[648] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2009 |
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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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[652] | 25 | /// \brief Network Simplex algorithm for finding a minimum cost flow. |
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[648] | 26 | |
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| 27 | #include <vector> |
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| 28 | #include <limits> |
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| 29 | #include <algorithm> |
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| 30 | |
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[650] | 31 | #include <lemon/core.h> |
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[648] | 32 | #include <lemon/math.h> |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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| 36 | /// \addtogroup min_cost_flow |
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| 37 | /// @{ |
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| 38 | |
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[652] | 39 | /// \brief Implementation of the primal Network Simplex algorithm |
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[648] | 40 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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| 41 | /// |
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[652] | 42 | /// \ref NetworkSimplex implements the primal Network Simplex algorithm |
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[648] | 43 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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[653] | 44 | /// This algorithm is a specialized version of the linear programming |
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| 45 | /// simplex method directly for the minimum cost flow problem. |
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| 46 | /// It is one of the most efficient solution methods. |
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| 47 | /// |
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| 48 | /// In general this class is the fastest implementation available |
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| 49 | /// in LEMON for the minimum cost flow problem. |
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[648] | 50 | /// |
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[652] | 51 | /// \tparam GR The digraph type the algorithm runs on. |
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[654] | 52 | /// \tparam F The value type used for flow amounts, capacity bounds |
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| 53 | /// and supply values in the algorithm. By default it is \c int. |
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| 54 | /// \tparam C The value type used for costs and potentials in the |
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| 55 | /// algorithm. By default it is the same as \c F. |
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[648] | 56 | /// |
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[655] | 57 | /// \warning Both value types must be signed and all input data must |
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| 58 | /// be integer. |
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[648] | 59 | /// |
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[652] | 60 | /// \note %NetworkSimplex provides five different pivot rule |
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| 61 | /// implementations. For more information see \ref PivotRule. |
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[654] | 62 | template <typename GR, typename F = int, typename C = F> |
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[648] | 63 | class NetworkSimplex |
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| 64 | { |
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[652] | 65 | public: |
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[648] | 66 | |
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[654] | 67 | /// The flow type of the algorithm |
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| 68 | typedef F Flow; |
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| 69 | /// The cost type of the algorithm |
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| 70 | typedef C Cost; |
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[652] | 71 | /// The type of the flow map |
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[654] | 72 | typedef typename GR::template ArcMap<Flow> FlowMap; |
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[652] | 73 | /// The type of the potential map |
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[654] | 74 | typedef typename GR::template NodeMap<Cost> PotentialMap; |
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[652] | 75 | |
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| 76 | public: |
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| 77 | |
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| 78 | /// \brief Enum type for selecting the pivot rule. |
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| 79 | /// |
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| 80 | /// Enum type for selecting the pivot rule for the \ref run() |
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| 81 | /// function. |
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| 82 | /// |
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| 83 | /// \ref NetworkSimplex provides five different pivot rule |
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| 84 | /// implementations that significantly affect the running time |
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| 85 | /// of the algorithm. |
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| 86 | /// By default \ref BLOCK_SEARCH "Block Search" is used, which |
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| 87 | /// proved to be the most efficient and the most robust on various |
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| 88 | /// test inputs according to our benchmark tests. |
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| 89 | /// However another pivot rule can be selected using the \ref run() |
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| 90 | /// function with the proper parameter. |
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| 91 | enum PivotRule { |
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| 92 | |
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| 93 | /// The First Eligible pivot rule. |
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| 94 | /// The next eligible arc is selected in a wraparound fashion |
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| 95 | /// in every iteration. |
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| 96 | FIRST_ELIGIBLE, |
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| 97 | |
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| 98 | /// The Best Eligible pivot rule. |
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| 99 | /// The best eligible arc is selected in every iteration. |
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| 100 | BEST_ELIGIBLE, |
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| 101 | |
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| 102 | /// The Block Search pivot rule. |
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| 103 | /// A specified number of arcs are examined in every iteration |
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| 104 | /// in a wraparound fashion and the best eligible arc is selected |
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| 105 | /// from this block. |
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| 106 | BLOCK_SEARCH, |
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| 107 | |
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| 108 | /// The Candidate List pivot rule. |
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| 109 | /// In a major iteration a candidate list is built from eligible arcs |
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| 110 | /// in a wraparound fashion and in the following minor iterations |
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| 111 | /// the best eligible arc is selected from this list. |
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| 112 | CANDIDATE_LIST, |
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| 113 | |
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| 114 | /// The Altering Candidate List pivot rule. |
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| 115 | /// It is a modified version of the Candidate List method. |
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| 116 | /// It keeps only the several best eligible arcs from the former |
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| 117 | /// candidate list and extends this list in every iteration. |
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| 118 | ALTERING_LIST |
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| 119 | }; |
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| 120 | |
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| 121 | private: |
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| 122 | |
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| 123 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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| 124 | |
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[654] | 125 | typedef typename GR::template ArcMap<Flow> FlowArcMap; |
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| 126 | typedef typename GR::template ArcMap<Cost> CostArcMap; |
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| 127 | typedef typename GR::template NodeMap<Flow> FlowNodeMap; |
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[648] | 128 | |
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| 129 | typedef std::vector<Arc> ArcVector; |
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| 130 | typedef std::vector<Node> NodeVector; |
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| 131 | typedef std::vector<int> IntVector; |
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| 132 | typedef std::vector<bool> BoolVector; |
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[654] | 133 | typedef std::vector<Flow> FlowVector; |
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| 134 | typedef std::vector<Cost> CostVector; |
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[648] | 135 | |
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| 136 | // State constants for arcs |
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| 137 | enum ArcStateEnum { |
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| 138 | STATE_UPPER = -1, |
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| 139 | STATE_TREE = 0, |
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| 140 | STATE_LOWER = 1 |
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| 141 | }; |
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| 142 | |
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| 143 | private: |
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| 144 | |
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[652] | 145 | // Data related to the underlying digraph |
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| 146 | const GR &_graph; |
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| 147 | int _node_num; |
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| 148 | int _arc_num; |
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| 149 | |
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| 150 | // Parameters of the problem |
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[654] | 151 | FlowArcMap *_plower; |
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| 152 | FlowArcMap *_pupper; |
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| 153 | CostArcMap *_pcost; |
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| 154 | FlowNodeMap *_psupply; |
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[652] | 155 | bool _pstsup; |
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| 156 | Node _psource, _ptarget; |
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[654] | 157 | Flow _pstflow; |
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[648] | 158 | |
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| 159 | // Result maps |
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[650] | 160 | FlowMap *_flow_map; |
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| 161 | PotentialMap *_potential_map; |
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[648] | 162 | bool _local_flow; |
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| 163 | bool _local_potential; |
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| 164 | |
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[652] | 165 | // Data structures for storing the digraph |
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[650] | 166 | IntNodeMap _node_id; |
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| 167 | ArcVector _arc_ref; |
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| 168 | IntVector _source; |
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| 169 | IntVector _target; |
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| 170 | |
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[652] | 171 | // Node and arc data |
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[654] | 172 | FlowVector _cap; |
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| 173 | CostVector _cost; |
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| 174 | FlowVector _supply; |
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| 175 | FlowVector _flow; |
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| 176 | CostVector _pi; |
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[648] | 177 | |
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[650] | 178 | // Data for storing the spanning tree structure |
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[648] | 179 | IntVector _parent; |
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| 180 | IntVector _pred; |
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| 181 | IntVector _thread; |
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[651] | 182 | IntVector _rev_thread; |
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| 183 | IntVector _succ_num; |
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| 184 | IntVector _last_succ; |
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| 185 | IntVector _dirty_revs; |
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[648] | 186 | BoolVector _forward; |
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| 187 | IntVector _state; |
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| 188 | int _root; |
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| 189 | |
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| 190 | // Temporary data used in the current pivot iteration |
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[650] | 191 | int in_arc, join, u_in, v_in, u_out, v_out; |
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| 192 | int first, second, right, last; |
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[648] | 193 | int stem, par_stem, new_stem; |
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[654] | 194 | Flow delta; |
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[648] | 195 | |
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| 196 | private: |
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| 197 | |
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[652] | 198 | // Implementation of the First Eligible pivot rule |
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[648] | 199 | class FirstEligiblePivotRule |
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| 200 | { |
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| 201 | private: |
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| 202 | |
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| 203 | // References to the NetworkSimplex class |
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| 204 | const IntVector &_source; |
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| 205 | const IntVector &_target; |
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[654] | 206 | const CostVector &_cost; |
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[648] | 207 | const IntVector &_state; |
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[654] | 208 | const CostVector &_pi; |
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[648] | 209 | int &_in_arc; |
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| 210 | int _arc_num; |
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| 211 | |
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| 212 | // Pivot rule data |
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| 213 | int _next_arc; |
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| 214 | |
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| 215 | public: |
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| 216 | |
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[652] | 217 | // Constructor |
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[648] | 218 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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[650] | 219 | _source(ns._source), _target(ns._target), |
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[648] | 220 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[650] | 221 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[648] | 222 | {} |
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| 223 | |
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[652] | 224 | // Find next entering arc |
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[648] | 225 | bool findEnteringArc() { |
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[654] | 226 | Cost c; |
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[648] | 227 | for (int e = _next_arc; e < _arc_num; ++e) { |
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| 228 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 229 | if (c < 0) { |
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| 230 | _in_arc = e; |
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| 231 | _next_arc = e + 1; |
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| 232 | return true; |
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| 233 | } |
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| 234 | } |
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| 235 | for (int e = 0; e < _next_arc; ++e) { |
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| 236 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 237 | if (c < 0) { |
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| 238 | _in_arc = e; |
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| 239 | _next_arc = e + 1; |
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| 240 | return true; |
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| 241 | } |
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| 242 | } |
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| 243 | return false; |
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| 244 | } |
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| 245 | |
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| 246 | }; //class FirstEligiblePivotRule |
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| 247 | |
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| 248 | |
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[652] | 249 | // Implementation of the Best Eligible pivot rule |
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[648] | 250 | class BestEligiblePivotRule |
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| 251 | { |
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| 252 | private: |
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| 253 | |
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| 254 | // References to the NetworkSimplex class |
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| 255 | const IntVector &_source; |
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| 256 | const IntVector &_target; |
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[654] | 257 | const CostVector &_cost; |
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[648] | 258 | const IntVector &_state; |
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[654] | 259 | const CostVector &_pi; |
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[648] | 260 | int &_in_arc; |
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| 261 | int _arc_num; |
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| 262 | |
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| 263 | public: |
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| 264 | |
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[652] | 265 | // Constructor |
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[648] | 266 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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[650] | 267 | _source(ns._source), _target(ns._target), |
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[648] | 268 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[650] | 269 | _in_arc(ns.in_arc), _arc_num(ns._arc_num) |
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[648] | 270 | {} |
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| 271 | |
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[652] | 272 | // Find next entering arc |
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[648] | 273 | bool findEnteringArc() { |
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[654] | 274 | Cost c, min = 0; |
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[648] | 275 | for (int e = 0; e < _arc_num; ++e) { |
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| 276 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 277 | if (c < min) { |
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| 278 | min = c; |
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| 279 | _in_arc = e; |
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| 280 | } |
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| 281 | } |
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| 282 | return min < 0; |
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| 283 | } |
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| 284 | |
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| 285 | }; //class BestEligiblePivotRule |
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| 286 | |
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| 287 | |
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[652] | 288 | // Implementation of the Block Search pivot rule |
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[648] | 289 | class BlockSearchPivotRule |
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| 290 | { |
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| 291 | private: |
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| 292 | |
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| 293 | // References to the NetworkSimplex class |
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| 294 | const IntVector &_source; |
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| 295 | const IntVector &_target; |
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[654] | 296 | const CostVector &_cost; |
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[648] | 297 | const IntVector &_state; |
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[654] | 298 | const CostVector &_pi; |
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[648] | 299 | int &_in_arc; |
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| 300 | int _arc_num; |
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| 301 | |
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| 302 | // Pivot rule data |
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| 303 | int _block_size; |
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| 304 | int _next_arc; |
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| 305 | |
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| 306 | public: |
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| 307 | |
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[652] | 308 | // Constructor |
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[648] | 309 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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[650] | 310 | _source(ns._source), _target(ns._target), |
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[648] | 311 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[650] | 312 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[648] | 313 | { |
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| 314 | // The main parameters of the pivot rule |
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| 315 | const double BLOCK_SIZE_FACTOR = 2.0; |
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| 316 | const int MIN_BLOCK_SIZE = 10; |
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| 317 | |
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| 318 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
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| 319 | MIN_BLOCK_SIZE ); |
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| 320 | } |
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| 321 | |
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[652] | 322 | // Find next entering arc |
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[648] | 323 | bool findEnteringArc() { |
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[654] | 324 | Cost c, min = 0; |
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[648] | 325 | int cnt = _block_size; |
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| 326 | int e, min_arc = _next_arc; |
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| 327 | for (e = _next_arc; e < _arc_num; ++e) { |
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| 328 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 329 | if (c < min) { |
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| 330 | min = c; |
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| 331 | min_arc = e; |
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| 332 | } |
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| 333 | if (--cnt == 0) { |
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| 334 | if (min < 0) break; |
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| 335 | cnt = _block_size; |
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| 336 | } |
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| 337 | } |
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| 338 | if (min == 0 || cnt > 0) { |
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| 339 | for (e = 0; e < _next_arc; ++e) { |
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| 340 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 341 | if (c < min) { |
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| 342 | min = c; |
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| 343 | min_arc = e; |
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| 344 | } |
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| 345 | if (--cnt == 0) { |
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| 346 | if (min < 0) break; |
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| 347 | cnt = _block_size; |
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| 348 | } |
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| 349 | } |
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| 350 | } |
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| 351 | if (min >= 0) return false; |
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| 352 | _in_arc = min_arc; |
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| 353 | _next_arc = e; |
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| 354 | return true; |
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| 355 | } |
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| 356 | |
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| 357 | }; //class BlockSearchPivotRule |
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| 358 | |
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| 359 | |
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[652] | 360 | // Implementation of the Candidate List pivot rule |
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[648] | 361 | class CandidateListPivotRule |
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| 362 | { |
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| 363 | private: |
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| 364 | |
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| 365 | // References to the NetworkSimplex class |
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| 366 | const IntVector &_source; |
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| 367 | const IntVector &_target; |
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[654] | 368 | const CostVector &_cost; |
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[648] | 369 | const IntVector &_state; |
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[654] | 370 | const CostVector &_pi; |
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[648] | 371 | int &_in_arc; |
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| 372 | int _arc_num; |
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| 373 | |
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| 374 | // Pivot rule data |
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| 375 | IntVector _candidates; |
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| 376 | int _list_length, _minor_limit; |
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| 377 | int _curr_length, _minor_count; |
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| 378 | int _next_arc; |
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| 379 | |
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| 380 | public: |
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| 381 | |
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| 382 | /// Constructor |
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| 383 | CandidateListPivotRule(NetworkSimplex &ns) : |
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[650] | 384 | _source(ns._source), _target(ns._target), |
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[648] | 385 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[650] | 386 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[648] | 387 | { |
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| 388 | // The main parameters of the pivot rule |
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| 389 | const double LIST_LENGTH_FACTOR = 1.0; |
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| 390 | const int MIN_LIST_LENGTH = 10; |
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| 391 | const double MINOR_LIMIT_FACTOR = 0.1; |
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| 392 | const int MIN_MINOR_LIMIT = 3; |
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| 393 | |
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| 394 | _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)), |
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| 395 | MIN_LIST_LENGTH ); |
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| 396 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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| 397 | MIN_MINOR_LIMIT ); |
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| 398 | _curr_length = _minor_count = 0; |
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| 399 | _candidates.resize(_list_length); |
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| 400 | } |
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| 401 | |
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| 402 | /// Find next entering arc |
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| 403 | bool findEnteringArc() { |
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[654] | 404 | Cost min, c; |
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[648] | 405 | int e, min_arc = _next_arc; |
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| 406 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
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| 407 | // Minor iteration: select the best eligible arc from the |
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| 408 | // current candidate list |
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| 409 | ++_minor_count; |
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| 410 | min = 0; |
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| 411 | for (int i = 0; i < _curr_length; ++i) { |
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| 412 | e = _candidates[i]; |
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| 413 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 414 | if (c < min) { |
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| 415 | min = c; |
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| 416 | min_arc = e; |
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| 417 | } |
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| 418 | if (c >= 0) { |
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| 419 | _candidates[i--] = _candidates[--_curr_length]; |
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| 420 | } |
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| 421 | } |
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| 422 | if (min < 0) { |
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| 423 | _in_arc = min_arc; |
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| 424 | return true; |
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| 425 | } |
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| 426 | } |
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| 427 | |
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| 428 | // Major iteration: build a new candidate list |
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| 429 | min = 0; |
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| 430 | _curr_length = 0; |
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| 431 | for (e = _next_arc; e < _arc_num; ++e) { |
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| 432 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 433 | if (c < 0) { |
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| 434 | _candidates[_curr_length++] = e; |
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| 435 | if (c < min) { |
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| 436 | min = c; |
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| 437 | min_arc = e; |
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| 438 | } |
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| 439 | if (_curr_length == _list_length) break; |
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| 440 | } |
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| 441 | } |
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| 442 | if (_curr_length < _list_length) { |
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| 443 | for (e = 0; e < _next_arc; ++e) { |
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| 444 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 445 | if (c < 0) { |
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| 446 | _candidates[_curr_length++] = e; |
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| 447 | if (c < min) { |
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| 448 | min = c; |
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| 449 | min_arc = e; |
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| 450 | } |
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| 451 | if (_curr_length == _list_length) break; |
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| 452 | } |
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| 453 | } |
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| 454 | } |
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| 455 | if (_curr_length == 0) return false; |
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| 456 | _minor_count = 1; |
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| 457 | _in_arc = min_arc; |
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| 458 | _next_arc = e; |
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| 459 | return true; |
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| 460 | } |
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| 461 | |
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| 462 | }; //class CandidateListPivotRule |
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| 463 | |
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| 464 | |
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[652] | 465 | // Implementation of the Altering Candidate List pivot rule |
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[648] | 466 | class AlteringListPivotRule |
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| 467 | { |
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| 468 | private: |
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| 469 | |
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| 470 | // References to the NetworkSimplex class |
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| 471 | const IntVector &_source; |
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| 472 | const IntVector &_target; |
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[654] | 473 | const CostVector &_cost; |
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[648] | 474 | const IntVector &_state; |
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[654] | 475 | const CostVector &_pi; |
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[648] | 476 | int &_in_arc; |
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| 477 | int _arc_num; |
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| 478 | |
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| 479 | // Pivot rule data |
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| 480 | int _block_size, _head_length, _curr_length; |
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| 481 | int _next_arc; |
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| 482 | IntVector _candidates; |
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[654] | 483 | CostVector _cand_cost; |
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[648] | 484 | |
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| 485 | // Functor class to compare arcs during sort of the candidate list |
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| 486 | class SortFunc |
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| 487 | { |
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| 488 | private: |
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[654] | 489 | const CostVector &_map; |
---|
[648] | 490 | public: |
---|
[654] | 491 | SortFunc(const CostVector &map) : _map(map) {} |
---|
[648] | 492 | bool operator()(int left, int right) { |
---|
| 493 | return _map[left] > _map[right]; |
---|
| 494 | } |
---|
| 495 | }; |
---|
| 496 | |
---|
| 497 | SortFunc _sort_func; |
---|
| 498 | |
---|
| 499 | public: |
---|
| 500 | |
---|
[652] | 501 | // Constructor |
---|
[648] | 502 | AlteringListPivotRule(NetworkSimplex &ns) : |
---|
[650] | 503 | _source(ns._source), _target(ns._target), |
---|
[648] | 504 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
[650] | 505 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), |
---|
[648] | 506 | _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) |
---|
| 507 | { |
---|
| 508 | // The main parameters of the pivot rule |
---|
| 509 | const double BLOCK_SIZE_FACTOR = 1.5; |
---|
| 510 | const int MIN_BLOCK_SIZE = 10; |
---|
| 511 | const double HEAD_LENGTH_FACTOR = 0.1; |
---|
| 512 | const int MIN_HEAD_LENGTH = 3; |
---|
| 513 | |
---|
| 514 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
---|
| 515 | MIN_BLOCK_SIZE ); |
---|
| 516 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
---|
| 517 | MIN_HEAD_LENGTH ); |
---|
| 518 | _candidates.resize(_head_length + _block_size); |
---|
| 519 | _curr_length = 0; |
---|
| 520 | } |
---|
| 521 | |
---|
[652] | 522 | // Find next entering arc |
---|
[648] | 523 | bool findEnteringArc() { |
---|
| 524 | // Check the current candidate list |
---|
| 525 | int e; |
---|
| 526 | for (int i = 0; i < _curr_length; ++i) { |
---|
| 527 | e = _candidates[i]; |
---|
| 528 | _cand_cost[e] = _state[e] * |
---|
| 529 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 530 | if (_cand_cost[e] >= 0) { |
---|
| 531 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 532 | } |
---|
| 533 | } |
---|
| 534 | |
---|
| 535 | // Extend the list |
---|
| 536 | int cnt = _block_size; |
---|
[650] | 537 | int last_arc = 0; |
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[648] | 538 | int limit = _head_length; |
---|
| 539 | |
---|
| 540 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
| 541 | _cand_cost[e] = _state[e] * |
---|
| 542 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 543 | if (_cand_cost[e] < 0) { |
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| 544 | _candidates[_curr_length++] = e; |
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[650] | 545 | last_arc = e; |
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[648] | 546 | } |
---|
| 547 | if (--cnt == 0) { |
---|
| 548 | if (_curr_length > limit) break; |
---|
| 549 | limit = 0; |
---|
| 550 | cnt = _block_size; |
---|
| 551 | } |
---|
| 552 | } |
---|
| 553 | if (_curr_length <= limit) { |
---|
| 554 | for (int e = 0; e < _next_arc; ++e) { |
---|
| 555 | _cand_cost[e] = _state[e] * |
---|
| 556 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 557 | if (_cand_cost[e] < 0) { |
---|
| 558 | _candidates[_curr_length++] = e; |
---|
[650] | 559 | last_arc = e; |
---|
[648] | 560 | } |
---|
| 561 | if (--cnt == 0) { |
---|
| 562 | if (_curr_length > limit) break; |
---|
| 563 | limit = 0; |
---|
| 564 | cnt = _block_size; |
---|
| 565 | } |
---|
| 566 | } |
---|
| 567 | } |
---|
| 568 | if (_curr_length == 0) return false; |
---|
[650] | 569 | _next_arc = last_arc + 1; |
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[648] | 570 | |
---|
| 571 | // Make heap of the candidate list (approximating a partial sort) |
---|
| 572 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 573 | _sort_func ); |
---|
| 574 | |
---|
| 575 | // Pop the first element of the heap |
---|
| 576 | _in_arc = _candidates[0]; |
---|
| 577 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 578 | _sort_func ); |
---|
| 579 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
| 580 | return true; |
---|
| 581 | } |
---|
| 582 | |
---|
| 583 | }; //class AlteringListPivotRule |
---|
| 584 | |
---|
| 585 | public: |
---|
| 586 | |
---|
[652] | 587 | /// \brief Constructor. |
---|
[648] | 588 | /// |
---|
[652] | 589 | /// Constructor. |
---|
[648] | 590 | /// |
---|
[650] | 591 | /// \param graph The digraph the algorithm runs on. |
---|
[652] | 592 | NetworkSimplex(const GR& graph) : |
---|
| 593 | _graph(graph), |
---|
| 594 | _plower(NULL), _pupper(NULL), _pcost(NULL), |
---|
| 595 | _psupply(NULL), _pstsup(false), |
---|
[650] | 596 | _flow_map(NULL), _potential_map(NULL), |
---|
[648] | 597 | _local_flow(false), _local_potential(false), |
---|
[650] | 598 | _node_id(graph) |
---|
[652] | 599 | { |
---|
[654] | 600 | LEMON_ASSERT(std::numeric_limits<Flow>::is_integer && |
---|
| 601 | std::numeric_limits<Flow>::is_signed, |
---|
| 602 | "The flow type of NetworkSimplex must be signed integer"); |
---|
| 603 | LEMON_ASSERT(std::numeric_limits<Cost>::is_integer && |
---|
| 604 | std::numeric_limits<Cost>::is_signed, |
---|
| 605 | "The cost type of NetworkSimplex must be signed integer"); |
---|
[652] | 606 | } |
---|
[648] | 607 | |
---|
| 608 | /// Destructor. |
---|
| 609 | ~NetworkSimplex() { |
---|
[650] | 610 | if (_local_flow) delete _flow_map; |
---|
| 611 | if (_local_potential) delete _potential_map; |
---|
[648] | 612 | } |
---|
| 613 | |
---|
[652] | 614 | /// \brief Set the lower bounds on the arcs. |
---|
| 615 | /// |
---|
| 616 | /// This function sets the lower bounds on the arcs. |
---|
| 617 | /// If neither this function nor \ref boundMaps() is used before |
---|
| 618 | /// calling \ref run(), the lower bounds will be set to zero |
---|
| 619 | /// on all arcs. |
---|
| 620 | /// |
---|
| 621 | /// \param map An arc map storing the lower bounds. |
---|
[654] | 622 | /// Its \c Value type must be convertible to the \c Flow type |
---|
[652] | 623 | /// of the algorithm. |
---|
| 624 | /// |
---|
| 625 | /// \return <tt>(*this)</tt> |
---|
| 626 | template <typename LOWER> |
---|
| 627 | NetworkSimplex& lowerMap(const LOWER& map) { |
---|
| 628 | delete _plower; |
---|
[654] | 629 | _plower = new FlowArcMap(_graph); |
---|
[652] | 630 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 631 | (*_plower)[a] = map[a]; |
---|
| 632 | } |
---|
| 633 | return *this; |
---|
| 634 | } |
---|
| 635 | |
---|
| 636 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
| 637 | /// |
---|
| 638 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
| 639 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
| 640 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
| 641 | /// the upper bounds (capacities) will be set to |
---|
[654] | 642 | /// \c std::numeric_limits<Flow>::max() on all arcs. |
---|
[652] | 643 | /// |
---|
| 644 | /// \param map An arc map storing the upper bounds. |
---|
[654] | 645 | /// Its \c Value type must be convertible to the \c Flow type |
---|
[652] | 646 | /// of the algorithm. |
---|
| 647 | /// |
---|
| 648 | /// \return <tt>(*this)</tt> |
---|
| 649 | template<typename UPPER> |
---|
| 650 | NetworkSimplex& upperMap(const UPPER& map) { |
---|
| 651 | delete _pupper; |
---|
[654] | 652 | _pupper = new FlowArcMap(_graph); |
---|
[652] | 653 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 654 | (*_pupper)[a] = map[a]; |
---|
| 655 | } |
---|
| 656 | return *this; |
---|
| 657 | } |
---|
| 658 | |
---|
| 659 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
| 660 | /// |
---|
| 661 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
| 662 | /// It is just an alias for \ref upperMap(). |
---|
| 663 | /// |
---|
| 664 | /// \return <tt>(*this)</tt> |
---|
| 665 | template<typename CAP> |
---|
| 666 | NetworkSimplex& capacityMap(const CAP& map) { |
---|
| 667 | return upperMap(map); |
---|
| 668 | } |
---|
| 669 | |
---|
| 670 | /// \brief Set the lower and upper bounds on the arcs. |
---|
| 671 | /// |
---|
| 672 | /// This function sets the lower and upper bounds on the arcs. |
---|
| 673 | /// If neither this function nor \ref lowerMap() is used before |
---|
| 674 | /// calling \ref run(), the lower bounds will be set to zero |
---|
| 675 | /// on all arcs. |
---|
| 676 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
| 677 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
| 678 | /// the upper bounds (capacities) will be set to |
---|
[654] | 679 | /// \c std::numeric_limits<Flow>::max() on all arcs. |
---|
[652] | 680 | /// |
---|
| 681 | /// \param lower An arc map storing the lower bounds. |
---|
| 682 | /// \param upper An arc map storing the upper bounds. |
---|
| 683 | /// |
---|
| 684 | /// The \c Value type of the maps must be convertible to the |
---|
[654] | 685 | /// \c Flow type of the algorithm. |
---|
[652] | 686 | /// |
---|
| 687 | /// \note This function is just a shortcut of calling \ref lowerMap() |
---|
| 688 | /// and \ref upperMap() separately. |
---|
| 689 | /// |
---|
| 690 | /// \return <tt>(*this)</tt> |
---|
| 691 | template <typename LOWER, typename UPPER> |
---|
| 692 | NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) { |
---|
| 693 | return lowerMap(lower).upperMap(upper); |
---|
| 694 | } |
---|
| 695 | |
---|
| 696 | /// \brief Set the costs of the arcs. |
---|
| 697 | /// |
---|
| 698 | /// This function sets the costs of the arcs. |
---|
| 699 | /// If it is not used before calling \ref run(), the costs |
---|
| 700 | /// will be set to \c 1 on all arcs. |
---|
| 701 | /// |
---|
| 702 | /// \param map An arc map storing the costs. |
---|
[654] | 703 | /// Its \c Value type must be convertible to the \c Cost type |
---|
[652] | 704 | /// of the algorithm. |
---|
| 705 | /// |
---|
| 706 | /// \return <tt>(*this)</tt> |
---|
| 707 | template<typename COST> |
---|
| 708 | NetworkSimplex& costMap(const COST& map) { |
---|
| 709 | delete _pcost; |
---|
[654] | 710 | _pcost = new CostArcMap(_graph); |
---|
[652] | 711 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 712 | (*_pcost)[a] = map[a]; |
---|
| 713 | } |
---|
| 714 | return *this; |
---|
| 715 | } |
---|
| 716 | |
---|
| 717 | /// \brief Set the supply values of the nodes. |
---|
| 718 | /// |
---|
| 719 | /// This function sets the supply values of the nodes. |
---|
| 720 | /// If neither this function nor \ref stSupply() is used before |
---|
| 721 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 722 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
| 723 | /// |
---|
| 724 | /// \param map A node map storing the supply values. |
---|
[654] | 725 | /// Its \c Value type must be convertible to the \c Flow type |
---|
[652] | 726 | /// of the algorithm. |
---|
| 727 | /// |
---|
| 728 | /// \return <tt>(*this)</tt> |
---|
| 729 | template<typename SUP> |
---|
| 730 | NetworkSimplex& supplyMap(const SUP& map) { |
---|
| 731 | delete _psupply; |
---|
| 732 | _pstsup = false; |
---|
[654] | 733 | _psupply = new FlowNodeMap(_graph); |
---|
[652] | 734 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 735 | (*_psupply)[n] = map[n]; |
---|
| 736 | } |
---|
| 737 | return *this; |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | /// \brief Set single source and target nodes and a supply value. |
---|
| 741 | /// |
---|
| 742 | /// This function sets a single source node and a single target node |
---|
| 743 | /// and the required flow value. |
---|
| 744 | /// If neither this function nor \ref supplyMap() is used before |
---|
| 745 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 746 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
| 747 | /// |
---|
| 748 | /// \param s The source node. |
---|
| 749 | /// \param t The target node. |
---|
| 750 | /// \param k The required amount of flow from node \c s to node \c t |
---|
| 751 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
| 752 | /// |
---|
| 753 | /// \return <tt>(*this)</tt> |
---|
[654] | 754 | NetworkSimplex& stSupply(const Node& s, const Node& t, Flow k) { |
---|
[652] | 755 | delete _psupply; |
---|
| 756 | _psupply = NULL; |
---|
| 757 | _pstsup = true; |
---|
| 758 | _psource = s; |
---|
| 759 | _ptarget = t; |
---|
| 760 | _pstflow = k; |
---|
| 761 | return *this; |
---|
| 762 | } |
---|
| 763 | |
---|
[648] | 764 | /// \brief Set the flow map. |
---|
| 765 | /// |
---|
| 766 | /// This function sets the flow map. |
---|
[652] | 767 | /// If it is not used before calling \ref run(), an instance will |
---|
| 768 | /// be allocated automatically. The destructor deallocates this |
---|
| 769 | /// automatically allocated map, of course. |
---|
[648] | 770 | /// |
---|
| 771 | /// \return <tt>(*this)</tt> |
---|
[652] | 772 | NetworkSimplex& flowMap(FlowMap& map) { |
---|
[648] | 773 | if (_local_flow) { |
---|
[650] | 774 | delete _flow_map; |
---|
[648] | 775 | _local_flow = false; |
---|
| 776 | } |
---|
[650] | 777 | _flow_map = ↦ |
---|
[648] | 778 | return *this; |
---|
| 779 | } |
---|
| 780 | |
---|
| 781 | /// \brief Set the potential map. |
---|
| 782 | /// |
---|
[652] | 783 | /// This function sets the potential map, which is used for storing |
---|
| 784 | /// the dual solution. |
---|
| 785 | /// If it is not used before calling \ref run(), an instance will |
---|
| 786 | /// be allocated automatically. The destructor deallocates this |
---|
| 787 | /// automatically allocated map, of course. |
---|
[648] | 788 | /// |
---|
| 789 | /// \return <tt>(*this)</tt> |
---|
[652] | 790 | NetworkSimplex& potentialMap(PotentialMap& map) { |
---|
[648] | 791 | if (_local_potential) { |
---|
[650] | 792 | delete _potential_map; |
---|
[648] | 793 | _local_potential = false; |
---|
| 794 | } |
---|
[650] | 795 | _potential_map = ↦ |
---|
[648] | 796 | return *this; |
---|
| 797 | } |
---|
| 798 | |
---|
[652] | 799 | /// \name Execution Control |
---|
| 800 | /// The algorithm can be executed using \ref run(). |
---|
| 801 | |
---|
[648] | 802 | /// @{ |
---|
| 803 | |
---|
| 804 | /// \brief Run the algorithm. |
---|
| 805 | /// |
---|
| 806 | /// This function runs the algorithm. |
---|
[652] | 807 | /// The paramters can be specified using \ref lowerMap(), |
---|
[653] | 808 | /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), |
---|
[652] | 809 | /// \ref costMap(), \ref supplyMap() and \ref stSupply() |
---|
| 810 | /// functions. For example, |
---|
| 811 | /// \code |
---|
| 812 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
| 813 | /// ns.boundMaps(lower, upper).costMap(cost) |
---|
| 814 | /// .supplyMap(sup).run(); |
---|
| 815 | /// \endcode |
---|
[648] | 816 | /// |
---|
[653] | 817 | /// This function can be called more than once. All the parameters |
---|
| 818 | /// that have been given are kept for the next call, unless |
---|
| 819 | /// \ref reset() is called, thus only the modified parameters |
---|
| 820 | /// have to be set again. See \ref reset() for examples. |
---|
| 821 | /// |
---|
[652] | 822 | /// \param pivot_rule The pivot rule that will be used during the |
---|
| 823 | /// algorithm. For more information see \ref PivotRule. |
---|
[648] | 824 | /// |
---|
| 825 | /// \return \c true if a feasible flow can be found. |
---|
[652] | 826 | bool run(PivotRule pivot_rule = BLOCK_SEARCH) { |
---|
[648] | 827 | return init() && start(pivot_rule); |
---|
| 828 | } |
---|
| 829 | |
---|
[653] | 830 | /// \brief Reset all the parameters that have been given before. |
---|
| 831 | /// |
---|
| 832 | /// This function resets all the paramaters that have been given |
---|
| 833 | /// using \ref lowerMap(), \ref upperMap(), \ref capacityMap(), |
---|
| 834 | /// \ref boundMaps(), \ref costMap(), \ref supplyMap() and |
---|
| 835 | /// \ref stSupply() functions before. |
---|
| 836 | /// |
---|
| 837 | /// It is useful for multiple run() calls. If this function is not |
---|
| 838 | /// used, all the parameters given before are kept for the next |
---|
| 839 | /// \ref run() call. |
---|
| 840 | /// |
---|
| 841 | /// For example, |
---|
| 842 | /// \code |
---|
| 843 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
| 844 | /// |
---|
| 845 | /// // First run |
---|
| 846 | /// ns.lowerMap(lower).capacityMap(cap).costMap(cost) |
---|
| 847 | /// .supplyMap(sup).run(); |
---|
| 848 | /// |
---|
| 849 | /// // Run again with modified cost map (reset() is not called, |
---|
| 850 | /// // so only the cost map have to be set again) |
---|
| 851 | /// cost[e] += 100; |
---|
| 852 | /// ns.costMap(cost).run(); |
---|
| 853 | /// |
---|
| 854 | /// // Run again from scratch using reset() |
---|
| 855 | /// // (the lower bounds will be set to zero on all arcs) |
---|
| 856 | /// ns.reset(); |
---|
| 857 | /// ns.capacityMap(cap).costMap(cost) |
---|
| 858 | /// .supplyMap(sup).run(); |
---|
| 859 | /// \endcode |
---|
| 860 | /// |
---|
| 861 | /// \return <tt>(*this)</tt> |
---|
| 862 | NetworkSimplex& reset() { |
---|
| 863 | delete _plower; |
---|
| 864 | delete _pupper; |
---|
| 865 | delete _pcost; |
---|
| 866 | delete _psupply; |
---|
| 867 | _plower = NULL; |
---|
| 868 | _pupper = NULL; |
---|
| 869 | _pcost = NULL; |
---|
| 870 | _psupply = NULL; |
---|
| 871 | _pstsup = false; |
---|
| 872 | return *this; |
---|
| 873 | } |
---|
| 874 | |
---|
[648] | 875 | /// @} |
---|
| 876 | |
---|
| 877 | /// \name Query Functions |
---|
| 878 | /// The results of the algorithm can be obtained using these |
---|
| 879 | /// functions.\n |
---|
[652] | 880 | /// The \ref run() function must be called before using them. |
---|
| 881 | |
---|
[648] | 882 | /// @{ |
---|
| 883 | |
---|
[652] | 884 | /// \brief Return the total cost of the found flow. |
---|
| 885 | /// |
---|
| 886 | /// This function returns the total cost of the found flow. |
---|
[654] | 887 | /// The complexity of the function is O(e). |
---|
[652] | 888 | /// |
---|
| 889 | /// \note The return type of the function can be specified as a |
---|
| 890 | /// template parameter. For example, |
---|
| 891 | /// \code |
---|
| 892 | /// ns.totalCost<double>(); |
---|
| 893 | /// \endcode |
---|
[654] | 894 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
[652] | 895 | /// type of the algorithm, which is the default return type of the |
---|
| 896 | /// function. |
---|
| 897 | /// |
---|
| 898 | /// \pre \ref run() must be called before using this function. |
---|
| 899 | template <typename Num> |
---|
| 900 | Num totalCost() const { |
---|
| 901 | Num c = 0; |
---|
| 902 | if (_pcost) { |
---|
| 903 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 904 | c += (*_flow_map)[e] * (*_pcost)[e]; |
---|
| 905 | } else { |
---|
| 906 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 907 | c += (*_flow_map)[e]; |
---|
| 908 | } |
---|
| 909 | return c; |
---|
| 910 | } |
---|
| 911 | |
---|
| 912 | #ifndef DOXYGEN |
---|
[654] | 913 | Cost totalCost() const { |
---|
| 914 | return totalCost<Cost>(); |
---|
[652] | 915 | } |
---|
| 916 | #endif |
---|
| 917 | |
---|
| 918 | /// \brief Return the flow on the given arc. |
---|
| 919 | /// |
---|
| 920 | /// This function returns the flow on the given arc. |
---|
| 921 | /// |
---|
| 922 | /// \pre \ref run() must be called before using this function. |
---|
[654] | 923 | Flow flow(const Arc& a) const { |
---|
[652] | 924 | return (*_flow_map)[a]; |
---|
| 925 | } |
---|
| 926 | |
---|
[648] | 927 | /// \brief Return a const reference to the flow map. |
---|
| 928 | /// |
---|
| 929 | /// This function returns a const reference to an arc map storing |
---|
| 930 | /// the found flow. |
---|
| 931 | /// |
---|
| 932 | /// \pre \ref run() must be called before using this function. |
---|
| 933 | const FlowMap& flowMap() const { |
---|
[650] | 934 | return *_flow_map; |
---|
[648] | 935 | } |
---|
| 936 | |
---|
[652] | 937 | /// \brief Return the potential (dual value) of the given node. |
---|
| 938 | /// |
---|
| 939 | /// This function returns the potential (dual value) of the |
---|
| 940 | /// given node. |
---|
| 941 | /// |
---|
| 942 | /// \pre \ref run() must be called before using this function. |
---|
[654] | 943 | Cost potential(const Node& n) const { |
---|
[652] | 944 | return (*_potential_map)[n]; |
---|
| 945 | } |
---|
| 946 | |
---|
[648] | 947 | /// \brief Return a const reference to the potential map |
---|
| 948 | /// (the dual solution). |
---|
| 949 | /// |
---|
| 950 | /// This function returns a const reference to a node map storing |
---|
[652] | 951 | /// the found potentials, which form the dual solution of the |
---|
| 952 | /// \ref min_cost_flow "minimum cost flow" problem. |
---|
[648] | 953 | /// |
---|
| 954 | /// \pre \ref run() must be called before using this function. |
---|
| 955 | const PotentialMap& potentialMap() const { |
---|
[650] | 956 | return *_potential_map; |
---|
[648] | 957 | } |
---|
| 958 | |
---|
| 959 | /// @} |
---|
| 960 | |
---|
| 961 | private: |
---|
| 962 | |
---|
| 963 | // Initialize internal data structures |
---|
| 964 | bool init() { |
---|
| 965 | // Initialize result maps |
---|
[650] | 966 | if (!_flow_map) { |
---|
| 967 | _flow_map = new FlowMap(_graph); |
---|
[648] | 968 | _local_flow = true; |
---|
| 969 | } |
---|
[650] | 970 | if (!_potential_map) { |
---|
| 971 | _potential_map = new PotentialMap(_graph); |
---|
[648] | 972 | _local_potential = true; |
---|
| 973 | } |
---|
| 974 | |
---|
| 975 | // Initialize vectors |
---|
[650] | 976 | _node_num = countNodes(_graph); |
---|
| 977 | _arc_num = countArcs(_graph); |
---|
[648] | 978 | int all_node_num = _node_num + 1; |
---|
[650] | 979 | int all_arc_num = _arc_num + _node_num; |
---|
[652] | 980 | if (_node_num == 0) return false; |
---|
[648] | 981 | |
---|
[650] | 982 | _arc_ref.resize(_arc_num); |
---|
| 983 | _source.resize(all_arc_num); |
---|
| 984 | _target.resize(all_arc_num); |
---|
[648] | 985 | |
---|
[650] | 986 | _cap.resize(all_arc_num); |
---|
| 987 | _cost.resize(all_arc_num); |
---|
[648] | 988 | _supply.resize(all_node_num); |
---|
[653] | 989 | _flow.resize(all_arc_num); |
---|
| 990 | _pi.resize(all_node_num); |
---|
[648] | 991 | |
---|
| 992 | _parent.resize(all_node_num); |
---|
| 993 | _pred.resize(all_node_num); |
---|
[650] | 994 | _forward.resize(all_node_num); |
---|
[648] | 995 | _thread.resize(all_node_num); |
---|
[651] | 996 | _rev_thread.resize(all_node_num); |
---|
| 997 | _succ_num.resize(all_node_num); |
---|
| 998 | _last_succ.resize(all_node_num); |
---|
[653] | 999 | _state.resize(all_arc_num); |
---|
[648] | 1000 | |
---|
| 1001 | // Initialize node related data |
---|
| 1002 | bool valid_supply = true; |
---|
[652] | 1003 | if (!_pstsup && !_psupply) { |
---|
| 1004 | _pstsup = true; |
---|
| 1005 | _psource = _ptarget = NodeIt(_graph); |
---|
| 1006 | _pstflow = 0; |
---|
| 1007 | } |
---|
| 1008 | if (_psupply) { |
---|
[654] | 1009 | Flow sum = 0; |
---|
[648] | 1010 | int i = 0; |
---|
[650] | 1011 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
[648] | 1012 | _node_id[n] = i; |
---|
[652] | 1013 | _supply[i] = (*_psupply)[n]; |
---|
[648] | 1014 | sum += _supply[i]; |
---|
| 1015 | } |
---|
| 1016 | valid_supply = (sum == 0); |
---|
| 1017 | } else { |
---|
| 1018 | int i = 0; |
---|
[650] | 1019 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
[648] | 1020 | _node_id[n] = i; |
---|
| 1021 | _supply[i] = 0; |
---|
| 1022 | } |
---|
[652] | 1023 | _supply[_node_id[_psource]] = _pstflow; |
---|
| 1024 | _supply[_node_id[_ptarget]] = -_pstflow; |
---|
[648] | 1025 | } |
---|
| 1026 | if (!valid_supply) return false; |
---|
| 1027 | |
---|
| 1028 | // Set data for the artificial root node |
---|
| 1029 | _root = _node_num; |
---|
| 1030 | _parent[_root] = -1; |
---|
| 1031 | _pred[_root] = -1; |
---|
| 1032 | _thread[_root] = 0; |
---|
[651] | 1033 | _rev_thread[0] = _root; |
---|
| 1034 | _succ_num[_root] = all_node_num; |
---|
| 1035 | _last_succ[_root] = _root - 1; |
---|
[648] | 1036 | _supply[_root] = 0; |
---|
| 1037 | _pi[_root] = 0; |
---|
| 1038 | |
---|
| 1039 | // Store the arcs in a mixed order |
---|
| 1040 | int k = std::max(int(sqrt(_arc_num)), 10); |
---|
| 1041 | int i = 0; |
---|
[650] | 1042 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 1043 | _arc_ref[i] = e; |
---|
[648] | 1044 | if ((i += k) >= _arc_num) i = (i % k) + 1; |
---|
| 1045 | } |
---|
| 1046 | |
---|
| 1047 | // Initialize arc maps |
---|
[655] | 1048 | Flow inf_cap = |
---|
| 1049 | std::numeric_limits<Flow>::has_infinity ? |
---|
| 1050 | std::numeric_limits<Flow>::infinity() : |
---|
| 1051 | std::numeric_limits<Flow>::max(); |
---|
[652] | 1052 | if (_pupper && _pcost) { |
---|
| 1053 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1054 | Arc e = _arc_ref[i]; |
---|
| 1055 | _source[i] = _node_id[_graph.source(e)]; |
---|
| 1056 | _target[i] = _node_id[_graph.target(e)]; |
---|
| 1057 | _cap[i] = (*_pupper)[e]; |
---|
| 1058 | _cost[i] = (*_pcost)[e]; |
---|
[653] | 1059 | _flow[i] = 0; |
---|
| 1060 | _state[i] = STATE_LOWER; |
---|
[652] | 1061 | } |
---|
| 1062 | } else { |
---|
| 1063 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1064 | Arc e = _arc_ref[i]; |
---|
| 1065 | _source[i] = _node_id[_graph.source(e)]; |
---|
| 1066 | _target[i] = _node_id[_graph.target(e)]; |
---|
[653] | 1067 | _flow[i] = 0; |
---|
| 1068 | _state[i] = STATE_LOWER; |
---|
[652] | 1069 | } |
---|
| 1070 | if (_pupper) { |
---|
| 1071 | for (int i = 0; i != _arc_num; ++i) |
---|
| 1072 | _cap[i] = (*_pupper)[_arc_ref[i]]; |
---|
| 1073 | } else { |
---|
| 1074 | for (int i = 0; i != _arc_num; ++i) |
---|
[655] | 1075 | _cap[i] = inf_cap; |
---|
[652] | 1076 | } |
---|
| 1077 | if (_pcost) { |
---|
| 1078 | for (int i = 0; i != _arc_num; ++i) |
---|
| 1079 | _cost[i] = (*_pcost)[_arc_ref[i]]; |
---|
| 1080 | } else { |
---|
| 1081 | for (int i = 0; i != _arc_num; ++i) |
---|
| 1082 | _cost[i] = 1; |
---|
| 1083 | } |
---|
[648] | 1084 | } |
---|
[655] | 1085 | |
---|
| 1086 | // Initialize artifical cost |
---|
| 1087 | Cost art_cost; |
---|
| 1088 | if (std::numeric_limits<Cost>::is_exact) { |
---|
| 1089 | art_cost = std::numeric_limits<Cost>::max() / 4 + 1; |
---|
| 1090 | } else { |
---|
| 1091 | art_cost = std::numeric_limits<Cost>::min(); |
---|
| 1092 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1093 | if (_cost[i] > art_cost) art_cost = _cost[i]; |
---|
| 1094 | } |
---|
| 1095 | art_cost = (art_cost + 1) * _node_num; |
---|
| 1096 | } |
---|
[648] | 1097 | |
---|
| 1098 | // Remove non-zero lower bounds |
---|
[652] | 1099 | if (_plower) { |
---|
[648] | 1100 | for (int i = 0; i != _arc_num; ++i) { |
---|
[654] | 1101 | Flow c = (*_plower)[_arc_ref[i]]; |
---|
[648] | 1102 | if (c != 0) { |
---|
| 1103 | _cap[i] -= c; |
---|
| 1104 | _supply[_source[i]] -= c; |
---|
| 1105 | _supply[_target[i]] += c; |
---|
| 1106 | } |
---|
| 1107 | } |
---|
| 1108 | } |
---|
| 1109 | |
---|
| 1110 | // Add artificial arcs and initialize the spanning tree data structure |
---|
| 1111 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1112 | _thread[u] = u + 1; |
---|
[651] | 1113 | _rev_thread[u + 1] = u; |
---|
| 1114 | _succ_num[u] = 1; |
---|
| 1115 | _last_succ[u] = u; |
---|
[648] | 1116 | _parent[u] = _root; |
---|
| 1117 | _pred[u] = e; |
---|
[655] | 1118 | _cost[e] = art_cost; |
---|
| 1119 | _cap[e] = inf_cap; |
---|
[653] | 1120 | _state[e] = STATE_TREE; |
---|
[648] | 1121 | if (_supply[u] >= 0) { |
---|
| 1122 | _flow[e] = _supply[u]; |
---|
| 1123 | _forward[u] = true; |
---|
[655] | 1124 | _pi[u] = -art_cost; |
---|
[648] | 1125 | } else { |
---|
| 1126 | _flow[e] = -_supply[u]; |
---|
| 1127 | _forward[u] = false; |
---|
[655] | 1128 | _pi[u] = art_cost; |
---|
[648] | 1129 | } |
---|
| 1130 | } |
---|
| 1131 | |
---|
| 1132 | return true; |
---|
| 1133 | } |
---|
| 1134 | |
---|
| 1135 | // Find the join node |
---|
| 1136 | void findJoinNode() { |
---|
[650] | 1137 | int u = _source[in_arc]; |
---|
| 1138 | int v = _target[in_arc]; |
---|
[648] | 1139 | while (u != v) { |
---|
[651] | 1140 | if (_succ_num[u] < _succ_num[v]) { |
---|
| 1141 | u = _parent[u]; |
---|
| 1142 | } else { |
---|
| 1143 | v = _parent[v]; |
---|
| 1144 | } |
---|
[648] | 1145 | } |
---|
| 1146 | join = u; |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | // Find the leaving arc of the cycle and returns true if the |
---|
| 1150 | // leaving arc is not the same as the entering arc |
---|
| 1151 | bool findLeavingArc() { |
---|
| 1152 | // Initialize first and second nodes according to the direction |
---|
| 1153 | // of the cycle |
---|
[650] | 1154 | if (_state[in_arc] == STATE_LOWER) { |
---|
| 1155 | first = _source[in_arc]; |
---|
| 1156 | second = _target[in_arc]; |
---|
[648] | 1157 | } else { |
---|
[650] | 1158 | first = _target[in_arc]; |
---|
| 1159 | second = _source[in_arc]; |
---|
[648] | 1160 | } |
---|
[650] | 1161 | delta = _cap[in_arc]; |
---|
[648] | 1162 | int result = 0; |
---|
[654] | 1163 | Flow d; |
---|
[648] | 1164 | int e; |
---|
| 1165 | |
---|
| 1166 | // Search the cycle along the path form the first node to the root |
---|
| 1167 | for (int u = first; u != join; u = _parent[u]) { |
---|
| 1168 | e = _pred[u]; |
---|
| 1169 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
| 1170 | if (d < delta) { |
---|
| 1171 | delta = d; |
---|
| 1172 | u_out = u; |
---|
| 1173 | result = 1; |
---|
| 1174 | } |
---|
| 1175 | } |
---|
| 1176 | // Search the cycle along the path form the second node to the root |
---|
| 1177 | for (int u = second; u != join; u = _parent[u]) { |
---|
| 1178 | e = _pred[u]; |
---|
| 1179 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
| 1180 | if (d <= delta) { |
---|
| 1181 | delta = d; |
---|
| 1182 | u_out = u; |
---|
| 1183 | result = 2; |
---|
| 1184 | } |
---|
| 1185 | } |
---|
| 1186 | |
---|
| 1187 | if (result == 1) { |
---|
| 1188 | u_in = first; |
---|
| 1189 | v_in = second; |
---|
| 1190 | } else { |
---|
| 1191 | u_in = second; |
---|
| 1192 | v_in = first; |
---|
| 1193 | } |
---|
| 1194 | return result != 0; |
---|
| 1195 | } |
---|
| 1196 | |
---|
| 1197 | // Change _flow and _state vectors |
---|
| 1198 | void changeFlow(bool change) { |
---|
| 1199 | // Augment along the cycle |
---|
| 1200 | if (delta > 0) { |
---|
[654] | 1201 | Flow val = _state[in_arc] * delta; |
---|
[650] | 1202 | _flow[in_arc] += val; |
---|
| 1203 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
[648] | 1204 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
| 1205 | } |
---|
[650] | 1206 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
[648] | 1207 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
| 1208 | } |
---|
| 1209 | } |
---|
| 1210 | // Update the state of the entering and leaving arcs |
---|
| 1211 | if (change) { |
---|
[650] | 1212 | _state[in_arc] = STATE_TREE; |
---|
[648] | 1213 | _state[_pred[u_out]] = |
---|
| 1214 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
| 1215 | } else { |
---|
[650] | 1216 | _state[in_arc] = -_state[in_arc]; |
---|
[648] | 1217 | } |
---|
| 1218 | } |
---|
| 1219 | |
---|
[651] | 1220 | // Update the tree structure |
---|
| 1221 | void updateTreeStructure() { |
---|
| 1222 | int u, w; |
---|
| 1223 | int old_rev_thread = _rev_thread[u_out]; |
---|
| 1224 | int old_succ_num = _succ_num[u_out]; |
---|
| 1225 | int old_last_succ = _last_succ[u_out]; |
---|
[648] | 1226 | v_out = _parent[u_out]; |
---|
| 1227 | |
---|
[651] | 1228 | u = _last_succ[u_in]; // the last successor of u_in |
---|
| 1229 | right = _thread[u]; // the node after it |
---|
| 1230 | |
---|
| 1231 | // Handle the case when old_rev_thread equals to v_in |
---|
| 1232 | // (it also means that join and v_out coincide) |
---|
| 1233 | if (old_rev_thread == v_in) { |
---|
| 1234 | last = _thread[_last_succ[u_out]]; |
---|
| 1235 | } else { |
---|
| 1236 | last = _thread[v_in]; |
---|
[648] | 1237 | } |
---|
| 1238 | |
---|
[651] | 1239 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
| 1240 | // between u_in and u_out, whose parent have to be changed) |
---|
[648] | 1241 | _thread[v_in] = stem = u_in; |
---|
[651] | 1242 | _dirty_revs.clear(); |
---|
| 1243 | _dirty_revs.push_back(v_in); |
---|
[648] | 1244 | par_stem = v_in; |
---|
| 1245 | while (stem != u_out) { |
---|
[651] | 1246 | // Insert the next stem node into the thread list |
---|
| 1247 | new_stem = _parent[stem]; |
---|
| 1248 | _thread[u] = new_stem; |
---|
| 1249 | _dirty_revs.push_back(u); |
---|
[648] | 1250 | |
---|
[651] | 1251 | // Remove the subtree of stem from the thread list |
---|
| 1252 | w = _rev_thread[stem]; |
---|
| 1253 | _thread[w] = right; |
---|
| 1254 | _rev_thread[right] = w; |
---|
[648] | 1255 | |
---|
[651] | 1256 | // Change the parent node and shift stem nodes |
---|
[648] | 1257 | _parent[stem] = par_stem; |
---|
| 1258 | par_stem = stem; |
---|
| 1259 | stem = new_stem; |
---|
| 1260 | |
---|
[651] | 1261 | // Update u and right |
---|
| 1262 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
| 1263 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
[648] | 1264 | right = _thread[u]; |
---|
| 1265 | } |
---|
| 1266 | _parent[u_out] = par_stem; |
---|
| 1267 | _thread[u] = last; |
---|
[651] | 1268 | _rev_thread[last] = u; |
---|
| 1269 | _last_succ[u_out] = u; |
---|
[648] | 1270 | |
---|
[651] | 1271 | // Remove the subtree of u_out from the thread list except for |
---|
| 1272 | // the case when old_rev_thread equals to v_in |
---|
| 1273 | // (it also means that join and v_out coincide) |
---|
| 1274 | if (old_rev_thread != v_in) { |
---|
| 1275 | _thread[old_rev_thread] = right; |
---|
| 1276 | _rev_thread[right] = old_rev_thread; |
---|
| 1277 | } |
---|
| 1278 | |
---|
| 1279 | // Update _rev_thread using the new _thread values |
---|
| 1280 | for (int i = 0; i < int(_dirty_revs.size()); ++i) { |
---|
| 1281 | u = _dirty_revs[i]; |
---|
| 1282 | _rev_thread[_thread[u]] = u; |
---|
| 1283 | } |
---|
| 1284 | |
---|
| 1285 | // Update _pred, _forward, _last_succ and _succ_num for the |
---|
| 1286 | // stem nodes from u_out to u_in |
---|
| 1287 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
| 1288 | u = u_out; |
---|
| 1289 | while (u != u_in) { |
---|
| 1290 | w = _parent[u]; |
---|
| 1291 | _pred[u] = _pred[w]; |
---|
| 1292 | _forward[u] = !_forward[w]; |
---|
| 1293 | tmp_sc += _succ_num[u] - _succ_num[w]; |
---|
| 1294 | _succ_num[u] = tmp_sc; |
---|
| 1295 | _last_succ[w] = tmp_ls; |
---|
| 1296 | u = w; |
---|
| 1297 | } |
---|
| 1298 | _pred[u_in] = in_arc; |
---|
| 1299 | _forward[u_in] = (u_in == _source[in_arc]); |
---|
| 1300 | _succ_num[u_in] = old_succ_num; |
---|
| 1301 | |
---|
| 1302 | // Set limits for updating _last_succ form v_in and v_out |
---|
| 1303 | // towards the root |
---|
| 1304 | int up_limit_in = -1; |
---|
| 1305 | int up_limit_out = -1; |
---|
| 1306 | if (_last_succ[join] == v_in) { |
---|
| 1307 | up_limit_out = join; |
---|
[648] | 1308 | } else { |
---|
[651] | 1309 | up_limit_in = join; |
---|
| 1310 | } |
---|
| 1311 | |
---|
| 1312 | // Update _last_succ from v_in towards the root |
---|
| 1313 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
| 1314 | u = _parent[u]) { |
---|
| 1315 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1316 | } |
---|
| 1317 | // Update _last_succ from v_out towards the root |
---|
| 1318 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
| 1319 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1320 | u = _parent[u]) { |
---|
| 1321 | _last_succ[u] = old_rev_thread; |
---|
| 1322 | } |
---|
| 1323 | } else { |
---|
| 1324 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1325 | u = _parent[u]) { |
---|
| 1326 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1327 | } |
---|
| 1328 | } |
---|
| 1329 | |
---|
| 1330 | // Update _succ_num from v_in to join |
---|
| 1331 | for (u = v_in; u != join; u = _parent[u]) { |
---|
| 1332 | _succ_num[u] += old_succ_num; |
---|
| 1333 | } |
---|
| 1334 | // Update _succ_num from v_out to join |
---|
| 1335 | for (u = v_out; u != join; u = _parent[u]) { |
---|
| 1336 | _succ_num[u] -= old_succ_num; |
---|
[648] | 1337 | } |
---|
| 1338 | } |
---|
| 1339 | |
---|
[651] | 1340 | // Update potentials |
---|
| 1341 | void updatePotential() { |
---|
[654] | 1342 | Cost sigma = _forward[u_in] ? |
---|
[648] | 1343 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
| 1344 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
[655] | 1345 | // Update potentials in the subtree, which has been moved |
---|
| 1346 | int end = _thread[_last_succ[u_in]]; |
---|
| 1347 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
| 1348 | _pi[u] += sigma; |
---|
[648] | 1349 | } |
---|
| 1350 | } |
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| 1351 | |
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| 1352 | // Execute the algorithm |
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[652] | 1353 | bool start(PivotRule pivot_rule) { |
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[648] | 1354 | // Select the pivot rule implementation |
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| 1355 | switch (pivot_rule) { |
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[652] | 1356 | case FIRST_ELIGIBLE: |
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[648] | 1357 | return start<FirstEligiblePivotRule>(); |
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[652] | 1358 | case BEST_ELIGIBLE: |
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[648] | 1359 | return start<BestEligiblePivotRule>(); |
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[652] | 1360 | case BLOCK_SEARCH: |
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[648] | 1361 | return start<BlockSearchPivotRule>(); |
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[652] | 1362 | case CANDIDATE_LIST: |
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[648] | 1363 | return start<CandidateListPivotRule>(); |
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[652] | 1364 | case ALTERING_LIST: |
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[648] | 1365 | return start<AlteringListPivotRule>(); |
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| 1366 | } |
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| 1367 | return false; |
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| 1368 | } |
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| 1369 | |
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[652] | 1370 | template <typename PivotRuleImpl> |
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[648] | 1371 | bool start() { |
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[652] | 1372 | PivotRuleImpl pivot(*this); |
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[648] | 1373 | |
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[652] | 1374 | // Execute the Network Simplex algorithm |
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[648] | 1375 | while (pivot.findEnteringArc()) { |
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| 1376 | findJoinNode(); |
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| 1377 | bool change = findLeavingArc(); |
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| 1378 | changeFlow(change); |
---|
| 1379 | if (change) { |
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[651] | 1380 | updateTreeStructure(); |
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| 1381 | updatePotential(); |
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[648] | 1382 | } |
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| 1383 | } |
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| 1384 | |
---|
| 1385 | // Check if the flow amount equals zero on all the artificial arcs |
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| 1386 | for (int e = _arc_num; e != _arc_num + _node_num; ++e) { |
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| 1387 | if (_flow[e] > 0) return false; |
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| 1388 | } |
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| 1389 | |
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[650] | 1390 | // Copy flow values to _flow_map |
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[652] | 1391 | if (_plower) { |
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[648] | 1392 | for (int i = 0; i != _arc_num; ++i) { |
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[650] | 1393 | Arc e = _arc_ref[i]; |
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[652] | 1394 | _flow_map->set(e, (*_plower)[e] + _flow[i]); |
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[648] | 1395 | } |
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| 1396 | } else { |
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| 1397 | for (int i = 0; i != _arc_num; ++i) { |
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[650] | 1398 | _flow_map->set(_arc_ref[i], _flow[i]); |
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[648] | 1399 | } |
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| 1400 | } |
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[650] | 1401 | // Copy potential values to _potential_map |
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| 1402 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 1403 | _potential_map->set(n, _pi[_node_id[n]]); |
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[648] | 1404 | } |
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| 1405 | |
---|
| 1406 | return true; |
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| 1407 | } |
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| 1408 | |
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| 1409 | }; //class NetworkSimplex |
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| 1410 | |
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| 1411 | ///@} |
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| 1412 | |
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| 1413 | } //namespace lemon |
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| 1414 | |
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| 1415 | #endif //LEMON_NETWORK_SIMPLEX_H |
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