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