[601] | 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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[605] | 25 | /// \brief Network Simplex algorithm for finding a minimum cost flow. |
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[601] | 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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[603] | 31 | #include <lemon/core.h> |
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[601] | 32 | #include <lemon/math.h> |
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[609] | 33 | #include <lemon/maps.h> |
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| 34 | #include <lemon/circulation.h> |
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| 35 | #include <lemon/adaptors.h> |
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[601] | 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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| 39 | /// \addtogroup min_cost_flow |
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| 40 | /// @{ |
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| 41 | |
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[605] | 42 | /// \brief Implementation of the primal Network Simplex algorithm |
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[601] | 43 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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| 44 | /// |
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[605] | 45 | /// \ref NetworkSimplex implements the primal Network Simplex algorithm |
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[601] | 46 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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[606] | 47 | /// This algorithm is a specialized version of the linear programming |
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| 48 | /// simplex method directly for the minimum cost flow problem. |
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| 49 | /// It is one of the most efficient solution methods. |
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| 50 | /// |
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| 51 | /// In general this class is the fastest implementation available |
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| 52 | /// in LEMON for the minimum cost flow problem. |
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[609] | 53 | /// Moreover it supports both direction of the supply/demand inequality |
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| 54 | /// constraints. For more information see \ref ProblemType. |
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[601] | 55 | /// |
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[605] | 56 | /// \tparam GR The digraph type the algorithm runs on. |
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[607] | 57 | /// \tparam F The value type used for flow amounts, capacity bounds |
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| 58 | /// and supply values in the algorithm. By default it is \c int. |
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| 59 | /// \tparam C The value type used for costs and potentials in the |
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| 60 | /// algorithm. By default it is the same as \c F. |
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[601] | 61 | /// |
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[608] | 62 | /// \warning Both value types must be signed and all input data must |
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| 63 | /// be integer. |
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[601] | 64 | /// |
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[605] | 65 | /// \note %NetworkSimplex provides five different pivot rule |
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[609] | 66 | /// implementations, from which the most efficient one is used |
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| 67 | /// by default. For more information see \ref PivotRule. |
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[607] | 68 | template <typename GR, typename F = int, typename C = F> |
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[601] | 69 | class NetworkSimplex |
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| 70 | { |
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[605] | 71 | public: |
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[601] | 72 | |
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[607] | 73 | /// The flow type of the algorithm |
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| 74 | typedef F Flow; |
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| 75 | /// The cost type of the algorithm |
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| 76 | typedef C Cost; |
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[609] | 77 | #ifdef DOXYGEN |
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| 78 | /// The type of the flow map |
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| 79 | typedef GR::ArcMap<Flow> FlowMap; |
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| 80 | /// The type of the potential map |
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| 81 | typedef GR::NodeMap<Cost> PotentialMap; |
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| 82 | #else |
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[605] | 83 | /// The type of the flow map |
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[607] | 84 | typedef typename GR::template ArcMap<Flow> FlowMap; |
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[605] | 85 | /// The type of the potential map |
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[607] | 86 | typedef typename GR::template NodeMap<Cost> PotentialMap; |
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[609] | 87 | #endif |
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[605] | 88 | |
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| 89 | public: |
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| 90 | |
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| 91 | /// \brief Enum type for selecting the pivot rule. |
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| 92 | /// |
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| 93 | /// Enum type for selecting the pivot rule for the \ref run() |
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| 94 | /// function. |
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| 95 | /// |
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| 96 | /// \ref NetworkSimplex provides five different pivot rule |
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| 97 | /// implementations that significantly affect the running time |
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| 98 | /// of the algorithm. |
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| 99 | /// By default \ref BLOCK_SEARCH "Block Search" is used, which |
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| 100 | /// proved to be the most efficient and the most robust on various |
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| 101 | /// test inputs according to our benchmark tests. |
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| 102 | /// However another pivot rule can be selected using the \ref run() |
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| 103 | /// function with the proper parameter. |
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| 104 | enum PivotRule { |
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| 105 | |
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| 106 | /// The First Eligible pivot rule. |
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| 107 | /// The next eligible arc is selected in a wraparound fashion |
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| 108 | /// in every iteration. |
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| 109 | FIRST_ELIGIBLE, |
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| 110 | |
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| 111 | /// The Best Eligible pivot rule. |
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| 112 | /// The best eligible arc is selected in every iteration. |
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| 113 | BEST_ELIGIBLE, |
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| 114 | |
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| 115 | /// The Block Search pivot rule. |
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| 116 | /// A specified number of arcs are examined in every iteration |
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| 117 | /// in a wraparound fashion and the best eligible arc is selected |
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| 118 | /// from this block. |
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| 119 | BLOCK_SEARCH, |
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| 120 | |
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| 121 | /// The Candidate List pivot rule. |
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| 122 | /// In a major iteration a candidate list is built from eligible arcs |
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| 123 | /// in a wraparound fashion and in the following minor iterations |
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| 124 | /// the best eligible arc is selected from this list. |
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| 125 | CANDIDATE_LIST, |
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| 126 | |
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| 127 | /// The Altering Candidate List pivot rule. |
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| 128 | /// It is a modified version of the Candidate List method. |
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| 129 | /// It keeps only the several best eligible arcs from the former |
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| 130 | /// candidate list and extends this list in every iteration. |
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| 131 | ALTERING_LIST |
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| 132 | }; |
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[609] | 133 | |
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| 134 | /// \brief Enum type for selecting the problem type. |
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| 135 | /// |
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| 136 | /// Enum type for selecting the problem type, i.e. the direction of |
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| 137 | /// the inequalities in the supply/demand constraints of the |
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| 138 | /// \ref min_cost_flow "minimum cost flow problem". |
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| 139 | /// |
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| 140 | /// The default problem type is \c GEQ, since this form is supported |
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| 141 | /// by other minimum cost flow algorithms and the \ref Circulation |
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| 142 | /// algorithm as well. |
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| 143 | /// The \c LEQ problem type can be selected using the \ref problemType() |
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| 144 | /// function. |
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| 145 | /// |
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| 146 | /// Note that the equality form is a special case of both problem type. |
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| 147 | enum ProblemType { |
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| 148 | |
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| 149 | /// This option means that there are "<em>greater or equal</em>" |
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| 150 | /// constraints in the defintion, i.e. the exact formulation of the |
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| 151 | /// problem is the following. |
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| 152 | /** |
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| 153 | \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] |
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| 154 | \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq |
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| 155 | sup(u) \quad \forall u\in V \f] |
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| 156 | \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] |
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| 157 | */ |
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| 158 | /// It means that the total demand must be greater or equal to the |
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| 159 | /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or |
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| 160 | /// negative) and all the supplies have to be carried out from |
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| 161 | /// the supply nodes, but there could be demands that are not |
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| 162 | /// satisfied. |
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| 163 | GEQ, |
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| 164 | /// It is just an alias for the \c GEQ option. |
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| 165 | CARRY_SUPPLIES = GEQ, |
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| 166 | |
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| 167 | /// This option means that there are "<em>less or equal</em>" |
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| 168 | /// constraints in the defintion, i.e. the exact formulation of the |
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| 169 | /// problem is the following. |
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| 170 | /** |
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| 171 | \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] |
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| 172 | \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \leq |
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| 173 | sup(u) \quad \forall u\in V \f] |
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| 174 | \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] |
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| 175 | */ |
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| 176 | /// It means that the total demand must be less or equal to the |
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| 177 | /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or |
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| 178 | /// positive) and all the demands have to be satisfied, but there |
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| 179 | /// could be supplies that are not carried out from the supply |
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| 180 | /// nodes. |
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| 181 | LEQ, |
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| 182 | /// It is just an alias for the \c LEQ option. |
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| 183 | SATISFY_DEMANDS = LEQ |
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| 184 | }; |
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[605] | 185 | |
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| 186 | private: |
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| 187 | |
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| 188 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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| 189 | |
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[607] | 190 | typedef typename GR::template ArcMap<Flow> FlowArcMap; |
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| 191 | typedef typename GR::template ArcMap<Cost> CostArcMap; |
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| 192 | typedef typename GR::template NodeMap<Flow> FlowNodeMap; |
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[601] | 193 | |
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| 194 | typedef std::vector<Arc> ArcVector; |
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| 195 | typedef std::vector<Node> NodeVector; |
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| 196 | typedef std::vector<int> IntVector; |
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| 197 | typedef std::vector<bool> BoolVector; |
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[607] | 198 | typedef std::vector<Flow> FlowVector; |
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| 199 | typedef std::vector<Cost> CostVector; |
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[601] | 200 | |
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| 201 | // State constants for arcs |
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| 202 | enum ArcStateEnum { |
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| 203 | STATE_UPPER = -1, |
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| 204 | STATE_TREE = 0, |
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| 205 | STATE_LOWER = 1 |
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| 206 | }; |
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| 207 | |
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| 208 | private: |
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| 209 | |
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[605] | 210 | // Data related to the underlying digraph |
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| 211 | const GR &_graph; |
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| 212 | int _node_num; |
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| 213 | int _arc_num; |
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| 214 | |
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| 215 | // Parameters of the problem |
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[607] | 216 | FlowArcMap *_plower; |
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| 217 | FlowArcMap *_pupper; |
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| 218 | CostArcMap *_pcost; |
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| 219 | FlowNodeMap *_psupply; |
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[605] | 220 | bool _pstsup; |
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| 221 | Node _psource, _ptarget; |
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[607] | 222 | Flow _pstflow; |
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[609] | 223 | ProblemType _ptype; |
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[601] | 224 | |
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| 225 | // Result maps |
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[603] | 226 | FlowMap *_flow_map; |
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| 227 | PotentialMap *_potential_map; |
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[601] | 228 | bool _local_flow; |
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| 229 | bool _local_potential; |
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| 230 | |
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[605] | 231 | // Data structures for storing the digraph |
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[603] | 232 | IntNodeMap _node_id; |
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| 233 | ArcVector _arc_ref; |
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| 234 | IntVector _source; |
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| 235 | IntVector _target; |
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| 236 | |
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[605] | 237 | // Node and arc data |
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[607] | 238 | FlowVector _cap; |
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| 239 | CostVector _cost; |
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| 240 | FlowVector _supply; |
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| 241 | FlowVector _flow; |
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| 242 | CostVector _pi; |
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[601] | 243 | |
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[603] | 244 | // Data for storing the spanning tree structure |
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[601] | 245 | IntVector _parent; |
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| 246 | IntVector _pred; |
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| 247 | IntVector _thread; |
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[604] | 248 | IntVector _rev_thread; |
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| 249 | IntVector _succ_num; |
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| 250 | IntVector _last_succ; |
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| 251 | IntVector _dirty_revs; |
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[601] | 252 | BoolVector _forward; |
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| 253 | IntVector _state; |
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| 254 | int _root; |
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| 255 | |
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| 256 | // Temporary data used in the current pivot iteration |
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[603] | 257 | int in_arc, join, u_in, v_in, u_out, v_out; |
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| 258 | int first, second, right, last; |
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[601] | 259 | int stem, par_stem, new_stem; |
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[607] | 260 | Flow delta; |
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[601] | 261 | |
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| 262 | private: |
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| 263 | |
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[605] | 264 | // Implementation of the First Eligible pivot rule |
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[601] | 265 | class FirstEligiblePivotRule |
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| 266 | { |
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| 267 | private: |
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| 268 | |
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| 269 | // References to the NetworkSimplex class |
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| 270 | const IntVector &_source; |
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| 271 | const IntVector &_target; |
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[607] | 272 | const CostVector &_cost; |
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[601] | 273 | const IntVector &_state; |
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[607] | 274 | const CostVector &_pi; |
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[601] | 275 | int &_in_arc; |
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| 276 | int _arc_num; |
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| 277 | |
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| 278 | // Pivot rule data |
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| 279 | int _next_arc; |
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| 280 | |
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| 281 | public: |
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| 282 | |
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[605] | 283 | // Constructor |
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[601] | 284 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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[603] | 285 | _source(ns._source), _target(ns._target), |
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[601] | 286 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 287 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[601] | 288 | {} |
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| 289 | |
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[605] | 290 | // Find next entering arc |
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[601] | 291 | bool findEnteringArc() { |
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[607] | 292 | Cost c; |
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[601] | 293 | for (int e = _next_arc; e < _arc_num; ++e) { |
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| 294 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 295 | if (c < 0) { |
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| 296 | _in_arc = e; |
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| 297 | _next_arc = e + 1; |
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| 298 | return true; |
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| 299 | } |
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| 300 | } |
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| 301 | for (int e = 0; e < _next_arc; ++e) { |
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| 302 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 303 | if (c < 0) { |
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| 304 | _in_arc = e; |
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| 305 | _next_arc = e + 1; |
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| 306 | return true; |
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| 307 | } |
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| 308 | } |
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| 309 | return false; |
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| 310 | } |
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| 311 | |
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| 312 | }; //class FirstEligiblePivotRule |
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| 313 | |
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| 314 | |
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[605] | 315 | // Implementation of the Best Eligible pivot rule |
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[601] | 316 | class BestEligiblePivotRule |
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| 317 | { |
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| 318 | private: |
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| 319 | |
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| 320 | // References to the NetworkSimplex class |
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| 321 | const IntVector &_source; |
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| 322 | const IntVector &_target; |
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[607] | 323 | const CostVector &_cost; |
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[601] | 324 | const IntVector &_state; |
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[607] | 325 | const CostVector &_pi; |
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[601] | 326 | int &_in_arc; |
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| 327 | int _arc_num; |
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| 328 | |
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| 329 | public: |
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| 330 | |
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[605] | 331 | // Constructor |
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[601] | 332 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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[603] | 333 | _source(ns._source), _target(ns._target), |
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[601] | 334 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 335 | _in_arc(ns.in_arc), _arc_num(ns._arc_num) |
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[601] | 336 | {} |
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| 337 | |
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[605] | 338 | // Find next entering arc |
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[601] | 339 | bool findEnteringArc() { |
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[607] | 340 | Cost c, min = 0; |
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[601] | 341 | for (int e = 0; e < _arc_num; ++e) { |
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| 342 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 343 | if (c < min) { |
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| 344 | min = c; |
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| 345 | _in_arc = e; |
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| 346 | } |
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| 347 | } |
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| 348 | return min < 0; |
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| 349 | } |
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| 350 | |
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| 351 | }; //class BestEligiblePivotRule |
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| 352 | |
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| 353 | |
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[605] | 354 | // Implementation of the Block Search pivot rule |
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[601] | 355 | class BlockSearchPivotRule |
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| 356 | { |
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| 357 | private: |
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| 358 | |
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| 359 | // References to the NetworkSimplex class |
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| 360 | const IntVector &_source; |
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| 361 | const IntVector &_target; |
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[607] | 362 | const CostVector &_cost; |
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[601] | 363 | const IntVector &_state; |
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[607] | 364 | const CostVector &_pi; |
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[601] | 365 | int &_in_arc; |
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| 366 | int _arc_num; |
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| 367 | |
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| 368 | // Pivot rule data |
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| 369 | int _block_size; |
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| 370 | int _next_arc; |
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| 371 | |
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| 372 | public: |
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| 373 | |
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[605] | 374 | // Constructor |
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[601] | 375 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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[603] | 376 | _source(ns._source), _target(ns._target), |
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[601] | 377 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 378 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[601] | 379 | { |
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| 380 | // The main parameters of the pivot rule |
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| 381 | const double BLOCK_SIZE_FACTOR = 2.0; |
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| 382 | const int MIN_BLOCK_SIZE = 10; |
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| 383 | |
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[612] | 384 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
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| 385 | std::sqrt(double(_arc_num))), |
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[601] | 386 | MIN_BLOCK_SIZE ); |
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| 387 | } |
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| 388 | |
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[605] | 389 | // Find next entering arc |
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[601] | 390 | bool findEnteringArc() { |
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[607] | 391 | Cost c, min = 0; |
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[601] | 392 | int cnt = _block_size; |
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| 393 | int e, min_arc = _next_arc; |
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| 394 | for (e = _next_arc; e < _arc_num; ++e) { |
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| 395 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 396 | if (c < min) { |
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| 397 | min = c; |
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| 398 | min_arc = e; |
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| 399 | } |
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| 400 | if (--cnt == 0) { |
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| 401 | if (min < 0) break; |
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| 402 | cnt = _block_size; |
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| 403 | } |
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| 404 | } |
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| 405 | if (min == 0 || cnt > 0) { |
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| 406 | for (e = 0; e < _next_arc; ++e) { |
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| 407 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 408 | if (c < min) { |
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| 409 | min = c; |
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| 410 | min_arc = e; |
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| 411 | } |
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| 412 | if (--cnt == 0) { |
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| 413 | if (min < 0) break; |
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| 414 | cnt = _block_size; |
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| 415 | } |
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| 416 | } |
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| 417 | } |
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| 418 | if (min >= 0) return false; |
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| 419 | _in_arc = min_arc; |
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| 420 | _next_arc = e; |
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| 421 | return true; |
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| 422 | } |
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| 423 | |
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| 424 | }; //class BlockSearchPivotRule |
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| 425 | |
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| 426 | |
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[605] | 427 | // Implementation of the Candidate List pivot rule |
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[601] | 428 | class CandidateListPivotRule |
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| 429 | { |
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| 430 | private: |
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| 431 | |
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| 432 | // References to the NetworkSimplex class |
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| 433 | const IntVector &_source; |
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| 434 | const IntVector &_target; |
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[607] | 435 | const CostVector &_cost; |
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[601] | 436 | const IntVector &_state; |
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[607] | 437 | const CostVector &_pi; |
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[601] | 438 | int &_in_arc; |
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| 439 | int _arc_num; |
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| 440 | |
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| 441 | // Pivot rule data |
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| 442 | IntVector _candidates; |
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| 443 | int _list_length, _minor_limit; |
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| 444 | int _curr_length, _minor_count; |
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| 445 | int _next_arc; |
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| 446 | |
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| 447 | public: |
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| 448 | |
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| 449 | /// Constructor |
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| 450 | CandidateListPivotRule(NetworkSimplex &ns) : |
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[603] | 451 | _source(ns._source), _target(ns._target), |
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[601] | 452 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 453 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[601] | 454 | { |
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| 455 | // The main parameters of the pivot rule |
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| 456 | const double LIST_LENGTH_FACTOR = 1.0; |
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| 457 | const int MIN_LIST_LENGTH = 10; |
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| 458 | const double MINOR_LIMIT_FACTOR = 0.1; |
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| 459 | const int MIN_MINOR_LIMIT = 3; |
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| 460 | |
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[612] | 461 | _list_length = std::max( int(LIST_LENGTH_FACTOR * |
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| 462 | std::sqrt(double(_arc_num))), |
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[601] | 463 | MIN_LIST_LENGTH ); |
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| 464 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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| 465 | MIN_MINOR_LIMIT ); |
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| 466 | _curr_length = _minor_count = 0; |
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| 467 | _candidates.resize(_list_length); |
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| 468 | } |
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| 469 | |
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| 470 | /// Find next entering arc |
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| 471 | bool findEnteringArc() { |
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[607] | 472 | Cost min, c; |
---|
[601] | 473 | int e, min_arc = _next_arc; |
---|
| 474 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
---|
| 475 | // Minor iteration: select the best eligible arc from the |
---|
| 476 | // current candidate list |
---|
| 477 | ++_minor_count; |
---|
| 478 | min = 0; |
---|
| 479 | for (int i = 0; i < _curr_length; ++i) { |
---|
| 480 | e = _candidates[i]; |
---|
| 481 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 482 | if (c < min) { |
---|
| 483 | min = c; |
---|
| 484 | min_arc = e; |
---|
| 485 | } |
---|
| 486 | if (c >= 0) { |
---|
| 487 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 488 | } |
---|
| 489 | } |
---|
| 490 | if (min < 0) { |
---|
| 491 | _in_arc = min_arc; |
---|
| 492 | return true; |
---|
| 493 | } |
---|
| 494 | } |
---|
| 495 | |
---|
| 496 | // Major iteration: build a new candidate list |
---|
| 497 | min = 0; |
---|
| 498 | _curr_length = 0; |
---|
| 499 | for (e = _next_arc; e < _arc_num; ++e) { |
---|
| 500 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 501 | if (c < 0) { |
---|
| 502 | _candidates[_curr_length++] = e; |
---|
| 503 | if (c < min) { |
---|
| 504 | min = c; |
---|
| 505 | min_arc = e; |
---|
| 506 | } |
---|
| 507 | if (_curr_length == _list_length) break; |
---|
| 508 | } |
---|
| 509 | } |
---|
| 510 | if (_curr_length < _list_length) { |
---|
| 511 | for (e = 0; e < _next_arc; ++e) { |
---|
| 512 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 513 | if (c < 0) { |
---|
| 514 | _candidates[_curr_length++] = e; |
---|
| 515 | if (c < min) { |
---|
| 516 | min = c; |
---|
| 517 | min_arc = e; |
---|
| 518 | } |
---|
| 519 | if (_curr_length == _list_length) break; |
---|
| 520 | } |
---|
| 521 | } |
---|
| 522 | } |
---|
| 523 | if (_curr_length == 0) return false; |
---|
| 524 | _minor_count = 1; |
---|
| 525 | _in_arc = min_arc; |
---|
| 526 | _next_arc = e; |
---|
| 527 | return true; |
---|
| 528 | } |
---|
| 529 | |
---|
| 530 | }; //class CandidateListPivotRule |
---|
| 531 | |
---|
| 532 | |
---|
[605] | 533 | // Implementation of the Altering Candidate List pivot rule |
---|
[601] | 534 | class AlteringListPivotRule |
---|
| 535 | { |
---|
| 536 | private: |
---|
| 537 | |
---|
| 538 | // References to the NetworkSimplex class |
---|
| 539 | const IntVector &_source; |
---|
| 540 | const IntVector &_target; |
---|
[607] | 541 | const CostVector &_cost; |
---|
[601] | 542 | const IntVector &_state; |
---|
[607] | 543 | const CostVector &_pi; |
---|
[601] | 544 | int &_in_arc; |
---|
| 545 | int _arc_num; |
---|
| 546 | |
---|
| 547 | // Pivot rule data |
---|
| 548 | int _block_size, _head_length, _curr_length; |
---|
| 549 | int _next_arc; |
---|
| 550 | IntVector _candidates; |
---|
[607] | 551 | CostVector _cand_cost; |
---|
[601] | 552 | |
---|
| 553 | // Functor class to compare arcs during sort of the candidate list |
---|
| 554 | class SortFunc |
---|
| 555 | { |
---|
| 556 | private: |
---|
[607] | 557 | const CostVector &_map; |
---|
[601] | 558 | public: |
---|
[607] | 559 | SortFunc(const CostVector &map) : _map(map) {} |
---|
[601] | 560 | bool operator()(int left, int right) { |
---|
| 561 | return _map[left] > _map[right]; |
---|
| 562 | } |
---|
| 563 | }; |
---|
| 564 | |
---|
| 565 | SortFunc _sort_func; |
---|
| 566 | |
---|
| 567 | public: |
---|
| 568 | |
---|
[605] | 569 | // Constructor |
---|
[601] | 570 | AlteringListPivotRule(NetworkSimplex &ns) : |
---|
[603] | 571 | _source(ns._source), _target(ns._target), |
---|
[601] | 572 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
[603] | 573 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), |
---|
[601] | 574 | _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) |
---|
| 575 | { |
---|
| 576 | // The main parameters of the pivot rule |
---|
| 577 | const double BLOCK_SIZE_FACTOR = 1.5; |
---|
| 578 | const int MIN_BLOCK_SIZE = 10; |
---|
| 579 | const double HEAD_LENGTH_FACTOR = 0.1; |
---|
| 580 | const int MIN_HEAD_LENGTH = 3; |
---|
| 581 | |
---|
[612] | 582 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
---|
| 583 | std::sqrt(double(_arc_num))), |
---|
[601] | 584 | MIN_BLOCK_SIZE ); |
---|
| 585 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
---|
| 586 | MIN_HEAD_LENGTH ); |
---|
| 587 | _candidates.resize(_head_length + _block_size); |
---|
| 588 | _curr_length = 0; |
---|
| 589 | } |
---|
| 590 | |
---|
[605] | 591 | // Find next entering arc |
---|
[601] | 592 | bool findEnteringArc() { |
---|
| 593 | // Check the current candidate list |
---|
| 594 | int e; |
---|
| 595 | for (int i = 0; i < _curr_length; ++i) { |
---|
| 596 | e = _candidates[i]; |
---|
| 597 | _cand_cost[e] = _state[e] * |
---|
| 598 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 599 | if (_cand_cost[e] >= 0) { |
---|
| 600 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 601 | } |
---|
| 602 | } |
---|
| 603 | |
---|
| 604 | // Extend the list |
---|
| 605 | int cnt = _block_size; |
---|
[603] | 606 | int last_arc = 0; |
---|
[601] | 607 | int limit = _head_length; |
---|
| 608 | |
---|
| 609 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
| 610 | _cand_cost[e] = _state[e] * |
---|
| 611 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 612 | if (_cand_cost[e] < 0) { |
---|
| 613 | _candidates[_curr_length++] = e; |
---|
[603] | 614 | last_arc = e; |
---|
[601] | 615 | } |
---|
| 616 | if (--cnt == 0) { |
---|
| 617 | if (_curr_length > limit) break; |
---|
| 618 | limit = 0; |
---|
| 619 | cnt = _block_size; |
---|
| 620 | } |
---|
| 621 | } |
---|
| 622 | if (_curr_length <= limit) { |
---|
| 623 | for (int e = 0; e < _next_arc; ++e) { |
---|
| 624 | _cand_cost[e] = _state[e] * |
---|
| 625 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 626 | if (_cand_cost[e] < 0) { |
---|
| 627 | _candidates[_curr_length++] = e; |
---|
[603] | 628 | last_arc = e; |
---|
[601] | 629 | } |
---|
| 630 | if (--cnt == 0) { |
---|
| 631 | if (_curr_length > limit) break; |
---|
| 632 | limit = 0; |
---|
| 633 | cnt = _block_size; |
---|
| 634 | } |
---|
| 635 | } |
---|
| 636 | } |
---|
| 637 | if (_curr_length == 0) return false; |
---|
[603] | 638 | _next_arc = last_arc + 1; |
---|
[601] | 639 | |
---|
| 640 | // Make heap of the candidate list (approximating a partial sort) |
---|
| 641 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 642 | _sort_func ); |
---|
| 643 | |
---|
| 644 | // Pop the first element of the heap |
---|
| 645 | _in_arc = _candidates[0]; |
---|
| 646 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 647 | _sort_func ); |
---|
| 648 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
| 649 | return true; |
---|
| 650 | } |
---|
| 651 | |
---|
| 652 | }; //class AlteringListPivotRule |
---|
| 653 | |
---|
| 654 | public: |
---|
| 655 | |
---|
[605] | 656 | /// \brief Constructor. |
---|
[601] | 657 | /// |
---|
[609] | 658 | /// The constructor of the class. |
---|
[601] | 659 | /// |
---|
[603] | 660 | /// \param graph The digraph the algorithm runs on. |
---|
[605] | 661 | NetworkSimplex(const GR& graph) : |
---|
| 662 | _graph(graph), |
---|
| 663 | _plower(NULL), _pupper(NULL), _pcost(NULL), |
---|
[609] | 664 | _psupply(NULL), _pstsup(false), _ptype(GEQ), |
---|
[603] | 665 | _flow_map(NULL), _potential_map(NULL), |
---|
[601] | 666 | _local_flow(false), _local_potential(false), |
---|
[603] | 667 | _node_id(graph) |
---|
[605] | 668 | { |
---|
[607] | 669 | LEMON_ASSERT(std::numeric_limits<Flow>::is_integer && |
---|
| 670 | std::numeric_limits<Flow>::is_signed, |
---|
| 671 | "The flow type of NetworkSimplex must be signed integer"); |
---|
| 672 | LEMON_ASSERT(std::numeric_limits<Cost>::is_integer && |
---|
| 673 | std::numeric_limits<Cost>::is_signed, |
---|
| 674 | "The cost type of NetworkSimplex must be signed integer"); |
---|
[605] | 675 | } |
---|
[601] | 676 | |
---|
| 677 | /// Destructor. |
---|
| 678 | ~NetworkSimplex() { |
---|
[603] | 679 | if (_local_flow) delete _flow_map; |
---|
| 680 | if (_local_potential) delete _potential_map; |
---|
[601] | 681 | } |
---|
| 682 | |
---|
[609] | 683 | /// \name Parameters |
---|
| 684 | /// The parameters of the algorithm can be specified using these |
---|
| 685 | /// functions. |
---|
| 686 | |
---|
| 687 | /// @{ |
---|
| 688 | |
---|
[605] | 689 | /// \brief Set the lower bounds on the arcs. |
---|
| 690 | /// |
---|
| 691 | /// This function sets the lower bounds on the arcs. |
---|
| 692 | /// If neither this function nor \ref boundMaps() is used before |
---|
| 693 | /// calling \ref run(), the lower bounds will be set to zero |
---|
| 694 | /// on all arcs. |
---|
| 695 | /// |
---|
| 696 | /// \param map An arc map storing the lower bounds. |
---|
[607] | 697 | /// Its \c Value type must be convertible to the \c Flow type |
---|
[605] | 698 | /// of the algorithm. |
---|
| 699 | /// |
---|
| 700 | /// \return <tt>(*this)</tt> |
---|
| 701 | template <typename LOWER> |
---|
| 702 | NetworkSimplex& lowerMap(const LOWER& map) { |
---|
| 703 | delete _plower; |
---|
[607] | 704 | _plower = new FlowArcMap(_graph); |
---|
[605] | 705 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 706 | (*_plower)[a] = map[a]; |
---|
| 707 | } |
---|
| 708 | return *this; |
---|
| 709 | } |
---|
| 710 | |
---|
| 711 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
| 712 | /// |
---|
| 713 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
| 714 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
| 715 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
| 716 | /// the upper bounds (capacities) will be set to |
---|
[607] | 717 | /// \c std::numeric_limits<Flow>::max() on all arcs. |
---|
[605] | 718 | /// |
---|
| 719 | /// \param map An arc map storing the upper bounds. |
---|
[607] | 720 | /// Its \c Value type must be convertible to the \c Flow type |
---|
[605] | 721 | /// of the algorithm. |
---|
| 722 | /// |
---|
| 723 | /// \return <tt>(*this)</tt> |
---|
| 724 | template<typename UPPER> |
---|
| 725 | NetworkSimplex& upperMap(const UPPER& map) { |
---|
| 726 | delete _pupper; |
---|
[607] | 727 | _pupper = new FlowArcMap(_graph); |
---|
[605] | 728 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 729 | (*_pupper)[a] = map[a]; |
---|
| 730 | } |
---|
| 731 | return *this; |
---|
| 732 | } |
---|
| 733 | |
---|
| 734 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
| 735 | /// |
---|
| 736 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
| 737 | /// It is just an alias for \ref upperMap(). |
---|
| 738 | /// |
---|
| 739 | /// \return <tt>(*this)</tt> |
---|
| 740 | template<typename CAP> |
---|
| 741 | NetworkSimplex& capacityMap(const CAP& map) { |
---|
| 742 | return upperMap(map); |
---|
| 743 | } |
---|
| 744 | |
---|
| 745 | /// \brief Set the lower and upper bounds on the arcs. |
---|
| 746 | /// |
---|
| 747 | /// This function sets the lower and upper bounds on the arcs. |
---|
| 748 | /// If neither this function nor \ref lowerMap() is used before |
---|
| 749 | /// calling \ref run(), the lower bounds will be set to zero |
---|
| 750 | /// on all arcs. |
---|
| 751 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
| 752 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
| 753 | /// the upper bounds (capacities) will be set to |
---|
[607] | 754 | /// \c std::numeric_limits<Flow>::max() on all arcs. |
---|
[605] | 755 | /// |
---|
| 756 | /// \param lower An arc map storing the lower bounds. |
---|
| 757 | /// \param upper An arc map storing the upper bounds. |
---|
| 758 | /// |
---|
| 759 | /// The \c Value type of the maps must be convertible to the |
---|
[607] | 760 | /// \c Flow type of the algorithm. |
---|
[605] | 761 | /// |
---|
| 762 | /// \note This function is just a shortcut of calling \ref lowerMap() |
---|
| 763 | /// and \ref upperMap() separately. |
---|
| 764 | /// |
---|
| 765 | /// \return <tt>(*this)</tt> |
---|
| 766 | template <typename LOWER, typename UPPER> |
---|
| 767 | NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) { |
---|
| 768 | return lowerMap(lower).upperMap(upper); |
---|
| 769 | } |
---|
| 770 | |
---|
| 771 | /// \brief Set the costs of the arcs. |
---|
| 772 | /// |
---|
| 773 | /// This function sets the costs of the arcs. |
---|
| 774 | /// If it is not used before calling \ref run(), the costs |
---|
| 775 | /// will be set to \c 1 on all arcs. |
---|
| 776 | /// |
---|
| 777 | /// \param map An arc map storing the costs. |
---|
[607] | 778 | /// Its \c Value type must be convertible to the \c Cost type |
---|
[605] | 779 | /// of the algorithm. |
---|
| 780 | /// |
---|
| 781 | /// \return <tt>(*this)</tt> |
---|
| 782 | template<typename COST> |
---|
| 783 | NetworkSimplex& costMap(const COST& map) { |
---|
| 784 | delete _pcost; |
---|
[607] | 785 | _pcost = new CostArcMap(_graph); |
---|
[605] | 786 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 787 | (*_pcost)[a] = map[a]; |
---|
| 788 | } |
---|
| 789 | return *this; |
---|
| 790 | } |
---|
| 791 | |
---|
| 792 | /// \brief Set the supply values of the nodes. |
---|
| 793 | /// |
---|
| 794 | /// This function sets the supply values of the nodes. |
---|
| 795 | /// If neither this function nor \ref stSupply() is used before |
---|
| 796 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 797 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
| 798 | /// |
---|
| 799 | /// \param map A node map storing the supply values. |
---|
[607] | 800 | /// Its \c Value type must be convertible to the \c Flow type |
---|
[605] | 801 | /// of the algorithm. |
---|
| 802 | /// |
---|
| 803 | /// \return <tt>(*this)</tt> |
---|
| 804 | template<typename SUP> |
---|
| 805 | NetworkSimplex& supplyMap(const SUP& map) { |
---|
| 806 | delete _psupply; |
---|
| 807 | _pstsup = false; |
---|
[607] | 808 | _psupply = new FlowNodeMap(_graph); |
---|
[605] | 809 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 810 | (*_psupply)[n] = map[n]; |
---|
| 811 | } |
---|
| 812 | return *this; |
---|
| 813 | } |
---|
| 814 | |
---|
| 815 | /// \brief Set single source and target nodes and a supply value. |
---|
| 816 | /// |
---|
| 817 | /// This function sets a single source node and a single target node |
---|
| 818 | /// and the required flow value. |
---|
| 819 | /// If neither this function nor \ref supplyMap() is used before |
---|
| 820 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 821 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
| 822 | /// |
---|
| 823 | /// \param s The source node. |
---|
| 824 | /// \param t The target node. |
---|
| 825 | /// \param k The required amount of flow from node \c s to node \c t |
---|
| 826 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
| 827 | /// |
---|
| 828 | /// \return <tt>(*this)</tt> |
---|
[607] | 829 | NetworkSimplex& stSupply(const Node& s, const Node& t, Flow k) { |
---|
[605] | 830 | delete _psupply; |
---|
| 831 | _psupply = NULL; |
---|
| 832 | _pstsup = true; |
---|
| 833 | _psource = s; |
---|
| 834 | _ptarget = t; |
---|
| 835 | _pstflow = k; |
---|
| 836 | return *this; |
---|
| 837 | } |
---|
[609] | 838 | |
---|
| 839 | /// \brief Set the problem type. |
---|
| 840 | /// |
---|
| 841 | /// This function sets the problem type for the algorithm. |
---|
| 842 | /// If it is not used before calling \ref run(), the \ref GEQ problem |
---|
| 843 | /// type will be used. |
---|
| 844 | /// |
---|
| 845 | /// For more information see \ref ProblemType. |
---|
| 846 | /// |
---|
| 847 | /// \return <tt>(*this)</tt> |
---|
| 848 | NetworkSimplex& problemType(ProblemType problem_type) { |
---|
| 849 | _ptype = problem_type; |
---|
| 850 | return *this; |
---|
| 851 | } |
---|
[605] | 852 | |
---|
[601] | 853 | /// \brief Set the flow map. |
---|
| 854 | /// |
---|
| 855 | /// This function sets the flow map. |
---|
[605] | 856 | /// If it is not used before calling \ref run(), an instance will |
---|
| 857 | /// be allocated automatically. The destructor deallocates this |
---|
| 858 | /// automatically allocated map, of course. |
---|
[601] | 859 | /// |
---|
| 860 | /// \return <tt>(*this)</tt> |
---|
[605] | 861 | NetworkSimplex& flowMap(FlowMap& map) { |
---|
[601] | 862 | if (_local_flow) { |
---|
[603] | 863 | delete _flow_map; |
---|
[601] | 864 | _local_flow = false; |
---|
| 865 | } |
---|
[603] | 866 | _flow_map = ↦ |
---|
[601] | 867 | return *this; |
---|
| 868 | } |
---|
| 869 | |
---|
| 870 | /// \brief Set the potential map. |
---|
| 871 | /// |
---|
[605] | 872 | /// This function sets the potential map, which is used for storing |
---|
| 873 | /// the dual solution. |
---|
| 874 | /// If it is not used before calling \ref run(), an instance will |
---|
| 875 | /// be allocated automatically. The destructor deallocates this |
---|
| 876 | /// automatically allocated map, of course. |
---|
[601] | 877 | /// |
---|
| 878 | /// \return <tt>(*this)</tt> |
---|
[605] | 879 | NetworkSimplex& potentialMap(PotentialMap& map) { |
---|
[601] | 880 | if (_local_potential) { |
---|
[603] | 881 | delete _potential_map; |
---|
[601] | 882 | _local_potential = false; |
---|
| 883 | } |
---|
[603] | 884 | _potential_map = ↦ |
---|
[601] | 885 | return *this; |
---|
| 886 | } |
---|
[609] | 887 | |
---|
| 888 | /// @} |
---|
[601] | 889 | |
---|
[605] | 890 | /// \name Execution Control |
---|
| 891 | /// The algorithm can be executed using \ref run(). |
---|
| 892 | |
---|
[601] | 893 | /// @{ |
---|
| 894 | |
---|
| 895 | /// \brief Run the algorithm. |
---|
| 896 | /// |
---|
| 897 | /// This function runs the algorithm. |
---|
[609] | 898 | /// The paramters can be specified using functions \ref lowerMap(), |
---|
[606] | 899 | /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), |
---|
[609] | 900 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(), |
---|
| 901 | /// \ref problemType(), \ref flowMap() and \ref potentialMap(). |
---|
| 902 | /// For example, |
---|
[605] | 903 | /// \code |
---|
| 904 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
| 905 | /// ns.boundMaps(lower, upper).costMap(cost) |
---|
| 906 | /// .supplyMap(sup).run(); |
---|
| 907 | /// \endcode |
---|
[601] | 908 | /// |
---|
[606] | 909 | /// This function can be called more than once. All the parameters |
---|
| 910 | /// that have been given are kept for the next call, unless |
---|
| 911 | /// \ref reset() is called, thus only the modified parameters |
---|
| 912 | /// have to be set again. See \ref reset() for examples. |
---|
| 913 | /// |
---|
[605] | 914 | /// \param pivot_rule The pivot rule that will be used during the |
---|
| 915 | /// algorithm. For more information see \ref PivotRule. |
---|
[601] | 916 | /// |
---|
| 917 | /// \return \c true if a feasible flow can be found. |
---|
[605] | 918 | bool run(PivotRule pivot_rule = BLOCK_SEARCH) { |
---|
[601] | 919 | return init() && start(pivot_rule); |
---|
| 920 | } |
---|
| 921 | |
---|
[606] | 922 | /// \brief Reset all the parameters that have been given before. |
---|
| 923 | /// |
---|
| 924 | /// This function resets all the paramaters that have been given |
---|
[609] | 925 | /// before using functions \ref lowerMap(), \ref upperMap(), |
---|
| 926 | /// \ref capacityMap(), \ref boundMaps(), \ref costMap(), |
---|
| 927 | /// \ref supplyMap(), \ref stSupply(), \ref problemType(), |
---|
| 928 | /// \ref flowMap() and \ref potentialMap(). |
---|
[606] | 929 | /// |
---|
| 930 | /// It is useful for multiple run() calls. If this function is not |
---|
| 931 | /// used, all the parameters given before are kept for the next |
---|
| 932 | /// \ref run() call. |
---|
| 933 | /// |
---|
| 934 | /// For example, |
---|
| 935 | /// \code |
---|
| 936 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
| 937 | /// |
---|
| 938 | /// // First run |
---|
| 939 | /// ns.lowerMap(lower).capacityMap(cap).costMap(cost) |
---|
| 940 | /// .supplyMap(sup).run(); |
---|
| 941 | /// |
---|
| 942 | /// // Run again with modified cost map (reset() is not called, |
---|
| 943 | /// // so only the cost map have to be set again) |
---|
| 944 | /// cost[e] += 100; |
---|
| 945 | /// ns.costMap(cost).run(); |
---|
| 946 | /// |
---|
| 947 | /// // Run again from scratch using reset() |
---|
| 948 | /// // (the lower bounds will be set to zero on all arcs) |
---|
| 949 | /// ns.reset(); |
---|
| 950 | /// ns.capacityMap(cap).costMap(cost) |
---|
| 951 | /// .supplyMap(sup).run(); |
---|
| 952 | /// \endcode |
---|
| 953 | /// |
---|
| 954 | /// \return <tt>(*this)</tt> |
---|
| 955 | NetworkSimplex& reset() { |
---|
| 956 | delete _plower; |
---|
| 957 | delete _pupper; |
---|
| 958 | delete _pcost; |
---|
| 959 | delete _psupply; |
---|
| 960 | _plower = NULL; |
---|
| 961 | _pupper = NULL; |
---|
| 962 | _pcost = NULL; |
---|
| 963 | _psupply = NULL; |
---|
| 964 | _pstsup = false; |
---|
[609] | 965 | _ptype = GEQ; |
---|
| 966 | if (_local_flow) delete _flow_map; |
---|
| 967 | if (_local_potential) delete _potential_map; |
---|
| 968 | _flow_map = NULL; |
---|
| 969 | _potential_map = NULL; |
---|
| 970 | _local_flow = false; |
---|
| 971 | _local_potential = false; |
---|
| 972 | |
---|
[606] | 973 | return *this; |
---|
| 974 | } |
---|
| 975 | |
---|
[601] | 976 | /// @} |
---|
| 977 | |
---|
| 978 | /// \name Query Functions |
---|
| 979 | /// The results of the algorithm can be obtained using these |
---|
| 980 | /// functions.\n |
---|
[605] | 981 | /// The \ref run() function must be called before using them. |
---|
| 982 | |
---|
[601] | 983 | /// @{ |
---|
| 984 | |
---|
[605] | 985 | /// \brief Return the total cost of the found flow. |
---|
| 986 | /// |
---|
| 987 | /// This function returns the total cost of the found flow. |
---|
[607] | 988 | /// The complexity of the function is O(e). |
---|
[605] | 989 | /// |
---|
| 990 | /// \note The return type of the function can be specified as a |
---|
| 991 | /// template parameter. For example, |
---|
| 992 | /// \code |
---|
| 993 | /// ns.totalCost<double>(); |
---|
| 994 | /// \endcode |
---|
[607] | 995 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
[605] | 996 | /// type of the algorithm, which is the default return type of the |
---|
| 997 | /// function. |
---|
| 998 | /// |
---|
| 999 | /// \pre \ref run() must be called before using this function. |
---|
| 1000 | template <typename Num> |
---|
| 1001 | Num totalCost() const { |
---|
| 1002 | Num c = 0; |
---|
| 1003 | if (_pcost) { |
---|
| 1004 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 1005 | c += (*_flow_map)[e] * (*_pcost)[e]; |
---|
| 1006 | } else { |
---|
| 1007 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 1008 | c += (*_flow_map)[e]; |
---|
| 1009 | } |
---|
| 1010 | return c; |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | #ifndef DOXYGEN |
---|
[607] | 1014 | Cost totalCost() const { |
---|
| 1015 | return totalCost<Cost>(); |
---|
[605] | 1016 | } |
---|
| 1017 | #endif |
---|
| 1018 | |
---|
| 1019 | /// \brief Return the flow on the given arc. |
---|
| 1020 | /// |
---|
| 1021 | /// This function returns the flow on the given arc. |
---|
| 1022 | /// |
---|
| 1023 | /// \pre \ref run() must be called before using this function. |
---|
[607] | 1024 | Flow flow(const Arc& a) const { |
---|
[605] | 1025 | return (*_flow_map)[a]; |
---|
| 1026 | } |
---|
| 1027 | |
---|
[601] | 1028 | /// \brief Return a const reference to the flow map. |
---|
| 1029 | /// |
---|
| 1030 | /// This function returns a const reference to an arc map storing |
---|
| 1031 | /// the found flow. |
---|
| 1032 | /// |
---|
| 1033 | /// \pre \ref run() must be called before using this function. |
---|
| 1034 | const FlowMap& flowMap() const { |
---|
[603] | 1035 | return *_flow_map; |
---|
[601] | 1036 | } |
---|
| 1037 | |
---|
[605] | 1038 | /// \brief Return the potential (dual value) of the given node. |
---|
| 1039 | /// |
---|
| 1040 | /// This function returns the potential (dual value) of the |
---|
| 1041 | /// given node. |
---|
| 1042 | /// |
---|
| 1043 | /// \pre \ref run() must be called before using this function. |
---|
[607] | 1044 | Cost potential(const Node& n) const { |
---|
[605] | 1045 | return (*_potential_map)[n]; |
---|
| 1046 | } |
---|
| 1047 | |
---|
[601] | 1048 | /// \brief Return a const reference to the potential map |
---|
| 1049 | /// (the dual solution). |
---|
| 1050 | /// |
---|
| 1051 | /// This function returns a const reference to a node map storing |
---|
[605] | 1052 | /// the found potentials, which form the dual solution of the |
---|
| 1053 | /// \ref min_cost_flow "minimum cost flow" problem. |
---|
[601] | 1054 | /// |
---|
| 1055 | /// \pre \ref run() must be called before using this function. |
---|
| 1056 | const PotentialMap& potentialMap() const { |
---|
[603] | 1057 | return *_potential_map; |
---|
[601] | 1058 | } |
---|
| 1059 | |
---|
| 1060 | /// @} |
---|
| 1061 | |
---|
| 1062 | private: |
---|
| 1063 | |
---|
| 1064 | // Initialize internal data structures |
---|
| 1065 | bool init() { |
---|
| 1066 | // Initialize result maps |
---|
[603] | 1067 | if (!_flow_map) { |
---|
| 1068 | _flow_map = new FlowMap(_graph); |
---|
[601] | 1069 | _local_flow = true; |
---|
| 1070 | } |
---|
[603] | 1071 | if (!_potential_map) { |
---|
| 1072 | _potential_map = new PotentialMap(_graph); |
---|
[601] | 1073 | _local_potential = true; |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | // Initialize vectors |
---|
[603] | 1077 | _node_num = countNodes(_graph); |
---|
| 1078 | _arc_num = countArcs(_graph); |
---|
[601] | 1079 | int all_node_num = _node_num + 1; |
---|
[603] | 1080 | int all_arc_num = _arc_num + _node_num; |
---|
[605] | 1081 | if (_node_num == 0) return false; |
---|
[601] | 1082 | |
---|
[603] | 1083 | _arc_ref.resize(_arc_num); |
---|
| 1084 | _source.resize(all_arc_num); |
---|
| 1085 | _target.resize(all_arc_num); |
---|
[601] | 1086 | |
---|
[603] | 1087 | _cap.resize(all_arc_num); |
---|
| 1088 | _cost.resize(all_arc_num); |
---|
[601] | 1089 | _supply.resize(all_node_num); |
---|
[606] | 1090 | _flow.resize(all_arc_num); |
---|
| 1091 | _pi.resize(all_node_num); |
---|
[601] | 1092 | |
---|
| 1093 | _parent.resize(all_node_num); |
---|
| 1094 | _pred.resize(all_node_num); |
---|
[603] | 1095 | _forward.resize(all_node_num); |
---|
[601] | 1096 | _thread.resize(all_node_num); |
---|
[604] | 1097 | _rev_thread.resize(all_node_num); |
---|
| 1098 | _succ_num.resize(all_node_num); |
---|
| 1099 | _last_succ.resize(all_node_num); |
---|
[606] | 1100 | _state.resize(all_arc_num); |
---|
[601] | 1101 | |
---|
| 1102 | // Initialize node related data |
---|
| 1103 | bool valid_supply = true; |
---|
[609] | 1104 | Flow sum_supply = 0; |
---|
[605] | 1105 | if (!_pstsup && !_psupply) { |
---|
| 1106 | _pstsup = true; |
---|
| 1107 | _psource = _ptarget = NodeIt(_graph); |
---|
| 1108 | _pstflow = 0; |
---|
| 1109 | } |
---|
| 1110 | if (_psupply) { |
---|
[601] | 1111 | int i = 0; |
---|
[603] | 1112 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
[601] | 1113 | _node_id[n] = i; |
---|
[605] | 1114 | _supply[i] = (*_psupply)[n]; |
---|
[609] | 1115 | sum_supply += _supply[i]; |
---|
[601] | 1116 | } |
---|
[609] | 1117 | valid_supply = (_ptype == GEQ && sum_supply <= 0) || |
---|
| 1118 | (_ptype == LEQ && sum_supply >= 0); |
---|
[601] | 1119 | } else { |
---|
| 1120 | int i = 0; |
---|
[603] | 1121 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
[601] | 1122 | _node_id[n] = i; |
---|
| 1123 | _supply[i] = 0; |
---|
| 1124 | } |
---|
[605] | 1125 | _supply[_node_id[_psource]] = _pstflow; |
---|
[609] | 1126 | _supply[_node_id[_ptarget]] = -_pstflow; |
---|
[601] | 1127 | } |
---|
| 1128 | if (!valid_supply) return false; |
---|
| 1129 | |
---|
[609] | 1130 | // Infinite capacity value |
---|
| 1131 | Flow inf_cap = |
---|
| 1132 | std::numeric_limits<Flow>::has_infinity ? |
---|
| 1133 | std::numeric_limits<Flow>::infinity() : |
---|
| 1134 | std::numeric_limits<Flow>::max(); |
---|
| 1135 | |
---|
| 1136 | // Initialize artifical cost |
---|
| 1137 | Cost art_cost; |
---|
| 1138 | if (std::numeric_limits<Cost>::is_exact) { |
---|
| 1139 | art_cost = std::numeric_limits<Cost>::max() / 4 + 1; |
---|
| 1140 | } else { |
---|
| 1141 | art_cost = std::numeric_limits<Cost>::min(); |
---|
| 1142 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1143 | if (_cost[i] > art_cost) art_cost = _cost[i]; |
---|
| 1144 | } |
---|
| 1145 | art_cost = (art_cost + 1) * _node_num; |
---|
| 1146 | } |
---|
| 1147 | |
---|
| 1148 | // Run Circulation to check if a feasible solution exists |
---|
| 1149 | typedef ConstMap<Arc, Flow> ConstArcMap; |
---|
[613] | 1150 | ConstArcMap zero_arc_map(0), inf_arc_map(inf_cap); |
---|
[609] | 1151 | FlowNodeMap *csup = NULL; |
---|
| 1152 | bool local_csup = false; |
---|
| 1153 | if (_psupply) { |
---|
| 1154 | csup = _psupply; |
---|
| 1155 | } else { |
---|
| 1156 | csup = new FlowNodeMap(_graph, 0); |
---|
| 1157 | (*csup)[_psource] = _pstflow; |
---|
| 1158 | (*csup)[_ptarget] = -_pstflow; |
---|
| 1159 | local_csup = true; |
---|
| 1160 | } |
---|
| 1161 | bool circ_result = false; |
---|
| 1162 | if (_ptype == GEQ || (_ptype == LEQ && sum_supply == 0)) { |
---|
| 1163 | // GEQ problem type |
---|
| 1164 | if (_plower) { |
---|
| 1165 | if (_pupper) { |
---|
| 1166 | Circulation<GR, FlowArcMap, FlowArcMap, FlowNodeMap> |
---|
| 1167 | circ(_graph, *_plower, *_pupper, *csup); |
---|
| 1168 | circ_result = circ.run(); |
---|
| 1169 | } else { |
---|
| 1170 | Circulation<GR, FlowArcMap, ConstArcMap, FlowNodeMap> |
---|
[613] | 1171 | circ(_graph, *_plower, inf_arc_map, *csup); |
---|
[609] | 1172 | circ_result = circ.run(); |
---|
| 1173 | } |
---|
| 1174 | } else { |
---|
| 1175 | if (_pupper) { |
---|
| 1176 | Circulation<GR, ConstArcMap, FlowArcMap, FlowNodeMap> |
---|
[613] | 1177 | circ(_graph, zero_arc_map, *_pupper, *csup); |
---|
[609] | 1178 | circ_result = circ.run(); |
---|
| 1179 | } else { |
---|
| 1180 | Circulation<GR, ConstArcMap, ConstArcMap, FlowNodeMap> |
---|
[613] | 1181 | circ(_graph, zero_arc_map, inf_arc_map, *csup); |
---|
[609] | 1182 | circ_result = circ.run(); |
---|
| 1183 | } |
---|
| 1184 | } |
---|
| 1185 | } else { |
---|
| 1186 | // LEQ problem type |
---|
| 1187 | typedef ReverseDigraph<const GR> RevGraph; |
---|
| 1188 | typedef NegMap<FlowNodeMap> NegNodeMap; |
---|
| 1189 | RevGraph rgraph(_graph); |
---|
| 1190 | NegNodeMap neg_csup(*csup); |
---|
| 1191 | if (_plower) { |
---|
| 1192 | if (_pupper) { |
---|
| 1193 | Circulation<RevGraph, FlowArcMap, FlowArcMap, NegNodeMap> |
---|
| 1194 | circ(rgraph, *_plower, *_pupper, neg_csup); |
---|
| 1195 | circ_result = circ.run(); |
---|
| 1196 | } else { |
---|
| 1197 | Circulation<RevGraph, FlowArcMap, ConstArcMap, NegNodeMap> |
---|
[613] | 1198 | circ(rgraph, *_plower, inf_arc_map, neg_csup); |
---|
[609] | 1199 | circ_result = circ.run(); |
---|
| 1200 | } |
---|
| 1201 | } else { |
---|
| 1202 | if (_pupper) { |
---|
| 1203 | Circulation<RevGraph, ConstArcMap, FlowArcMap, NegNodeMap> |
---|
[613] | 1204 | circ(rgraph, zero_arc_map, *_pupper, neg_csup); |
---|
[609] | 1205 | circ_result = circ.run(); |
---|
| 1206 | } else { |
---|
| 1207 | Circulation<RevGraph, ConstArcMap, ConstArcMap, NegNodeMap> |
---|
[613] | 1208 | circ(rgraph, zero_arc_map, inf_arc_map, neg_csup); |
---|
[609] | 1209 | circ_result = circ.run(); |
---|
| 1210 | } |
---|
| 1211 | } |
---|
| 1212 | } |
---|
| 1213 | if (local_csup) delete csup; |
---|
| 1214 | if (!circ_result) return false; |
---|
| 1215 | |
---|
[601] | 1216 | // Set data for the artificial root node |
---|
| 1217 | _root = _node_num; |
---|
| 1218 | _parent[_root] = -1; |
---|
| 1219 | _pred[_root] = -1; |
---|
| 1220 | _thread[_root] = 0; |
---|
[604] | 1221 | _rev_thread[0] = _root; |
---|
| 1222 | _succ_num[_root] = all_node_num; |
---|
| 1223 | _last_succ[_root] = _root - 1; |
---|
[609] | 1224 | _supply[_root] = -sum_supply; |
---|
| 1225 | if (sum_supply < 0) { |
---|
| 1226 | _pi[_root] = -art_cost; |
---|
| 1227 | } else { |
---|
| 1228 | _pi[_root] = art_cost; |
---|
| 1229 | } |
---|
[601] | 1230 | |
---|
| 1231 | // Store the arcs in a mixed order |
---|
[612] | 1232 | int k = std::max(int(std::sqrt(double(_arc_num))), 10); |
---|
[601] | 1233 | int i = 0; |
---|
[603] | 1234 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 1235 | _arc_ref[i] = e; |
---|
[601] | 1236 | if ((i += k) >= _arc_num) i = (i % k) + 1; |
---|
| 1237 | } |
---|
| 1238 | |
---|
| 1239 | // Initialize arc maps |
---|
[605] | 1240 | if (_pupper && _pcost) { |
---|
| 1241 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1242 | Arc e = _arc_ref[i]; |
---|
| 1243 | _source[i] = _node_id[_graph.source(e)]; |
---|
| 1244 | _target[i] = _node_id[_graph.target(e)]; |
---|
| 1245 | _cap[i] = (*_pupper)[e]; |
---|
| 1246 | _cost[i] = (*_pcost)[e]; |
---|
[606] | 1247 | _flow[i] = 0; |
---|
| 1248 | _state[i] = STATE_LOWER; |
---|
[605] | 1249 | } |
---|
| 1250 | } else { |
---|
| 1251 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1252 | Arc e = _arc_ref[i]; |
---|
| 1253 | _source[i] = _node_id[_graph.source(e)]; |
---|
| 1254 | _target[i] = _node_id[_graph.target(e)]; |
---|
[606] | 1255 | _flow[i] = 0; |
---|
| 1256 | _state[i] = STATE_LOWER; |
---|
[605] | 1257 | } |
---|
| 1258 | if (_pupper) { |
---|
| 1259 | for (int i = 0; i != _arc_num; ++i) |
---|
| 1260 | _cap[i] = (*_pupper)[_arc_ref[i]]; |
---|
| 1261 | } else { |
---|
| 1262 | for (int i = 0; i != _arc_num; ++i) |
---|
[608] | 1263 | _cap[i] = inf_cap; |
---|
[605] | 1264 | } |
---|
| 1265 | if (_pcost) { |
---|
| 1266 | for (int i = 0; i != _arc_num; ++i) |
---|
| 1267 | _cost[i] = (*_pcost)[_arc_ref[i]]; |
---|
| 1268 | } else { |
---|
| 1269 | for (int i = 0; i != _arc_num; ++i) |
---|
| 1270 | _cost[i] = 1; |
---|
| 1271 | } |
---|
[601] | 1272 | } |
---|
[608] | 1273 | |
---|
[601] | 1274 | // Remove non-zero lower bounds |
---|
[605] | 1275 | if (_plower) { |
---|
[601] | 1276 | for (int i = 0; i != _arc_num; ++i) { |
---|
[607] | 1277 | Flow c = (*_plower)[_arc_ref[i]]; |
---|
[601] | 1278 | if (c != 0) { |
---|
| 1279 | _cap[i] -= c; |
---|
| 1280 | _supply[_source[i]] -= c; |
---|
| 1281 | _supply[_target[i]] += c; |
---|
| 1282 | } |
---|
| 1283 | } |
---|
| 1284 | } |
---|
| 1285 | |
---|
| 1286 | // Add artificial arcs and initialize the spanning tree data structure |
---|
| 1287 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1288 | _thread[u] = u + 1; |
---|
[604] | 1289 | _rev_thread[u + 1] = u; |
---|
| 1290 | _succ_num[u] = 1; |
---|
| 1291 | _last_succ[u] = u; |
---|
[601] | 1292 | _parent[u] = _root; |
---|
| 1293 | _pred[u] = e; |
---|
[608] | 1294 | _cost[e] = art_cost; |
---|
| 1295 | _cap[e] = inf_cap; |
---|
[606] | 1296 | _state[e] = STATE_TREE; |
---|
[609] | 1297 | if (_supply[u] > 0 || (_supply[u] == 0 && sum_supply <= 0)) { |
---|
[601] | 1298 | _flow[e] = _supply[u]; |
---|
| 1299 | _forward[u] = true; |
---|
[609] | 1300 | _pi[u] = -art_cost + _pi[_root]; |
---|
[601] | 1301 | } else { |
---|
| 1302 | _flow[e] = -_supply[u]; |
---|
| 1303 | _forward[u] = false; |
---|
[609] | 1304 | _pi[u] = art_cost + _pi[_root]; |
---|
[601] | 1305 | } |
---|
| 1306 | } |
---|
| 1307 | |
---|
| 1308 | return true; |
---|
| 1309 | } |
---|
| 1310 | |
---|
| 1311 | // Find the join node |
---|
| 1312 | void findJoinNode() { |
---|
[603] | 1313 | int u = _source[in_arc]; |
---|
| 1314 | int v = _target[in_arc]; |
---|
[601] | 1315 | while (u != v) { |
---|
[604] | 1316 | if (_succ_num[u] < _succ_num[v]) { |
---|
| 1317 | u = _parent[u]; |
---|
| 1318 | } else { |
---|
| 1319 | v = _parent[v]; |
---|
| 1320 | } |
---|
[601] | 1321 | } |
---|
| 1322 | join = u; |
---|
| 1323 | } |
---|
| 1324 | |
---|
| 1325 | // Find the leaving arc of the cycle and returns true if the |
---|
| 1326 | // leaving arc is not the same as the entering arc |
---|
| 1327 | bool findLeavingArc() { |
---|
| 1328 | // Initialize first and second nodes according to the direction |
---|
| 1329 | // of the cycle |
---|
[603] | 1330 | if (_state[in_arc] == STATE_LOWER) { |
---|
| 1331 | first = _source[in_arc]; |
---|
| 1332 | second = _target[in_arc]; |
---|
[601] | 1333 | } else { |
---|
[603] | 1334 | first = _target[in_arc]; |
---|
| 1335 | second = _source[in_arc]; |
---|
[601] | 1336 | } |
---|
[603] | 1337 | delta = _cap[in_arc]; |
---|
[601] | 1338 | int result = 0; |
---|
[607] | 1339 | Flow d; |
---|
[601] | 1340 | int e; |
---|
| 1341 | |
---|
| 1342 | // Search the cycle along the path form the first node to the root |
---|
| 1343 | for (int u = first; u != join; u = _parent[u]) { |
---|
| 1344 | e = _pred[u]; |
---|
| 1345 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
| 1346 | if (d < delta) { |
---|
| 1347 | delta = d; |
---|
| 1348 | u_out = u; |
---|
| 1349 | result = 1; |
---|
| 1350 | } |
---|
| 1351 | } |
---|
| 1352 | // Search the cycle along the path form the second node to the root |
---|
| 1353 | for (int u = second; u != join; u = _parent[u]) { |
---|
| 1354 | e = _pred[u]; |
---|
| 1355 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
| 1356 | if (d <= delta) { |
---|
| 1357 | delta = d; |
---|
| 1358 | u_out = u; |
---|
| 1359 | result = 2; |
---|
| 1360 | } |
---|
| 1361 | } |
---|
| 1362 | |
---|
| 1363 | if (result == 1) { |
---|
| 1364 | u_in = first; |
---|
| 1365 | v_in = second; |
---|
| 1366 | } else { |
---|
| 1367 | u_in = second; |
---|
| 1368 | v_in = first; |
---|
| 1369 | } |
---|
| 1370 | return result != 0; |
---|
| 1371 | } |
---|
| 1372 | |
---|
| 1373 | // Change _flow and _state vectors |
---|
| 1374 | void changeFlow(bool change) { |
---|
| 1375 | // Augment along the cycle |
---|
| 1376 | if (delta > 0) { |
---|
[607] | 1377 | Flow val = _state[in_arc] * delta; |
---|
[603] | 1378 | _flow[in_arc] += val; |
---|
| 1379 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
[601] | 1380 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
| 1381 | } |
---|
[603] | 1382 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
[601] | 1383 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
| 1384 | } |
---|
| 1385 | } |
---|
| 1386 | // Update the state of the entering and leaving arcs |
---|
| 1387 | if (change) { |
---|
[603] | 1388 | _state[in_arc] = STATE_TREE; |
---|
[601] | 1389 | _state[_pred[u_out]] = |
---|
| 1390 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
| 1391 | } else { |
---|
[603] | 1392 | _state[in_arc] = -_state[in_arc]; |
---|
[601] | 1393 | } |
---|
| 1394 | } |
---|
| 1395 | |
---|
[604] | 1396 | // Update the tree structure |
---|
| 1397 | void updateTreeStructure() { |
---|
| 1398 | int u, w; |
---|
| 1399 | int old_rev_thread = _rev_thread[u_out]; |
---|
| 1400 | int old_succ_num = _succ_num[u_out]; |
---|
| 1401 | int old_last_succ = _last_succ[u_out]; |
---|
[601] | 1402 | v_out = _parent[u_out]; |
---|
| 1403 | |
---|
[604] | 1404 | u = _last_succ[u_in]; // the last successor of u_in |
---|
| 1405 | right = _thread[u]; // the node after it |
---|
| 1406 | |
---|
| 1407 | // Handle the case when old_rev_thread equals to v_in |
---|
| 1408 | // (it also means that join and v_out coincide) |
---|
| 1409 | if (old_rev_thread == v_in) { |
---|
| 1410 | last = _thread[_last_succ[u_out]]; |
---|
| 1411 | } else { |
---|
| 1412 | last = _thread[v_in]; |
---|
[601] | 1413 | } |
---|
| 1414 | |
---|
[604] | 1415 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
| 1416 | // between u_in and u_out, whose parent have to be changed) |
---|
[601] | 1417 | _thread[v_in] = stem = u_in; |
---|
[604] | 1418 | _dirty_revs.clear(); |
---|
| 1419 | _dirty_revs.push_back(v_in); |
---|
[601] | 1420 | par_stem = v_in; |
---|
| 1421 | while (stem != u_out) { |
---|
[604] | 1422 | // Insert the next stem node into the thread list |
---|
| 1423 | new_stem = _parent[stem]; |
---|
| 1424 | _thread[u] = new_stem; |
---|
| 1425 | _dirty_revs.push_back(u); |
---|
[601] | 1426 | |
---|
[604] | 1427 | // Remove the subtree of stem from the thread list |
---|
| 1428 | w = _rev_thread[stem]; |
---|
| 1429 | _thread[w] = right; |
---|
| 1430 | _rev_thread[right] = w; |
---|
[601] | 1431 | |
---|
[604] | 1432 | // Change the parent node and shift stem nodes |
---|
[601] | 1433 | _parent[stem] = par_stem; |
---|
| 1434 | par_stem = stem; |
---|
| 1435 | stem = new_stem; |
---|
| 1436 | |
---|
[604] | 1437 | // Update u and right |
---|
| 1438 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
| 1439 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
[601] | 1440 | right = _thread[u]; |
---|
| 1441 | } |
---|
| 1442 | _parent[u_out] = par_stem; |
---|
| 1443 | _thread[u] = last; |
---|
[604] | 1444 | _rev_thread[last] = u; |
---|
| 1445 | _last_succ[u_out] = u; |
---|
[601] | 1446 | |
---|
[604] | 1447 | // Remove the subtree of u_out from the thread list except for |
---|
| 1448 | // the case when old_rev_thread equals to v_in |
---|
| 1449 | // (it also means that join and v_out coincide) |
---|
| 1450 | if (old_rev_thread != v_in) { |
---|
| 1451 | _thread[old_rev_thread] = right; |
---|
| 1452 | _rev_thread[right] = old_rev_thread; |
---|
| 1453 | } |
---|
| 1454 | |
---|
| 1455 | // Update _rev_thread using the new _thread values |
---|
| 1456 | for (int i = 0; i < int(_dirty_revs.size()); ++i) { |
---|
| 1457 | u = _dirty_revs[i]; |
---|
| 1458 | _rev_thread[_thread[u]] = u; |
---|
| 1459 | } |
---|
| 1460 | |
---|
| 1461 | // Update _pred, _forward, _last_succ and _succ_num for the |
---|
| 1462 | // stem nodes from u_out to u_in |
---|
| 1463 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
| 1464 | u = u_out; |
---|
| 1465 | while (u != u_in) { |
---|
| 1466 | w = _parent[u]; |
---|
| 1467 | _pred[u] = _pred[w]; |
---|
| 1468 | _forward[u] = !_forward[w]; |
---|
| 1469 | tmp_sc += _succ_num[u] - _succ_num[w]; |
---|
| 1470 | _succ_num[u] = tmp_sc; |
---|
| 1471 | _last_succ[w] = tmp_ls; |
---|
| 1472 | u = w; |
---|
| 1473 | } |
---|
| 1474 | _pred[u_in] = in_arc; |
---|
| 1475 | _forward[u_in] = (u_in == _source[in_arc]); |
---|
| 1476 | _succ_num[u_in] = old_succ_num; |
---|
| 1477 | |
---|
| 1478 | // Set limits for updating _last_succ form v_in and v_out |
---|
| 1479 | // towards the root |
---|
| 1480 | int up_limit_in = -1; |
---|
| 1481 | int up_limit_out = -1; |
---|
| 1482 | if (_last_succ[join] == v_in) { |
---|
| 1483 | up_limit_out = join; |
---|
[601] | 1484 | } else { |
---|
[604] | 1485 | up_limit_in = join; |
---|
| 1486 | } |
---|
| 1487 | |
---|
| 1488 | // Update _last_succ from v_in towards the root |
---|
| 1489 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
| 1490 | u = _parent[u]) { |
---|
| 1491 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1492 | } |
---|
| 1493 | // Update _last_succ from v_out towards the root |
---|
| 1494 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
| 1495 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1496 | u = _parent[u]) { |
---|
| 1497 | _last_succ[u] = old_rev_thread; |
---|
| 1498 | } |
---|
| 1499 | } else { |
---|
| 1500 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1501 | u = _parent[u]) { |
---|
| 1502 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1503 | } |
---|
| 1504 | } |
---|
| 1505 | |
---|
| 1506 | // Update _succ_num from v_in to join |
---|
| 1507 | for (u = v_in; u != join; u = _parent[u]) { |
---|
| 1508 | _succ_num[u] += old_succ_num; |
---|
| 1509 | } |
---|
| 1510 | // Update _succ_num from v_out to join |
---|
| 1511 | for (u = v_out; u != join; u = _parent[u]) { |
---|
| 1512 | _succ_num[u] -= old_succ_num; |
---|
[601] | 1513 | } |
---|
| 1514 | } |
---|
| 1515 | |
---|
[604] | 1516 | // Update potentials |
---|
| 1517 | void updatePotential() { |
---|
[607] | 1518 | Cost sigma = _forward[u_in] ? |
---|
[601] | 1519 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
| 1520 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
[608] | 1521 | // Update potentials in the subtree, which has been moved |
---|
| 1522 | int end = _thread[_last_succ[u_in]]; |
---|
| 1523 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
| 1524 | _pi[u] += sigma; |
---|
[601] | 1525 | } |
---|
| 1526 | } |
---|
| 1527 | |
---|
| 1528 | // Execute the algorithm |
---|
[605] | 1529 | bool start(PivotRule pivot_rule) { |
---|
[601] | 1530 | // Select the pivot rule implementation |
---|
| 1531 | switch (pivot_rule) { |
---|
[605] | 1532 | case FIRST_ELIGIBLE: |
---|
[601] | 1533 | return start<FirstEligiblePivotRule>(); |
---|
[605] | 1534 | case BEST_ELIGIBLE: |
---|
[601] | 1535 | return start<BestEligiblePivotRule>(); |
---|
[605] | 1536 | case BLOCK_SEARCH: |
---|
[601] | 1537 | return start<BlockSearchPivotRule>(); |
---|
[605] | 1538 | case CANDIDATE_LIST: |
---|
[601] | 1539 | return start<CandidateListPivotRule>(); |
---|
[605] | 1540 | case ALTERING_LIST: |
---|
[601] | 1541 | return start<AlteringListPivotRule>(); |
---|
| 1542 | } |
---|
| 1543 | return false; |
---|
| 1544 | } |
---|
| 1545 | |
---|
[605] | 1546 | template <typename PivotRuleImpl> |
---|
[601] | 1547 | bool start() { |
---|
[605] | 1548 | PivotRuleImpl pivot(*this); |
---|
[601] | 1549 | |
---|
[605] | 1550 | // Execute the Network Simplex algorithm |
---|
[601] | 1551 | while (pivot.findEnteringArc()) { |
---|
| 1552 | findJoinNode(); |
---|
| 1553 | bool change = findLeavingArc(); |
---|
| 1554 | changeFlow(change); |
---|
| 1555 | if (change) { |
---|
[604] | 1556 | updateTreeStructure(); |
---|
| 1557 | updatePotential(); |
---|
[601] | 1558 | } |
---|
| 1559 | } |
---|
| 1560 | |
---|
[603] | 1561 | // Copy flow values to _flow_map |
---|
[605] | 1562 | if (_plower) { |
---|
[601] | 1563 | for (int i = 0; i != _arc_num; ++i) { |
---|
[603] | 1564 | Arc e = _arc_ref[i]; |
---|
[605] | 1565 | _flow_map->set(e, (*_plower)[e] + _flow[i]); |
---|
[601] | 1566 | } |
---|
| 1567 | } else { |
---|
| 1568 | for (int i = 0; i != _arc_num; ++i) { |
---|
[603] | 1569 | _flow_map->set(_arc_ref[i], _flow[i]); |
---|
[601] | 1570 | } |
---|
| 1571 | } |
---|
[603] | 1572 | // Copy potential values to _potential_map |
---|
| 1573 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1574 | _potential_map->set(n, _pi[_node_id[n]]); |
---|
[601] | 1575 | } |
---|
| 1576 | |
---|
| 1577 | return true; |
---|
| 1578 | } |
---|
| 1579 | |
---|
| 1580 | }; //class NetworkSimplex |
---|
| 1581 | |
---|
| 1582 | ///@} |
---|
| 1583 | |
---|
| 1584 | } //namespace lemon |
---|
| 1585 | |
---|
| 1586 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|