[2577] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_COST_SCALING_H |
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| 20 | #define LEMON_COST_SCALING_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow |
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| 23 | /// \file |
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| 24 | /// \brief Cost scaling algorithm for finding a minimum cost flow. |
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| 25 | |
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| 26 | #include <deque> |
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| 27 | #include <lemon/graph_adaptor.h> |
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| 28 | #include <lemon/graph_utils.h> |
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| 29 | #include <lemon/maps.h> |
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| 30 | #include <lemon/math.h> |
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| 31 | |
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| 32 | #include <lemon/circulation.h> |
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| 33 | #include <lemon/bellman_ford.h> |
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| 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | /// \addtogroup min_cost_flow |
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| 38 | /// @{ |
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| 39 | |
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| 40 | /// \brief Implementation of the cost scaling algorithm for finding a |
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| 41 | /// minimum cost flow. |
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| 42 | /// |
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| 43 | /// \ref CostScaling implements the cost scaling algorithm performing |
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[2625] | 44 | /// augment/push and relabel operations for finding a minimum cost |
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[2577] | 45 | /// flow. |
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| 46 | /// |
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| 47 | /// \tparam Graph The directed graph type the algorithm runs on. |
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| 48 | /// \tparam LowerMap The type of the lower bound map. |
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| 49 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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| 50 | /// \tparam CostMap The type of the cost (length) map. |
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| 51 | /// \tparam SupplyMap The type of the supply map. |
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| 52 | /// |
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| 53 | /// \warning |
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| 54 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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| 55 | /// - Supply values should be \e signed \e integers. |
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[2581] | 56 | /// - The value types of the maps should be convertible to each other. |
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| 57 | /// - \c CostMap::Value must be signed type. |
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[2577] | 58 | /// |
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| 59 | /// \note Edge costs are multiplied with the number of nodes during |
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| 60 | /// the algorithm so overflow problems may arise more easily than with |
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| 61 | /// other minimum cost flow algorithms. |
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| 62 | /// If it is available, <tt>long long int</tt> type is used instead of |
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| 63 | /// <tt>long int</tt> in the inside computations. |
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| 64 | /// |
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| 65 | /// \author Peter Kovacs |
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| 66 | template < typename Graph, |
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| 67 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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| 68 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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| 69 | typename CostMap = typename Graph::template EdgeMap<int>, |
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| 70 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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| 71 | class CostScaling |
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| 72 | { |
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| 73 | GRAPH_TYPEDEFS(typename Graph); |
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| 74 | |
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| 75 | typedef typename CapacityMap::Value Capacity; |
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| 76 | typedef typename CostMap::Value Cost; |
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| 77 | typedef typename SupplyMap::Value Supply; |
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| 78 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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| 79 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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| 80 | |
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| 81 | typedef ResGraphAdaptor< const Graph, Capacity, |
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| 82 | CapacityEdgeMap, CapacityEdgeMap > ResGraph; |
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| 83 | typedef typename ResGraph::Edge ResEdge; |
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| 84 | |
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| 85 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
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| 86 | typedef long long int LCost; |
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| 87 | #else |
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| 88 | typedef long int LCost; |
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| 89 | #endif |
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| 90 | typedef typename Graph::template EdgeMap<LCost> LargeCostMap; |
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| 91 | |
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| 92 | public: |
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| 93 | |
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| 94 | /// The type of the flow map. |
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[2581] | 95 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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[2577] | 96 | /// The type of the potential map. |
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| 97 | typedef typename Graph::template NodeMap<LCost> PotentialMap; |
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| 98 | |
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| 99 | private: |
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| 100 | |
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| 101 | /// \brief Map adaptor class for handling residual edge costs. |
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| 102 | /// |
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[2620] | 103 | /// Map adaptor class for handling residual edge costs. |
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[2581] | 104 | template <typename Map> |
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| 105 | class ResidualCostMap : public MapBase<ResEdge, typename Map::Value> |
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[2577] | 106 | { |
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| 107 | private: |
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| 108 | |
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[2581] | 109 | const Map &_cost_map; |
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[2577] | 110 | |
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| 111 | public: |
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| 112 | |
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| 113 | ///\e |
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[2581] | 114 | ResidualCostMap(const Map &cost_map) : |
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[2577] | 115 | _cost_map(cost_map) {} |
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| 116 | |
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| 117 | ///\e |
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[2625] | 118 | inline typename Map::Value operator[](const ResEdge &e) const { |
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| 119 | return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
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[2577] | 120 | } |
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| 121 | |
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| 122 | }; //class ResidualCostMap |
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| 123 | |
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| 124 | /// \brief Map adaptor class for handling reduced edge costs. |
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| 125 | /// |
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[2620] | 126 | /// Map adaptor class for handling reduced edge costs. |
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[2577] | 127 | class ReducedCostMap : public MapBase<Edge, LCost> |
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| 128 | { |
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| 129 | private: |
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| 130 | |
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| 131 | const Graph &_gr; |
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| 132 | const LargeCostMap &_cost_map; |
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| 133 | const PotentialMap &_pot_map; |
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| 134 | |
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| 135 | public: |
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| 136 | |
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| 137 | ///\e |
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| 138 | ReducedCostMap( const Graph &gr, |
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| 139 | const LargeCostMap &cost_map, |
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| 140 | const PotentialMap &pot_map ) : |
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| 141 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
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| 142 | |
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| 143 | ///\e |
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[2625] | 144 | inline LCost operator[](const Edge &e) const { |
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[2577] | 145 | return _cost_map[e] + _pot_map[_gr.source(e)] |
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| 146 | - _pot_map[_gr.target(e)]; |
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| 147 | } |
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| 148 | |
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| 149 | }; //class ReducedCostMap |
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| 150 | |
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| 151 | private: |
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| 152 | |
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| 153 | // The directed graph the algorithm runs on |
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| 154 | const Graph &_graph; |
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| 155 | // The original lower bound map |
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| 156 | const LowerMap *_lower; |
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| 157 | // The modified capacity map |
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| 158 | CapacityEdgeMap _capacity; |
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| 159 | // The original cost map |
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| 160 | const CostMap &_orig_cost; |
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| 161 | // The scaled cost map |
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| 162 | LargeCostMap _cost; |
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| 163 | // The modified supply map |
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| 164 | SupplyNodeMap _supply; |
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| 165 | bool _valid_supply; |
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| 166 | |
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| 167 | // Edge map of the current flow |
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[2581] | 168 | FlowMap *_flow; |
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| 169 | bool _local_flow; |
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[2577] | 170 | // Node map of the current potentials |
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[2581] | 171 | PotentialMap *_potential; |
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| 172 | bool _local_potential; |
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[2577] | 173 | |
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[2623] | 174 | // The residual cost map |
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| 175 | ResidualCostMap<LargeCostMap> _res_cost; |
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[2577] | 176 | // The residual graph |
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[2581] | 177 | ResGraph *_res_graph; |
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[2577] | 178 | // The reduced cost map |
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[2581] | 179 | ReducedCostMap *_red_cost; |
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[2577] | 180 | // The excess map |
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| 181 | SupplyNodeMap _excess; |
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| 182 | // The epsilon parameter used for cost scaling |
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| 183 | LCost _epsilon; |
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[2625] | 184 | // The scaling factor |
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| 185 | int _alpha; |
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[2577] | 186 | |
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| 187 | public: |
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| 188 | |
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[2581] | 189 | /// \brief General constructor (with lower bounds). |
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[2577] | 190 | /// |
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[2581] | 191 | /// General constructor (with lower bounds). |
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[2577] | 192 | /// |
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| 193 | /// \param graph The directed graph the algorithm runs on. |
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| 194 | /// \param lower The lower bounds of the edges. |
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| 195 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 196 | /// \param cost The cost (length) values of the edges. |
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| 197 | /// \param supply The supply values of the nodes (signed). |
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| 198 | CostScaling( const Graph &graph, |
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| 199 | const LowerMap &lower, |
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| 200 | const CapacityMap &capacity, |
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| 201 | const CostMap &cost, |
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| 202 | const SupplyMap &supply ) : |
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| 203 | _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost), |
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[2623] | 204 | _cost(graph), _supply(graph), _flow(NULL), _local_flow(false), |
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| 205 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 206 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 207 | { |
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[2625] | 208 | // Remove non-zero lower bounds |
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[2577] | 209 | _capacity = subMap(capacity, lower); |
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| 210 | Supply sum = 0; |
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| 211 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 212 | Supply s = supply[n]; |
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| 213 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 214 | s += lower[e]; |
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| 215 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 216 | s -= lower[e]; |
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| 217 | _supply[n] = s; |
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| 218 | sum += s; |
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| 219 | } |
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| 220 | _valid_supply = sum == 0; |
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| 221 | } |
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| 222 | |
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[2581] | 223 | /// \brief General constructor (without lower bounds). |
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[2577] | 224 | /// |
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[2581] | 225 | /// General constructor (without lower bounds). |
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[2577] | 226 | /// |
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| 227 | /// \param graph The directed graph the algorithm runs on. |
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| 228 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 229 | /// \param cost The cost (length) values of the edges. |
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| 230 | /// \param supply The supply values of the nodes (signed). |
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| 231 | CostScaling( const Graph &graph, |
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| 232 | const CapacityMap &capacity, |
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| 233 | const CostMap &cost, |
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| 234 | const SupplyMap &supply ) : |
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| 235 | _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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[2623] | 236 | _cost(graph), _supply(supply), _flow(NULL), _local_flow(false), |
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| 237 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 238 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 239 | { |
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[2625] | 240 | // Check the sum of supply values |
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[2577] | 241 | Supply sum = 0; |
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| 242 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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| 243 | _valid_supply = sum == 0; |
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| 244 | } |
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| 245 | |
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[2581] | 246 | /// \brief Simple constructor (with lower bounds). |
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[2577] | 247 | /// |
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[2581] | 248 | /// Simple constructor (with lower bounds). |
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[2577] | 249 | /// |
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| 250 | /// \param graph The directed graph the algorithm runs on. |
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| 251 | /// \param lower The lower bounds of the edges. |
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| 252 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 253 | /// \param cost The cost (length) values of the edges. |
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| 254 | /// \param s The source node. |
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| 255 | /// \param t The target node. |
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| 256 | /// \param flow_value The required amount of flow from node \c s |
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| 257 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 258 | CostScaling( const Graph &graph, |
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| 259 | const LowerMap &lower, |
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| 260 | const CapacityMap &capacity, |
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| 261 | const CostMap &cost, |
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| 262 | Node s, Node t, |
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| 263 | Supply flow_value ) : |
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| 264 | _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost), |
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[2623] | 265 | _cost(graph), _supply(graph), _flow(NULL), _local_flow(false), |
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| 266 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 267 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 268 | { |
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[2625] | 269 | // Remove nonzero lower bounds |
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[2577] | 270 | _capacity = subMap(capacity, lower); |
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| 271 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 272 | Supply sum = 0; |
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| 273 | if (n == s) sum = flow_value; |
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| 274 | if (n == t) sum = -flow_value; |
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| 275 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 276 | sum += lower[e]; |
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| 277 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 278 | sum -= lower[e]; |
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| 279 | _supply[n] = sum; |
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| 280 | } |
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| 281 | _valid_supply = true; |
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| 282 | } |
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| 283 | |
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[2581] | 284 | /// \brief Simple constructor (without lower bounds). |
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[2577] | 285 | /// |
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[2581] | 286 | /// Simple constructor (without lower bounds). |
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[2577] | 287 | /// |
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| 288 | /// \param graph The directed graph the algorithm runs on. |
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| 289 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 290 | /// \param cost The cost (length) values of the edges. |
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| 291 | /// \param s The source node. |
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| 292 | /// \param t The target node. |
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| 293 | /// \param flow_value The required amount of flow from node \c s |
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| 294 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 295 | CostScaling( const Graph &graph, |
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| 296 | const CapacityMap &capacity, |
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| 297 | const CostMap &cost, |
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| 298 | Node s, Node t, |
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| 299 | Supply flow_value ) : |
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| 300 | _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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[2623] | 301 | _cost(graph), _supply(graph, 0), _flow(NULL), _local_flow(false), |
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| 302 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 303 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 304 | { |
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| 305 | _supply[s] = flow_value; |
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| 306 | _supply[t] = -flow_value; |
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| 307 | _valid_supply = true; |
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| 308 | } |
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| 309 | |
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[2581] | 310 | /// Destructor. |
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| 311 | ~CostScaling() { |
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| 312 | if (_local_flow) delete _flow; |
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| 313 | if (_local_potential) delete _potential; |
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| 314 | delete _res_graph; |
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| 315 | delete _red_cost; |
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| 316 | } |
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| 317 | |
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[2620] | 318 | /// \brief Set the flow map. |
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[2581] | 319 | /// |
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[2620] | 320 | /// Set the flow map. |
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[2581] | 321 | /// |
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| 322 | /// \return \c (*this) |
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| 323 | CostScaling& flowMap(FlowMap &map) { |
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| 324 | if (_local_flow) { |
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| 325 | delete _flow; |
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| 326 | _local_flow = false; |
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| 327 | } |
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| 328 | _flow = ↦ |
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| 329 | return *this; |
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| 330 | } |
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| 331 | |
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[2620] | 332 | /// \brief Set the potential map. |
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[2581] | 333 | /// |
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[2620] | 334 | /// Set the potential map. |
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[2581] | 335 | /// |
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| 336 | /// \return \c (*this) |
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| 337 | CostScaling& potentialMap(PotentialMap &map) { |
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| 338 | if (_local_potential) { |
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| 339 | delete _potential; |
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| 340 | _local_potential = false; |
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| 341 | } |
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| 342 | _potential = ↦ |
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| 343 | return *this; |
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| 344 | } |
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| 345 | |
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| 346 | /// \name Execution control |
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| 347 | |
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| 348 | /// @{ |
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| 349 | |
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[2620] | 350 | /// \brief Run the algorithm. |
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[2577] | 351 | /// |
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[2620] | 352 | /// Run the algorithm. |
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[2577] | 353 | /// |
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[2625] | 354 | /// \param partial_augment By default the algorithm performs |
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| 355 | /// partial augment and relabel operations in the cost scaling |
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| 356 | /// phases. Set this parameter to \c false for using local push and |
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| 357 | /// relabel operations instead. |
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| 358 | /// |
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[2577] | 359 | /// \return \c true if a feasible flow can be found. |
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[2625] | 360 | bool run(bool partial_augment = true) { |
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| 361 | if (partial_augment) { |
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| 362 | return init() && startPartialAugment(); |
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| 363 | } else { |
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| 364 | return init() && startPushRelabel(); |
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| 365 | } |
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[2577] | 366 | } |
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| 367 | |
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[2581] | 368 | /// @} |
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| 369 | |
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| 370 | /// \name Query Functions |
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| 371 | /// The result of the algorithm can be obtained using these |
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[2620] | 372 | /// functions.\n |
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| 373 | /// \ref lemon::CostScaling::run() "run()" must be called before |
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| 374 | /// using them. |
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[2581] | 375 | |
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| 376 | /// @{ |
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| 377 | |
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[2620] | 378 | /// \brief Return a const reference to the edge map storing the |
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[2577] | 379 | /// found flow. |
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| 380 | /// |
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[2620] | 381 | /// Return a const reference to the edge map storing the found flow. |
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[2577] | 382 | /// |
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| 383 | /// \pre \ref run() must be called before using this function. |
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| 384 | const FlowMap& flowMap() const { |
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[2581] | 385 | return *_flow; |
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[2577] | 386 | } |
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| 387 | |
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[2620] | 388 | /// \brief Return a const reference to the node map storing the |
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[2577] | 389 | /// found potentials (the dual solution). |
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| 390 | /// |
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[2620] | 391 | /// Return a const reference to the node map storing the found |
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[2577] | 392 | /// potentials (the dual solution). |
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| 393 | /// |
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| 394 | /// \pre \ref run() must be called before using this function. |
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| 395 | const PotentialMap& potentialMap() const { |
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[2581] | 396 | return *_potential; |
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| 397 | } |
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| 398 | |
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[2620] | 399 | /// \brief Return the flow on the given edge. |
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[2581] | 400 | /// |
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[2620] | 401 | /// Return the flow on the given edge. |
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[2581] | 402 | /// |
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| 403 | /// \pre \ref run() must be called before using this function. |
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| 404 | Capacity flow(const Edge& edge) const { |
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| 405 | return (*_flow)[edge]; |
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| 406 | } |
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| 407 | |
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[2620] | 408 | /// \brief Return the potential of the given node. |
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[2581] | 409 | /// |
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[2620] | 410 | /// Return the potential of the given node. |
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[2581] | 411 | /// |
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| 412 | /// \pre \ref run() must be called before using this function. |
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| 413 | Cost potential(const Node& node) const { |
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| 414 | return (*_potential)[node]; |
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[2577] | 415 | } |
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| 416 | |
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[2620] | 417 | /// \brief Return the total cost of the found flow. |
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[2577] | 418 | /// |
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[2620] | 419 | /// Return the total cost of the found flow. The complexity of the |
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[2577] | 420 | /// function is \f$ O(e) \f$. |
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| 421 | /// |
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| 422 | /// \pre \ref run() must be called before using this function. |
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| 423 | Cost totalCost() const { |
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| 424 | Cost c = 0; |
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| 425 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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[2581] | 426 | c += (*_flow)[e] * _orig_cost[e]; |
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[2577] | 427 | return c; |
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| 428 | } |
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| 429 | |
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[2581] | 430 | /// @} |
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| 431 | |
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[2577] | 432 | private: |
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| 433 | |
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[2620] | 434 | /// Initialize the algorithm. |
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[2577] | 435 | bool init() { |
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| 436 | if (!_valid_supply) return false; |
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[2625] | 437 | // The scaling factor |
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| 438 | _alpha = 8; |
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[2577] | 439 | |
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[2625] | 440 | // Initialize flow and potential maps |
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[2581] | 441 | if (!_flow) { |
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| 442 | _flow = new FlowMap(_graph); |
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| 443 | _local_flow = true; |
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| 444 | } |
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| 445 | if (!_potential) { |
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| 446 | _potential = new PotentialMap(_graph); |
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| 447 | _local_potential = true; |
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| 448 | } |
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| 449 | |
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| 450 | _red_cost = new ReducedCostMap(_graph, _cost, *_potential); |
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| 451 | _res_graph = new ResGraph(_graph, _capacity, *_flow); |
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| 452 | |
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[2625] | 453 | // Initialize the scaled cost map and the epsilon parameter |
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[2577] | 454 | Cost max_cost = 0; |
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| 455 | int node_num = countNodes(_graph); |
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| 456 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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[2625] | 457 | _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha; |
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[2577] | 458 | if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e]; |
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| 459 | } |
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| 460 | _epsilon = max_cost * node_num; |
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| 461 | |
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[2625] | 462 | // Find a feasible flow using Circulation |
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[2577] | 463 | Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap, |
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| 464 | SupplyMap > |
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[2581] | 465 | circulation( _graph, constMap<Edge>(Capacity(0)), _capacity, |
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[2577] | 466 | _supply ); |
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[2581] | 467 | return circulation.flowMap(*_flow).run(); |
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[2577] | 468 | } |
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| 469 | |
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[2625] | 470 | /// Execute the algorithm performing partial augmentation and |
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| 471 | /// relabel operations. |
---|
| 472 | bool startPartialAugment() { |
---|
| 473 | // Paramters for heuristics |
---|
| 474 | const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
---|
| 475 | const int BF_HEURISTIC_BOUND_FACTOR = 3; |
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| 476 | // Maximum augment path length |
---|
| 477 | const int MAX_PATH_LENGTH = 4; |
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[2577] | 478 | |
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[2625] | 479 | // Variables |
---|
| 480 | typename Graph::template NodeMap<Edge> pred_edge(_graph); |
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| 481 | typename Graph::template NodeMap<bool> forward(_graph); |
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| 482 | typename Graph::template NodeMap<OutEdgeIt> next_out(_graph); |
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| 483 | typename Graph::template NodeMap<InEdgeIt> next_in(_graph); |
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| 484 | typename Graph::template NodeMap<bool> next_dir(_graph); |
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[2577] | 485 | std::deque<Node> active_nodes; |
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[2625] | 486 | std::vector<Node> path_nodes; |
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[2577] | 487 | |
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| 488 | int node_num = countNodes(_graph); |
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[2625] | 489 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
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| 490 | 1 : _epsilon / _alpha ) |
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[2577] | 491 | { |
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[2625] | 492 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
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| 493 | // to check if the current flow is optimal |
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[2577] | 494 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
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[2581] | 495 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
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[2625] | 496 | ShiftCostMap shift_cost(_res_cost, 1); |
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[2581] | 497 | BellmanFord<ResGraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
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[2577] | 498 | bf.init(0); |
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| 499 | bool done = false; |
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| 500 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
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| 501 | for (int i = 0; i < K && !done; ++i) |
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| 502 | done = bf.processNextWeakRound(); |
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[2625] | 503 | if (done) break; |
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[2577] | 504 | } |
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| 505 | |
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[2625] | 506 | // Saturate edges not satisfying the optimality condition |
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[2577] | 507 | Capacity delta; |
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| 508 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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[2581] | 509 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 510 | delta = _capacity[e] - (*_flow)[e]; |
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[2577] | 511 | _excess[_graph.source(e)] -= delta; |
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| 512 | _excess[_graph.target(e)] += delta; |
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[2581] | 513 | (*_flow)[e] = _capacity[e]; |
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[2577] | 514 | } |
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[2581] | 515 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 516 | _excess[_graph.target(e)] -= (*_flow)[e]; |
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| 517 | _excess[_graph.source(e)] += (*_flow)[e]; |
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| 518 | (*_flow)[e] = 0; |
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[2577] | 519 | } |
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| 520 | } |
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| 521 | |
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[2625] | 522 | // Find active nodes (i.e. nodes with positive excess) |
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| 523 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[2577] | 524 | if (_excess[n] > 0) active_nodes.push_back(n); |
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[2625] | 525 | } |
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[2577] | 526 | |
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[2625] | 527 | // Initialize the next edge maps |
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| 528 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 529 | next_out[n] = OutEdgeIt(_graph, n); |
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| 530 | next_in[n] = InEdgeIt(_graph, n); |
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| 531 | next_dir[n] = true; |
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| 532 | } |
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| 533 | |
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| 534 | // Perform partial augment and relabel operations |
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[2577] | 535 | while (active_nodes.size() > 0) { |
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[2625] | 536 | // Select an active node (FIFO selection) |
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| 537 | if (_excess[active_nodes[0]] <= 0) { |
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| 538 | active_nodes.pop_front(); |
---|
| 539 | continue; |
---|
| 540 | } |
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| 541 | Node start = active_nodes[0]; |
---|
| 542 | path_nodes.clear(); |
---|
| 543 | path_nodes.push_back(start); |
---|
| 544 | |
---|
| 545 | // Find an augmenting path from the start node |
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| 546 | Node u, tip = start; |
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| 547 | LCost min_red_cost; |
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| 548 | while ( _excess[tip] >= 0 && |
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| 549 | int(path_nodes.size()) <= MAX_PATH_LENGTH ) |
---|
| 550 | { |
---|
| 551 | if (next_dir[tip]) { |
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| 552 | for (OutEdgeIt e = next_out[tip]; e != INVALID; ++e) { |
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| 553 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
| 554 | u = _graph.target(e); |
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| 555 | pred_edge[u] = e; |
---|
| 556 | forward[u] = true; |
---|
| 557 | next_out[tip] = e; |
---|
| 558 | tip = u; |
---|
| 559 | path_nodes.push_back(tip); |
---|
| 560 | goto next_step; |
---|
| 561 | } |
---|
| 562 | } |
---|
| 563 | next_dir[tip] = false; |
---|
| 564 | } |
---|
| 565 | for (InEdgeIt e = next_in[tip]; e != INVALID; ++e) { |
---|
| 566 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 567 | u = _graph.source(e); |
---|
| 568 | pred_edge[u] = e; |
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| 569 | forward[u] = false; |
---|
| 570 | next_in[tip] = e; |
---|
| 571 | tip = u; |
---|
| 572 | path_nodes.push_back(tip); |
---|
| 573 | goto next_step; |
---|
| 574 | } |
---|
| 575 | } |
---|
| 576 | |
---|
| 577 | // Relabel tip node |
---|
| 578 | min_red_cost = std::numeric_limits<LCost>::max() / 2; |
---|
| 579 | for (OutEdgeIt oe(_graph, tip); oe != INVALID; ++oe) { |
---|
| 580 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
---|
| 581 | (*_red_cost)[oe] < min_red_cost ) |
---|
| 582 | min_red_cost = (*_red_cost)[oe]; |
---|
| 583 | } |
---|
| 584 | for (InEdgeIt ie(_graph, tip); ie != INVALID; ++ie) { |
---|
| 585 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
---|
| 586 | min_red_cost = -(*_red_cost)[ie]; |
---|
| 587 | } |
---|
| 588 | (*_potential)[tip] -= min_red_cost + _epsilon; |
---|
| 589 | |
---|
| 590 | // Reset the next edge maps |
---|
| 591 | next_out[tip] = OutEdgeIt(_graph, tip); |
---|
| 592 | next_in[tip] = InEdgeIt(_graph, tip); |
---|
| 593 | next_dir[tip] = true; |
---|
| 594 | |
---|
| 595 | // Step back |
---|
| 596 | if (tip != start) { |
---|
| 597 | path_nodes.pop_back(); |
---|
| 598 | tip = path_nodes[path_nodes.size()-1]; |
---|
| 599 | } |
---|
| 600 | |
---|
| 601 | next_step: |
---|
| 602 | continue; |
---|
| 603 | } |
---|
| 604 | |
---|
| 605 | // Augment along the found path (as much flow as possible) |
---|
| 606 | Capacity delta; |
---|
| 607 | for (int i = 1; i < int(path_nodes.size()); ++i) { |
---|
| 608 | u = path_nodes[i]; |
---|
| 609 | delta = forward[u] ? |
---|
| 610 | _capacity[pred_edge[u]] - (*_flow)[pred_edge[u]] : |
---|
| 611 | (*_flow)[pred_edge[u]]; |
---|
| 612 | delta = std::min(delta, _excess[path_nodes[i-1]]); |
---|
| 613 | (*_flow)[pred_edge[u]] += forward[u] ? delta : -delta; |
---|
| 614 | _excess[path_nodes[i-1]] -= delta; |
---|
| 615 | _excess[u] += delta; |
---|
| 616 | if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u); |
---|
| 617 | } |
---|
| 618 | } |
---|
| 619 | } |
---|
| 620 | |
---|
| 621 | // Compute node potentials for the original costs |
---|
| 622 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
---|
| 623 | BellmanFord< ResGraph, ResidualCostMap<CostMap> > |
---|
| 624 | bf(*_res_graph, res_cost); |
---|
| 625 | bf.init(0); bf.start(); |
---|
| 626 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
| 627 | (*_potential)[n] = bf.dist(n); |
---|
| 628 | |
---|
| 629 | // Handle non-zero lower bounds |
---|
| 630 | if (_lower) { |
---|
| 631 | for (EdgeIt e(_graph); e != INVALID; ++e) |
---|
| 632 | (*_flow)[e] += (*_lower)[e]; |
---|
| 633 | } |
---|
| 634 | return true; |
---|
| 635 | } |
---|
| 636 | |
---|
| 637 | /// Execute the algorithm performing push and relabel operations. |
---|
| 638 | bool startPushRelabel() { |
---|
| 639 | // Paramters for heuristics |
---|
| 640 | const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
---|
| 641 | const int BF_HEURISTIC_BOUND_FACTOR = 3; |
---|
| 642 | |
---|
| 643 | typename Graph::template NodeMap<bool> hyper(_graph, false); |
---|
| 644 | typename Graph::template NodeMap<Edge> pred_edge(_graph); |
---|
| 645 | typename Graph::template NodeMap<bool> forward(_graph); |
---|
| 646 | typename Graph::template NodeMap<OutEdgeIt> next_out(_graph); |
---|
| 647 | typename Graph::template NodeMap<InEdgeIt> next_in(_graph); |
---|
| 648 | typename Graph::template NodeMap<bool> next_dir(_graph); |
---|
| 649 | std::deque<Node> active_nodes; |
---|
| 650 | |
---|
| 651 | int node_num = countNodes(_graph); |
---|
| 652 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
| 653 | 1 : _epsilon / _alpha ) |
---|
| 654 | { |
---|
| 655 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
---|
| 656 | // to check if the current flow is optimal |
---|
| 657 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
---|
| 658 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
---|
| 659 | ShiftCostMap shift_cost(_res_cost, 1); |
---|
| 660 | BellmanFord<ResGraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
---|
| 661 | bf.init(0); |
---|
| 662 | bool done = false; |
---|
| 663 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
---|
| 664 | for (int i = 0; i < K && !done; ++i) |
---|
| 665 | done = bf.processNextWeakRound(); |
---|
| 666 | if (done) break; |
---|
| 667 | } |
---|
| 668 | |
---|
| 669 | // Saturate edges not satisfying the optimality condition |
---|
| 670 | Capacity delta; |
---|
| 671 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 672 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
| 673 | delta = _capacity[e] - (*_flow)[e]; |
---|
| 674 | _excess[_graph.source(e)] -= delta; |
---|
| 675 | _excess[_graph.target(e)] += delta; |
---|
| 676 | (*_flow)[e] = _capacity[e]; |
---|
| 677 | } |
---|
| 678 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
---|
| 679 | _excess[_graph.target(e)] -= (*_flow)[e]; |
---|
| 680 | _excess[_graph.source(e)] += (*_flow)[e]; |
---|
| 681 | (*_flow)[e] = 0; |
---|
| 682 | } |
---|
| 683 | } |
---|
| 684 | |
---|
| 685 | // Find active nodes (i.e. nodes with positive excess) |
---|
| 686 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 687 | if (_excess[n] > 0) active_nodes.push_back(n); |
---|
| 688 | } |
---|
| 689 | |
---|
| 690 | // Initialize the next edge maps |
---|
| 691 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 692 | next_out[n] = OutEdgeIt(_graph, n); |
---|
| 693 | next_in[n] = InEdgeIt(_graph, n); |
---|
| 694 | next_dir[n] = true; |
---|
| 695 | } |
---|
| 696 | |
---|
| 697 | // Perform push and relabel operations |
---|
| 698 | while (active_nodes.size() > 0) { |
---|
| 699 | // Select an active node (FIFO selection) |
---|
[2577] | 700 | Node n = active_nodes[0], t; |
---|
| 701 | bool relabel_enabled = true; |
---|
| 702 | |
---|
[2625] | 703 | // Perform push operations if there are admissible edges |
---|
| 704 | if (_excess[n] > 0 && next_dir[n]) { |
---|
| 705 | OutEdgeIt e = next_out[n]; |
---|
| 706 | for ( ; e != INVALID; ++e) { |
---|
[2581] | 707 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
[2625] | 708 | delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]); |
---|
[2577] | 709 | t = _graph.target(e); |
---|
| 710 | |
---|
| 711 | // Push-look-ahead heuristic |
---|
| 712 | Capacity ahead = -_excess[t]; |
---|
| 713 | for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) { |
---|
[2581] | 714 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
---|
| 715 | ahead += _capacity[oe] - (*_flow)[oe]; |
---|
[2577] | 716 | } |
---|
| 717 | for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) { |
---|
[2581] | 718 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
---|
| 719 | ahead += (*_flow)[ie]; |
---|
[2577] | 720 | } |
---|
| 721 | if (ahead < 0) ahead = 0; |
---|
| 722 | |
---|
[2625] | 723 | // Push flow along the edge |
---|
[2577] | 724 | if (ahead < delta) { |
---|
[2581] | 725 | (*_flow)[e] += ahead; |
---|
[2577] | 726 | _excess[n] -= ahead; |
---|
| 727 | _excess[t] += ahead; |
---|
| 728 | active_nodes.push_front(t); |
---|
| 729 | hyper[t] = true; |
---|
| 730 | relabel_enabled = false; |
---|
| 731 | break; |
---|
| 732 | } else { |
---|
[2581] | 733 | (*_flow)[e] += delta; |
---|
[2577] | 734 | _excess[n] -= delta; |
---|
| 735 | _excess[t] += delta; |
---|
| 736 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
| 737 | active_nodes.push_back(t); |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | if (_excess[n] == 0) break; |
---|
| 741 | } |
---|
| 742 | } |
---|
[2625] | 743 | if (e != INVALID) { |
---|
| 744 | next_out[n] = e; |
---|
| 745 | } else { |
---|
| 746 | next_dir[n] = false; |
---|
| 747 | } |
---|
[2577] | 748 | } |
---|
| 749 | |
---|
[2625] | 750 | if (_excess[n] > 0 && !next_dir[n]) { |
---|
| 751 | InEdgeIt e = next_in[n]; |
---|
| 752 | for ( ; e != INVALID; ++e) { |
---|
[2581] | 753 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
---|
[2625] | 754 | delta = std::min((*_flow)[e], _excess[n]); |
---|
[2577] | 755 | t = _graph.source(e); |
---|
| 756 | |
---|
| 757 | // Push-look-ahead heuristic |
---|
| 758 | Capacity ahead = -_excess[t]; |
---|
| 759 | for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) { |
---|
[2581] | 760 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
---|
| 761 | ahead += _capacity[oe] - (*_flow)[oe]; |
---|
[2577] | 762 | } |
---|
| 763 | for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) { |
---|
[2581] | 764 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
---|
| 765 | ahead += (*_flow)[ie]; |
---|
[2577] | 766 | } |
---|
| 767 | if (ahead < 0) ahead = 0; |
---|
| 768 | |
---|
[2625] | 769 | // Push flow along the edge |
---|
[2577] | 770 | if (ahead < delta) { |
---|
[2581] | 771 | (*_flow)[e] -= ahead; |
---|
[2577] | 772 | _excess[n] -= ahead; |
---|
| 773 | _excess[t] += ahead; |
---|
| 774 | active_nodes.push_front(t); |
---|
| 775 | hyper[t] = true; |
---|
| 776 | relabel_enabled = false; |
---|
| 777 | break; |
---|
| 778 | } else { |
---|
[2581] | 779 | (*_flow)[e] -= delta; |
---|
[2577] | 780 | _excess[n] -= delta; |
---|
| 781 | _excess[t] += delta; |
---|
| 782 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
| 783 | active_nodes.push_back(t); |
---|
| 784 | } |
---|
| 785 | |
---|
| 786 | if (_excess[n] == 0) break; |
---|
| 787 | } |
---|
| 788 | } |
---|
[2625] | 789 | next_in[n] = e; |
---|
[2577] | 790 | } |
---|
| 791 | |
---|
[2625] | 792 | // Relabel the node if it is still active (or hyper) |
---|
[2577] | 793 | if (relabel_enabled && (_excess[n] > 0 || hyper[n])) { |
---|
[2625] | 794 | LCost min_red_cost = std::numeric_limits<LCost>::max() / 2; |
---|
[2577] | 795 | for (OutEdgeIt oe(_graph, n); oe != INVALID; ++oe) { |
---|
[2581] | 796 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
---|
| 797 | (*_red_cost)[oe] < min_red_cost ) |
---|
| 798 | min_red_cost = (*_red_cost)[oe]; |
---|
[2577] | 799 | } |
---|
| 800 | for (InEdgeIt ie(_graph, n); ie != INVALID; ++ie) { |
---|
[2581] | 801 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
---|
| 802 | min_red_cost = -(*_red_cost)[ie]; |
---|
[2577] | 803 | } |
---|
[2581] | 804 | (*_potential)[n] -= min_red_cost + _epsilon; |
---|
[2577] | 805 | hyper[n] = false; |
---|
[2625] | 806 | |
---|
| 807 | // Reset the next edge maps |
---|
| 808 | next_out[n] = OutEdgeIt(_graph, n); |
---|
| 809 | next_in[n] = InEdgeIt(_graph, n); |
---|
| 810 | next_dir[n] = true; |
---|
[2577] | 811 | } |
---|
| 812 | |
---|
[2625] | 813 | // Remove nodes that are not active nor hyper |
---|
[2577] | 814 | while ( active_nodes.size() > 0 && |
---|
| 815 | _excess[active_nodes[0]] <= 0 && |
---|
| 816 | !hyper[active_nodes[0]] ) { |
---|
| 817 | active_nodes.pop_front(); |
---|
| 818 | } |
---|
| 819 | } |
---|
| 820 | } |
---|
| 821 | |
---|
[2625] | 822 | // Compute node potentials for the original costs |
---|
[2581] | 823 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
---|
| 824 | BellmanFord< ResGraph, ResidualCostMap<CostMap> > |
---|
| 825 | bf(*_res_graph, res_cost); |
---|
| 826 | bf.init(0); bf.start(); |
---|
| 827 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
| 828 | (*_potential)[n] = bf.dist(n); |
---|
| 829 | |
---|
[2625] | 830 | // Handle non-zero lower bounds |
---|
[2577] | 831 | if (_lower) { |
---|
| 832 | for (EdgeIt e(_graph); e != INVALID; ++e) |
---|
[2581] | 833 | (*_flow)[e] += (*_lower)[e]; |
---|
[2577] | 834 | } |
---|
| 835 | return true; |
---|
| 836 | } |
---|
| 837 | |
---|
| 838 | }; //class CostScaling |
---|
| 839 | |
---|
| 840 | ///@} |
---|
| 841 | |
---|
| 842 | } //namespace lemon |
---|
| 843 | |
---|
| 844 | #endif //LEMON_COST_SCALING_H |
---|