[2440] | 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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[2553] | 5 | * Copyright (C) 2003-2008 |
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[2440] | 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_CYCLE_CANCELING_H |
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| 20 | #define LEMON_CYCLE_CANCELING_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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[2573] | 25 | /// \brief Cycle-canceling algorithm for finding a minimum cost flow. |
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[2440] | 26 | |
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| 27 | #include <vector> |
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[2509] | 28 | #include <lemon/graph_adaptor.h> |
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[2573] | 29 | #include <lemon/path.h> |
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| 30 | |
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[2440] | 31 | #include <lemon/circulation.h> |
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[2573] | 32 | #include <lemon/bellman_ford.h> |
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| 33 | #include <lemon/min_mean_cycle.h> |
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[2556] | 34 | |
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[2440] | 35 | namespace lemon { |
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| 36 | |
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| 37 | /// \addtogroup min_cost_flow |
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| 38 | /// @{ |
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| 39 | |
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[2556] | 40 | /// \brief Implementation of a cycle-canceling algorithm for |
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| 41 | /// finding a minimum cost flow. |
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[2440] | 42 | /// |
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[2556] | 43 | /// \ref CycleCanceling implements a cycle-canceling algorithm for |
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| 44 | /// finding a minimum cost flow. |
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[2440] | 45 | /// |
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[2573] | 46 | /// \tparam Graph The directed graph type the algorithm runs on. |
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| 47 | /// \tparam LowerMap The type of the lower bound map. |
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| 48 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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| 49 | /// \tparam CostMap The type of the cost (length) map. |
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| 50 | /// \tparam SupplyMap The type of the supply map. |
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[2440] | 51 | /// |
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| 52 | /// \warning |
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[2573] | 53 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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| 54 | /// - Supply values should be \e signed \e integers. |
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| 55 | /// - \c LowerMap::Value must be convertible to \c CapacityMap::Value. |
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| 56 | /// - \c CapacityMap::Value and \c SupplyMap::Value must be |
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| 57 | /// convertible to each other. |
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| 58 | /// - All value types must be convertible to \c CostMap::Value, which |
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| 59 | /// must be signed type. |
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| 60 | /// |
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| 61 | /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is |
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| 62 | /// used for negative cycle detection with limited iteration number. |
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| 63 | /// However \ref CycleCanceling also provides the "Minimum Mean |
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| 64 | /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial, |
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| 65 | /// but rather slower in practice. |
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| 66 | /// To use this version of the algorithm, call \ref run() with \c true |
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| 67 | /// parameter. |
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[2440] | 68 | /// |
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| 69 | /// \author Peter Kovacs |
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| 70 | |
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[2533] | 71 | template < typename Graph, |
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| 72 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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[2573] | 73 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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[2533] | 74 | typename CostMap = typename Graph::template EdgeMap<int>, |
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[2573] | 75 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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[2440] | 76 | class CycleCanceling |
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| 77 | { |
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[2556] | 78 | GRAPH_TYPEDEFS(typename Graph); |
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[2440] | 79 | |
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| 80 | typedef typename CapacityMap::Value Capacity; |
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| 81 | typedef typename CostMap::Value Cost; |
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| 82 | typedef typename SupplyMap::Value Supply; |
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[2556] | 83 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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| 84 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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[2440] | 85 | |
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| 86 | typedef ResGraphAdaptor< const Graph, Capacity, |
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[2556] | 87 | CapacityEdgeMap, CapacityEdgeMap > ResGraph; |
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[2440] | 88 | typedef typename ResGraph::Node ResNode; |
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| 89 | typedef typename ResGraph::NodeIt ResNodeIt; |
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| 90 | typedef typename ResGraph::Edge ResEdge; |
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| 91 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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| 92 | |
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| 93 | public: |
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| 94 | |
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[2556] | 95 | /// The type of the flow map. |
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| 96 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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[2440] | 97 | |
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[2573] | 98 | private: |
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[2440] | 99 | |
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[2573] | 100 | /// \brief Map adaptor class for handling residual edge costs. |
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| 101 | /// |
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| 102 | /// \ref ResidualCostMap is a map adaptor class for handling |
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| 103 | /// residual edge costs. |
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| 104 | class ResidualCostMap : public MapBase<ResEdge, Cost> |
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[2440] | 105 | { |
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| 106 | private: |
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| 107 | |
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[2573] | 108 | const CostMap &_cost_map; |
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[2440] | 109 | |
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| 110 | public: |
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| 111 | |
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[2573] | 112 | ///\e |
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| 113 | ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {} |
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[2440] | 114 | |
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[2573] | 115 | ///\e |
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[2509] | 116 | Cost operator[](const ResEdge &e) const { |
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[2573] | 117 | return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
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[2440] | 118 | } |
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| 119 | |
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[2573] | 120 | }; //class ResidualCostMap |
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[2440] | 121 | |
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[2573] | 122 | private: |
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[2440] | 123 | |
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[2573] | 124 | // The maximum number of iterations for the first execution of the |
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| 125 | // Bellman-Ford algorithm. It should be at least 2. |
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| 126 | static const int BF_FIRST_LIMIT = 2; |
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| 127 | // The iteration limit for the Bellman-Ford algorithm is multiplied |
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| 128 | // by BF_ALPHA in every round. |
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| 129 | static const double BF_ALPHA = 1.5; |
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[2440] | 130 | |
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[2573] | 131 | private: |
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[2440] | 132 | |
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[2573] | 133 | // The directed graph the algorithm runs on |
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| 134 | const Graph &_graph; |
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| 135 | // The original lower bound map |
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| 136 | const LowerMap *_lower; |
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| 137 | // The modified capacity map |
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| 138 | CapacityEdgeMap _capacity; |
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| 139 | // The original cost map |
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| 140 | const CostMap &_cost; |
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| 141 | // The modified supply map |
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| 142 | SupplyNodeMap _supply; |
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| 143 | bool _valid_supply; |
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| 144 | |
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| 145 | // Edge map of the current flow |
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| 146 | FlowMap _flow; |
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| 147 | |
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| 148 | // The residual graph |
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| 149 | ResGraph _res_graph; |
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| 150 | // The residual cost map |
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| 151 | ResidualCostMap _res_cost; |
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| 152 | |
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| 153 | public: |
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[2440] | 154 | |
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| 155 | /// \brief General constructor of the class (with lower bounds). |
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| 156 | /// |
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| 157 | /// General constructor of the class (with lower bounds). |
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| 158 | /// |
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[2573] | 159 | /// \param graph The directed graph the algorithm runs on. |
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| 160 | /// \param lower The lower bounds of the edges. |
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| 161 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 162 | /// \param cost The cost (length) values of the edges. |
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| 163 | /// \param supply The supply values of the nodes (signed). |
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| 164 | CycleCanceling( const Graph &graph, |
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| 165 | const LowerMap &lower, |
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| 166 | const CapacityMap &capacity, |
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| 167 | const CostMap &cost, |
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| 168 | const SupplyMap &supply ) : |
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| 169 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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| 170 | _supply(graph), _flow(graph, 0), |
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| 171 | _res_graph(graph, _capacity, _flow), _res_cost(_cost) |
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[2440] | 172 | { |
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[2556] | 173 | // Removing non-zero lower bounds |
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[2573] | 174 | _capacity = subMap(capacity, lower); |
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[2440] | 175 | Supply sum = 0; |
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[2573] | 176 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 177 | Supply s = supply[n]; |
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| 178 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 179 | s += lower[e]; |
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| 180 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 181 | s -= lower[e]; |
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| 182 | sum += (_supply[n] = s); |
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[2440] | 183 | } |
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[2573] | 184 | _valid_supply = sum == 0; |
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[2440] | 185 | } |
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| 186 | |
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| 187 | /// \brief General constructor of the class (without lower bounds). |
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| 188 | /// |
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| 189 | /// General constructor of the class (without lower bounds). |
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| 190 | /// |
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[2573] | 191 | /// \param graph The directed graph the algorithm runs on. |
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| 192 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 193 | /// \param cost The cost (length) values of the edges. |
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| 194 | /// \param supply The supply values of the nodes (signed). |
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| 195 | CycleCanceling( const Graph &graph, |
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| 196 | const CapacityMap &capacity, |
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| 197 | const CostMap &cost, |
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| 198 | const SupplyMap &supply ) : |
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| 199 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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| 200 | _supply(supply), _flow(graph, 0), |
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| 201 | _res_graph(graph, _capacity, _flow), _res_cost(_cost) |
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[2440] | 202 | { |
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| 203 | // Checking the sum of supply values |
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| 204 | Supply sum = 0; |
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[2573] | 205 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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| 206 | _valid_supply = sum == 0; |
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[2440] | 207 | } |
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| 208 | |
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| 209 | /// \brief Simple constructor of the class (with lower bounds). |
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| 210 | /// |
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| 211 | /// Simple constructor of the class (with lower bounds). |
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| 212 | /// |
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[2573] | 213 | /// \param graph The directed graph the algorithm runs on. |
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| 214 | /// \param lower The lower bounds of the edges. |
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| 215 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 216 | /// \param cost The cost (length) values of the edges. |
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| 217 | /// \param s The source node. |
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| 218 | /// \param t The target node. |
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| 219 | /// \param flow_value The required amount of flow from node \c s |
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| 220 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 221 | CycleCanceling( const Graph &graph, |
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| 222 | const LowerMap &lower, |
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| 223 | const CapacityMap &capacity, |
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| 224 | const CostMap &cost, |
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| 225 | Node s, Node t, |
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| 226 | Supply flow_value ) : |
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| 227 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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| 228 | _supply(graph), _flow(graph, 0), |
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| 229 | _res_graph(graph, _capacity, _flow), _res_cost(_cost) |
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[2440] | 230 | { |
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[2556] | 231 | // Removing non-zero lower bounds |
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[2573] | 232 | _capacity = subMap(capacity, lower); |
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| 233 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 234 | Supply sum = 0; |
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| 235 | if (n == s) sum = flow_value; |
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| 236 | if (n == t) sum = -flow_value; |
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| 237 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 238 | sum += lower[e]; |
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| 239 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 240 | sum -= lower[e]; |
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| 241 | _supply[n] = sum; |
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[2440] | 242 | } |
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[2573] | 243 | _valid_supply = true; |
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[2440] | 244 | } |
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| 245 | |
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| 246 | /// \brief Simple constructor of the class (without lower bounds). |
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| 247 | /// |
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| 248 | /// Simple constructor of the class (without lower bounds). |
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| 249 | /// |
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[2573] | 250 | /// \param graph The directed graph the algorithm runs on. |
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| 251 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 252 | /// \param cost The cost (length) values of the edges. |
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| 253 | /// \param s The source node. |
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| 254 | /// \param t The target node. |
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| 255 | /// \param flow_value The required amount of flow from node \c s |
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| 256 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 257 | CycleCanceling( const Graph &graph, |
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| 258 | const CapacityMap &capacity, |
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| 259 | const CostMap &cost, |
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| 260 | Node s, Node t, |
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| 261 | Supply flow_value ) : |
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| 262 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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| 263 | _supply(graph, 0), _flow(graph, 0), |
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| 264 | _res_graph(graph, _capacity, _flow), _res_cost(_cost) |
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[2440] | 265 | { |
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[2573] | 266 | _supply[s] = flow_value; |
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| 267 | _supply[t] = -flow_value; |
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| 268 | _valid_supply = true; |
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[2440] | 269 | } |
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| 270 | |
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[2556] | 271 | /// \brief Runs the algorithm. |
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| 272 | /// |
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| 273 | /// Runs the algorithm. |
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| 274 | /// |
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[2573] | 275 | /// \param min_mean_cc Set this parameter to \c true to run the |
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| 276 | /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly |
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| 277 | /// polynomial, but rather slower in practice. |
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| 278 | /// |
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[2556] | 279 | /// \return \c true if a feasible flow can be found. |
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[2573] | 280 | bool run(bool min_mean_cc = false) { |
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| 281 | return init() && start(min_mean_cc); |
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[2556] | 282 | } |
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| 283 | |
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[2573] | 284 | /// \brief Returns a const reference to the edge map storing the |
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| 285 | /// found flow. |
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[2440] | 286 | /// |
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[2573] | 287 | /// Returns a const reference to the edge map storing the found flow. |
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[2440] | 288 | /// |
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| 289 | /// \pre \ref run() must be called before using this function. |
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| 290 | const FlowMap& flowMap() const { |
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[2573] | 291 | return _flow; |
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[2440] | 292 | } |
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| 293 | |
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| 294 | /// \brief Returns the total cost of the found flow. |
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| 295 | /// |
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| 296 | /// Returns the total cost of the found flow. The complexity of the |
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| 297 | /// function is \f$ O(e) \f$. |
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| 298 | /// |
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| 299 | /// \pre \ref run() must be called before using this function. |
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| 300 | Cost totalCost() const { |
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| 301 | Cost c = 0; |
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[2573] | 302 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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| 303 | c += _flow[e] * _cost[e]; |
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[2440] | 304 | return c; |
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| 305 | } |
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| 306 | |
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[2573] | 307 | private: |
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[2440] | 308 | |
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[2556] | 309 | /// Initializes the algorithm. |
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[2440] | 310 | bool init() { |
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[2573] | 311 | if (!_valid_supply) return false; |
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[2440] | 312 | |
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[2573] | 313 | // Finding a feasible flow using Circulation |
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[2556] | 314 | Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap, |
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| 315 | SupplyMap > |
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[2573] | 316 | circulation( _graph, constMap<Edge>((Capacity)0), _capacity, |
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| 317 | _supply ); |
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| 318 | return circulation.flowMap(_flow).run(); |
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[2440] | 319 | } |
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| 320 | |
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[2573] | 321 | bool start(bool min_mean_cc) { |
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| 322 | if (min_mean_cc) |
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| 323 | return startMinMean(); |
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| 324 | else |
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| 325 | return start(); |
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| 326 | } |
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| 327 | |
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| 328 | /// \brief Executes the algorithm using \ref BellmanFord. |
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| 329 | /// |
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| 330 | /// Executes the algorithm using the \ref BellmanFord |
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| 331 | /// "Bellman-Ford" algorithm for negative cycle detection with |
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| 332 | /// successively larger limit for the number of iterations. |
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[2440] | 333 | bool start() { |
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[2573] | 334 | typename BellmanFord<ResGraph, ResidualCostMap>::PredMap pred(_res_graph); |
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| 335 | typename ResGraph::template NodeMap<int> visited(_res_graph); |
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[2440] | 336 | std::vector<ResEdge> cycle; |
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[2573] | 337 | int node_num = countNodes(_graph); |
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[2440] | 338 | |
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[2573] | 339 | int length_bound = BF_FIRST_LIMIT; |
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[2440] | 340 | bool optimal = false; |
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| 341 | while (!optimal) { |
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[2573] | 342 | BellmanFord<ResGraph, ResidualCostMap> bf(_res_graph, _res_cost); |
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[2556] | 343 | bf.predMap(pred); |
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| 344 | bf.init(0); |
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| 345 | int iter_num = 0; |
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| 346 | bool cycle_found = false; |
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| 347 | while (!cycle_found) { |
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| 348 | int curr_iter_num = iter_num + length_bound <= node_num ? |
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| 349 | length_bound : node_num - iter_num; |
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| 350 | iter_num += curr_iter_num; |
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| 351 | int real_iter_num = curr_iter_num; |
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| 352 | for (int i = 0; i < curr_iter_num; ++i) { |
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| 353 | if (bf.processNextWeakRound()) { |
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| 354 | real_iter_num = i; |
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| 355 | break; |
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| 356 | } |
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| 357 | } |
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| 358 | if (real_iter_num < curr_iter_num) { |
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| 359 | optimal = true; |
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| 360 | break; |
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| 361 | } else { |
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| 362 | // Searching for node disjoint negative cycles |
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[2573] | 363 | for (ResNodeIt n(_res_graph); n != INVALID; ++n) |
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[2556] | 364 | visited[n] = 0; |
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| 365 | int id = 0; |
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[2573] | 366 | for (ResNodeIt n(_res_graph); n != INVALID; ++n) { |
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[2556] | 367 | if (visited[n] > 0) continue; |
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| 368 | visited[n] = ++id; |
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| 369 | ResNode u = pred[n] == INVALID ? |
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[2573] | 370 | INVALID : _res_graph.source(pred[n]); |
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[2556] | 371 | while (u != INVALID && visited[u] == 0) { |
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| 372 | visited[u] = id; |
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| 373 | u = pred[u] == INVALID ? |
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[2573] | 374 | INVALID : _res_graph.source(pred[u]); |
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[2556] | 375 | } |
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| 376 | if (u != INVALID && visited[u] == id) { |
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| 377 | // Finding the negative cycle |
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| 378 | cycle_found = true; |
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| 379 | cycle.clear(); |
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| 380 | ResEdge e = pred[u]; |
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| 381 | cycle.push_back(e); |
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[2573] | 382 | Capacity d = _res_graph.rescap(e); |
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| 383 | while (_res_graph.source(e) != u) { |
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| 384 | cycle.push_back(e = pred[_res_graph.source(e)]); |
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| 385 | if (_res_graph.rescap(e) < d) |
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| 386 | d = _res_graph.rescap(e); |
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[2556] | 387 | } |
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[2573] | 388 | |
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[2556] | 389 | // Augmenting along the cycle |
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[2573] | 390 | for (int i = 0; i < int(cycle.size()); ++i) |
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| 391 | _res_graph.augment(cycle[i], d); |
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[2556] | 392 | } |
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| 393 | } |
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| 394 | } |
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[2440] | 395 | |
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[2556] | 396 | if (!cycle_found) |
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[2573] | 397 | length_bound = int(length_bound * BF_ALPHA); |
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[2556] | 398 | } |
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[2440] | 399 | } |
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| 400 | |
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[2556] | 401 | // Handling non-zero lower bounds |
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[2573] | 402 | if (_lower) { |
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| 403 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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| 404 | _flow[e] += (*_lower)[e]; |
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[2440] | 405 | } |
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| 406 | return true; |
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| 407 | } |
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| 408 | |
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[2573] | 409 | /// \brief Executes the algorithm using \ref MinMeanCycle. |
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| 410 | /// |
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| 411 | /// Executes the algorithm using \ref MinMeanCycle for negative |
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| 412 | /// cycle detection. |
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| 413 | bool startMinMean() { |
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[2440] | 414 | typedef Path<ResGraph> ResPath; |
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[2573] | 415 | MinMeanCycle<ResGraph, ResidualCostMap> mmc(_res_graph, _res_cost); |
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[2440] | 416 | ResPath cycle; |
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| 417 | |
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| 418 | mmc.cyclePath(cycle).init(); |
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| 419 | if (mmc.findMinMean()) { |
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[2556] | 420 | while (mmc.cycleLength() < 0) { |
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| 421 | // Finding the cycle |
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| 422 | mmc.findCycle(); |
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[2440] | 423 | |
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[2556] | 424 | // Finding the largest flow amount that can be augmented |
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| 425 | // along the cycle |
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| 426 | Capacity delta = 0; |
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| 427 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) { |
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[2573] | 428 | if (delta == 0 || _res_graph.rescap(e) < delta) |
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| 429 | delta = _res_graph.rescap(e); |
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[2556] | 430 | } |
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[2440] | 431 | |
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[2556] | 432 | // Augmenting along the cycle |
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| 433 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) |
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[2573] | 434 | _res_graph.augment(e, delta); |
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[2440] | 435 | |
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[2556] | 436 | // Finding the minimum cycle mean for the modified residual |
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| 437 | // graph |
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| 438 | mmc.reset(); |
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| 439 | if (!mmc.findMinMean()) break; |
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| 440 | } |
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[2440] | 441 | } |
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| 442 | |
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[2556] | 443 | // Handling non-zero lower bounds |
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[2573] | 444 | if (_lower) { |
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| 445 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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| 446 | _flow[e] += (*_lower)[e]; |
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[2440] | 447 | } |
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| 448 | return true; |
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| 449 | } |
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| 450 | |
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| 451 | }; //class CycleCanceling |
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| 452 | |
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| 453 | ///@} |
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| 454 | |
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| 455 | } //namespace lemon |
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| 456 | |
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| 457 | #endif //LEMON_CYCLE_CANCELING_H |
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