[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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| 5 | * Copyright (C) 2003-2007 |
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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_NETWORK_SIMPLEX_H |
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| 20 | #define LEMON_NETWORK_SIMPLEX_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow |
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| 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief The network simplex algorithm for finding a minimum cost |
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| 26 | /// flow. |
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| 27 | |
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| 28 | #include <limits> |
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[2509] | 29 | #include <lemon/graph_adaptor.h> |
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| 30 | #include <lemon/graph_utils.h> |
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[2440] | 31 | #include <lemon/smart_graph.h> |
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| 32 | |
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| 33 | /// \brief The pivot rule used in the algorithm. |
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| 34 | //#define FIRST_ELIGIBLE_PIVOT |
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| 35 | //#define BEST_ELIGIBLE_PIVOT |
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[2444] | 36 | #define EDGE_BLOCK_PIVOT |
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[2440] | 37 | //#define CANDIDATE_LIST_PIVOT |
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| 38 | //#define SORTED_LIST_PIVOT |
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| 39 | |
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[2444] | 40 | //#define _DEBUG_ITER_ |
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| 41 | |
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| 42 | |
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[2440] | 43 | /// \brief State constant for edges at their lower bounds. |
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| 44 | #define LOWER 1 |
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| 45 | /// \brief State constant for edges in the spanning tree. |
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| 46 | #define TREE 0 |
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| 47 | /// \brief State constant for edges at their upper bounds. |
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| 48 | #define UPPER -1 |
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| 49 | |
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| 50 | #ifdef EDGE_BLOCK_PIVOT |
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[2471] | 51 | #include <cmath> |
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[2444] | 52 | /// \brief Lower bound for the size of blocks. |
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| 53 | #define MIN_BLOCK_SIZE 10 |
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[2440] | 54 | #endif |
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| 55 | |
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| 56 | #ifdef CANDIDATE_LIST_PIVOT |
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[2471] | 57 | #include <vector> |
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| 58 | #define LIST_LENGTH_DIV 50 |
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| 59 | #define MINOR_LIMIT_DIV 200 |
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[2440] | 60 | #endif |
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| 61 | |
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| 62 | #ifdef SORTED_LIST_PIVOT |
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[2471] | 63 | #include <vector> |
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[2440] | 64 | #include <algorithm> |
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[2471] | 65 | #define LIST_LENGTH_DIV 100 |
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| 66 | #define LOWER_DIV 4 |
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[2440] | 67 | #endif |
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| 68 | |
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| 69 | namespace lemon { |
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| 70 | |
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| 71 | /// \addtogroup min_cost_flow |
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| 72 | /// @{ |
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| 73 | |
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| 74 | /// \brief Implementation of the network simplex algorithm for |
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| 75 | /// finding a minimum cost flow. |
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| 76 | /// |
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| 77 | /// \ref lemon::NetworkSimplex "NetworkSimplex" implements the |
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| 78 | /// network simplex algorithm for finding a minimum cost flow. |
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| 79 | /// |
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| 80 | /// \param Graph The directed graph type the algorithm runs on. |
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| 81 | /// \param LowerMap The type of the lower bound map. |
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| 82 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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| 83 | /// \param CostMap The type of the cost (length) map. |
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| 84 | /// \param SupplyMap The type of the supply map. |
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| 85 | /// |
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| 86 | /// \warning |
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| 87 | /// - Edge capacities and costs should be nonnegative integers. |
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| 88 | /// However \c CostMap::Value should be signed type. |
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[2509] | 89 | /// - Supply values should be signed integers. |
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[2440] | 90 | /// - \c LowerMap::Value must be convertible to |
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| 91 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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| 92 | /// convertible to \c SupplyMap::Value. |
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| 93 | /// |
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| 94 | /// \author Peter Kovacs |
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| 95 | |
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| 96 | template < typename Graph, |
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| 97 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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| 98 | typename CapacityMap = LowerMap, |
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| 99 | typename CostMap = typename Graph::template EdgeMap<int>, |
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| 100 | typename SupplyMap = typename Graph::template NodeMap |
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| 101 | <typename CapacityMap::Value> > |
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| 102 | class NetworkSimplex |
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| 103 | { |
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| 104 | typedef typename LowerMap::Value Lower; |
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| 105 | typedef typename CapacityMap::Value Capacity; |
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| 106 | typedef typename CostMap::Value Cost; |
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| 107 | typedef typename SupplyMap::Value Supply; |
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| 108 | |
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| 109 | typedef SmartGraph SGraph; |
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| 110 | typedef typename SGraph::Node Node; |
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| 111 | typedef typename SGraph::NodeIt NodeIt; |
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| 112 | typedef typename SGraph::Edge Edge; |
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| 113 | typedef typename SGraph::EdgeIt EdgeIt; |
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| 114 | typedef typename SGraph::InEdgeIt InEdgeIt; |
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| 115 | typedef typename SGraph::OutEdgeIt OutEdgeIt; |
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| 116 | |
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| 117 | typedef typename SGraph::template EdgeMap<Lower> SLowerMap; |
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| 118 | typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap; |
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| 119 | typedef typename SGraph::template EdgeMap<Cost> SCostMap; |
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| 120 | typedef typename SGraph::template NodeMap<Supply> SSupplyMap; |
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| 121 | typedef typename SGraph::template NodeMap<Cost> SPotentialMap; |
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| 122 | |
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| 123 | typedef typename SGraph::template NodeMap<int> IntNodeMap; |
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| 124 | typedef typename SGraph::template NodeMap<bool> BoolNodeMap; |
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| 125 | typedef typename SGraph::template NodeMap<Node> NodeNodeMap; |
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| 126 | typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap; |
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| 127 | typedef typename SGraph::template EdgeMap<int> IntEdgeMap; |
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| 128 | |
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| 129 | typedef typename Graph::template NodeMap<Node> NodeRefMap; |
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| 130 | typedef typename Graph::template EdgeMap<Edge> EdgeRefMap; |
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| 131 | |
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| 132 | public: |
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| 133 | |
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| 134 | /// \brief The type of the flow map. |
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| 135 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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| 136 | /// \brief The type of the potential map. |
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| 137 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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| 138 | |
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| 139 | protected: |
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| 140 | |
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| 141 | /// \brief Map adaptor class for handling reduced edge costs. |
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| 142 | class ReducedCostMap : public MapBase<Edge, Cost> |
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| 143 | { |
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| 144 | private: |
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| 145 | |
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| 146 | const SGraph &gr; |
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| 147 | const SCostMap &cost_map; |
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| 148 | const SPotentialMap &pot_map; |
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| 149 | |
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| 150 | public: |
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| 151 | |
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| 152 | ReducedCostMap( const SGraph &_gr, |
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| 153 | const SCostMap &_cm, |
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| 154 | const SPotentialMap &_pm ) : |
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| 155 | gr(_gr), cost_map(_cm), pot_map(_pm) {} |
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| 156 | |
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[2509] | 157 | Cost operator[](const Edge &e) const { |
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[2440] | 158 | return cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)]; |
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| 159 | } |
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| 160 | |
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| 161 | }; //class ReducedCostMap |
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| 162 | |
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| 163 | protected: |
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| 164 | |
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| 165 | /// \brief The directed graph the algorithm runs on. |
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| 166 | SGraph graph; |
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| 167 | /// \brief The original graph. |
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| 168 | const Graph &graph_ref; |
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| 169 | /// \brief The original lower bound map. |
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| 170 | const LowerMap *lower; |
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| 171 | /// \brief The capacity map. |
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| 172 | SCapacityMap capacity; |
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| 173 | /// \brief The cost map. |
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| 174 | SCostMap cost; |
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| 175 | /// \brief The supply map. |
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| 176 | SSupplyMap supply; |
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| 177 | /// \brief The reduced cost map. |
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| 178 | ReducedCostMap red_cost; |
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| 179 | /// \brief The sum of supply values equals zero. |
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| 180 | bool valid_supply; |
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| 181 | |
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| 182 | /// \brief The edge map of the current flow. |
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| 183 | SCapacityMap flow; |
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| 184 | /// \brief The edge map of the found flow on the original graph. |
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| 185 | FlowMap flow_result; |
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| 186 | /// \brief The potential node map. |
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| 187 | SPotentialMap potential; |
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| 188 | /// \brief The potential node map on the original graph. |
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| 189 | PotentialMap potential_result; |
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| 190 | |
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| 191 | /// \brief Node reference for the original graph. |
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| 192 | NodeRefMap node_ref; |
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| 193 | /// \brief Edge reference for the original graph. |
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| 194 | EdgeRefMap edge_ref; |
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| 195 | |
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| 196 | /// \brief The depth node map of the spanning tree structure. |
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| 197 | IntNodeMap depth; |
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| 198 | /// \brief The parent node map of the spanning tree structure. |
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| 199 | NodeNodeMap parent; |
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| 200 | /// \brief The pred_edge node map of the spanning tree structure. |
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| 201 | EdgeNodeMap pred_edge; |
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| 202 | /// \brief The thread node map of the spanning tree structure. |
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| 203 | NodeNodeMap thread; |
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| 204 | /// \brief The forward node map of the spanning tree structure. |
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| 205 | BoolNodeMap forward; |
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| 206 | /// \brief The state edge map. |
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| 207 | IntEdgeMap state; |
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| 208 | |
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| 209 | |
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| 210 | #ifdef EDGE_BLOCK_PIVOT |
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| 211 | /// \brief The size of blocks for the "Edge Block" pivot rule. |
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| 212 | int block_size; |
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| 213 | #endif |
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| 214 | #ifdef CANDIDATE_LIST_PIVOT |
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| 215 | /// \brief The list of candidate edges for the "Candidate List" |
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| 216 | /// pivot rule. |
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[2471] | 217 | std::vector<Edge> candidates; |
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| 218 | /// \brief The maximum length of the edge list for the |
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| 219 | /// "Candidate List" pivot rule. |
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| 220 | int list_length; |
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| 221 | /// \brief The maximum number of minor iterations between two major |
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| 222 | /// itarations. |
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| 223 | int minor_limit; |
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[2440] | 224 | /// \brief The number of minor iterations. |
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| 225 | int minor_count; |
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| 226 | #endif |
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| 227 | #ifdef SORTED_LIST_PIVOT |
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| 228 | /// \brief The list of candidate edges for the "Sorted List" |
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| 229 | /// pivot rule. |
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[2471] | 230 | std::vector<Edge> candidates; |
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| 231 | /// \brief The maximum length of the edge list for the |
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| 232 | /// "Sorted List" pivot rule. |
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| 233 | int list_length; |
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| 234 | int list_index; |
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[2440] | 235 | #endif |
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| 236 | |
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| 237 | // Root node of the starting spanning tree. |
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| 238 | Node root; |
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| 239 | // The entering edge of the current pivot iteration. |
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| 240 | Edge in_edge; |
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| 241 | // Temporary nodes used in the current pivot iteration. |
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| 242 | Node join, u_in, v_in, u_out, v_out; |
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| 243 | Node right, first, second, last; |
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| 244 | Node stem, par_stem, new_stem; |
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| 245 | // The maximum augment amount along the cycle in the current pivot |
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| 246 | // iteration. |
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| 247 | Capacity delta; |
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| 248 | |
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| 249 | public : |
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| 250 | |
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| 251 | /// \brief General constructor of the class (with lower bounds). |
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| 252 | /// |
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| 253 | /// General constructor of the class (with lower bounds). |
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| 254 | /// |
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| 255 | /// \param _graph The directed graph the algorithm runs on. |
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| 256 | /// \param _lower The lower bounds of the edges. |
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| 257 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 258 | /// \param _cost The cost (length) values of the edges. |
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| 259 | /// \param _supply The supply values of the nodes (signed). |
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| 260 | NetworkSimplex( const Graph &_graph, |
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| 261 | const LowerMap &_lower, |
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| 262 | const CapacityMap &_capacity, |
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| 263 | const CostMap &_cost, |
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| 264 | const SupplyMap &_supply ) : |
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| 265 | graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph), |
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| 266 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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| 267 | potential_result(_graph), depth(graph), parent(graph), |
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| 268 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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| 269 | node_ref(graph_ref), edge_ref(graph_ref), |
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| 270 | red_cost(graph, cost, potential) |
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| 271 | { |
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| 272 | // Checking the sum of supply values |
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| 273 | Supply sum = 0; |
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| 274 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
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| 275 | sum += _supply[n]; |
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| 276 | if (!(valid_supply = sum == 0)) return; |
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| 277 | |
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| 278 | // Copying graph_ref to graph |
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[2457] | 279 | graph.reserveNode(countNodes(graph_ref) + 1); |
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| 280 | graph.reserveEdge(countEdges(graph_ref) + countNodes(graph_ref)); |
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[2440] | 281 | copyGraph(graph, graph_ref) |
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| 282 | .edgeMap(cost, _cost) |
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| 283 | .nodeRef(node_ref) |
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| 284 | .edgeRef(edge_ref) |
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| 285 | .run(); |
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| 286 | |
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| 287 | // Removing nonzero lower bounds |
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| 288 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) { |
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| 289 | capacity[edge_ref[e]] = _capacity[e] - _lower[e]; |
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| 290 | } |
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| 291 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) { |
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| 292 | Supply s = _supply[n]; |
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| 293 | for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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| 294 | s += _lower[e]; |
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| 295 | for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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| 296 | s -= _lower[e]; |
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| 297 | supply[node_ref[n]] = s; |
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| 298 | } |
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| 299 | } |
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| 300 | |
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| 301 | /// \brief General constructor of the class (without lower bounds). |
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| 302 | /// |
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| 303 | /// General constructor of the class (without lower bounds). |
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| 304 | /// |
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| 305 | /// \param _graph The directed graph the algorithm runs on. |
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| 306 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 307 | /// \param _cost The cost (length) values of the edges. |
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| 308 | /// \param _supply The supply values of the nodes (signed). |
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| 309 | NetworkSimplex( const Graph &_graph, |
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| 310 | const CapacityMap &_capacity, |
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| 311 | const CostMap &_cost, |
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| 312 | const SupplyMap &_supply ) : |
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| 313 | graph_ref(_graph), lower(NULL), capacity(graph), cost(graph), |
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| 314 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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| 315 | potential_result(_graph), depth(graph), parent(graph), |
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| 316 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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| 317 | node_ref(graph_ref), edge_ref(graph_ref), |
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| 318 | red_cost(graph, cost, potential) |
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| 319 | { |
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| 320 | // Checking the sum of supply values |
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| 321 | Supply sum = 0; |
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| 322 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
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| 323 | sum += _supply[n]; |
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| 324 | if (!(valid_supply = sum == 0)) return; |
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| 325 | |
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| 326 | // Copying graph_ref to graph |
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| 327 | copyGraph(graph, graph_ref) |
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| 328 | .edgeMap(capacity, _capacity) |
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| 329 | .edgeMap(cost, _cost) |
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| 330 | .nodeMap(supply, _supply) |
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| 331 | .nodeRef(node_ref) |
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| 332 | .edgeRef(edge_ref) |
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| 333 | .run(); |
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| 334 | } |
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| 335 | |
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| 336 | /// \brief Simple constructor of the class (with lower bounds). |
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| 337 | /// |
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| 338 | /// Simple constructor of the class (with lower bounds). |
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| 339 | /// |
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| 340 | /// \param _graph The directed graph the algorithm runs on. |
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| 341 | /// \param _lower The lower bounds of the edges. |
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| 342 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 343 | /// \param _cost The cost (length) values of the edges. |
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| 344 | /// \param _s The source node. |
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| 345 | /// \param _t The target node. |
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| 346 | /// \param _flow_value The required amount of flow from node \c _s |
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| 347 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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| 348 | /// \c _t). |
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| 349 | NetworkSimplex( const Graph &_graph, |
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| 350 | const LowerMap &_lower, |
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| 351 | const CapacityMap &_capacity, |
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| 352 | const CostMap &_cost, |
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| 353 | typename Graph::Node _s, |
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| 354 | typename Graph::Node _t, |
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| 355 | typename SupplyMap::Value _flow_value ) : |
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| 356 | graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph), |
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| 357 | supply(graph), flow(graph), flow_result(_graph), potential(graph), |
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| 358 | potential_result(_graph), depth(graph), parent(graph), |
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| 359 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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| 360 | node_ref(graph_ref), edge_ref(graph_ref), |
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| 361 | red_cost(graph, cost, potential) |
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| 362 | { |
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| 363 | // Copying graph_ref to graph |
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| 364 | copyGraph(graph, graph_ref) |
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| 365 | .edgeMap(cost, _cost) |
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| 366 | .nodeRef(node_ref) |
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| 367 | .edgeRef(edge_ref) |
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| 368 | .run(); |
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| 369 | |
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| 370 | // Removing nonzero lower bounds |
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| 371 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) { |
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| 372 | capacity[edge_ref[e]] = _capacity[e] - _lower[e]; |
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| 373 | } |
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| 374 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) { |
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| 375 | Supply s = 0; |
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| 376 | if (n == _s) s = _flow_value; |
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| 377 | if (n == _t) s = -_flow_value; |
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| 378 | for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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| 379 | s += _lower[e]; |
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| 380 | for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e) |
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| 381 | s -= _lower[e]; |
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| 382 | supply[node_ref[n]] = s; |
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| 383 | } |
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| 384 | valid_supply = true; |
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| 385 | } |
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| 386 | |
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| 387 | /// \brief Simple constructor of the class (without lower bounds). |
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| 388 | /// |
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| 389 | /// Simple constructor of the class (without lower bounds). |
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| 390 | /// |
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| 391 | /// \param _graph The directed graph the algorithm runs on. |
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| 392 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 393 | /// \param _cost The cost (length) values of the edges. |
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| 394 | /// \param _s The source node. |
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| 395 | /// \param _t The target node. |
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| 396 | /// \param _flow_value The required amount of flow from node \c _s |
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| 397 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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| 398 | /// \c _t). |
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| 399 | NetworkSimplex( const Graph &_graph, |
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| 400 | const CapacityMap &_capacity, |
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| 401 | const CostMap &_cost, |
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| 402 | typename Graph::Node _s, |
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| 403 | typename Graph::Node _t, |
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| 404 | typename SupplyMap::Value _flow_value ) : |
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| 405 | graph_ref(_graph), lower(NULL), capacity(graph), cost(graph), |
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| 406 | supply(graph, 0), flow(graph), flow_result(_graph), potential(graph), |
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| 407 | potential_result(_graph), depth(graph), parent(graph), |
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| 408 | pred_edge(graph), thread(graph), forward(graph), state(graph), |
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| 409 | node_ref(graph_ref), edge_ref(graph_ref), |
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| 410 | red_cost(graph, cost, potential) |
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| 411 | { |
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| 412 | // Copying graph_ref to graph |
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| 413 | copyGraph(graph, graph_ref) |
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| 414 | .edgeMap(capacity, _capacity) |
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| 415 | .edgeMap(cost, _cost) |
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| 416 | .nodeRef(node_ref) |
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| 417 | .edgeRef(edge_ref) |
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| 418 | .run(); |
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| 419 | supply[node_ref[_s]] = _flow_value; |
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| 420 | supply[node_ref[_t]] = -_flow_value; |
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| 421 | valid_supply = true; |
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| 422 | } |
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| 423 | |
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| 424 | /// \brief Returns a const reference to the flow map. |
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| 425 | /// |
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| 426 | /// Returns a const reference to the flow map. |
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| 427 | /// |
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| 428 | /// \pre \ref run() must be called before using this function. |
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| 429 | const FlowMap& flowMap() const { |
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| 430 | return flow_result; |
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| 431 | } |
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| 432 | |
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| 433 | /// \brief Returns a const reference to the potential map (the dual |
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| 434 | /// solution). |
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| 435 | /// |
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| 436 | /// Returns a const reference to the potential map (the dual |
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| 437 | /// solution). |
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| 438 | /// |
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| 439 | /// \pre \ref run() must be called before using this function. |
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| 440 | const PotentialMap& potentialMap() const { |
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| 441 | return potential_result; |
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| 442 | } |
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| 443 | |
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| 444 | /// \brief Returns the total cost of the found flow. |
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| 445 | /// |
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| 446 | /// Returns the total cost of the found flow. The complexity of the |
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| 447 | /// function is \f$ O(e) \f$. |
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| 448 | /// |
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| 449 | /// \pre \ref run() must be called before using this function. |
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| 450 | Cost totalCost() const { |
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| 451 | Cost c = 0; |
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| 452 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
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| 453 | c += flow_result[e] * cost[edge_ref[e]]; |
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| 454 | return c; |
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| 455 | } |
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| 456 | |
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| 457 | /// \brief Runs the algorithm. |
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| 458 | /// |
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| 459 | /// Runs the algorithm. |
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| 460 | /// |
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| 461 | /// \return \c true if a feasible flow can be found. |
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| 462 | bool run() { |
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| 463 | return init() && start(); |
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| 464 | } |
---|
| 465 | |
---|
| 466 | protected: |
---|
| 467 | |
---|
| 468 | /// \brief Extends the underlaying graph and initializes all the |
---|
| 469 | /// node and edge maps. |
---|
| 470 | bool init() { |
---|
| 471 | if (!valid_supply) return false; |
---|
| 472 | |
---|
| 473 | // Initializing state and flow maps |
---|
| 474 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
| 475 | flow[e] = 0; |
---|
| 476 | state[e] = LOWER; |
---|
| 477 | } |
---|
| 478 | |
---|
| 479 | // Adding an artificial root node to the graph |
---|
| 480 | root = graph.addNode(); |
---|
| 481 | parent[root] = INVALID; |
---|
| 482 | pred_edge[root] = INVALID; |
---|
[2457] | 483 | depth[root] = 0; |
---|
| 484 | supply[root] = 0; |
---|
| 485 | potential[root] = 0; |
---|
[2440] | 486 | |
---|
| 487 | // Adding artificial edges to the graph and initializing the node |
---|
| 488 | // maps of the spanning tree data structure |
---|
| 489 | Supply sum = 0; |
---|
| 490 | Node last = root; |
---|
| 491 | Edge e; |
---|
| 492 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
---|
| 493 | for (NodeIt u(graph); u != INVALID; ++u) { |
---|
| 494 | if (u == root) continue; |
---|
| 495 | thread[last] = u; |
---|
| 496 | last = u; |
---|
| 497 | parent[u] = root; |
---|
| 498 | depth[u] = 1; |
---|
| 499 | sum += supply[u]; |
---|
| 500 | if (supply[u] >= 0) { |
---|
| 501 | e = graph.addEdge(u, root); |
---|
| 502 | flow[e] = supply[u]; |
---|
| 503 | forward[u] = true; |
---|
| 504 | potential[u] = max_cost; |
---|
| 505 | } else { |
---|
| 506 | e = graph.addEdge(root, u); |
---|
| 507 | flow[e] = -supply[u]; |
---|
| 508 | forward[u] = false; |
---|
| 509 | potential[u] = -max_cost; |
---|
| 510 | } |
---|
| 511 | cost[e] = max_cost; |
---|
| 512 | capacity[e] = std::numeric_limits<Capacity>::max(); |
---|
| 513 | state[e] = TREE; |
---|
| 514 | pred_edge[u] = e; |
---|
| 515 | } |
---|
| 516 | thread[last] = root; |
---|
| 517 | |
---|
| 518 | #ifdef EDGE_BLOCK_PIVOT |
---|
| 519 | // Initializing block_size for the edge block pivot rule |
---|
| 520 | int edge_num = countEdges(graph); |
---|
[2471] | 521 | block_size = 2 * int(sqrt(countEdges(graph))); |
---|
| 522 | if (block_size < MIN_BLOCK_SIZE) block_size = MIN_BLOCK_SIZE; |
---|
| 523 | // block_size = edge_num >= BLOCK_NUM * MIN_BLOCK_SIZE ? |
---|
| 524 | // edge_num / BLOCK_NUM : MIN_BLOCK_SIZE; |
---|
[2440] | 525 | #endif |
---|
| 526 | #ifdef CANDIDATE_LIST_PIVOT |
---|
[2471] | 527 | int edge_num = countEdges(graph); |
---|
[2440] | 528 | minor_count = 0; |
---|
[2471] | 529 | list_length = edge_num / LIST_LENGTH_DIV; |
---|
| 530 | minor_limit = edge_num / MINOR_LIMIT_DIV; |
---|
| 531 | #endif |
---|
| 532 | #ifdef SORTED_LIST_PIVOT |
---|
| 533 | int edge_num = countEdges(graph); |
---|
| 534 | list_index = 0; |
---|
| 535 | list_length = edge_num / LIST_LENGTH_DIV; |
---|
[2440] | 536 | #endif |
---|
| 537 | |
---|
| 538 | return sum == 0; |
---|
| 539 | } |
---|
| 540 | |
---|
| 541 | #ifdef FIRST_ELIGIBLE_PIVOT |
---|
| 542 | /// \brief Finds entering edge according to the "First Eligible" |
---|
| 543 | /// pivot rule. |
---|
| 544 | bool findEnteringEdge(EdgeIt &next_edge) { |
---|
| 545 | for (EdgeIt e = next_edge; e != INVALID; ++e) { |
---|
| 546 | if (state[e] * red_cost[e] < 0) { |
---|
| 547 | in_edge = e; |
---|
| 548 | next_edge = ++e; |
---|
| 549 | return true; |
---|
| 550 | } |
---|
| 551 | } |
---|
| 552 | for (EdgeIt e(graph); e != next_edge; ++e) { |
---|
| 553 | if (state[e] * red_cost[e] < 0) { |
---|
| 554 | in_edge = e; |
---|
| 555 | next_edge = ++e; |
---|
| 556 | return true; |
---|
| 557 | } |
---|
| 558 | } |
---|
| 559 | return false; |
---|
| 560 | } |
---|
| 561 | #endif |
---|
| 562 | |
---|
| 563 | #ifdef BEST_ELIGIBLE_PIVOT |
---|
| 564 | /// \brief Finds entering edge according to the "Best Eligible" |
---|
| 565 | /// pivot rule. |
---|
| 566 | bool findEnteringEdge() { |
---|
| 567 | Cost min = 0; |
---|
| 568 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
| 569 | if (state[e] * red_cost[e] < min) { |
---|
| 570 | min = state[e] * red_cost[e]; |
---|
| 571 | in_edge = e; |
---|
| 572 | } |
---|
| 573 | } |
---|
| 574 | return min < 0; |
---|
| 575 | } |
---|
| 576 | #endif |
---|
| 577 | |
---|
| 578 | #ifdef EDGE_BLOCK_PIVOT |
---|
| 579 | /// \brief Finds entering edge according to the "Edge Block" |
---|
| 580 | /// pivot rule. |
---|
| 581 | bool findEnteringEdge(EdgeIt &next_edge) { |
---|
[2444] | 582 | // Performing edge block selection |
---|
| 583 | Cost curr, min = 0; |
---|
| 584 | EdgeIt min_edge(graph); |
---|
| 585 | int cnt = 0; |
---|
| 586 | for (EdgeIt e = next_edge; e != INVALID; ++e) { |
---|
| 587 | if ((curr = state[e] * red_cost[e]) < min) { |
---|
| 588 | min = curr; |
---|
| 589 | min_edge = e; |
---|
[2440] | 590 | } |
---|
[2444] | 591 | if (++cnt == block_size) { |
---|
| 592 | if (min < 0) break; |
---|
| 593 | cnt = 0; |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | if (!(min < 0)) { |
---|
[2440] | 597 | for (EdgeIt e(graph); e != next_edge; ++e) { |
---|
| 598 | if ((curr = state[e] * red_cost[e]) < min) { |
---|
| 599 | min = curr; |
---|
| 600 | min_edge = e; |
---|
| 601 | } |
---|
| 602 | if (++cnt == block_size) { |
---|
| 603 | if (min < 0) break; |
---|
| 604 | cnt = 0; |
---|
| 605 | } |
---|
| 606 | } |
---|
| 607 | } |
---|
[2444] | 608 | in_edge = min_edge; |
---|
| 609 | if ((next_edge = ++min_edge) == INVALID) |
---|
| 610 | next_edge = EdgeIt(graph); |
---|
| 611 | return min < 0; |
---|
[2440] | 612 | } |
---|
| 613 | #endif |
---|
| 614 | |
---|
| 615 | #ifdef CANDIDATE_LIST_PIVOT |
---|
| 616 | /// \brief Finds entering edge according to the "Candidate List" |
---|
| 617 | /// pivot rule. |
---|
| 618 | bool findEnteringEdge() { |
---|
[2471] | 619 | typedef typename std::vector<Edge>::iterator ListIt; |
---|
[2440] | 620 | |
---|
[2471] | 621 | if (minor_count >= minor_limit || candidates.size() == 0) { |
---|
[2440] | 622 | // Major iteration |
---|
[2471] | 623 | candidates.clear(); |
---|
[2440] | 624 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
| 625 | if (state[e] * red_cost[e] < 0) { |
---|
| 626 | candidates.push_back(e); |
---|
[2471] | 627 | if (candidates.size() == list_length) break; |
---|
[2440] | 628 | } |
---|
| 629 | } |
---|
| 630 | if (candidates.size() == 0) return false; |
---|
| 631 | } |
---|
| 632 | |
---|
| 633 | // Minor iteration |
---|
| 634 | ++minor_count; |
---|
| 635 | Cost min = 0; |
---|
[2471] | 636 | Edge e; |
---|
| 637 | for (int i = 0; i < candidates.size(); ++i) { |
---|
| 638 | e = candidates[i]; |
---|
| 639 | if (state[e] * red_cost[e] < min) { |
---|
| 640 | min = state[e] * red_cost[e]; |
---|
| 641 | in_edge = e; |
---|
[2440] | 642 | } |
---|
| 643 | } |
---|
| 644 | return true; |
---|
| 645 | } |
---|
| 646 | #endif |
---|
| 647 | |
---|
| 648 | #ifdef SORTED_LIST_PIVOT |
---|
| 649 | /// \brief Functor class to compare edges during sort of the |
---|
| 650 | /// candidate list. |
---|
| 651 | class SortFunc |
---|
| 652 | { |
---|
| 653 | private: |
---|
| 654 | const IntEdgeMap &st; |
---|
| 655 | const ReducedCostMap &rc; |
---|
| 656 | public: |
---|
| 657 | SortFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) : |
---|
| 658 | st(_st), rc(_rc) {} |
---|
| 659 | bool operator()(const Edge &e1, const Edge &e2) { |
---|
| 660 | return st[e1] * rc[e1] < st[e2] * rc[e2]; |
---|
| 661 | } |
---|
| 662 | }; |
---|
| 663 | |
---|
| 664 | /// \brief Finds entering edge according to the "Sorted List" |
---|
| 665 | /// pivot rule. |
---|
| 666 | bool findEnteringEdge() { |
---|
| 667 | static SortFunc sort_func(state, red_cost); |
---|
| 668 | |
---|
| 669 | // Minor iteration |
---|
[2471] | 670 | while (list_index < candidates.size()) { |
---|
| 671 | in_edge = candidates[list_index++]; |
---|
[2440] | 672 | if (state[in_edge] * red_cost[in_edge] < 0) return true; |
---|
| 673 | } |
---|
| 674 | |
---|
| 675 | // Major iteration |
---|
[2471] | 676 | candidates.clear(); |
---|
[2440] | 677 | Cost curr, min = 0; |
---|
| 678 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
| 679 | if ((curr = state[e] * red_cost[e]) < min / LOWER_DIV) { |
---|
| 680 | candidates.push_back(e); |
---|
| 681 | if (curr < min) min = curr; |
---|
[2471] | 682 | if (candidates.size() == list_length) break; |
---|
[2440] | 683 | } |
---|
| 684 | } |
---|
| 685 | if (candidates.size() == 0) return false; |
---|
| 686 | sort(candidates.begin(), candidates.end(), sort_func); |
---|
[2471] | 687 | in_edge = candidates[0]; |
---|
| 688 | list_index = 1; |
---|
[2440] | 689 | return true; |
---|
| 690 | } |
---|
| 691 | #endif |
---|
| 692 | |
---|
| 693 | /// \brief Finds the join node. |
---|
| 694 | Node findJoinNode() { |
---|
| 695 | // Finding the join node |
---|
| 696 | Node u = graph.source(in_edge); |
---|
| 697 | Node v = graph.target(in_edge); |
---|
| 698 | while (u != v) { |
---|
| 699 | if (depth[u] == depth[v]) { |
---|
| 700 | u = parent[u]; |
---|
| 701 | v = parent[v]; |
---|
| 702 | } |
---|
| 703 | else if (depth[u] > depth[v]) u = parent[u]; |
---|
| 704 | else v = parent[v]; |
---|
| 705 | } |
---|
| 706 | return u; |
---|
| 707 | } |
---|
| 708 | |
---|
| 709 | /// \brief Finds the leaving edge of the cycle. Returns \c true if |
---|
| 710 | /// the leaving edge is not the same as the entering edge. |
---|
| 711 | bool findLeavingEdge() { |
---|
| 712 | // Initializing first and second nodes according to the direction |
---|
| 713 | // of the cycle |
---|
| 714 | if (state[in_edge] == LOWER) { |
---|
| 715 | first = graph.source(in_edge); |
---|
| 716 | second = graph.target(in_edge); |
---|
| 717 | } else { |
---|
| 718 | first = graph.target(in_edge); |
---|
| 719 | second = graph.source(in_edge); |
---|
| 720 | } |
---|
| 721 | delta = capacity[in_edge]; |
---|
| 722 | bool result = false; |
---|
| 723 | Capacity d; |
---|
| 724 | Edge e; |
---|
| 725 | |
---|
| 726 | // Searching the cycle along the path form the first node to the |
---|
| 727 | // root node |
---|
| 728 | for (Node u = first; u != join; u = parent[u]) { |
---|
| 729 | e = pred_edge[u]; |
---|
| 730 | d = forward[u] ? flow[e] : capacity[e] - flow[e]; |
---|
| 731 | if (d < delta) { |
---|
| 732 | delta = d; |
---|
| 733 | u_out = u; |
---|
| 734 | u_in = first; |
---|
| 735 | v_in = second; |
---|
| 736 | result = true; |
---|
| 737 | } |
---|
| 738 | } |
---|
| 739 | // Searching the cycle along the path form the second node to the |
---|
| 740 | // root node |
---|
| 741 | for (Node u = second; u != join; u = parent[u]) { |
---|
| 742 | e = pred_edge[u]; |
---|
| 743 | d = forward[u] ? capacity[e] - flow[e] : flow[e]; |
---|
| 744 | if (d <= delta) { |
---|
| 745 | delta = d; |
---|
| 746 | u_out = u; |
---|
| 747 | u_in = second; |
---|
| 748 | v_in = first; |
---|
| 749 | result = true; |
---|
| 750 | } |
---|
| 751 | } |
---|
| 752 | return result; |
---|
| 753 | } |
---|
| 754 | |
---|
| 755 | /// \brief Changes flow and state edge maps. |
---|
| 756 | void changeFlows(bool change) { |
---|
| 757 | // Augmenting along the cycle |
---|
| 758 | if (delta > 0) { |
---|
| 759 | Capacity val = state[in_edge] * delta; |
---|
| 760 | flow[in_edge] += val; |
---|
| 761 | for (Node u = graph.source(in_edge); u != join; u = parent[u]) { |
---|
| 762 | flow[pred_edge[u]] += forward[u] ? -val : val; |
---|
| 763 | } |
---|
| 764 | for (Node u = graph.target(in_edge); u != join; u = parent[u]) { |
---|
| 765 | flow[pred_edge[u]] += forward[u] ? val : -val; |
---|
| 766 | } |
---|
| 767 | } |
---|
| 768 | // Updating the state of the entering and leaving edges |
---|
| 769 | if (change) { |
---|
| 770 | state[in_edge] = TREE; |
---|
| 771 | state[pred_edge[u_out]] = |
---|
| 772 | (flow[pred_edge[u_out]] == 0) ? LOWER : UPPER; |
---|
| 773 | } else { |
---|
| 774 | state[in_edge] = -state[in_edge]; |
---|
| 775 | } |
---|
| 776 | } |
---|
| 777 | |
---|
| 778 | /// \brief Updates thread and parent node maps. |
---|
| 779 | void updateThreadParent() { |
---|
| 780 | Node u; |
---|
| 781 | v_out = parent[u_out]; |
---|
| 782 | |
---|
| 783 | // Handling the case when join and v_out coincide |
---|
| 784 | bool par_first = false; |
---|
| 785 | if (join == v_out) { |
---|
| 786 | for (u = join; u != u_in && u != v_in; u = thread[u]) ; |
---|
| 787 | if (u == v_in) { |
---|
| 788 | par_first = true; |
---|
| 789 | while (thread[u] != u_out) u = thread[u]; |
---|
| 790 | first = u; |
---|
| 791 | } |
---|
| 792 | } |
---|
| 793 | |
---|
| 794 | // Finding the last successor of u_in (u) and the node after it |
---|
| 795 | // (right) according to the thread index |
---|
| 796 | for (u = u_in; depth[thread[u]] > depth[u_in]; u = thread[u]) ; |
---|
| 797 | right = thread[u]; |
---|
| 798 | if (thread[v_in] == u_out) { |
---|
| 799 | for (last = u; depth[last] > depth[u_out]; last = thread[last]) ; |
---|
| 800 | if (last == u_out) last = thread[last]; |
---|
| 801 | } |
---|
| 802 | else last = thread[v_in]; |
---|
| 803 | |
---|
| 804 | // Updating stem nodes |
---|
| 805 | thread[v_in] = stem = u_in; |
---|
| 806 | par_stem = v_in; |
---|
| 807 | while (stem != u_out) { |
---|
| 808 | thread[u] = new_stem = parent[stem]; |
---|
| 809 | |
---|
| 810 | // Finding the node just before the stem node (u) according to |
---|
| 811 | // the original thread index |
---|
| 812 | for (u = new_stem; thread[u] != stem; u = thread[u]) ; |
---|
| 813 | thread[u] = right; |
---|
| 814 | |
---|
| 815 | // Changing the parent node of stem and shifting stem and |
---|
| 816 | // par_stem nodes |
---|
| 817 | parent[stem] = par_stem; |
---|
| 818 | par_stem = stem; |
---|
| 819 | stem = new_stem; |
---|
| 820 | |
---|
| 821 | // Finding the last successor of stem (u) and the node after it |
---|
| 822 | // (right) according to the thread index |
---|
| 823 | for (u = stem; depth[thread[u]] > depth[stem]; u = thread[u]) ; |
---|
| 824 | right = thread[u]; |
---|
| 825 | } |
---|
| 826 | parent[u_out] = par_stem; |
---|
| 827 | thread[u] = last; |
---|
| 828 | |
---|
| 829 | if (join == v_out && par_first) { |
---|
| 830 | if (first != v_in) thread[first] = right; |
---|
| 831 | } else { |
---|
| 832 | for (u = v_out; thread[u] != u_out; u = thread[u]) ; |
---|
| 833 | thread[u] = right; |
---|
| 834 | } |
---|
| 835 | } |
---|
| 836 | |
---|
| 837 | /// \brief Updates pred_edge and forward node maps. |
---|
| 838 | void updatePredEdge() { |
---|
| 839 | Node u = u_out, v; |
---|
| 840 | while (u != u_in) { |
---|
| 841 | v = parent[u]; |
---|
| 842 | pred_edge[u] = pred_edge[v]; |
---|
| 843 | forward[u] = !forward[v]; |
---|
| 844 | u = v; |
---|
| 845 | } |
---|
| 846 | pred_edge[u_in] = in_edge; |
---|
| 847 | forward[u_in] = (u_in == graph.source(in_edge)); |
---|
| 848 | } |
---|
| 849 | |
---|
| 850 | /// \brief Updates depth and potential node maps. |
---|
| 851 | void updateDepthPotential() { |
---|
| 852 | depth[u_in] = depth[v_in] + 1; |
---|
| 853 | potential[u_in] = forward[u_in] ? |
---|
| 854 | potential[v_in] + cost[pred_edge[u_in]] : |
---|
| 855 | potential[v_in] - cost[pred_edge[u_in]]; |
---|
| 856 | |
---|
| 857 | Node u = thread[u_in], v; |
---|
| 858 | while (true) { |
---|
| 859 | v = parent[u]; |
---|
| 860 | if (v == INVALID) break; |
---|
| 861 | depth[u] = depth[v] + 1; |
---|
| 862 | potential[u] = forward[u] ? |
---|
| 863 | potential[v] + cost[pred_edge[u]] : |
---|
| 864 | potential[v] - cost[pred_edge[u]]; |
---|
| 865 | if (depth[u] <= depth[v_in]) break; |
---|
| 866 | u = thread[u]; |
---|
| 867 | } |
---|
| 868 | } |
---|
| 869 | |
---|
| 870 | /// \brief Executes the algorithm. |
---|
| 871 | bool start() { |
---|
| 872 | // Processing pivots |
---|
| 873 | #ifdef _DEBUG_ITER_ |
---|
| 874 | int iter_num = 0; |
---|
| 875 | #endif |
---|
| 876 | #if defined(FIRST_ELIGIBLE_PIVOT) || defined(EDGE_BLOCK_PIVOT) |
---|
| 877 | EdgeIt next_edge(graph); |
---|
| 878 | while (findEnteringEdge(next_edge)) |
---|
| 879 | #else |
---|
| 880 | while (findEnteringEdge()) |
---|
| 881 | #endif |
---|
| 882 | { |
---|
| 883 | join = findJoinNode(); |
---|
| 884 | bool change = findLeavingEdge(); |
---|
| 885 | changeFlows(change); |
---|
| 886 | if (change) { |
---|
| 887 | updateThreadParent(); |
---|
| 888 | updatePredEdge(); |
---|
| 889 | updateDepthPotential(); |
---|
| 890 | } |
---|
| 891 | #ifdef _DEBUG_ITER_ |
---|
| 892 | ++iter_num; |
---|
| 893 | #endif |
---|
| 894 | } |
---|
| 895 | |
---|
| 896 | #ifdef _DEBUG_ITER_ |
---|
| 897 | std::cout << "Network Simplex algorithm finished. " << iter_num |
---|
[2444] | 898 | << " pivot iterations performed." << std::endl; |
---|
[2440] | 899 | #endif |
---|
| 900 | |
---|
| 901 | // Checking if the flow amount equals zero on all the |
---|
| 902 | // artificial edges |
---|
| 903 | for (InEdgeIt e(graph, root); e != INVALID; ++e) |
---|
| 904 | if (flow[e] > 0) return false; |
---|
| 905 | for (OutEdgeIt e(graph, root); e != INVALID; ++e) |
---|
| 906 | if (flow[e] > 0) return false; |
---|
| 907 | |
---|
| 908 | // Copying flow values to flow_result |
---|
| 909 | if (lower) { |
---|
| 910 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
---|
| 911 | flow_result[e] = (*lower)[e] + flow[edge_ref[e]]; |
---|
| 912 | } else { |
---|
| 913 | for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) |
---|
| 914 | flow_result[e] = flow[edge_ref[e]]; |
---|
| 915 | } |
---|
| 916 | // Copying potential values to potential_result |
---|
| 917 | for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) |
---|
| 918 | potential_result[n] = potential[node_ref[n]]; |
---|
| 919 | |
---|
| 920 | return true; |
---|
| 921 | } |
---|
| 922 | |
---|
| 923 | }; //class NetworkSimplex |
---|
| 924 | |
---|
| 925 | ///@} |
---|
| 926 | |
---|
| 927 | } //namespace lemon |
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| 928 | |
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| 929 | #endif //LEMON_NETWORK_SIMPLEX_H |
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