[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 | /// |
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| 24 | /// \file |
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| 25 | /// \brief Cost scaling algorithm for finding a minimum cost flow. |
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| 26 | |
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| 27 | #include <deque> |
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| 28 | #include <lemon/graph_adaptor.h> |
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| 29 | #include <lemon/graph_utils.h> |
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| 30 | #include <lemon/maps.h> |
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| 31 | #include <lemon/math.h> |
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| 32 | |
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| 33 | #include <lemon/circulation.h> |
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| 34 | #include <lemon/bellman_ford.h> |
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| 35 | |
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| 36 | namespace lemon { |
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| 37 | |
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| 38 | /// \addtogroup min_cost_flow |
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| 39 | /// @{ |
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| 40 | |
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| 41 | /// \brief Implementation of the cost scaling algorithm for finding a |
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| 42 | /// minimum cost flow. |
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| 43 | /// |
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| 44 | /// \ref CostScaling implements the cost scaling algorithm performing |
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| 45 | /// generalized push-relabel operations for finding a minimum cost |
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| 46 | /// flow. |
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| 47 | /// |
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| 48 | /// \tparam Graph The directed graph type the algorithm runs on. |
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| 49 | /// \tparam LowerMap The type of the lower bound map. |
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| 50 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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| 51 | /// \tparam CostMap The type of the cost (length) map. |
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| 52 | /// \tparam SupplyMap The type of the supply map. |
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| 53 | /// |
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| 54 | /// \warning |
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| 55 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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| 56 | /// - Supply values should be \e signed \e integers. |
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[2581] | 57 | /// - The value types of the maps should be convertible to each other. |
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| 58 | /// - \c CostMap::Value must be signed type. |
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[2577] | 59 | /// |
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| 60 | /// \note Edge costs are multiplied with the number of nodes during |
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| 61 | /// the algorithm so overflow problems may arise more easily than with |
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| 62 | /// other minimum cost flow algorithms. |
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| 63 | /// If it is available, <tt>long long int</tt> type is used instead of |
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| 64 | /// <tt>long int</tt> in the inside computations. |
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| 65 | /// |
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| 66 | /// \author Peter Kovacs |
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| 67 | template < typename Graph, |
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| 68 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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| 69 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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| 70 | typename CostMap = typename Graph::template EdgeMap<int>, |
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| 71 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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| 72 | class CostScaling |
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| 73 | { |
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| 74 | GRAPH_TYPEDEFS(typename Graph); |
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| 75 | |
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| 76 | typedef typename CapacityMap::Value Capacity; |
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| 77 | typedef typename CostMap::Value Cost; |
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| 78 | typedef typename SupplyMap::Value Supply; |
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| 79 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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| 80 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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| 81 | |
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| 82 | typedef ResGraphAdaptor< const Graph, Capacity, |
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| 83 | CapacityEdgeMap, CapacityEdgeMap > ResGraph; |
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| 84 | typedef typename ResGraph::Edge ResEdge; |
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| 85 | |
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| 86 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
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| 87 | typedef long long int LCost; |
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| 88 | #else |
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| 89 | typedef long int LCost; |
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| 90 | #endif |
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| 91 | typedef typename Graph::template EdgeMap<LCost> LargeCostMap; |
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| 92 | |
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| 93 | public: |
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| 94 | |
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| 95 | /// The type of the flow map. |
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[2581] | 96 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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[2577] | 97 | /// The type of the potential map. |
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| 98 | typedef typename Graph::template NodeMap<LCost> PotentialMap; |
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| 99 | |
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| 100 | private: |
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| 101 | |
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| 102 | /// \brief Map adaptor class for handling residual edge costs. |
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| 103 | /// |
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[2620] | 104 | /// Map adaptor class for handling residual edge costs. |
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[2581] | 105 | template <typename Map> |
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| 106 | class ResidualCostMap : public MapBase<ResEdge, typename Map::Value> |
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[2577] | 107 | { |
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| 108 | private: |
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| 109 | |
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[2581] | 110 | const Map &_cost_map; |
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[2577] | 111 | |
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| 112 | public: |
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| 113 | |
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| 114 | ///\e |
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[2581] | 115 | ResidualCostMap(const Map &cost_map) : |
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[2577] | 116 | _cost_map(cost_map) {} |
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| 117 | |
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| 118 | ///\e |
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[2581] | 119 | typename Map::Value operator[](const ResEdge &e) const { |
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[2577] | 120 | return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
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| 121 | } |
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| 122 | |
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| 123 | }; //class ResidualCostMap |
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| 124 | |
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| 125 | /// \brief Map adaptor class for handling reduced edge costs. |
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| 126 | /// |
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[2620] | 127 | /// Map adaptor class for handling reduced edge costs. |
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[2577] | 128 | class ReducedCostMap : public MapBase<Edge, LCost> |
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| 129 | { |
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| 130 | private: |
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| 131 | |
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| 132 | const Graph &_gr; |
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| 133 | const LargeCostMap &_cost_map; |
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| 134 | const PotentialMap &_pot_map; |
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| 135 | |
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| 136 | public: |
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| 137 | |
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| 138 | ///\e |
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| 139 | ReducedCostMap( const Graph &gr, |
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| 140 | const LargeCostMap &cost_map, |
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| 141 | const PotentialMap &pot_map ) : |
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| 142 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
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| 143 | |
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| 144 | ///\e |
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| 145 | LCost operator[](const Edge &e) const { |
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| 146 | return _cost_map[e] + _pot_map[_gr.source(e)] |
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| 147 | - _pot_map[_gr.target(e)]; |
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| 148 | } |
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| 149 | |
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| 150 | }; //class ReducedCostMap |
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| 151 | |
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| 152 | private: |
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| 153 | |
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| 154 | // Scaling factor |
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| 155 | static const int ALPHA = 4; |
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| 156 | |
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| 157 | // Paramters for heuristics |
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[2581] | 158 | static const int BF_HEURISTIC_EPSILON_BOUND = 5000; |
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| 159 | static const int BF_HEURISTIC_BOUND_FACTOR = 3; |
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[2577] | 160 | |
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| 161 | private: |
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| 162 | |
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| 163 | // The directed graph the algorithm runs on |
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| 164 | const Graph &_graph; |
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| 165 | // The original lower bound map |
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| 166 | const LowerMap *_lower; |
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| 167 | // The modified capacity map |
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| 168 | CapacityEdgeMap _capacity; |
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| 169 | // The original cost map |
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| 170 | const CostMap &_orig_cost; |
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| 171 | // The scaled cost map |
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| 172 | LargeCostMap _cost; |
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| 173 | // The modified supply map |
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| 174 | SupplyNodeMap _supply; |
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| 175 | bool _valid_supply; |
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| 176 | |
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| 177 | // Edge map of the current flow |
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[2581] | 178 | FlowMap *_flow; |
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| 179 | bool _local_flow; |
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[2577] | 180 | // Node map of the current potentials |
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[2581] | 181 | PotentialMap *_potential; |
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| 182 | bool _local_potential; |
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[2577] | 183 | |
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[2623] | 184 | // The residual cost map |
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| 185 | ResidualCostMap<LargeCostMap> _res_cost; |
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[2577] | 186 | // The residual graph |
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[2581] | 187 | ResGraph *_res_graph; |
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[2577] | 188 | // The reduced cost map |
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[2581] | 189 | ReducedCostMap *_red_cost; |
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[2577] | 190 | // The excess map |
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| 191 | SupplyNodeMap _excess; |
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| 192 | // The epsilon parameter used for cost scaling |
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| 193 | LCost _epsilon; |
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| 194 | |
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| 195 | public: |
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| 196 | |
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[2581] | 197 | /// \brief General constructor (with lower bounds). |
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[2577] | 198 | /// |
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[2581] | 199 | /// General constructor (with lower bounds). |
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[2577] | 200 | /// |
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| 201 | /// \param graph The directed graph the algorithm runs on. |
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| 202 | /// \param lower The lower bounds of the edges. |
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| 203 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 204 | /// \param cost The cost (length) values of the edges. |
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| 205 | /// \param supply The supply values of the nodes (signed). |
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| 206 | CostScaling( const Graph &graph, |
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| 207 | const LowerMap &lower, |
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| 208 | const CapacityMap &capacity, |
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| 209 | const CostMap &cost, |
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| 210 | const SupplyMap &supply ) : |
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| 211 | _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost), |
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[2623] | 212 | _cost(graph), _supply(graph), _flow(NULL), _local_flow(false), |
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| 213 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 214 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 215 | { |
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| 216 | // Removing non-zero lower bounds |
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| 217 | _capacity = subMap(capacity, lower); |
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| 218 | Supply sum = 0; |
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| 219 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 220 | Supply s = supply[n]; |
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| 221 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 222 | s += lower[e]; |
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| 223 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 224 | s -= lower[e]; |
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| 225 | _supply[n] = s; |
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| 226 | sum += s; |
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| 227 | } |
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| 228 | _valid_supply = sum == 0; |
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| 229 | } |
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| 230 | |
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[2581] | 231 | /// \brief General constructor (without lower bounds). |
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[2577] | 232 | /// |
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[2581] | 233 | /// General constructor (without lower bounds). |
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[2577] | 234 | /// |
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| 235 | /// \param graph The directed graph the algorithm runs on. |
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| 236 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 237 | /// \param cost The cost (length) values of the edges. |
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| 238 | /// \param supply The supply values of the nodes (signed). |
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| 239 | CostScaling( const Graph &graph, |
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| 240 | const CapacityMap &capacity, |
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| 241 | const CostMap &cost, |
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| 242 | const SupplyMap &supply ) : |
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| 243 | _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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[2623] | 244 | _cost(graph), _supply(supply), _flow(NULL), _local_flow(false), |
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| 245 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 246 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 247 | { |
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| 248 | // Checking the sum of supply values |
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| 249 | Supply sum = 0; |
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| 250 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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| 251 | _valid_supply = sum == 0; |
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| 252 | } |
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| 253 | |
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[2581] | 254 | /// \brief Simple constructor (with lower bounds). |
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[2577] | 255 | /// |
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[2581] | 256 | /// Simple constructor (with lower bounds). |
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[2577] | 257 | /// |
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| 258 | /// \param graph The directed graph the algorithm runs on. |
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| 259 | /// \param lower The lower bounds of the edges. |
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| 260 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 261 | /// \param cost The cost (length) values of the edges. |
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| 262 | /// \param s The source node. |
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| 263 | /// \param t The target node. |
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| 264 | /// \param flow_value The required amount of flow from node \c s |
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| 265 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 266 | CostScaling( const Graph &graph, |
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| 267 | const LowerMap &lower, |
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| 268 | const CapacityMap &capacity, |
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| 269 | const CostMap &cost, |
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| 270 | Node s, Node t, |
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| 271 | Supply flow_value ) : |
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| 272 | _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost), |
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[2623] | 273 | _cost(graph), _supply(graph), _flow(NULL), _local_flow(false), |
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| 274 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 275 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 276 | { |
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| 277 | // Removing nonzero lower bounds |
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| 278 | _capacity = subMap(capacity, lower); |
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| 279 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 280 | Supply sum = 0; |
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| 281 | if (n == s) sum = flow_value; |
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| 282 | if (n == t) sum = -flow_value; |
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| 283 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 284 | sum += lower[e]; |
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| 285 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 286 | sum -= lower[e]; |
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| 287 | _supply[n] = sum; |
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| 288 | } |
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| 289 | _valid_supply = true; |
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| 290 | } |
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| 291 | |
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[2581] | 292 | /// \brief Simple constructor (without lower bounds). |
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[2577] | 293 | /// |
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[2581] | 294 | /// Simple constructor (without lower bounds). |
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[2577] | 295 | /// |
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| 296 | /// \param graph The directed graph the algorithm runs on. |
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| 297 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 298 | /// \param cost The cost (length) values of the edges. |
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| 299 | /// \param s The source node. |
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| 300 | /// \param t The target node. |
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| 301 | /// \param flow_value The required amount of flow from node \c s |
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| 302 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 303 | CostScaling( const Graph &graph, |
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| 304 | const CapacityMap &capacity, |
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| 305 | const CostMap &cost, |
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| 306 | Node s, Node t, |
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| 307 | Supply flow_value ) : |
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| 308 | _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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[2623] | 309 | _cost(graph), _supply(graph, 0), _flow(NULL), _local_flow(false), |
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| 310 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 311 | _res_graph(NULL), _red_cost(NULL), _excess(graph, 0) |
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[2577] | 312 | { |
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| 313 | _supply[s] = flow_value; |
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| 314 | _supply[t] = -flow_value; |
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| 315 | _valid_supply = true; |
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| 316 | } |
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| 317 | |
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[2581] | 318 | /// Destructor. |
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| 319 | ~CostScaling() { |
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| 320 | if (_local_flow) delete _flow; |
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| 321 | if (_local_potential) delete _potential; |
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| 322 | delete _res_graph; |
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| 323 | delete _red_cost; |
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| 324 | } |
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| 325 | |
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[2620] | 326 | /// \brief Set the flow map. |
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[2581] | 327 | /// |
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[2620] | 328 | /// Set the flow map. |
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[2581] | 329 | /// |
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| 330 | /// \return \c (*this) |
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| 331 | CostScaling& flowMap(FlowMap &map) { |
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| 332 | if (_local_flow) { |
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| 333 | delete _flow; |
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| 334 | _local_flow = false; |
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| 335 | } |
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| 336 | _flow = ↦ |
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| 337 | return *this; |
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| 338 | } |
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| 339 | |
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[2620] | 340 | /// \brief Set the potential map. |
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[2581] | 341 | /// |
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[2620] | 342 | /// Set the potential map. |
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[2581] | 343 | /// |
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| 344 | /// \return \c (*this) |
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| 345 | CostScaling& potentialMap(PotentialMap &map) { |
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| 346 | if (_local_potential) { |
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| 347 | delete _potential; |
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| 348 | _local_potential = false; |
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| 349 | } |
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| 350 | _potential = ↦ |
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| 351 | return *this; |
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| 352 | } |
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| 353 | |
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| 354 | /// \name Execution control |
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| 355 | |
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| 356 | /// @{ |
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| 357 | |
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[2620] | 358 | /// \brief Run the algorithm. |
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[2577] | 359 | /// |
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[2620] | 360 | /// Run the algorithm. |
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[2577] | 361 | /// |
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| 362 | /// \return \c true if a feasible flow can be found. |
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| 363 | bool run() { |
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[2581] | 364 | return init() && start(); |
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[2577] | 365 | } |
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| 366 | |
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[2581] | 367 | /// @} |
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| 368 | |
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| 369 | /// \name Query Functions |
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| 370 | /// The result of the algorithm can be obtained using these |
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[2620] | 371 | /// functions.\n |
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| 372 | /// \ref lemon::CostScaling::run() "run()" must be called before |
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| 373 | /// using them. |
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[2581] | 374 | |
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| 375 | /// @{ |
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| 376 | |
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[2620] | 377 | /// \brief Return a const reference to the edge map storing the |
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[2577] | 378 | /// found flow. |
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| 379 | /// |
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[2620] | 380 | /// Return a const reference to the edge map storing the found flow. |
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[2577] | 381 | /// |
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| 382 | /// \pre \ref run() must be called before using this function. |
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| 383 | const FlowMap& flowMap() const { |
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[2581] | 384 | return *_flow; |
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[2577] | 385 | } |
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| 386 | |
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[2620] | 387 | /// \brief Return a const reference to the node map storing the |
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[2577] | 388 | /// found potentials (the dual solution). |
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| 389 | /// |
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[2620] | 390 | /// Return a const reference to the node map storing the found |
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[2577] | 391 | /// potentials (the dual solution). |
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| 392 | /// |
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| 393 | /// \pre \ref run() must be called before using this function. |
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| 394 | const PotentialMap& potentialMap() const { |
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[2581] | 395 | return *_potential; |
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| 396 | } |
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| 397 | |
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[2620] | 398 | /// \brief Return the flow on the given edge. |
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[2581] | 399 | /// |
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[2620] | 400 | /// Return the flow on the given edge. |
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[2581] | 401 | /// |
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| 402 | /// \pre \ref run() must be called before using this function. |
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| 403 | Capacity flow(const Edge& edge) const { |
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| 404 | return (*_flow)[edge]; |
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| 405 | } |
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| 406 | |
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[2620] | 407 | /// \brief Return the potential of the given node. |
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[2581] | 408 | /// |
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[2620] | 409 | /// Return the potential of the given node. |
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[2581] | 410 | /// |
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| 411 | /// \pre \ref run() must be called before using this function. |
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| 412 | Cost potential(const Node& node) const { |
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| 413 | return (*_potential)[node]; |
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[2577] | 414 | } |
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| 415 | |
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[2620] | 416 | /// \brief Return the total cost of the found flow. |
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[2577] | 417 | /// |
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[2620] | 418 | /// Return the total cost of the found flow. The complexity of the |
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[2577] | 419 | /// function is \f$ O(e) \f$. |
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| 420 | /// |
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| 421 | /// \pre \ref run() must be called before using this function. |
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| 422 | Cost totalCost() const { |
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| 423 | Cost c = 0; |
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| 424 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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[2581] | 425 | c += (*_flow)[e] * _orig_cost[e]; |
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[2577] | 426 | return c; |
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| 427 | } |
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| 428 | |
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[2581] | 429 | /// @} |
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| 430 | |
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[2577] | 431 | private: |
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| 432 | |
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[2620] | 433 | /// Initialize the algorithm. |
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[2577] | 434 | bool init() { |
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| 435 | if (!_valid_supply) return false; |
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| 436 | |
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[2581] | 437 | // Initializing flow and potential maps |
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| 438 | if (!_flow) { |
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| 439 | _flow = new FlowMap(_graph); |
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| 440 | _local_flow = true; |
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| 441 | } |
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| 442 | if (!_potential) { |
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| 443 | _potential = new PotentialMap(_graph); |
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| 444 | _local_potential = true; |
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| 445 | } |
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| 446 | |
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| 447 | _red_cost = new ReducedCostMap(_graph, _cost, *_potential); |
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| 448 | _res_graph = new ResGraph(_graph, _capacity, *_flow); |
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| 449 | |
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[2577] | 450 | // Initializing the scaled cost map and the epsilon parameter |
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| 451 | Cost max_cost = 0; |
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| 452 | int node_num = countNodes(_graph); |
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| 453 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 454 | _cost[e] = LCost(_orig_cost[e]) * node_num * ALPHA; |
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| 455 | if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e]; |
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| 456 | } |
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| 457 | _epsilon = max_cost * node_num; |
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| 458 | |
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| 459 | // Finding a feasible flow using Circulation |
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| 460 | Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap, |
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| 461 | SupplyMap > |
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[2581] | 462 | circulation( _graph, constMap<Edge>(Capacity(0)), _capacity, |
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[2577] | 463 | _supply ); |
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[2581] | 464 | return circulation.flowMap(*_flow).run(); |
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[2577] | 465 | } |
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| 466 | |
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| 467 | |
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[2620] | 468 | /// Execute the algorithm. |
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[2577] | 469 | bool start() { |
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| 470 | std::deque<Node> active_nodes; |
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| 471 | typename Graph::template NodeMap<bool> hyper(_graph, false); |
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| 472 | |
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| 473 | int node_num = countNodes(_graph); |
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| 474 | for ( ; _epsilon >= 1; _epsilon = _epsilon < ALPHA && _epsilon > 1 ? |
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| 475 | 1 : _epsilon / ALPHA ) |
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| 476 | { |
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| 477 | // Performing price refinement heuristic using Bellman-Ford |
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| 478 | // algorithm |
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| 479 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
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[2581] | 480 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
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[2577] | 481 | ShiftCostMap shift_cost(_res_cost, _epsilon); |
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[2581] | 482 | BellmanFord<ResGraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
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[2577] | 483 | bf.init(0); |
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| 484 | bool done = false; |
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| 485 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
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| 486 | for (int i = 0; i < K && !done; ++i) |
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| 487 | done = bf.processNextWeakRound(); |
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| 488 | if (done) { |
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| 489 | for (NodeIt n(_graph); n != INVALID; ++n) |
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[2581] | 490 | (*_potential)[n] = bf.dist(n); |
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[2577] | 491 | continue; |
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| 492 | } |
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| 493 | } |
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| 494 | |
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| 495 | // Saturating edges not satisfying the optimality condition |
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| 496 | Capacity delta; |
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| 497 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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[2581] | 498 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 499 | delta = _capacity[e] - (*_flow)[e]; |
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[2577] | 500 | _excess[_graph.source(e)] -= delta; |
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| 501 | _excess[_graph.target(e)] += delta; |
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[2581] | 502 | (*_flow)[e] = _capacity[e]; |
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[2577] | 503 | } |
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[2581] | 504 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 505 | _excess[_graph.target(e)] -= (*_flow)[e]; |
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| 506 | _excess[_graph.source(e)] += (*_flow)[e]; |
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| 507 | (*_flow)[e] = 0; |
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[2577] | 508 | } |
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| 509 | } |
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| 510 | |
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| 511 | // Finding active nodes (i.e. nodes with positive excess) |
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| 512 | for (NodeIt n(_graph); n != INVALID; ++n) |
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| 513 | if (_excess[n] > 0) active_nodes.push_back(n); |
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| 514 | |
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| 515 | // Performing push and relabel operations |
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| 516 | while (active_nodes.size() > 0) { |
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| 517 | Node n = active_nodes[0], t; |
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| 518 | bool relabel_enabled = true; |
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| 519 | |
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| 520 | // Performing push operations if there are admissible edges |
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| 521 | if (_excess[n] > 0) { |
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| 522 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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[2581] | 523 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 524 | delta = _capacity[e] - (*_flow)[e] <= _excess[n] ? |
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| 525 | _capacity[e] - (*_flow)[e] : _excess[n]; |
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[2577] | 526 | t = _graph.target(e); |
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| 527 | |
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| 528 | // Push-look-ahead heuristic |
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| 529 | Capacity ahead = -_excess[t]; |
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| 530 | for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) { |
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[2581] | 531 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
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| 532 | ahead += _capacity[oe] - (*_flow)[oe]; |
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[2577] | 533 | } |
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| 534 | for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) { |
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[2581] | 535 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
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| 536 | ahead += (*_flow)[ie]; |
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[2577] | 537 | } |
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| 538 | if (ahead < 0) ahead = 0; |
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| 539 | |
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| 540 | // Pushing flow along the edge |
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| 541 | if (ahead < delta) { |
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[2581] | 542 | (*_flow)[e] += ahead; |
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[2577] | 543 | _excess[n] -= ahead; |
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| 544 | _excess[t] += ahead; |
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| 545 | active_nodes.push_front(t); |
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| 546 | hyper[t] = true; |
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| 547 | relabel_enabled = false; |
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| 548 | break; |
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| 549 | } else { |
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[2581] | 550 | (*_flow)[e] += delta; |
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[2577] | 551 | _excess[n] -= delta; |
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| 552 | _excess[t] += delta; |
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| 553 | if (_excess[t] > 0 && _excess[t] <= delta) |
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| 554 | active_nodes.push_back(t); |
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| 555 | } |
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| 556 | |
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| 557 | if (_excess[n] == 0) break; |
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| 558 | } |
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| 559 | } |
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| 560 | } |
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| 561 | |
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| 562 | if (_excess[n] > 0) { |
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| 563 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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[2581] | 564 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 565 | delta = (*_flow)[e] <= _excess[n] ? (*_flow)[e] : _excess[n]; |
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[2577] | 566 | t = _graph.source(e); |
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| 567 | |
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| 568 | // Push-look-ahead heuristic |
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| 569 | Capacity ahead = -_excess[t]; |
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| 570 | for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) { |
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[2581] | 571 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
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| 572 | ahead += _capacity[oe] - (*_flow)[oe]; |
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[2577] | 573 | } |
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| 574 | for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) { |
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[2581] | 575 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
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| 576 | ahead += (*_flow)[ie]; |
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[2577] | 577 | } |
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| 578 | if (ahead < 0) ahead = 0; |
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| 579 | |
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| 580 | // Pushing flow along the edge |
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| 581 | if (ahead < delta) { |
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[2581] | 582 | (*_flow)[e] -= ahead; |
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[2577] | 583 | _excess[n] -= ahead; |
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| 584 | _excess[t] += ahead; |
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| 585 | active_nodes.push_front(t); |
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| 586 | hyper[t] = true; |
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| 587 | relabel_enabled = false; |
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| 588 | break; |
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| 589 | } else { |
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[2581] | 590 | (*_flow)[e] -= delta; |
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[2577] | 591 | _excess[n] -= delta; |
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| 592 | _excess[t] += delta; |
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| 593 | if (_excess[t] > 0 && _excess[t] <= delta) |
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| 594 | active_nodes.push_back(t); |
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| 595 | } |
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| 596 | |
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| 597 | if (_excess[n] == 0) break; |
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| 598 | } |
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| 599 | } |
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| 600 | } |
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| 601 | |
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| 602 | if (relabel_enabled && (_excess[n] > 0 || hyper[n])) { |
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| 603 | // Performing relabel operation if the node is still active |
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| 604 | LCost min_red_cost = std::numeric_limits<LCost>::max(); |
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| 605 | for (OutEdgeIt oe(_graph, n); oe != INVALID; ++oe) { |
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[2581] | 606 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
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| 607 | (*_red_cost)[oe] < min_red_cost ) |
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| 608 | min_red_cost = (*_red_cost)[oe]; |
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[2577] | 609 | } |
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| 610 | for (InEdgeIt ie(_graph, n); ie != INVALID; ++ie) { |
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[2581] | 611 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
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| 612 | min_red_cost = -(*_red_cost)[ie]; |
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[2577] | 613 | } |
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[2581] | 614 | (*_potential)[n] -= min_red_cost + _epsilon; |
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[2577] | 615 | hyper[n] = false; |
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| 616 | } |
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| 617 | |
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| 618 | // Removing active nodes with non-positive excess |
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| 619 | while ( active_nodes.size() > 0 && |
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| 620 | _excess[active_nodes[0]] <= 0 && |
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| 621 | !hyper[active_nodes[0]] ) { |
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| 622 | active_nodes.pop_front(); |
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| 623 | } |
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| 624 | } |
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| 625 | } |
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| 626 | |
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[2581] | 627 | // Computing node potentials for the original costs |
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| 628 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
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| 629 | BellmanFord< ResGraph, ResidualCostMap<CostMap> > |
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| 630 | bf(*_res_graph, res_cost); |
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| 631 | bf.init(0); bf.start(); |
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| 632 | for (NodeIt n(_graph); n != INVALID; ++n) |
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| 633 | (*_potential)[n] = bf.dist(n); |
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| 634 | |
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[2577] | 635 | // Handling non-zero lower bounds |
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| 636 | if (_lower) { |
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| 637 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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[2581] | 638 | (*_flow)[e] += (*_lower)[e]; |
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[2577] | 639 | } |
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| 640 | return true; |
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| 641 | } |
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| 642 | |
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| 643 | }; //class CostScaling |
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| 644 | |
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| 645 | ///@} |
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| 646 | |
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| 647 | } //namespace lemon |
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| 648 | |
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| 649 | #endif //LEMON_COST_SCALING_H |
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