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 the minimum cost flow of given value in an uncapacitated network |
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8 | |
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9 | #include <hugo/dijkstra.h> |
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10 | #include <hugo/graph_wrapper.h> |
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11 | #include <hugo/maps.h> |
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12 | #include <vector> |
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13 | #include <list> |
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14 | #include <for_each_macros.h> |
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15 | #include <hugo/union_find.h> |
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16 | |
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17 | namespace hugo { |
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18 | |
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19 | /// \addtogroup galgs |
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20 | /// @{ |
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21 | |
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22 | ///\brief Implementation of an algorithm for finding the minimum cost flow |
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23 | /// of given value in an uncapacitated network |
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24 | /// |
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25 | /// |
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26 | /// The class \ref hugo::MinCostFlow "MinCostFlow" implements |
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27 | /// an algorithm for solving the following general minimum cost flow problem> |
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28 | /// |
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29 | /// |
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30 | /// |
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31 | /// \warning It is assumed here that the problem has a feasible solution |
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32 | /// |
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33 | /// The range of the length (weight) function is nonnegative reals but |
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34 | /// the range of capacity function is the set of nonnegative integers. |
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35 | /// It is not a polinomial time algorithm for counting the minimum cost |
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36 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
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37 | /// where \c M is the value of the maximal flow. |
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38 | /// |
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39 | ///\author Attila Bernath |
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40 | template <typename Graph, typename LengthMap, typename SupplyDemandMap> |
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41 | class MinCostFlow { |
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42 | |
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43 | typedef typename LengthMap::ValueType Length; |
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44 | |
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45 | |
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46 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
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47 | |
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48 | typedef typename Graph::Node Node; |
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49 | typedef typename Graph::NodeIt NodeIt; |
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50 | typedef typename Graph::Edge Edge; |
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51 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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52 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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53 | |
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54 | // typedef ConstMap<Edge,int> ConstMap; |
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55 | |
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56 | typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType; |
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57 | typedef typename ResGraphType::Edge ResGraphEdge; |
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58 | |
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59 | class ModLengthMap { |
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60 | //typedef typename ResGraphType::template NodeMap<Length> NodeMap; |
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61 | typedef typename Graph::template NodeMap<Length> NodeMap; |
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62 | const ResGraphType& res_graph; |
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63 | // const EdgeIntMap& rev; |
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64 | const LengthMap &ol; |
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65 | const NodeMap &pot; |
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66 | public : |
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67 | typedef typename LengthMap::KeyType KeyType; |
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68 | typedef typename LengthMap::ValueType ValueType; |
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69 | |
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70 | ValueType operator[](typename ResGraphType::Edge e) const { |
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71 | if (res_graph.forward(e)) |
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72 | return ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]); |
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73 | else |
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74 | return -ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]); |
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75 | } |
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76 | |
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77 | ModLengthMap(const ResGraphType& _res_graph, |
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78 | const LengthMap &o, const NodeMap &p) : |
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79 | res_graph(_res_graph), /*rev(_rev),*/ ol(o), pot(p){}; |
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80 | };//ModLengthMap |
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81 | |
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82 | |
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83 | protected: |
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84 | |
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85 | //Input |
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86 | const Graph& graph; |
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87 | const LengthMap& length; |
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88 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
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89 | |
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90 | |
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91 | //auxiliary variables |
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92 | |
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93 | //To store the flow |
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94 | EdgeIntMap flow; |
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95 | //To store the potentila (dual variables) |
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96 | typename Graph::template NodeMap<Length> potential; |
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97 | //To store excess-deficit values |
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98 | SupplyDemandMap excess_deficit; |
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99 | |
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100 | |
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101 | Length total_length; |
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102 | |
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103 | |
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104 | public : |
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105 | |
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106 | |
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107 | MinCostFlow(Graph& _graph, LengthMap& _length, SupplyDemandMap& _supply_demand) : graph(_graph), |
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108 | length(_length), supply_demand(_supply_demand), flow(_graph), potential(_graph){ } |
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109 | |
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110 | |
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111 | ///Runs the algorithm. |
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112 | |
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113 | ///Runs the algorithm. |
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114 | |
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115 | ///\todo May be it does make sense to be able to start with a nonzero |
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116 | /// feasible primal-dual solution pair as well. |
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117 | void run() { |
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118 | |
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119 | //Resetting variables from previous runs |
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120 | //total_length = 0; |
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121 | |
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122 | typedef typename Graph::template NodeMap<int> HeapMap; |
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123 | typedef Heap< Node, SupplyDemand, typename Graph::template NodeMap<int>, |
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124 | std::greater<SupplyDemand> > HeapType; |
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125 | |
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126 | //A heap for the excess nodes |
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127 | HeapMap excess_nodes_map(graph,-1); |
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128 | HeapType excess_nodes(excess_nodes_map); |
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129 | |
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130 | //A heap for the deficit nodes |
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131 | HeapMap deficit_nodes_map(graph,-1); |
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132 | HeapType deficit_nodes(deficit_nodes_map); |
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133 | |
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134 | //A container to store nonabundant arcs |
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135 | list<Edge> nonabundant_arcs; |
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136 | |
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137 | |
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138 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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139 | flow.set(e,0); |
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140 | nonabundant_arcs.push_back(e); |
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141 | } |
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142 | |
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143 | //Initial value for delta |
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144 | SupplyDemand delta = 0; |
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145 | |
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146 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
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147 | |
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148 | //A union-find structure to store the abundant components |
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149 | UFE::MapType abund_comp_map(graph); |
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150 | UFE abundant_components(abund_comp_map); |
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151 | |
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152 | |
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153 | |
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154 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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155 | excess_deficit.set(n,supply_demand[n]); |
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156 | //A supply node |
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157 | if (excess_deficit[n] > 0){ |
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158 | excess_nodes.push(n,excess_deficit[n]); |
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159 | } |
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160 | //A demand node |
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161 | if (excess_deficit[n] < 0){ |
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162 | deficit_nodes.push(n, - excess_deficit[n]); |
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163 | } |
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164 | //Finding out starting value of delta |
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165 | if (delta < abs(excess_deficit[n])){ |
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166 | delta = abs(excess_deficit[n]); |
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167 | } |
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168 | //Initialize the copy of the Dijkstra potential to zero |
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169 | potential.set(n,0); |
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170 | //Every single point is an abundant component initially |
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171 | abundant_components.insert(n); |
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172 | } |
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173 | |
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174 | //It'll be allright as an initial value, though this value |
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175 | //can be the maximum deficit here |
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176 | SupplyDemand max_excess = delta; |
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177 | |
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178 | //ConstMap<Edge,SupplyDemand> ConstEdgeMap; |
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179 | |
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180 | //We need a residual graph which is uncapacitated |
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181 | ResGraphType res_graph(graph, flow); |
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182 | |
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183 | //An EdgeMap to tell which arcs are abundant |
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184 | template typename Graph::EdgeMap<bool> abundant_arcs(graph); |
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185 | |
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186 | //Let's construct the sugraph consisting only of the abundant edges |
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187 | typedef ConstMap< typename Graph::Node, bool > ConstNodeMap; |
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188 | ConstNodeMap const_true_map(true); |
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189 | typedef SubGraphWrapper< Graph, ConstNodeMap, |
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190 | template typename Graph::EdgeMap<bool> > |
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191 | AbundantGraph; |
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192 | AbundantGraph abundant_graph(graph, const_true_map, abundant_arcs ); |
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193 | |
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194 | //Let's construct the residual graph for the abundant graph |
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195 | typedef ResGraphWrapper<const AbundantGraph,int,CapacityMap,EdgeIntMap> |
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196 | ResAbGraph; |
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197 | //Again uncapacitated |
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198 | ResAbGraph res_ab_graph(abundant_graph, flow); |
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199 | |
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200 | //We need things for the bfs |
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201 | typename ResAbGraph::NodeMap<bool> bfs_reached(res_ab_graph); |
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202 | typename ResAbGraph::NodeMap<typename ResAbGraph::Edge> |
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203 | bfs_pred(res_ab_graph); |
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204 | NullMap<typename ResAbGraph::Node, int> bfs_dist_dummy(res_ab_graph); |
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205 | //We want to run bfs-es (more) on this graph 'res_ab_graph' |
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206 | Bfs < ResAbGraph , |
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207 | typename ResAbGraph::NodeMap<bool>, |
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208 | typename ResAbGraph::NodeMap<typename ResAbGraph::Edge>, |
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209 | NullMap<typename ResAbGraph::Node, int> > |
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210 | bfs(res_ab_graph, bfs_reached, bfs_pred, bfs_dist_dummy); |
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211 | |
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212 | ModLengthMap mod_length(res_graph, length, potential); |
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213 | |
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214 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
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215 | |
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216 | |
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217 | while (max_excess > 0){ |
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218 | |
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219 | //Reset delta if still too big |
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220 | if (8*number_of_nodes*max_excess <= delta){ |
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221 | delta = max_excess; |
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222 | |
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223 | } |
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224 | |
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225 | /* |
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226 | * Beginning of the delta scaling phase |
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227 | */ |
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228 | //Merge and stuff |
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229 | { |
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230 | SupplyDemand buf=8*number_of_nodes*delta; |
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231 | list<Edge>::iterator i = nonabundant_arcs.begin(); |
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232 | while ( i != nonabundant_arcs.end() ){ |
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233 | if (flow[i]>=buf){ |
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234 | Node a = abundant_components.find(res_graph.head(i)); |
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235 | Node b = abundant_components.find(res_graph.tail(i)); |
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236 | //Merge |
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237 | if (a != b){ |
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238 | abundant_components.join(a,b); |
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239 | //We want to push the smaller |
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240 | //Which has greater absolut value excess/deficit |
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241 | Node root=(abs(excess_deficit[a])>abs(excess_deficit[b]))?a:b; |
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242 | //Which is the other |
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243 | Node non_root = ( a == root ) ? b : a ; |
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244 | abundant_components.makeRep(root); |
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245 | SupplyDemand qty_to_augment = abs(excess_deficit[non_root]); |
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246 | //Push the positive value |
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247 | if (excess_deficit[non_root] < 0) |
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248 | swap(root, non_root); |
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249 | //If the non_root node has excess/deficit at all |
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250 | if (qty_to_augment>0){ |
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251 | //Find path and augment |
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252 | bfs.run(non_root); |
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253 | //root should be reached |
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254 | |
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255 | //Augmenting on the found path |
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256 | Node n=root; |
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257 | ResGraphEdge e; |
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258 | while (n!=non_root){ |
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259 | e = bfs_pred(n); |
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260 | n = res_graph.tail(e); |
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261 | res_graph.augment(e,qty_to_augment); |
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262 | } |
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263 | |
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264 | //We know that non_root had positive excess |
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265 | excess_nodes[non_root] -= qty_to_augment; |
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266 | //But what about root node |
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267 | //It might have been positive and so became larger |
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268 | if (excess_deficit[root]>0){ |
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269 | excess_nodes[root] += qty_to_augment; |
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270 | } |
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271 | else{ |
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272 | //Or negative but not turned into positive |
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273 | deficit_nodes[root] -= qty_to_augment; |
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274 | } |
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275 | |
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276 | //Update the excess_deficit map |
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277 | excess_deficit[non_root] -= qty_to_augment; |
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278 | excess_deficit[root] += qty_to_augment; |
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279 | |
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280 | |
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281 | } |
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282 | } |
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283 | //What happens to i? |
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284 | //Marci and Zsolt says I shouldn't do such things |
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285 | nonabundant_arcs.erase(i++); |
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286 | abundant_arcs[i] = true; |
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287 | } |
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288 | else |
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289 | ++i; |
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290 | } |
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291 | } |
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292 | |
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293 | |
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294 | Node s = excess_nodes.top(); |
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295 | SupplyDemand max_excess = excess_nodes[s]; |
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296 | Node t = deficit_nodes.top(); |
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297 | if (max_excess < deficit_nodes[t]){ |
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298 | max_excess = deficit_nodes[t]; |
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299 | } |
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300 | |
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301 | |
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302 | while(max_excess > (n-1)*delta/n){ |
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303 | |
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304 | |
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305 | //s es t valasztasa |
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306 | |
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307 | //Dijkstra part |
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308 | dijkstra.run(s); |
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309 | |
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310 | /*We know from theory that t can be reached |
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311 | if (!dijkstra.reached(t)){ |
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312 | //There are no k paths from s to t |
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313 | break; |
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314 | }; |
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315 | */ |
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316 | |
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317 | //We have to change the potential |
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318 | FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){ |
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319 | potential[n] += dijkstra.distMap()[n]; |
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320 | } |
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321 | |
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322 | |
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323 | //Augmenting on the sortest path |
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324 | Node n=t; |
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325 | ResGraphEdge e; |
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326 | while (n!=s){ |
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327 | e = dijkstra.pred(n); |
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328 | n = dijkstra.predNode(n); |
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329 | res_graph.augment(e,delta); |
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330 | /* |
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331 | //Let's update the total length |
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332 | if (res_graph.forward(e)) |
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333 | total_length += length[e]; |
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334 | else |
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335 | total_length -= length[e]; |
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336 | */ |
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337 | } |
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338 | |
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339 | //Update the excess_deficit map |
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340 | excess_deficit[s] -= delta; |
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341 | excess_deficit[t] += delta; |
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342 | |
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343 | |
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344 | //Update the excess_nodes heap |
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345 | if (delta >= excess_nodes[s]){ |
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346 | if (delta > excess_nodes[s]) |
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347 | deficit_nodes.push(s,delta - excess_nodes[s]); |
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348 | excess_nodes.pop(); |
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349 | |
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350 | } |
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351 | else{ |
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352 | excess_nodes[s] -= delta; |
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353 | } |
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354 | //Update the deficit_nodes heap |
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355 | if (delta >= deficit_nodes[t]){ |
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356 | if (delta > deficit_nodes[t]) |
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357 | excess_nodes.push(t,delta - deficit_nodes[t]); |
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358 | deficit_nodes.pop(); |
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359 | |
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360 | } |
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361 | else{ |
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362 | deficit_nodes[t] -= delta; |
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363 | } |
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364 | //Dijkstra part ends here |
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365 | |
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366 | //Choose s and t again |
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367 | s = excess_nodes.top(); |
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368 | max_excess = excess_nodes[s]; |
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369 | t = deficit_nodes.top(); |
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370 | if (max_excess < deficit_nodes[t]){ |
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371 | max_excess = deficit_nodes[t]; |
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372 | } |
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373 | |
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374 | } |
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375 | |
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376 | /* |
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377 | * End of the delta scaling phase |
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378 | */ |
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379 | |
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380 | //Whatever this means |
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381 | delta = delta / 2; |
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382 | |
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383 | /*This is not necessary here |
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384 | //Update the max_excess |
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385 | max_excess = 0; |
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386 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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387 | if (max_excess < excess_deficit[n]){ |
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388 | max_excess = excess_deficit[n]; |
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389 | } |
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390 | } |
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391 | */ |
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392 | |
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393 | |
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394 | }//while(max_excess > 0) |
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395 | |
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396 | |
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397 | return i; |
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398 | } |
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399 | |
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400 | |
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401 | |
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402 | |
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403 | ///This function gives back the total length of the found paths. |
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404 | ///Assumes that \c run() has been run and nothing changed since then. |
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405 | Length totalLength(){ |
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406 | return total_length; |
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407 | } |
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408 | |
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409 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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410 | ///be called before using this function. |
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411 | const EdgeIntMap &getFlow() const { return flow;} |
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412 | |
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413 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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414 | /// \pre \ref run() must be called before using this function. |
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415 | const EdgeIntMap &getPotential() const { return potential;} |
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416 | |
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417 | ///This function checks, whether the given solution is optimal |
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418 | ///Running after a \c run() should return with true |
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419 | ///In this "state of the art" this only check optimality, doesn't bother with feasibility |
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420 | /// |
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421 | ///\todo Is this OK here? |
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422 | bool checkComplementarySlackness(){ |
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423 | Length mod_pot; |
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424 | Length fl_e; |
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425 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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426 | //C^{\Pi}_{i,j} |
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427 | mod_pot = length[e]-potential[graph.head(e)]+potential[graph.tail(e)]; |
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428 | fl_e = flow[e]; |
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429 | // std::cout << fl_e << std::endl; |
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430 | if (0<fl_e && fl_e<capacity[e]){ |
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431 | if (mod_pot != 0) |
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432 | return false; |
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433 | } |
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434 | else{ |
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435 | if (mod_pot > 0 && fl_e != 0) |
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436 | return false; |
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437 | if (mod_pot < 0 && fl_e != capacity[e]) |
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438 | return false; |
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439 | } |
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440 | } |
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441 | return true; |
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442 | } |
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443 | |
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444 | |
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445 | }; //class MinCostFlow |
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446 | |
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447 | ///@} |
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448 | |
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449 | } //namespace hugo |
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450 | |
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451 | #endif //HUGO_MINCOSTFLOW_H |
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