[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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[610] | 14 | #include <for_each_macros.h> |
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[657] | 15 | #include <hugo/union_find.h> |
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[610] | 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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[645] | 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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[610] | 24 | /// |
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| 25 | /// |
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[633] | 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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[610] | 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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[635] | 40 | template <typename Graph, typename LengthMap, typename SupplyDemandMap> |
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[633] | 41 | class MinCostFlow { |
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[610] | 42 | |
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| 43 | typedef typename LengthMap::ValueType Length; |
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| 44 | |
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[633] | 45 | |
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[635] | 46 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
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[610] | 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& G; |
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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 (G.forward(e)) |
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| 72 | return ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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| 73 | else |
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| 74 | return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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| 75 | } |
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| 76 | |
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| 77 | ModLengthMap(const ResGraphType& _G, |
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| 78 | const LengthMap &o, const NodeMap &p) : |
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| 79 | G(_G), /*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& G; |
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| 87 | const LengthMap& length; |
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[635] | 88 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
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[610] | 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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[633] | 97 | //To store excess-deficit values |
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[635] | 98 | SupplyDemandMap excess_deficit; |
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[610] | 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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[635] | 107 | MinCostFlow(Graph& _G, LengthMap& _length, SupplyDemandMap& _supply_demand) : G(_G), |
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| 108 | length(_length), supply_demand(_supply_demand), flow(_G), potential(_G){ } |
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[610] | 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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[635] | 114 | |
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[610] | 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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[633] | 117 | int run() { |
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[610] | 118 | |
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| 119 | //Resetting variables from previous runs |
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[635] | 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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[657] | 123 | typedef Heap< Node, SupplyDemand, typename Graph::template NodeMap<int>, |
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[635] | 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(G,-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(G,-1); |
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| 132 | HeapType deficit_nodes(deficit_nodes_map); |
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| 133 | |
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[657] | 134 | //A container to store nonabundant arcs |
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| 135 | list<Edge> nonabundant_arcs; |
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[610] | 136 | |
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| 137 | FOR_EACH_LOC(typename Graph::EdgeIt, e, G){ |
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| 138 | flow.set(e,0); |
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[657] | 139 | nonabundant_arcs.push_back(e); |
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[610] | 140 | } |
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[633] | 141 | |
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| 142 | //Initial value for delta |
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[635] | 143 | SupplyDemand delta = 0; |
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| 144 | |
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[657] | 145 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
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| 146 | |
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| 147 | //A union-find structure to store the abundant components |
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| 148 | UFE::MapType abund_comp_map(G); |
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| 149 | UFE abundant_components(abund_comp_map); |
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| 150 | |
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| 151 | |
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| 152 | |
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[610] | 153 | FOR_EACH_LOC(typename Graph::NodeIt, n, G){ |
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[635] | 154 | excess_deficit.set(n,supply_demand[n]); |
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| 155 | //A supply node |
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| 156 | if (excess_deficit[n] > 0){ |
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| 157 | excess_nodes.push(n,excess_deficit[n]); |
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[633] | 158 | } |
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[635] | 159 | //A demand node |
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| 160 | if (excess_deficit[n] < 0){ |
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| 161 | deficit_nodes.push(n, - excess_deficit[n]); |
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| 162 | } |
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| 163 | //Finding out starting value of delta |
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| 164 | if (delta < abs(excess_deficit[n])){ |
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| 165 | delta = abs(excess_deficit[n]); |
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| 166 | } |
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[633] | 167 | //Initialize the copy of the Dijkstra potential to zero |
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[610] | 168 | potential.set(n,0); |
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[657] | 169 | //Every single point is an abundant component initially |
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| 170 | abundant_components.insert(n); |
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[610] | 171 | } |
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| 172 | |
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[635] | 173 | //It'll be allright as an initial value, though this value |
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| 174 | //can be the maximum deficit here |
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| 175 | SupplyDemand max_excess = delta; |
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[610] | 176 | |
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[633] | 177 | //We need a residual graph which is uncapacitated |
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| 178 | ResGraphType res_graph(G, flow); |
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[610] | 179 | |
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[633] | 180 | |
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[610] | 181 | |
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| 182 | ModLengthMap mod_length(res_graph, length, potential); |
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| 183 | |
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| 184 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
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| 185 | |
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[633] | 186 | |
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[635] | 187 | while (max_excess > 0){ |
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| 188 | |
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[657] | 189 | //Reset delta if still too big |
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| 190 | if (8*number_of_nodes*max_excess <= delta){ |
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| 191 | delta = max_excess; |
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| 192 | |
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| 193 | } |
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| 194 | |
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[645] | 195 | /* |
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| 196 | * Beginning of the delta scaling phase |
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| 197 | */ |
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[635] | 198 | //Merge and stuff |
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[657] | 199 | { |
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| 200 | SupplyDemand buf=8*number_of_nodes*delta; |
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| 201 | list<Edge>::iterator i = nonabundant_arcs.begin(); |
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| 202 | while ( i != nonabundant_arcs.end() ){ |
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| 203 | if (flow[i]>=buf){ |
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| 204 | Node a = abundant_components.find(res_graph.head(i)); |
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| 205 | Node b = abundant_components.find(res_graph.tail(i)); |
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| 206 | //Merge |
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| 207 | if (a != b){ |
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| 208 | //Find path and augment |
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| 209 | //!!! |
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| 210 | //Find path and augment |
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| 211 | abundant_components.join(a,b); |
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| 212 | } |
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| 213 | //What happens to i? |
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| 214 | nonabundant_arcs.erase(i); |
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| 215 | } |
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| 216 | else |
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| 217 | ++i; |
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| 218 | } |
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| 219 | } |
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| 220 | |
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[635] | 221 | |
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| 222 | Node s = excess_nodes.top(); |
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| 223 | SupplyDemand max_excess = excess_nodes[s]; |
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| 224 | Node t = deficit_nodes.top(); |
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| 225 | if (max_excess < dificit_nodes[t]){ |
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| 226 | max_excess = dificit_nodes[t]; |
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| 227 | } |
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| 228 | |
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| 229 | |
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[645] | 230 | while(max_excess > 0){ |
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[635] | 231 | |
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| 232 | |
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| 233 | //s es t valasztasa |
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| 234 | |
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| 235 | //Dijkstra part |
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| 236 | dijkstra.run(s); |
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| 237 | |
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| 238 | /*We know from theory that t can be reached |
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| 239 | if (!dijkstra.reached(t)){ |
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| 240 | //There are no k paths from s to t |
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| 241 | break; |
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| 242 | }; |
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| 243 | */ |
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| 244 | |
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| 245 | //We have to change the potential |
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| 246 | FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){ |
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| 247 | potential[n] += dijkstra.distMap()[n]; |
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| 248 | } |
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| 249 | |
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| 250 | |
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| 251 | //Augmenting on the sortest path |
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| 252 | Node n=t; |
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| 253 | ResGraphEdge e; |
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| 254 | while (n!=s){ |
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| 255 | e = dijkstra.pred(n); |
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| 256 | n = dijkstra.predNode(n); |
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| 257 | res_graph.augment(e,delta); |
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| 258 | /* |
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| 259 | //Let's update the total length |
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| 260 | if (res_graph.forward(e)) |
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| 261 | total_length += length[e]; |
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| 262 | else |
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| 263 | total_length -= length[e]; |
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| 264 | */ |
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| 265 | } |
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| 266 | |
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| 267 | //Update the excess_nodes heap |
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| 268 | if (delta >= excess_nodes[s]){ |
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| 269 | if (delta > excess_nodes[s]) |
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| 270 | deficit_nodes.push(s,delta - excess_nodes[s]); |
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| 271 | excess_nodes.pop(); |
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| 272 | |
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| 273 | } |
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| 274 | else{ |
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| 275 | excess_nodes[s] -= delta; |
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| 276 | } |
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| 277 | //Update the deficit_nodes heap |
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| 278 | if (delta >= deficit_nodes[t]){ |
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| 279 | if (delta > deficit_nodes[t]) |
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| 280 | excess_nodes.push(t,delta - deficit_nodes[t]); |
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| 281 | deficit_nodes.pop(); |
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| 282 | |
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| 283 | } |
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| 284 | else{ |
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| 285 | deficit_nodes[t] -= delta; |
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| 286 | } |
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| 287 | //Dijkstra part ends here |
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[633] | 288 | } |
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| 289 | |
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| 290 | /* |
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[635] | 291 | * End of the delta scaling phase |
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| 292 | */ |
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[633] | 293 | |
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[635] | 294 | //Whatever this means |
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| 295 | delta = delta / 2; |
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| 296 | |
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| 297 | /*This is not necessary here |
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| 298 | //Update the max_excess |
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| 299 | max_excess = 0; |
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| 300 | FOR_EACH_LOC(typename Graph::NodeIt, n, G){ |
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| 301 | if (max_excess < excess_deficit[n]){ |
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| 302 | max_excess = excess_deficit[n]; |
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[610] | 303 | } |
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| 304 | } |
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[633] | 305 | */ |
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[657] | 306 | |
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[610] | 307 | |
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[635] | 308 | }//while(max_excess > 0) |
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[610] | 309 | |
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| 310 | |
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| 311 | return i; |
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| 312 | } |
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| 313 | |
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| 314 | |
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| 315 | |
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| 316 | |
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| 317 | ///This function gives back the total length of the found paths. |
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| 318 | ///Assumes that \c run() has been run and nothing changed since then. |
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| 319 | Length totalLength(){ |
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| 320 | return total_length; |
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| 321 | } |
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| 322 | |
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| 323 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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| 324 | ///be called before using this function. |
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| 325 | const EdgeIntMap &getFlow() const { return flow;} |
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| 326 | |
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| 327 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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| 328 | /// \pre \ref run() must be called before using this function. |
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| 329 | const EdgeIntMap &getPotential() const { return potential;} |
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| 330 | |
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| 331 | ///This function checks, whether the given solution is optimal |
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| 332 | ///Running after a \c run() should return with true |
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| 333 | ///In this "state of the art" this only check optimality, doesn't bother with feasibility |
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| 334 | /// |
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| 335 | ///\todo Is this OK here? |
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| 336 | bool checkComplementarySlackness(){ |
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| 337 | Length mod_pot; |
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| 338 | Length fl_e; |
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| 339 | FOR_EACH_LOC(typename Graph::EdgeIt, e, G){ |
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| 340 | //C^{\Pi}_{i,j} |
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| 341 | mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)]; |
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| 342 | fl_e = flow[e]; |
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| 343 | // std::cout << fl_e << std::endl; |
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| 344 | if (0<fl_e && fl_e<capacity[e]){ |
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| 345 | if (mod_pot != 0) |
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| 346 | return false; |
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| 347 | } |
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| 348 | else{ |
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| 349 | if (mod_pot > 0 && fl_e != 0) |
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| 350 | return false; |
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| 351 | if (mod_pot < 0 && fl_e != capacity[e]) |
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| 352 | return false; |
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| 353 | } |
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| 354 | } |
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| 355 | return true; |
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| 356 | } |
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| 357 | |
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| 358 | |
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[633] | 359 | }; //class MinCostFlow |
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[610] | 360 | |
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| 361 | ///@} |
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| 362 | |
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| 363 | } //namespace hugo |
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| 364 | |
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| 365 | #endif //HUGO_MINCOSTFLOW_H |
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