[808] | 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_algs |
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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 <vector> |
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| 27 | #include <deque> |
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| 28 | #include <limits> |
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| 29 | |
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| 30 | #include <lemon/core.h> |
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| 31 | #include <lemon/maps.h> |
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| 32 | #include <lemon/math.h> |
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| 33 | #include <lemon/adaptors.h> |
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| 34 | #include <lemon/circulation.h> |
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| 35 | #include <lemon/bellman_ford.h> |
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| 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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| 39 | /// \addtogroup min_cost_flow_algs |
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| 40 | /// @{ |
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| 41 | |
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| 42 | /// \brief Implementation of the cost scaling algorithm for finding a |
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| 43 | /// minimum cost flow. |
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| 44 | /// |
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| 45 | /// \ref CostScaling implements the cost scaling algorithm performing |
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| 46 | /// augment/push and relabel operations for finding a minimum cost |
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| 47 | /// flow. |
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| 48 | /// |
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| 49 | /// \tparam Digraph The digraph type the algorithm runs on. |
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| 50 | /// \tparam LowerMap The type of the lower bound map. |
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| 51 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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| 52 | /// \tparam CostMap The type of the cost (length) map. |
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| 53 | /// \tparam SupplyMap The type of the supply map. |
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| 54 | /// |
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| 55 | /// \warning |
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| 56 | /// - Arc capacities and costs should be \e non-negative \e integers. |
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| 57 | /// - Supply values should be \e signed \e integers. |
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| 58 | /// - The value types of the maps should be convertible to each other. |
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| 59 | /// - \c CostMap::Value must be signed type. |
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| 60 | /// |
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| 61 | /// \note Arc costs are multiplied with the number of nodes during |
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| 62 | /// the algorithm so overflow problems may arise more easily than with |
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| 63 | /// other minimum cost flow algorithms. |
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| 64 | /// If it is available, <tt>long long int</tt> type is used instead of |
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| 65 | /// <tt>long int</tt> in the inside computations. |
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| 66 | /// |
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| 67 | /// \author Peter Kovacs |
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| 68 | template < typename Digraph, |
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| 69 | typename LowerMap = typename Digraph::template ArcMap<int>, |
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| 70 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
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| 71 | typename CostMap = typename Digraph::template ArcMap<int>, |
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| 72 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
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| 73 | class CostScaling |
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| 74 | { |
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| 75 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 76 | |
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| 77 | typedef typename CapacityMap::Value Capacity; |
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| 78 | typedef typename CostMap::Value Cost; |
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| 79 | typedef typename SupplyMap::Value Supply; |
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| 80 | typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap; |
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| 81 | typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap; |
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| 82 | |
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| 83 | typedef ResidualDigraph< const Digraph, |
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| 84 | CapacityArcMap, CapacityArcMap > ResDigraph; |
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| 85 | typedef typename ResDigraph::Arc ResArc; |
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| 86 | |
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| 87 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
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| 88 | typedef long long int LCost; |
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| 89 | #else |
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| 90 | typedef long int LCost; |
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| 91 | #endif |
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| 92 | typedef typename Digraph::template ArcMap<LCost> LargeCostMap; |
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| 93 | |
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| 94 | public: |
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| 95 | |
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| 96 | /// The type of the flow map. |
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| 97 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
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| 98 | /// The type of the potential map. |
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| 99 | typedef typename Digraph::template NodeMap<LCost> PotentialMap; |
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| 100 | |
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| 101 | private: |
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| 102 | |
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| 103 | /// \brief Map adaptor class for handling residual arc costs. |
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| 104 | /// |
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| 105 | /// Map adaptor class for handling residual arc costs. |
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| 106 | template <typename Map> |
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| 107 | class ResidualCostMap : public MapBase<ResArc, typename Map::Value> |
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| 108 | { |
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| 109 | private: |
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| 110 | |
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| 111 | const Map &_cost_map; |
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| 112 | |
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| 113 | public: |
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| 114 | |
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| 115 | ///\e |
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| 116 | ResidualCostMap(const Map &cost_map) : |
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| 117 | _cost_map(cost_map) {} |
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| 118 | |
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| 119 | ///\e |
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| 120 | inline typename Map::Value operator[](const ResArc &e) const { |
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| 121 | return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
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| 122 | } |
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| 123 | |
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| 124 | }; //class ResidualCostMap |
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| 125 | |
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| 126 | /// \brief Map adaptor class for handling reduced arc costs. |
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| 127 | /// |
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| 128 | /// Map adaptor class for handling reduced arc costs. |
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| 129 | class ReducedCostMap : public MapBase<Arc, LCost> |
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| 130 | { |
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| 131 | private: |
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| 132 | |
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| 133 | const Digraph &_gr; |
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| 134 | const LargeCostMap &_cost_map; |
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| 135 | const PotentialMap &_pot_map; |
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| 136 | |
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| 137 | public: |
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| 138 | |
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| 139 | ///\e |
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| 140 | ReducedCostMap( const Digraph &gr, |
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| 141 | const LargeCostMap &cost_map, |
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| 142 | const PotentialMap &pot_map ) : |
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| 143 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
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| 144 | |
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| 145 | ///\e |
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| 146 | inline LCost operator[](const Arc &e) const { |
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| 147 | return _cost_map[e] + _pot_map[_gr.source(e)] |
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| 148 | - _pot_map[_gr.target(e)]; |
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| 149 | } |
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| 150 | |
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| 151 | }; //class ReducedCostMap |
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| 152 | |
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| 153 | private: |
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| 154 | |
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| 155 | // The digraph the algorithm runs on |
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| 156 | const Digraph &_graph; |
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| 157 | // The original lower bound map |
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| 158 | const LowerMap *_lower; |
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| 159 | // The modified capacity map |
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| 160 | CapacityArcMap _capacity; |
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| 161 | // The original cost map |
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| 162 | const CostMap &_orig_cost; |
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| 163 | // The scaled cost map |
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| 164 | LargeCostMap _cost; |
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| 165 | // The modified supply map |
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| 166 | SupplyNodeMap _supply; |
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| 167 | bool _valid_supply; |
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| 168 | |
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| 169 | // Arc map of the current flow |
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| 170 | FlowMap *_flow; |
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| 171 | bool _local_flow; |
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| 172 | // Node map of the current potentials |
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| 173 | PotentialMap *_potential; |
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| 174 | bool _local_potential; |
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| 175 | |
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| 176 | // The residual cost map |
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| 177 | ResidualCostMap<LargeCostMap> _res_cost; |
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| 178 | // The residual digraph |
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| 179 | ResDigraph *_res_graph; |
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| 180 | // The reduced cost map |
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| 181 | ReducedCostMap *_red_cost; |
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| 182 | // The excess map |
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| 183 | SupplyNodeMap _excess; |
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| 184 | // The epsilon parameter used for cost scaling |
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| 185 | LCost _epsilon; |
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| 186 | // The scaling factor |
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| 187 | int _alpha; |
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| 188 | |
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| 189 | public: |
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| 190 | |
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| 191 | /// \brief General constructor (with lower bounds). |
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| 192 | /// |
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| 193 | /// General constructor (with lower bounds). |
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| 194 | /// |
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| 195 | /// \param digraph The digraph the algorithm runs on. |
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| 196 | /// \param lower The lower bounds of the arcs. |
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| 197 | /// \param capacity The capacities (upper bounds) of the arcs. |
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| 198 | /// \param cost The cost (length) values of the arcs. |
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| 199 | /// \param supply The supply values of the nodes (signed). |
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| 200 | CostScaling( const Digraph &digraph, |
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| 201 | const LowerMap &lower, |
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| 202 | const CapacityMap &capacity, |
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| 203 | const CostMap &cost, |
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| 204 | const SupplyMap &supply ) : |
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| 205 | _graph(digraph), _lower(&lower), _capacity(digraph), _orig_cost(cost), |
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| 206 | _cost(digraph), _supply(digraph), _flow(NULL), _local_flow(false), |
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| 207 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 208 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
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| 209 | { |
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| 210 | // Check the sum of supply values |
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| 211 | Supply sum = 0; |
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| 212 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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| 213 | _valid_supply = sum == 0; |
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| 214 | |
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| 215 | for (ArcIt e(_graph); e != INVALID; ++e) _capacity[e] = capacity[e]; |
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| 216 | for (NodeIt n(_graph); n != INVALID; ++n) _supply[n] = supply[n]; |
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| 217 | |
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| 218 | // Remove non-zero lower bounds |
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| 219 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 220 | if (lower[e] != 0) { |
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| 221 | _capacity[e] -= lower[e]; |
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| 222 | _supply[_graph.source(e)] -= lower[e]; |
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| 223 | _supply[_graph.target(e)] += lower[e]; |
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| 224 | } |
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| 225 | } |
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| 226 | } |
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| 227 | /* |
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| 228 | /// \brief General constructor (without lower bounds). |
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| 229 | /// |
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| 230 | /// General constructor (without lower bounds). |
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| 231 | /// |
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| 232 | /// \param digraph The digraph the algorithm runs on. |
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| 233 | /// \param capacity The capacities (upper bounds) of the arcs. |
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| 234 | /// \param cost The cost (length) values of the arcs. |
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| 235 | /// \param supply The supply values of the nodes (signed). |
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| 236 | CostScaling( const Digraph &digraph, |
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| 237 | const CapacityMap &capacity, |
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| 238 | const CostMap &cost, |
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| 239 | const SupplyMap &supply ) : |
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| 240 | _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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| 241 | _cost(digraph), _supply(supply), _flow(NULL), _local_flow(false), |
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| 242 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 243 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
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| 244 | { |
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| 245 | // Check the sum of supply values |
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| 246 | Supply sum = 0; |
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| 247 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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| 248 | _valid_supply = sum == 0; |
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| 249 | } |
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| 250 | |
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| 251 | /// \brief Simple constructor (with lower bounds). |
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| 252 | /// |
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| 253 | /// Simple constructor (with lower bounds). |
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| 254 | /// |
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| 255 | /// \param digraph The digraph the algorithm runs on. |
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| 256 | /// \param lower The lower bounds of the arcs. |
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| 257 | /// \param capacity The capacities (upper bounds) of the arcs. |
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| 258 | /// \param cost The cost (length) values of the arcs. |
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| 259 | /// \param s The source node. |
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| 260 | /// \param t The target node. |
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| 261 | /// \param flow_value The required amount of flow from node \c s |
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| 262 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 263 | CostScaling( const Digraph &digraph, |
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| 264 | const LowerMap &lower, |
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| 265 | const CapacityMap &capacity, |
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| 266 | const CostMap &cost, |
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| 267 | Node s, Node t, |
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| 268 | Supply flow_value ) : |
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| 269 | _graph(digraph), _lower(&lower), _capacity(capacity), _orig_cost(cost), |
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| 270 | _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false), |
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| 271 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 272 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
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| 273 | { |
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| 274 | // Remove non-zero lower bounds |
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| 275 | _supply[s] = flow_value; |
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| 276 | _supply[t] = -flow_value; |
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| 277 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 278 | if (lower[e] != 0) { |
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| 279 | _capacity[e] -= lower[e]; |
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| 280 | _supply[_graph.source(e)] -= lower[e]; |
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| 281 | _supply[_graph.target(e)] += lower[e]; |
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| 282 | } |
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| 283 | } |
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| 284 | _valid_supply = true; |
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| 285 | } |
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| 286 | |
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| 287 | /// \brief Simple constructor (without lower bounds). |
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| 288 | /// |
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| 289 | /// Simple constructor (without lower bounds). |
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| 290 | /// |
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| 291 | /// \param digraph The digraph the algorithm runs on. |
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| 292 | /// \param capacity The capacities (upper bounds) of the arcs. |
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| 293 | /// \param cost The cost (length) values of the arcs. |
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| 294 | /// \param s The source node. |
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| 295 | /// \param t The target node. |
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| 296 | /// \param flow_value The required amount of flow from node \c s |
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| 297 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 298 | CostScaling( const Digraph &digraph, |
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| 299 | const CapacityMap &capacity, |
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| 300 | const CostMap &cost, |
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| 301 | Node s, Node t, |
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| 302 | Supply flow_value ) : |
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| 303 | _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
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| 304 | _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false), |
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| 305 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
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| 306 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
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| 307 | { |
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| 308 | _supply[s] = flow_value; |
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| 309 | _supply[t] = -flow_value; |
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| 310 | _valid_supply = true; |
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| 311 | } |
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| 312 | */ |
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| 313 | /// Destructor. |
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| 314 | ~CostScaling() { |
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| 315 | if (_local_flow) delete _flow; |
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| 316 | if (_local_potential) delete _potential; |
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| 317 | delete _res_graph; |
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| 318 | delete _red_cost; |
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| 319 | } |
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| 320 | |
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| 321 | /// \brief Set the flow map. |
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| 322 | /// |
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| 323 | /// Set the flow map. |
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| 324 | /// |
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| 325 | /// \return \c (*this) |
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| 326 | CostScaling& flowMap(FlowMap &map) { |
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| 327 | if (_local_flow) { |
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| 328 | delete _flow; |
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| 329 | _local_flow = false; |
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| 330 | } |
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| 331 | _flow = ↦ |
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| 332 | return *this; |
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| 333 | } |
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| 334 | |
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| 335 | /// \brief Set the potential map. |
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| 336 | /// |
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| 337 | /// Set the potential map. |
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| 338 | /// |
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| 339 | /// \return \c (*this) |
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| 340 | CostScaling& potentialMap(PotentialMap &map) { |
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| 341 | if (_local_potential) { |
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| 342 | delete _potential; |
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| 343 | _local_potential = false; |
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| 344 | } |
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| 345 | _potential = ↦ |
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| 346 | return *this; |
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| 347 | } |
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| 348 | |
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| 349 | /// \name Execution control |
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| 350 | |
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| 351 | /// @{ |
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| 352 | |
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| 353 | /// \brief Run the algorithm. |
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| 354 | /// |
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| 355 | /// Run the algorithm. |
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| 356 | /// |
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| 357 | /// \param partial_augment By default the algorithm performs |
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| 358 | /// partial augment and relabel operations in the cost scaling |
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| 359 | /// phases. Set this parameter to \c false for using local push and |
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| 360 | /// relabel operations instead. |
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| 361 | /// |
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| 362 | /// \return \c true if a feasible flow can be found. |
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| 363 | bool run(bool partial_augment = true) { |
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| 364 | if (partial_augment) { |
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| 365 | return init() && startPartialAugment(); |
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| 366 | } else { |
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| 367 | return init() && startPushRelabel(); |
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| 368 | } |
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| 369 | } |
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| 370 | |
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| 371 | /// @} |
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| 372 | |
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| 373 | /// \name Query Functions |
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| 374 | /// The result of the algorithm can be obtained using these |
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| 375 | /// functions.\n |
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| 376 | /// \ref lemon::CostScaling::run() "run()" must be called before |
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| 377 | /// using them. |
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| 378 | |
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| 379 | /// @{ |
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| 380 | |
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| 381 | /// \brief Return a const reference to the arc map storing the |
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| 382 | /// found flow. |
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| 383 | /// |
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| 384 | /// Return a const reference to the arc map storing the found flow. |
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| 385 | /// |
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| 386 | /// \pre \ref run() must be called before using this function. |
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| 387 | const FlowMap& flowMap() const { |
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| 388 | return *_flow; |
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| 389 | } |
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| 390 | |
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| 391 | /// \brief Return a const reference to the node map storing the |
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| 392 | /// found potentials (the dual solution). |
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| 393 | /// |
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| 394 | /// Return a const reference to the node map storing the found |
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| 395 | /// potentials (the dual solution). |
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| 396 | /// |
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| 397 | /// \pre \ref run() must be called before using this function. |
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| 398 | const PotentialMap& potentialMap() const { |
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| 399 | return *_potential; |
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| 400 | } |
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| 401 | |
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| 402 | /// \brief Return the flow on the given arc. |
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| 403 | /// |
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| 404 | /// Return the flow on the given arc. |
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| 405 | /// |
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| 406 | /// \pre \ref run() must be called before using this function. |
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| 407 | Capacity flow(const Arc& arc) const { |
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| 408 | return (*_flow)[arc]; |
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| 409 | } |
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| 410 | |
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| 411 | /// \brief Return the potential of the given node. |
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| 412 | /// |
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| 413 | /// Return the potential of the given node. |
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| 414 | /// |
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| 415 | /// \pre \ref run() must be called before using this function. |
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| 416 | Cost potential(const Node& node) const { |
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| 417 | return (*_potential)[node]; |
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| 418 | } |
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| 419 | |
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| 420 | /// \brief Return the total cost of the found flow. |
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| 421 | /// |
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| 422 | /// Return the total cost of the found flow. The complexity of the |
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| 423 | /// function is \f$ O(e) \f$. |
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| 424 | /// |
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| 425 | /// \pre \ref run() must be called before using this function. |
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| 426 | Cost totalCost() const { |
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| 427 | Cost c = 0; |
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| 428 | for (ArcIt e(_graph); e != INVALID; ++e) |
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| 429 | c += (*_flow)[e] * _orig_cost[e]; |
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| 430 | return c; |
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| 431 | } |
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| 432 | |
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| 433 | /// @} |
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| 434 | |
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| 435 | private: |
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| 436 | |
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| 437 | /// Initialize the algorithm. |
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| 438 | bool init() { |
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| 439 | if (!_valid_supply) return false; |
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| 440 | // The scaling factor |
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| 441 | _alpha = 8; |
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| 442 | |
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| 443 | // Initialize flow and potential maps |
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| 444 | if (!_flow) { |
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| 445 | _flow = new FlowMap(_graph); |
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| 446 | _local_flow = true; |
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| 447 | } |
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| 448 | if (!_potential) { |
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| 449 | _potential = new PotentialMap(_graph); |
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| 450 | _local_potential = true; |
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| 451 | } |
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| 452 | |
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| 453 | _red_cost = new ReducedCostMap(_graph, _cost, *_potential); |
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| 454 | _res_graph = new ResDigraph(_graph, _capacity, *_flow); |
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| 455 | |
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| 456 | // Initialize the scaled cost map and the epsilon parameter |
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| 457 | Cost max_cost = 0; |
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| 458 | int node_num = countNodes(_graph); |
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| 459 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 460 | _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha; |
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| 461 | if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e]; |
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| 462 | } |
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| 463 | _epsilon = max_cost * node_num; |
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| 464 | |
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| 465 | // Find a feasible flow using Circulation |
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| 466 | Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap, |
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| 467 | SupplyMap > |
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| 468 | circulation( _graph, constMap<Arc>(Capacity(0)), _capacity, |
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| 469 | _supply ); |
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| 470 | return circulation.flowMap(*_flow).run(); |
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| 471 | } |
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| 472 | |
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| 473 | /// Execute the algorithm performing partial augmentation and |
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| 474 | /// relabel operations. |
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| 475 | bool startPartialAugment() { |
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| 476 | // Paramters for heuristics |
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| 477 | // const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
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| 478 | // const int BF_HEURISTIC_BOUND_FACTOR = 3; |
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| 479 | // Maximum augment path length |
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| 480 | const int MAX_PATH_LENGTH = 4; |
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| 481 | |
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| 482 | // Variables |
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| 483 | typename Digraph::template NodeMap<Arc> pred_arc(_graph); |
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| 484 | typename Digraph::template NodeMap<bool> forward(_graph); |
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| 485 | typename Digraph::template NodeMap<OutArcIt> next_out(_graph); |
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| 486 | typename Digraph::template NodeMap<InArcIt> next_in(_graph); |
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| 487 | typename Digraph::template NodeMap<bool> next_dir(_graph); |
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| 488 | std::deque<Node> active_nodes; |
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| 489 | std::vector<Node> path_nodes; |
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| 490 | |
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| 491 | // int node_num = countNodes(_graph); |
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| 492 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
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| 493 | 1 : _epsilon / _alpha ) |
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| 494 | { |
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| 495 | /* |
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| 496 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
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| 497 | // to check if the current flow is optimal |
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| 498 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
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| 499 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
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| 500 | ShiftCostMap shift_cost(_res_cost, 1); |
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| 501 | BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
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| 502 | bf.init(0); |
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| 503 | bool done = false; |
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| 504 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
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| 505 | for (int i = 0; i < K && !done; ++i) |
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| 506 | done = bf.processNextWeakRound(); |
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| 507 | if (done) break; |
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| 508 | } |
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| 509 | */ |
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| 510 | // Saturate arcs not satisfying the optimality condition |
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| 511 | Capacity delta; |
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| 512 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 513 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 514 | delta = _capacity[e] - (*_flow)[e]; |
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| 515 | _excess[_graph.source(e)] -= delta; |
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| 516 | _excess[_graph.target(e)] += delta; |
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| 517 | (*_flow)[e] = _capacity[e]; |
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| 518 | } |
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| 519 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 520 | _excess[_graph.target(e)] -= (*_flow)[e]; |
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| 521 | _excess[_graph.source(e)] += (*_flow)[e]; |
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| 522 | (*_flow)[e] = 0; |
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| 523 | } |
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| 524 | } |
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| 525 | |
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| 526 | // Find active nodes (i.e. nodes with positive excess) |
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| 527 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 528 | if (_excess[n] > 0) active_nodes.push_back(n); |
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| 529 | } |
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| 530 | |
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| 531 | // Initialize the next arc maps |
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| 532 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 533 | next_out[n] = OutArcIt(_graph, n); |
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| 534 | next_in[n] = InArcIt(_graph, n); |
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| 535 | next_dir[n] = true; |
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| 536 | } |
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| 537 | |
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| 538 | // Perform partial augment and relabel operations |
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| 539 | while (active_nodes.size() > 0) { |
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| 540 | // Select an active node (FIFO selection) |
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| 541 | if (_excess[active_nodes[0]] <= 0) { |
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| 542 | active_nodes.pop_front(); |
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| 543 | continue; |
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| 544 | } |
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| 545 | Node start = active_nodes[0]; |
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| 546 | path_nodes.clear(); |
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| 547 | path_nodes.push_back(start); |
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| 548 | |
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| 549 | // Find an augmenting path from the start node |
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| 550 | Node u, tip = start; |
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| 551 | LCost min_red_cost; |
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| 552 | while ( _excess[tip] >= 0 && |
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| 553 | int(path_nodes.size()) <= MAX_PATH_LENGTH ) |
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| 554 | { |
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| 555 | if (next_dir[tip]) { |
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| 556 | for (OutArcIt e = next_out[tip]; e != INVALID; ++e) { |
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| 557 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 558 | u = _graph.target(e); |
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| 559 | pred_arc[u] = e; |
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| 560 | forward[u] = true; |
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| 561 | next_out[tip] = e; |
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| 562 | tip = u; |
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| 563 | path_nodes.push_back(tip); |
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| 564 | goto next_step; |
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| 565 | } |
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| 566 | } |
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| 567 | next_dir[tip] = false; |
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| 568 | } |
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| 569 | for (InArcIt e = next_in[tip]; e != INVALID; ++e) { |
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| 570 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 571 | u = _graph.source(e); |
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| 572 | pred_arc[u] = e; |
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| 573 | forward[u] = false; |
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| 574 | next_in[tip] = e; |
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| 575 | tip = u; |
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| 576 | path_nodes.push_back(tip); |
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| 577 | goto next_step; |
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| 578 | } |
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| 579 | } |
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| 580 | |
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| 581 | // Relabel tip node |
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| 582 | min_red_cost = std::numeric_limits<LCost>::max() / 2; |
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| 583 | for (OutArcIt oe(_graph, tip); oe != INVALID; ++oe) { |
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| 584 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
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| 585 | (*_red_cost)[oe] < min_red_cost ) |
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| 586 | min_red_cost = (*_red_cost)[oe]; |
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| 587 | } |
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| 588 | for (InArcIt ie(_graph, tip); ie != INVALID; ++ie) { |
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| 589 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
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| 590 | min_red_cost = -(*_red_cost)[ie]; |
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| 591 | } |
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| 592 | (*_potential)[tip] -= min_red_cost + _epsilon; |
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| 593 | |
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| 594 | // Reset the next arc maps |
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| 595 | next_out[tip] = OutArcIt(_graph, tip); |
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| 596 | next_in[tip] = InArcIt(_graph, tip); |
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| 597 | next_dir[tip] = true; |
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| 598 | |
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| 599 | // Step back |
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| 600 | if (tip != start) { |
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| 601 | path_nodes.pop_back(); |
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| 602 | tip = path_nodes[path_nodes.size()-1]; |
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| 603 | } |
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| 604 | |
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| 605 | next_step: |
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| 606 | continue; |
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| 607 | } |
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| 608 | |
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| 609 | // Augment along the found path (as much flow as possible) |
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| 610 | Capacity delta; |
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| 611 | for (int i = 1; i < int(path_nodes.size()); ++i) { |
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| 612 | u = path_nodes[i]; |
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| 613 | delta = forward[u] ? |
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| 614 | _capacity[pred_arc[u]] - (*_flow)[pred_arc[u]] : |
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| 615 | (*_flow)[pred_arc[u]]; |
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| 616 | delta = std::min(delta, _excess[path_nodes[i-1]]); |
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| 617 | (*_flow)[pred_arc[u]] += forward[u] ? delta : -delta; |
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| 618 | _excess[path_nodes[i-1]] -= delta; |
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| 619 | _excess[u] += delta; |
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| 620 | if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u); |
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| 621 | } |
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| 622 | } |
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| 623 | } |
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| 624 | |
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| 625 | // Compute node potentials for the original costs |
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| 626 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
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| 627 | BellmanFord< ResDigraph, ResidualCostMap<CostMap> > |
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| 628 | bf(*_res_graph, res_cost); |
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| 629 | bf.init(0); bf.start(); |
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| 630 | for (NodeIt n(_graph); n != INVALID; ++n) |
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| 631 | (*_potential)[n] = bf.dist(n); |
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| 632 | |
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| 633 | // Handle non-zero lower bounds |
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| 634 | if (_lower) { |
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| 635 | for (ArcIt e(_graph); e != INVALID; ++e) |
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| 636 | (*_flow)[e] += (*_lower)[e]; |
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| 637 | } |
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| 638 | return true; |
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| 639 | } |
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| 640 | |
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| 641 | /// Execute the algorithm performing push and relabel operations. |
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| 642 | bool startPushRelabel() { |
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| 643 | // Paramters for heuristics |
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| 644 | // const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
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| 645 | // const int BF_HEURISTIC_BOUND_FACTOR = 3; |
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| 646 | |
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| 647 | typename Digraph::template NodeMap<bool> hyper(_graph, false); |
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| 648 | typename Digraph::template NodeMap<Arc> pred_arc(_graph); |
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| 649 | typename Digraph::template NodeMap<bool> forward(_graph); |
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| 650 | typename Digraph::template NodeMap<OutArcIt> next_out(_graph); |
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| 651 | typename Digraph::template NodeMap<InArcIt> next_in(_graph); |
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| 652 | typename Digraph::template NodeMap<bool> next_dir(_graph); |
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| 653 | std::deque<Node> active_nodes; |
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| 654 | |
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| 655 | // int node_num = countNodes(_graph); |
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| 656 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
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| 657 | 1 : _epsilon / _alpha ) |
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| 658 | { |
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| 659 | /* |
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| 660 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
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| 661 | // to check if the current flow is optimal |
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| 662 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
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| 663 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
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| 664 | ShiftCostMap shift_cost(_res_cost, 1); |
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| 665 | BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
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| 666 | bf.init(0); |
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| 667 | bool done = false; |
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| 668 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
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| 669 | for (int i = 0; i < K && !done; ++i) |
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| 670 | done = bf.processNextWeakRound(); |
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| 671 | if (done) break; |
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| 672 | } |
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| 673 | */ |
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| 674 | |
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| 675 | // Saturate arcs not satisfying the optimality condition |
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| 676 | Capacity delta; |
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| 677 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 678 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 679 | delta = _capacity[e] - (*_flow)[e]; |
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| 680 | _excess[_graph.source(e)] -= delta; |
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| 681 | _excess[_graph.target(e)] += delta; |
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| 682 | (*_flow)[e] = _capacity[e]; |
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| 683 | } |
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| 684 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 685 | _excess[_graph.target(e)] -= (*_flow)[e]; |
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| 686 | _excess[_graph.source(e)] += (*_flow)[e]; |
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| 687 | (*_flow)[e] = 0; |
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| 688 | } |
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| 689 | } |
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| 690 | |
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| 691 | // Find active nodes (i.e. nodes with positive excess) |
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| 692 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 693 | if (_excess[n] > 0) active_nodes.push_back(n); |
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| 694 | } |
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| 695 | |
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| 696 | // Initialize the next arc maps |
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| 697 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 698 | next_out[n] = OutArcIt(_graph, n); |
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| 699 | next_in[n] = InArcIt(_graph, n); |
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| 700 | next_dir[n] = true; |
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| 701 | } |
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| 702 | |
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| 703 | // Perform push and relabel operations |
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| 704 | while (active_nodes.size() > 0) { |
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| 705 | // Select an active node (FIFO selection) |
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| 706 | Node n = active_nodes[0], t; |
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| 707 | bool relabel_enabled = true; |
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| 708 | |
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| 709 | // Perform push operations if there are admissible arcs |
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| 710 | if (_excess[n] > 0 && next_dir[n]) { |
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| 711 | OutArcIt e = next_out[n]; |
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| 712 | for ( ; e != INVALID; ++e) { |
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| 713 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
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| 714 | delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]); |
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| 715 | t = _graph.target(e); |
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| 716 | |
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| 717 | // Push-look-ahead heuristic |
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| 718 | Capacity ahead = -_excess[t]; |
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| 719 | for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) { |
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| 720 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
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| 721 | ahead += _capacity[oe] - (*_flow)[oe]; |
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| 722 | } |
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| 723 | for (InArcIt ie(_graph, t); ie != INVALID; ++ie) { |
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| 724 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
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| 725 | ahead += (*_flow)[ie]; |
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| 726 | } |
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| 727 | if (ahead < 0) ahead = 0; |
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| 728 | |
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| 729 | // Push flow along the arc |
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| 730 | if (ahead < delta) { |
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| 731 | (*_flow)[e] += ahead; |
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| 732 | _excess[n] -= ahead; |
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| 733 | _excess[t] += ahead; |
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| 734 | active_nodes.push_front(t); |
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| 735 | hyper[t] = true; |
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| 736 | relabel_enabled = false; |
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| 737 | break; |
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| 738 | } else { |
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| 739 | (*_flow)[e] += delta; |
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| 740 | _excess[n] -= delta; |
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| 741 | _excess[t] += delta; |
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| 742 | if (_excess[t] > 0 && _excess[t] <= delta) |
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| 743 | active_nodes.push_back(t); |
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| 744 | } |
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| 745 | |
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| 746 | if (_excess[n] == 0) break; |
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| 747 | } |
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| 748 | } |
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| 749 | if (e != INVALID) { |
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| 750 | next_out[n] = e; |
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| 751 | } else { |
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| 752 | next_dir[n] = false; |
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| 753 | } |
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| 754 | } |
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| 755 | |
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| 756 | if (_excess[n] > 0 && !next_dir[n]) { |
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| 757 | InArcIt e = next_in[n]; |
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| 758 | for ( ; e != INVALID; ++e) { |
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| 759 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
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| 760 | delta = std::min((*_flow)[e], _excess[n]); |
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| 761 | t = _graph.source(e); |
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| 762 | |
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| 763 | // Push-look-ahead heuristic |
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| 764 | Capacity ahead = -_excess[t]; |
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| 765 | for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) { |
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| 766 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
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| 767 | ahead += _capacity[oe] - (*_flow)[oe]; |
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| 768 | } |
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| 769 | for (InArcIt ie(_graph, t); ie != INVALID; ++ie) { |
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| 770 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
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| 771 | ahead += (*_flow)[ie]; |
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| 772 | } |
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| 773 | if (ahead < 0) ahead = 0; |
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| 774 | |
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| 775 | // Push flow along the arc |
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| 776 | if (ahead < delta) { |
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| 777 | (*_flow)[e] -= ahead; |
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| 778 | _excess[n] -= ahead; |
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| 779 | _excess[t] += ahead; |
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| 780 | active_nodes.push_front(t); |
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| 781 | hyper[t] = true; |
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| 782 | relabel_enabled = false; |
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| 783 | break; |
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| 784 | } else { |
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| 785 | (*_flow)[e] -= delta; |
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| 786 | _excess[n] -= delta; |
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| 787 | _excess[t] += delta; |
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| 788 | if (_excess[t] > 0 && _excess[t] <= delta) |
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| 789 | active_nodes.push_back(t); |
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| 790 | } |
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| 791 | |
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| 792 | if (_excess[n] == 0) break; |
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| 793 | } |
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| 794 | } |
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| 795 | next_in[n] = e; |
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| 796 | } |
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| 797 | |
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| 798 | // Relabel the node if it is still active (or hyper) |
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| 799 | if (relabel_enabled && (_excess[n] > 0 || hyper[n])) { |
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| 800 | LCost min_red_cost = std::numeric_limits<LCost>::max() / 2; |
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| 801 | for (OutArcIt oe(_graph, n); oe != INVALID; ++oe) { |
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| 802 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
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| 803 | (*_red_cost)[oe] < min_red_cost ) |
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| 804 | min_red_cost = (*_red_cost)[oe]; |
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| 805 | } |
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| 806 | for (InArcIt ie(_graph, n); ie != INVALID; ++ie) { |
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| 807 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
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| 808 | min_red_cost = -(*_red_cost)[ie]; |
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| 809 | } |
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| 810 | (*_potential)[n] -= min_red_cost + _epsilon; |
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| 811 | hyper[n] = false; |
---|
| 812 | |
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| 813 | // Reset the next arc maps |
---|
| 814 | next_out[n] = OutArcIt(_graph, n); |
---|
| 815 | next_in[n] = InArcIt(_graph, n); |
---|
| 816 | next_dir[n] = true; |
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| 817 | } |
---|
| 818 | |
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| 819 | // Remove nodes that are not active nor hyper |
---|
| 820 | while ( active_nodes.size() > 0 && |
---|
| 821 | _excess[active_nodes[0]] <= 0 && |
---|
| 822 | !hyper[active_nodes[0]] ) { |
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| 823 | active_nodes.pop_front(); |
---|
| 824 | } |
---|
| 825 | } |
---|
| 826 | } |
---|
| 827 | |
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| 828 | // Compute node potentials for the original costs |
---|
| 829 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
---|
| 830 | BellmanFord< ResDigraph, ResidualCostMap<CostMap> > |
---|
| 831 | bf(*_res_graph, res_cost); |
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| 832 | bf.init(0); bf.start(); |
---|
| 833 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
| 834 | (*_potential)[n] = bf.dist(n); |
---|
| 835 | |
---|
| 836 | // Handle non-zero lower bounds |
---|
| 837 | if (_lower) { |
---|
| 838 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 839 | (*_flow)[e] += (*_lower)[e]; |
---|
| 840 | } |
---|
| 841 | return true; |
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| 842 | } |
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| 843 | |
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| 844 | }; //class CostScaling |
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| 845 | |
---|
| 846 | ///@} |
---|
| 847 | |
---|
| 848 | } //namespace lemon |
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| 849 | |
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| 850 | #endif //LEMON_COST_SCALING_H |
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