotential() const { return potential;} |
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182 | |
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183 | ///This function checks, whether the given solution is optimal |
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184 | ///Running after a \c run() should return with true |
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185 | ///In this "state of the art" this only check optimality, doesn't bother with feasibility |
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186 | /// |
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187 | ///\todo Is this OK here? |
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188 | bool checkComplementarySlackness(){ |
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189 | Length mod_pot; |
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190 | Length fl_e; |
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191 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) { |
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192 | //C^{\Pi}_{i,j} |
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193 | mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)]; |
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194 | fl_e = flow[e]; |
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195 | // std::cout << fl_e << std::endl; |
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196 | if (0<fl_e && fl_e<capacity[e]){ |
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197 | if (mod_pot != 0) |
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198 | return false; |
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199 | } |
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200 | else{ |
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201 | if (mod_pot > 0 && fl_e != 0) |
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202 | return false; |
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203 | if (mod_pot < 0 && fl_e != capacity[e]) |
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204 | return false; |
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205 | } |
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206 | } |
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207 | return true; |
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208 | } |
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209 | |
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210 | |
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211 | }; //class MinCostFlows |
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212 | |
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213 | ///@} |
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214 | |
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215 | } //namespace hugo |
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216 | |
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217 | #endif //HUGO_MINCOSTFLOWS_H |
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