[610] | 1 | // -*- c++ -*- |
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[633] | 2 | #ifndef HUGO_MINCOSTFLOW_H |
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| 3 | #define HUGO_MINCOSTFLOW_H |
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[610] | 4 | |
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| 5 | ///\ingroup galgs |
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| 6 | ///\file |
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[645] | 7 | ///\brief An algorithm for finding the minimum cost flow of given value in an uncapacitated network |
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[611] | 8 | |
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[610] | 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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[657] | 13 | #include <list> |
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[662] | 14 | #include <values.h> |
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[661] | 15 | #include <hugo/for_each_macros.h> |
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| 16 | #include <hugo/unionfind.h> |
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[662] | 17 | #include <hugo/bin_heap.h> |
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| 18 | #include <bfs_dfs.h> |
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[610] | 19 | |
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| 20 | namespace hugo { |
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| 21 | |
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| 22 | /// \addtogroup galgs |
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| 23 | /// @{ |
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| 24 | |
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[661] | 25 | ///\brief Implementation of an algorithm for solving the minimum cost general |
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| 26 | /// flow problem in an uncapacitated network |
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[610] | 27 | /// |
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| 28 | /// |
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[633] | 29 | /// The class \ref hugo::MinCostFlow "MinCostFlow" implements |
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| 30 | /// an algorithm for solving the following general minimum cost flow problem> |
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| 31 | /// |
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| 32 | /// |
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| 33 | /// |
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| 34 | /// \warning It is assumed here that the problem has a feasible solution |
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| 35 | /// |
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[661] | 36 | /// The range of the cost (weight) function is nonnegative reals but |
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[610] | 37 | /// the range of capacity function is the set of nonnegative integers. |
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| 38 | /// It is not a polinomial time algorithm for counting the minimum cost |
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| 39 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
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| 40 | /// where \c M is the value of the maximal flow. |
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| 41 | /// |
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| 42 | ///\author Attila Bernath |
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[661] | 43 | template <typename Graph, typename CostMap, typename SupplyDemandMap> |
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[633] | 44 | class MinCostFlow { |
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[610] | 45 | |
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[661] | 46 | typedef typename CostMap::ValueType Cost; |
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[610] | 47 | |
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[633] | 48 | |
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[635] | 49 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
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[610] | 50 | |
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| 51 | typedef typename Graph::Node Node; |
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| 52 | typedef typename Graph::NodeIt NodeIt; |
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| 53 | typedef typename Graph::Edge Edge; |
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| 54 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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[661] | 55 | typedef typename Graph::template EdgeMap<SupplyDemand> FlowMap; |
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| 56 | typedef ConstMap<Edge,SupplyDemand> ConstEdgeMap; |
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[610] | 57 | |
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| 58 | // typedef ConstMap<Edge,int> ConstMap; |
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| 59 | |
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[661] | 60 | typedef ResGraphWrapper<const Graph,int,ConstEdgeMap,FlowMap> ResGraph; |
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| 61 | typedef typename ResGraph::Edge ResGraphEdge; |
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[610] | 62 | |
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[661] | 63 | class ModCostMap { |
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| 64 | //typedef typename ResGraph::template NodeMap<Cost> NodeMap; |
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| 65 | typedef typename Graph::template NodeMap<Cost> NodeMap; |
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| 66 | const ResGraph& res_graph; |
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[610] | 67 | // const EdgeIntMap& rev; |
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[661] | 68 | const CostMap &ol; |
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[610] | 69 | const NodeMap &pot; |
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| 70 | public : |
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[661] | 71 | typedef typename CostMap::KeyType KeyType; |
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| 72 | typedef typename CostMap::ValueType ValueType; |
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[610] | 73 | |
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[661] | 74 | ValueType operator[](typename ResGraph::Edge e) const { |
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[659] | 75 | if (res_graph.forward(e)) |
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| 76 | return ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]); |
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[610] | 77 | else |
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[659] | 78 | return -ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]); |
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[610] | 79 | } |
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| 80 | |
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[661] | 81 | ModCostMap(const ResGraph& _res_graph, |
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| 82 | const CostMap &o, const NodeMap &p) : |
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[659] | 83 | res_graph(_res_graph), /*rev(_rev),*/ ol(o), pot(p){}; |
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[661] | 84 | };//ModCostMap |
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[610] | 85 | |
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| 86 | |
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| 87 | protected: |
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| 88 | |
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| 89 | //Input |
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[659] | 90 | const Graph& graph; |
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[661] | 91 | const CostMap& cost; |
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[635] | 92 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
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[610] | 93 | |
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| 94 | |
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| 95 | //auxiliary variables |
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| 96 | |
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| 97 | //To store the flow |
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[661] | 98 | FlowMap flow; |
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[662] | 99 | //To store the potential (dual variables) |
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| 100 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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| 101 | PotentialMap potential; |
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[633] | 102 | //To store excess-deficit values |
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[635] | 103 | SupplyDemandMap excess_deficit; |
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[610] | 104 | |
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| 105 | |
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[661] | 106 | Cost total_cost; |
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[610] | 107 | |
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| 108 | |
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| 109 | public : |
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| 110 | |
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| 111 | |
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[662] | 112 | MinCostFlow(Graph& _graph, CostMap& _cost, SupplyDemandMap& _supply_demand): |
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| 113 | graph(_graph), |
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| 114 | cost(_cost), |
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| 115 | supply_demand(_supply_demand), |
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| 116 | flow(_graph), |
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| 117 | potential(_graph), |
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| 118 | excess_deficit(_graph){ } |
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[610] | 119 | |
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| 120 | |
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| 121 | ///Runs the algorithm. |
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| 122 | |
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| 123 | ///Runs the algorithm. |
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[635] | 124 | |
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[610] | 125 | ///\todo May be it does make sense to be able to start with a nonzero |
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| 126 | /// feasible primal-dual solution pair as well. |
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[659] | 127 | void run() { |
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[610] | 128 | |
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| 129 | //Resetting variables from previous runs |
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[661] | 130 | //total_cost = 0; |
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[635] | 131 | |
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| 132 | typedef typename Graph::template NodeMap<int> HeapMap; |
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[662] | 133 | typedef BinHeap< Node, SupplyDemand, typename Graph::template NodeMap<int>, |
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[635] | 134 | std::greater<SupplyDemand> > HeapType; |
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| 135 | |
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| 136 | //A heap for the excess nodes |
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[659] | 137 | HeapMap excess_nodes_map(graph,-1); |
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[635] | 138 | HeapType excess_nodes(excess_nodes_map); |
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| 139 | |
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| 140 | //A heap for the deficit nodes |
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[659] | 141 | HeapMap deficit_nodes_map(graph,-1); |
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[635] | 142 | HeapType deficit_nodes(deficit_nodes_map); |
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| 143 | |
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[657] | 144 | //A container to store nonabundant arcs |
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[662] | 145 | std::list<Edge> nonabundant_arcs; |
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[659] | 146 | |
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| 147 | |
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| 148 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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[610] | 149 | flow.set(e,0); |
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[657] | 150 | nonabundant_arcs.push_back(e); |
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[610] | 151 | } |
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[633] | 152 | |
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| 153 | //Initial value for delta |
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[635] | 154 | SupplyDemand delta = 0; |
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| 155 | |
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[657] | 156 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
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| 157 | |
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| 158 | //A union-find structure to store the abundant components |
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[662] | 159 | typename UFE::MapType abund_comp_map(graph); |
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[657] | 160 | UFE abundant_components(abund_comp_map); |
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| 161 | |
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| 162 | |
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| 163 | |
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[659] | 164 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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[635] | 165 | excess_deficit.set(n,supply_demand[n]); |
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| 166 | //A supply node |
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| 167 | if (excess_deficit[n] > 0){ |
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| 168 | excess_nodes.push(n,excess_deficit[n]); |
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[633] | 169 | } |
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[635] | 170 | //A demand node |
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| 171 | if (excess_deficit[n] < 0){ |
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| 172 | deficit_nodes.push(n, - excess_deficit[n]); |
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| 173 | } |
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| 174 | //Finding out starting value of delta |
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| 175 | if (delta < abs(excess_deficit[n])){ |
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| 176 | delta = abs(excess_deficit[n]); |
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| 177 | } |
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[633] | 178 | //Initialize the copy of the Dijkstra potential to zero |
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[610] | 179 | potential.set(n,0); |
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[657] | 180 | //Every single point is an abundant component initially |
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| 181 | abundant_components.insert(n); |
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[610] | 182 | } |
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| 183 | |
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[635] | 184 | //It'll be allright as an initial value, though this value |
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| 185 | //can be the maximum deficit here |
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| 186 | SupplyDemand max_excess = delta; |
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[610] | 187 | |
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[661] | 188 | ///\bug This is a serious cheat here, before we have an uncapacitated ResGraph |
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[662] | 189 | ConstEdgeMap const_inf_map(MAXINT); |
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[661] | 190 | |
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[633] | 191 | //We need a residual graph which is uncapacitated |
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[661] | 192 | ResGraph res_graph(graph, const_inf_map, flow); |
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[659] | 193 | |
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| 194 | //An EdgeMap to tell which arcs are abundant |
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[662] | 195 | typename Graph::template EdgeMap<bool> abundant_arcs(graph); |
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[610] | 196 | |
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[659] | 197 | //Let's construct the sugraph consisting only of the abundant edges |
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| 198 | typedef ConstMap< typename Graph::Node, bool > ConstNodeMap; |
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| 199 | ConstNodeMap const_true_map(true); |
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[662] | 200 | typedef SubGraphWrapper< const Graph, ConstNodeMap, |
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| 201 | typename Graph::template EdgeMap<bool> > |
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[659] | 202 | AbundantGraph; |
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| 203 | AbundantGraph abundant_graph(graph, const_true_map, abundant_arcs ); |
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| 204 | |
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| 205 | //Let's construct the residual graph for the abundant graph |
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[662] | 206 | typedef ResGraphWrapper<const AbundantGraph,int,ConstEdgeMap,FlowMap> |
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[659] | 207 | ResAbGraph; |
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| 208 | //Again uncapacitated |
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[661] | 209 | ResAbGraph res_ab_graph(abundant_graph, const_inf_map, flow); |
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[659] | 210 | |
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| 211 | //We need things for the bfs |
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[662] | 212 | typename ResAbGraph::template NodeMap<bool> bfs_reached(res_ab_graph); |
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| 213 | typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge> |
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[659] | 214 | bfs_pred(res_ab_graph); |
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[662] | 215 | NullMap<typename ResAbGraph::Node, int> bfs_dist_dummy; |
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[659] | 216 | //We want to run bfs-es (more) on this graph 'res_ab_graph' |
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| 217 | Bfs < ResAbGraph , |
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[662] | 218 | typename ResAbGraph::template NodeMap<bool>, |
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| 219 | typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge>, |
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[659] | 220 | NullMap<typename ResAbGraph::Node, int> > |
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| 221 | bfs(res_ab_graph, bfs_reached, bfs_pred, bfs_dist_dummy); |
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[662] | 222 | /*This is what Marci wants for a bfs |
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| 223 | template <typename Graph, |
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| 224 | typename ReachedMap=typename Graph::template NodeMap<bool>, |
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| 225 | typename PredMap |
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| 226 | =typename Graph::template NodeMap<typename Graph::Edge>, |
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| 227 | typename DistMap=typename Graph::template NodeMap<int> > |
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| 228 | class Bfs : public BfsIterator<Graph, ReachedMap> { |
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| 229 | |
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| 230 | */ |
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[610] | 231 | |
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[661] | 232 | ModCostMap mod_cost(res_graph, cost, potential); |
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[610] | 233 | |
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[661] | 234 | Dijkstra<ResGraph, ModCostMap> dijkstra(res_graph, mod_cost); |
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[610] | 235 | |
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[633] | 236 | |
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[635] | 237 | while (max_excess > 0){ |
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| 238 | |
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[657] | 239 | //Reset delta if still too big |
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| 240 | if (8*number_of_nodes*max_excess <= delta){ |
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| 241 | delta = max_excess; |
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| 242 | |
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| 243 | } |
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| 244 | |
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[645] | 245 | /* |
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| 246 | * Beginning of the delta scaling phase |
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| 247 | */ |
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[635] | 248 | //Merge and stuff |
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[657] | 249 | { |
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| 250 | SupplyDemand buf=8*number_of_nodes*delta; |
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[662] | 251 | typename std::list<Edge>::iterator i = nonabundant_arcs.begin(); |
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[657] | 252 | while ( i != nonabundant_arcs.end() ){ |
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| 253 | if (flow[i]>=buf){ |
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| 254 | Node a = abundant_components.find(res_graph.head(i)); |
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| 255 | Node b = abundant_components.find(res_graph.tail(i)); |
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| 256 | //Merge |
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| 257 | if (a != b){ |
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| 258 | abundant_components.join(a,b); |
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[659] | 259 | //We want to push the smaller |
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| 260 | //Which has greater absolut value excess/deficit |
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| 261 | Node root=(abs(excess_deficit[a])>abs(excess_deficit[b]))?a:b; |
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| 262 | //Which is the other |
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| 263 | Node non_root = ( a == root ) ? b : a ; |
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| 264 | abundant_components.makeRep(root); |
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| 265 | SupplyDemand qty_to_augment = abs(excess_deficit[non_root]); |
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| 266 | //Push the positive value |
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| 267 | if (excess_deficit[non_root] < 0) |
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| 268 | swap(root, non_root); |
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| 269 | //If the non_root node has excess/deficit at all |
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| 270 | if (qty_to_augment>0){ |
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| 271 | //Find path and augment |
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| 272 | bfs.run(non_root); |
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| 273 | //root should be reached |
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| 274 | |
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| 275 | //Augmenting on the found path |
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| 276 | Node n=root; |
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| 277 | ResGraphEdge e; |
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| 278 | while (n!=non_root){ |
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| 279 | e = bfs_pred(n); |
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| 280 | n = res_graph.tail(e); |
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| 281 | res_graph.augment(e,qty_to_augment); |
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| 282 | } |
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| 283 | |
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| 284 | //We know that non_root had positive excess |
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| 285 | excess_nodes[non_root] -= qty_to_augment; |
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| 286 | //But what about root node |
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| 287 | //It might have been positive and so became larger |
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| 288 | if (excess_deficit[root]>0){ |
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| 289 | excess_nodes[root] += qty_to_augment; |
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| 290 | } |
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| 291 | else{ |
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| 292 | //Or negative but not turned into positive |
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| 293 | deficit_nodes[root] -= qty_to_augment; |
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| 294 | } |
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| 295 | |
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| 296 | //Update the excess_deficit map |
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| 297 | excess_deficit[non_root] -= qty_to_augment; |
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| 298 | excess_deficit[root] += qty_to_augment; |
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| 299 | |
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| 300 | |
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| 301 | } |
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[657] | 302 | } |
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| 303 | //What happens to i? |
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[659] | 304 | //Marci and Zsolt says I shouldn't do such things |
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| 305 | nonabundant_arcs.erase(i++); |
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| 306 | abundant_arcs[i] = true; |
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[657] | 307 | } |
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| 308 | else |
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| 309 | ++i; |
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| 310 | } |
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| 311 | } |
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| 312 | |
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[635] | 313 | |
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| 314 | Node s = excess_nodes.top(); |
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| 315 | SupplyDemand max_excess = excess_nodes[s]; |
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| 316 | Node t = deficit_nodes.top(); |
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[659] | 317 | if (max_excess < deficit_nodes[t]){ |
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| 318 | max_excess = deficit_nodes[t]; |
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[635] | 319 | } |
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| 320 | |
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| 321 | |
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[662] | 322 | while(max_excess > (number_of_nodes-1)*delta/number_of_nodes){ |
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[659] | 323 | |
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[635] | 324 | |
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| 325 | //s es t valasztasa |
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[659] | 326 | |
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[635] | 327 | //Dijkstra part |
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| 328 | dijkstra.run(s); |
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[659] | 329 | |
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[635] | 330 | /*We know from theory that t can be reached |
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| 331 | if (!dijkstra.reached(t)){ |
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| 332 | //There are no k paths from s to t |
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| 333 | break; |
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| 334 | }; |
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| 335 | */ |
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| 336 | |
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| 337 | //We have to change the potential |
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[661] | 338 | FOR_EACH_LOC(typename ResGraph::NodeIt, n, res_graph){ |
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[635] | 339 | potential[n] += dijkstra.distMap()[n]; |
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| 340 | } |
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| 341 | |
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| 342 | |
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| 343 | //Augmenting on the sortest path |
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| 344 | Node n=t; |
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| 345 | ResGraphEdge e; |
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| 346 | while (n!=s){ |
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| 347 | e = dijkstra.pred(n); |
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| 348 | n = dijkstra.predNode(n); |
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| 349 | res_graph.augment(e,delta); |
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| 350 | /* |
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[661] | 351 | //Let's update the total cost |
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[635] | 352 | if (res_graph.forward(e)) |
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[661] | 353 | total_cost += cost[e]; |
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[635] | 354 | else |
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[661] | 355 | total_cost -= cost[e]; |
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[635] | 356 | */ |
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| 357 | } |
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[659] | 358 | |
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| 359 | //Update the excess_deficit map |
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| 360 | excess_deficit[s] -= delta; |
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| 361 | excess_deficit[t] += delta; |
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| 362 | |
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[635] | 363 | |
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| 364 | //Update the excess_nodes heap |
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| 365 | if (delta >= excess_nodes[s]){ |
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| 366 | if (delta > excess_nodes[s]) |
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| 367 | deficit_nodes.push(s,delta - excess_nodes[s]); |
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| 368 | excess_nodes.pop(); |
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| 369 | |
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| 370 | } |
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| 371 | else{ |
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| 372 | excess_nodes[s] -= delta; |
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| 373 | } |
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| 374 | //Update the deficit_nodes heap |
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| 375 | if (delta >= deficit_nodes[t]){ |
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| 376 | if (delta > deficit_nodes[t]) |
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| 377 | excess_nodes.push(t,delta - deficit_nodes[t]); |
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| 378 | deficit_nodes.pop(); |
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| 379 | |
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| 380 | } |
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| 381 | else{ |
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| 382 | deficit_nodes[t] -= delta; |
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| 383 | } |
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| 384 | //Dijkstra part ends here |
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[659] | 385 | |
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| 386 | //Choose s and t again |
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| 387 | s = excess_nodes.top(); |
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| 388 | max_excess = excess_nodes[s]; |
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| 389 | t = deficit_nodes.top(); |
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| 390 | if (max_excess < deficit_nodes[t]){ |
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| 391 | max_excess = deficit_nodes[t]; |
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| 392 | } |
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| 393 | |
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[633] | 394 | } |
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| 395 | |
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| 396 | /* |
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[635] | 397 | * End of the delta scaling phase |
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| 398 | */ |
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[633] | 399 | |
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[635] | 400 | //Whatever this means |
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| 401 | delta = delta / 2; |
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| 402 | |
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| 403 | /*This is not necessary here |
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| 404 | //Update the max_excess |
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| 405 | max_excess = 0; |
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[659] | 406 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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[635] | 407 | if (max_excess < excess_deficit[n]){ |
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| 408 | max_excess = excess_deficit[n]; |
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[610] | 409 | } |
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| 410 | } |
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[633] | 411 | */ |
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[657] | 412 | |
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[610] | 413 | |
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[635] | 414 | }//while(max_excess > 0) |
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[610] | 415 | |
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| 416 | |
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| 417 | return i; |
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| 418 | } |
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| 419 | |
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| 420 | |
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| 421 | |
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| 422 | |
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[661] | 423 | ///This function gives back the total cost of the found paths. |
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[610] | 424 | ///Assumes that \c run() has been run and nothing changed since then. |
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[661] | 425 | Cost totalCost(){ |
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| 426 | return total_cost; |
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[610] | 427 | } |
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| 428 | |
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| 429 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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| 430 | ///be called before using this function. |
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[662] | 431 | const FlowMap &getFlow() const { return flow;} |
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[610] | 432 | |
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| 433 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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| 434 | /// \pre \ref run() must be called before using this function. |
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[662] | 435 | const PotentialMap &getPotential() const { return potential;} |
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[610] | 436 | |
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| 437 | ///This function checks, whether the given solution is optimal |
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| 438 | ///Running after a \c run() should return with true |
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| 439 | ///In this "state of the art" this only check optimality, doesn't bother with feasibility |
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| 440 | /// |
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| 441 | ///\todo Is this OK here? |
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| 442 | bool checkComplementarySlackness(){ |
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[661] | 443 | Cost mod_pot; |
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| 444 | Cost fl_e; |
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[659] | 445 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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[610] | 446 | //C^{\Pi}_{i,j} |
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[661] | 447 | mod_pot = cost[e]-potential[graph.head(e)]+potential[graph.tail(e)]; |
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[610] | 448 | fl_e = flow[e]; |
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| 449 | // std::cout << fl_e << std::endl; |
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| 450 | if (0<fl_e && fl_e<capacity[e]){ |
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| 451 | if (mod_pot != 0) |
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| 452 | return false; |
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| 453 | } |
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| 454 | else{ |
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| 455 | if (mod_pot > 0 && fl_e != 0) |
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| 456 | return false; |
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| 457 | if (mod_pot < 0 && fl_e != capacity[e]) |
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| 458 | return false; |
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| 459 | } |
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| 460 | } |
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| 461 | return true; |
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| 462 | } |
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| 463 | |
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| 464 | |
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[633] | 465 | }; //class MinCostFlow |
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[610] | 466 | |
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| 467 | ///@} |
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| 468 | |
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| 469 | } //namespace hugo |
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| 470 | |
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| 471 | #endif //HUGO_MINCOSTFLOW_H |
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