[648] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2009 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_NETWORK_SIMPLEX_H |
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| 20 | #define LEMON_NETWORK_SIMPLEX_H |
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| 21 | |
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[710] | 22 | /// \ingroup min_cost_flow_algs |
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[648] | 23 | /// |
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| 24 | /// \file |
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[652] | 25 | /// \brief Network Simplex algorithm for finding a minimum cost flow. |
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[648] | 26 | |
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| 27 | #include <vector> |
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| 28 | #include <limits> |
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| 29 | #include <algorithm> |
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| 30 | |
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[650] | 31 | #include <lemon/core.h> |
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[648] | 32 | #include <lemon/math.h> |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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[710] | 36 | /// \addtogroup min_cost_flow_algs |
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[648] | 37 | /// @{ |
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| 38 | |
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[652] | 39 | /// \brief Implementation of the primal Network Simplex algorithm |
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[648] | 40 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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| 41 | /// |
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[652] | 42 | /// \ref NetworkSimplex implements the primal Network Simplex algorithm |
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[802] | 43 | /// for finding a \ref min_cost_flow "minimum cost flow" |
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| 44 | /// \ref amo93networkflows, \ref dantzig63linearprog, |
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| 45 | /// \ref kellyoneill91netsimplex. |
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[878] | 46 | /// This algorithm is a highly efficient specialized version of the |
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| 47 | /// linear programming simplex method directly for the minimum cost |
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| 48 | /// flow problem. |
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[653] | 49 | /// |
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[878] | 50 | /// In general, %NetworkSimplex is the fastest implementation available |
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| 51 | /// in LEMON for this problem. |
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| 52 | /// Moreover, it supports both directions of the supply/demand inequality |
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[833] | 53 | /// constraints. For more information, see \ref SupplyType. |
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[687] | 54 | /// |
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| 55 | /// Most of the parameters of the problem (except for the digraph) |
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| 56 | /// can be given using separate functions, and the algorithm can be |
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| 57 | /// executed using the \ref run() function. If some parameters are not |
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| 58 | /// specified, then default values will be used. |
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[648] | 59 | /// |
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[652] | 60 | /// \tparam GR The digraph type the algorithm runs on. |
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[878] | 61 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[833] | 62 | /// and supply values in the algorithm. By default, it is \c int. |
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[878] | 63 | /// \tparam C The number type used for costs and potentials in the |
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[833] | 64 | /// algorithm. By default, it is the same as \c V. |
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[648] | 65 | /// |
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[878] | 66 | /// \warning Both number types must be signed and all input data must |
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[655] | 67 | /// be integer. |
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[648] | 68 | /// |
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[652] | 69 | /// \note %NetworkSimplex provides five different pivot rule |
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[656] | 70 | /// implementations, from which the most efficient one is used |
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[833] | 71 | /// by default. For more information, see \ref PivotRule. |
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[688] | 72 | template <typename GR, typename V = int, typename C = V> |
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[648] | 73 | class NetworkSimplex |
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| 74 | { |
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[652] | 75 | public: |
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[648] | 76 | |
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[689] | 77 | /// The type of the flow amounts, capacity bounds and supply values |
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[688] | 78 | typedef V Value; |
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[689] | 79 | /// The type of the arc costs |
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[654] | 80 | typedef C Cost; |
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[652] | 81 | |
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| 82 | public: |
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| 83 | |
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[687] | 84 | /// \brief Problem type constants for the \c run() function. |
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[652] | 85 | /// |
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[687] | 86 | /// Enum type containing the problem type constants that can be |
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| 87 | /// returned by the \ref run() function of the algorithm. |
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| 88 | enum ProblemType { |
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| 89 | /// The problem has no feasible solution (flow). |
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| 90 | INFEASIBLE, |
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| 91 | /// The problem has optimal solution (i.e. it is feasible and |
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| 92 | /// bounded), and the algorithm has found optimal flow and node |
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| 93 | /// potentials (primal and dual solutions). |
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| 94 | OPTIMAL, |
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| 95 | /// The objective function of the problem is unbounded, i.e. |
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| 96 | /// there is a directed cycle having negative total cost and |
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| 97 | /// infinite upper bound. |
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| 98 | UNBOUNDED |
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| 99 | }; |
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| 100 | |
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| 101 | /// \brief Constants for selecting the type of the supply constraints. |
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| 102 | /// |
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| 103 | /// Enum type containing constants for selecting the supply type, |
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| 104 | /// i.e. the direction of the inequalities in the supply/demand |
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| 105 | /// constraints of the \ref min_cost_flow "minimum cost flow problem". |
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| 106 | /// |
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[710] | 107 | /// The default supply type is \c GEQ, the \c LEQ type can be |
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| 108 | /// selected using \ref supplyType(). |
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| 109 | /// The equality form is a special case of both supply types. |
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[687] | 110 | enum SupplyType { |
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| 111 | /// This option means that there are <em>"greater or equal"</em> |
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[710] | 112 | /// supply/demand constraints in the definition of the problem. |
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[687] | 113 | GEQ, |
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| 114 | /// This option means that there are <em>"less or equal"</em> |
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[710] | 115 | /// supply/demand constraints in the definition of the problem. |
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| 116 | LEQ |
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[687] | 117 | }; |
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| 118 | |
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| 119 | /// \brief Constants for selecting the pivot rule. |
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| 120 | /// |
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| 121 | /// Enum type containing constants for selecting the pivot rule for |
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| 122 | /// the \ref run() function. |
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| 123 | /// |
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[652] | 124 | /// \ref NetworkSimplex provides five different pivot rule |
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| 125 | /// implementations that significantly affect the running time |
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| 126 | /// of the algorithm. |
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[833] | 127 | /// By default, \ref BLOCK_SEARCH "Block Search" is used, which |
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[652] | 128 | /// proved to be the most efficient and the most robust on various |
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[878] | 129 | /// test inputs. |
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[833] | 130 | /// However, another pivot rule can be selected using the \ref run() |
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[652] | 131 | /// function with the proper parameter. |
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| 132 | enum PivotRule { |
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| 133 | |
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[833] | 134 | /// The \e First \e Eligible pivot rule. |
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[652] | 135 | /// The next eligible arc is selected in a wraparound fashion |
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| 136 | /// in every iteration. |
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| 137 | FIRST_ELIGIBLE, |
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| 138 | |
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[833] | 139 | /// The \e Best \e Eligible pivot rule. |
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[652] | 140 | /// The best eligible arc is selected in every iteration. |
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| 141 | BEST_ELIGIBLE, |
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| 142 | |
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[833] | 143 | /// The \e Block \e Search pivot rule. |
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[652] | 144 | /// A specified number of arcs are examined in every iteration |
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| 145 | /// in a wraparound fashion and the best eligible arc is selected |
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| 146 | /// from this block. |
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| 147 | BLOCK_SEARCH, |
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| 148 | |
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[833] | 149 | /// The \e Candidate \e List pivot rule. |
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[652] | 150 | /// In a major iteration a candidate list is built from eligible arcs |
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| 151 | /// in a wraparound fashion and in the following minor iterations |
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| 152 | /// the best eligible arc is selected from this list. |
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| 153 | CANDIDATE_LIST, |
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| 154 | |
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[833] | 155 | /// The \e Altering \e Candidate \e List pivot rule. |
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[652] | 156 | /// It is a modified version of the Candidate List method. |
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| 157 | /// It keeps only the several best eligible arcs from the former |
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| 158 | /// candidate list and extends this list in every iteration. |
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| 159 | ALTERING_LIST |
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| 160 | }; |
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[656] | 161 | |
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[652] | 162 | private: |
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| 163 | |
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| 164 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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| 165 | |
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[648] | 166 | typedef std::vector<int> IntVector; |
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[689] | 167 | typedef std::vector<Value> ValueVector; |
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[654] | 168 | typedef std::vector<Cost> CostVector; |
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[910] | 169 | typedef std::vector<char> BoolVector; |
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| 170 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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[648] | 171 | |
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| 172 | // State constants for arcs |
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| 173 | enum ArcStateEnum { |
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| 174 | STATE_UPPER = -1, |
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| 175 | STATE_TREE = 0, |
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| 176 | STATE_LOWER = 1 |
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| 177 | }; |
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| 178 | |
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| 179 | private: |
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| 180 | |
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[652] | 181 | // Data related to the underlying digraph |
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| 182 | const GR &_graph; |
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| 183 | int _node_num; |
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| 184 | int _arc_num; |
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[710] | 185 | int _all_arc_num; |
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| 186 | int _search_arc_num; |
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[652] | 187 | |
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| 188 | // Parameters of the problem |
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[689] | 189 | bool _have_lower; |
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[687] | 190 | SupplyType _stype; |
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[688] | 191 | Value _sum_supply; |
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[648] | 192 | |
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[652] | 193 | // Data structures for storing the digraph |
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[650] | 194 | IntNodeMap _node_id; |
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[689] | 195 | IntArcMap _arc_id; |
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[650] | 196 | IntVector _source; |
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| 197 | IntVector _target; |
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| 198 | |
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[652] | 199 | // Node and arc data |
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[689] | 200 | ValueVector _lower; |
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| 201 | ValueVector _upper; |
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| 202 | ValueVector _cap; |
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[654] | 203 | CostVector _cost; |
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[689] | 204 | ValueVector _supply; |
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| 205 | ValueVector _flow; |
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[654] | 206 | CostVector _pi; |
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[648] | 207 | |
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[650] | 208 | // Data for storing the spanning tree structure |
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[648] | 209 | IntVector _parent; |
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| 210 | IntVector _pred; |
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| 211 | IntVector _thread; |
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[651] | 212 | IntVector _rev_thread; |
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| 213 | IntVector _succ_num; |
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| 214 | IntVector _last_succ; |
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| 215 | IntVector _dirty_revs; |
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[910] | 216 | BoolVector _forward; |
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| 217 | BoolVector _state; |
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[648] | 218 | int _root; |
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| 219 | |
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| 220 | // Temporary data used in the current pivot iteration |
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[650] | 221 | int in_arc, join, u_in, v_in, u_out, v_out; |
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| 222 | int first, second, right, last; |
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[648] | 223 | int stem, par_stem, new_stem; |
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[688] | 224 | Value delta; |
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[877] | 225 | |
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| 226 | const Value MAX; |
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[648] | 227 | |
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[687] | 228 | public: |
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| 229 | |
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| 230 | /// \brief Constant for infinite upper bounds (capacities). |
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| 231 | /// |
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| 232 | /// Constant for infinite upper bounds (capacities). |
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[688] | 233 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 234 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 235 | const Value INF; |
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[687] | 236 | |
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[648] | 237 | private: |
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| 238 | |
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[652] | 239 | // Implementation of the First Eligible pivot rule |
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[648] | 240 | class FirstEligiblePivotRule |
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| 241 | { |
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| 242 | private: |
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| 243 | |
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| 244 | // References to the NetworkSimplex class |
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| 245 | const IntVector &_source; |
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| 246 | const IntVector &_target; |
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[654] | 247 | const CostVector &_cost; |
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[910] | 248 | const BoolVector &_state; |
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[654] | 249 | const CostVector &_pi; |
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[648] | 250 | int &_in_arc; |
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[710] | 251 | int _search_arc_num; |
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[648] | 252 | |
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| 253 | // Pivot rule data |
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| 254 | int _next_arc; |
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| 255 | |
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| 256 | public: |
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| 257 | |
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[652] | 258 | // Constructor |
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[648] | 259 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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[650] | 260 | _source(ns._source), _target(ns._target), |
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[648] | 261 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 262 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
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| 263 | _next_arc(0) |
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[648] | 264 | {} |
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| 265 | |
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[652] | 266 | // Find next entering arc |
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[648] | 267 | bool findEnteringArc() { |
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[654] | 268 | Cost c; |
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[910] | 269 | for (int e = _next_arc; e != _search_arc_num; ++e) { |
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[648] | 270 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 271 | if (c < 0) { |
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| 272 | _in_arc = e; |
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| 273 | _next_arc = e + 1; |
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| 274 | return true; |
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| 275 | } |
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| 276 | } |
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[910] | 277 | for (int e = 0; e != _next_arc; ++e) { |
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[648] | 278 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 279 | if (c < 0) { |
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| 280 | _in_arc = e; |
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| 281 | _next_arc = e + 1; |
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| 282 | return true; |
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| 283 | } |
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| 284 | } |
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| 285 | return false; |
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| 286 | } |
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| 287 | |
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| 288 | }; //class FirstEligiblePivotRule |
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| 289 | |
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| 290 | |
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[652] | 291 | // Implementation of the Best Eligible pivot rule |
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[648] | 292 | class BestEligiblePivotRule |
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| 293 | { |
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| 294 | private: |
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| 295 | |
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| 296 | // References to the NetworkSimplex class |
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| 297 | const IntVector &_source; |
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| 298 | const IntVector &_target; |
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[654] | 299 | const CostVector &_cost; |
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[910] | 300 | const BoolVector &_state; |
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[654] | 301 | const CostVector &_pi; |
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[648] | 302 | int &_in_arc; |
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[710] | 303 | int _search_arc_num; |
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[648] | 304 | |
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| 305 | public: |
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| 306 | |
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[652] | 307 | // Constructor |
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[648] | 308 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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[650] | 309 | _source(ns._source), _target(ns._target), |
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[648] | 310 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 311 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num) |
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[648] | 312 | {} |
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| 313 | |
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[652] | 314 | // Find next entering arc |
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[648] | 315 | bool findEnteringArc() { |
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[654] | 316 | Cost c, min = 0; |
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[910] | 317 | for (int e = 0; e != _search_arc_num; ++e) { |
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[648] | 318 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 319 | if (c < min) { |
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| 320 | min = c; |
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| 321 | _in_arc = e; |
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| 322 | } |
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| 323 | } |
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| 324 | return min < 0; |
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| 325 | } |
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| 326 | |
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| 327 | }; //class BestEligiblePivotRule |
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| 328 | |
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| 329 | |
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[652] | 330 | // Implementation of the Block Search pivot rule |
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[648] | 331 | class BlockSearchPivotRule |
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| 332 | { |
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| 333 | private: |
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| 334 | |
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| 335 | // References to the NetworkSimplex class |
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| 336 | const IntVector &_source; |
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| 337 | const IntVector &_target; |
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[654] | 338 | const CostVector &_cost; |
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[910] | 339 | const BoolVector &_state; |
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[654] | 340 | const CostVector &_pi; |
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[648] | 341 | int &_in_arc; |
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[710] | 342 | int _search_arc_num; |
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[648] | 343 | |
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| 344 | // Pivot rule data |
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| 345 | int _block_size; |
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| 346 | int _next_arc; |
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| 347 | |
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| 348 | public: |
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| 349 | |
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[652] | 350 | // Constructor |
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[648] | 351 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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[650] | 352 | _source(ns._source), _target(ns._target), |
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[648] | 353 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 354 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
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| 355 | _next_arc(0) |
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[648] | 356 | { |
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| 357 | // The main parameters of the pivot rule |
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[910] | 358 | const double BLOCK_SIZE_FACTOR = 1.0; |
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[648] | 359 | const int MIN_BLOCK_SIZE = 10; |
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| 360 | |
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[659] | 361 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
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[710] | 362 | std::sqrt(double(_search_arc_num))), |
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[648] | 363 | MIN_BLOCK_SIZE ); |
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| 364 | } |
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| 365 | |
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[652] | 366 | // Find next entering arc |
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[648] | 367 | bool findEnteringArc() { |
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[654] | 368 | Cost c, min = 0; |
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[648] | 369 | int cnt = _block_size; |
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[774] | 370 | int e; |
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[910] | 371 | for (e = _next_arc; e != _search_arc_num; ++e) { |
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[648] | 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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[774] | 375 | _in_arc = e; |
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[648] | 376 | } |
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| 377 | if (--cnt == 0) { |
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[774] | 378 | if (min < 0) goto search_end; |
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[648] | 379 | cnt = _block_size; |
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| 380 | } |
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| 381 | } |
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[910] | 382 | for (e = 0; e != _next_arc; ++e) { |
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[774] | 383 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 384 | if (c < min) { |
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| 385 | min = c; |
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| 386 | _in_arc = e; |
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| 387 | } |
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| 388 | if (--cnt == 0) { |
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| 389 | if (min < 0) goto search_end; |
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| 390 | cnt = _block_size; |
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[648] | 391 | } |
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| 392 | } |
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| 393 | if (min >= 0) return false; |
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[774] | 394 | |
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| 395 | search_end: |
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[648] | 396 | _next_arc = e; |
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| 397 | return true; |
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| 398 | } |
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| 399 | |
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| 400 | }; //class BlockSearchPivotRule |
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| 401 | |
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| 402 | |
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[652] | 403 | // Implementation of the Candidate List pivot rule |
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[648] | 404 | class CandidateListPivotRule |
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| 405 | { |
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| 406 | private: |
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| 407 | |
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| 408 | // References to the NetworkSimplex class |
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| 409 | const IntVector &_source; |
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| 410 | const IntVector &_target; |
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[654] | 411 | const CostVector &_cost; |
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[910] | 412 | const BoolVector &_state; |
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[654] | 413 | const CostVector &_pi; |
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[648] | 414 | int &_in_arc; |
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[710] | 415 | int _search_arc_num; |
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[648] | 416 | |
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| 417 | // Pivot rule data |
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| 418 | IntVector _candidates; |
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| 419 | int _list_length, _minor_limit; |
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| 420 | int _curr_length, _minor_count; |
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| 421 | int _next_arc; |
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| 422 | |
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| 423 | public: |
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| 424 | |
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| 425 | /// Constructor |
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| 426 | CandidateListPivotRule(NetworkSimplex &ns) : |
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[650] | 427 | _source(ns._source), _target(ns._target), |
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[648] | 428 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 429 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
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| 430 | _next_arc(0) |
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[648] | 431 | { |
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| 432 | // The main parameters of the pivot rule |
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[774] | 433 | const double LIST_LENGTH_FACTOR = 0.25; |
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[648] | 434 | const int MIN_LIST_LENGTH = 10; |
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| 435 | const double MINOR_LIMIT_FACTOR = 0.1; |
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| 436 | const int MIN_MINOR_LIMIT = 3; |
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| 437 | |
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[659] | 438 | _list_length = std::max( int(LIST_LENGTH_FACTOR * |
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[710] | 439 | std::sqrt(double(_search_arc_num))), |
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[648] | 440 | MIN_LIST_LENGTH ); |
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| 441 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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| 442 | MIN_MINOR_LIMIT ); |
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| 443 | _curr_length = _minor_count = 0; |
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| 444 | _candidates.resize(_list_length); |
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| 445 | } |
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| 446 | |
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| 447 | /// Find next entering arc |
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| 448 | bool findEnteringArc() { |
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[654] | 449 | Cost min, c; |
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[774] | 450 | int e; |
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[648] | 451 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
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| 452 | // Minor iteration: select the best eligible arc from the |
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| 453 | // current candidate list |
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| 454 | ++_minor_count; |
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| 455 | min = 0; |
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| 456 | for (int i = 0; i < _curr_length; ++i) { |
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| 457 | e = _candidates[i]; |
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| 458 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 459 | if (c < min) { |
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| 460 | min = c; |
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[774] | 461 | _in_arc = e; |
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[648] | 462 | } |
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[774] | 463 | else if (c >= 0) { |
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[648] | 464 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 465 | } |
---|
| 466 | } |
---|
[774] | 467 | if (min < 0) return true; |
---|
[648] | 468 | } |
---|
| 469 | |
---|
| 470 | // Major iteration: build a new candidate list |
---|
| 471 | min = 0; |
---|
| 472 | _curr_length = 0; |
---|
[910] | 473 | for (e = _next_arc; e != _search_arc_num; ++e) { |
---|
[648] | 474 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 475 | if (c < 0) { |
---|
| 476 | _candidates[_curr_length++] = e; |
---|
| 477 | if (c < min) { |
---|
| 478 | min = c; |
---|
[774] | 479 | _in_arc = e; |
---|
[648] | 480 | } |
---|
[774] | 481 | if (_curr_length == _list_length) goto search_end; |
---|
[648] | 482 | } |
---|
| 483 | } |
---|
[910] | 484 | for (e = 0; e != _next_arc; ++e) { |
---|
[774] | 485 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 486 | if (c < 0) { |
---|
| 487 | _candidates[_curr_length++] = e; |
---|
| 488 | if (c < min) { |
---|
| 489 | min = c; |
---|
| 490 | _in_arc = e; |
---|
[648] | 491 | } |
---|
[774] | 492 | if (_curr_length == _list_length) goto search_end; |
---|
[648] | 493 | } |
---|
| 494 | } |
---|
| 495 | if (_curr_length == 0) return false; |
---|
[774] | 496 | |
---|
| 497 | search_end: |
---|
[648] | 498 | _minor_count = 1; |
---|
| 499 | _next_arc = e; |
---|
| 500 | return true; |
---|
| 501 | } |
---|
| 502 | |
---|
| 503 | }; //class CandidateListPivotRule |
---|
| 504 | |
---|
| 505 | |
---|
[652] | 506 | // Implementation of the Altering Candidate List pivot rule |
---|
[648] | 507 | class AlteringListPivotRule |
---|
| 508 | { |
---|
| 509 | private: |
---|
| 510 | |
---|
| 511 | // References to the NetworkSimplex class |
---|
| 512 | const IntVector &_source; |
---|
| 513 | const IntVector &_target; |
---|
[654] | 514 | const CostVector &_cost; |
---|
[910] | 515 | const BoolVector &_state; |
---|
[654] | 516 | const CostVector &_pi; |
---|
[648] | 517 | int &_in_arc; |
---|
[710] | 518 | int _search_arc_num; |
---|
[648] | 519 | |
---|
| 520 | // Pivot rule data |
---|
| 521 | int _block_size, _head_length, _curr_length; |
---|
| 522 | int _next_arc; |
---|
| 523 | IntVector _candidates; |
---|
[654] | 524 | CostVector _cand_cost; |
---|
[648] | 525 | |
---|
| 526 | // Functor class to compare arcs during sort of the candidate list |
---|
| 527 | class SortFunc |
---|
| 528 | { |
---|
| 529 | private: |
---|
[654] | 530 | const CostVector &_map; |
---|
[648] | 531 | public: |
---|
[654] | 532 | SortFunc(const CostVector &map) : _map(map) {} |
---|
[648] | 533 | bool operator()(int left, int right) { |
---|
| 534 | return _map[left] > _map[right]; |
---|
| 535 | } |
---|
| 536 | }; |
---|
| 537 | |
---|
| 538 | SortFunc _sort_func; |
---|
| 539 | |
---|
| 540 | public: |
---|
| 541 | |
---|
[652] | 542 | // Constructor |
---|
[648] | 543 | AlteringListPivotRule(NetworkSimplex &ns) : |
---|
[650] | 544 | _source(ns._source), _target(ns._target), |
---|
[648] | 545 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
[710] | 546 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
---|
| 547 | _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost) |
---|
[648] | 548 | { |
---|
| 549 | // The main parameters of the pivot rule |
---|
[774] | 550 | const double BLOCK_SIZE_FACTOR = 1.0; |
---|
[648] | 551 | const int MIN_BLOCK_SIZE = 10; |
---|
| 552 | const double HEAD_LENGTH_FACTOR = 0.1; |
---|
| 553 | const int MIN_HEAD_LENGTH = 3; |
---|
| 554 | |
---|
[659] | 555 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
---|
[710] | 556 | std::sqrt(double(_search_arc_num))), |
---|
[648] | 557 | MIN_BLOCK_SIZE ); |
---|
| 558 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
---|
| 559 | MIN_HEAD_LENGTH ); |
---|
| 560 | _candidates.resize(_head_length + _block_size); |
---|
| 561 | _curr_length = 0; |
---|
| 562 | } |
---|
| 563 | |
---|
[652] | 564 | // Find next entering arc |
---|
[648] | 565 | bool findEnteringArc() { |
---|
| 566 | // Check the current candidate list |
---|
| 567 | int e; |
---|
[910] | 568 | for (int i = 0; i != _curr_length; ++i) { |
---|
[648] | 569 | e = _candidates[i]; |
---|
| 570 | _cand_cost[e] = _state[e] * |
---|
| 571 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 572 | if (_cand_cost[e] >= 0) { |
---|
| 573 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 574 | } |
---|
| 575 | } |
---|
| 576 | |
---|
| 577 | // Extend the list |
---|
| 578 | int cnt = _block_size; |
---|
| 579 | int limit = _head_length; |
---|
| 580 | |
---|
[910] | 581 | for (e = _next_arc; e != _search_arc_num; ++e) { |
---|
[648] | 582 | _cand_cost[e] = _state[e] * |
---|
| 583 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 584 | if (_cand_cost[e] < 0) { |
---|
| 585 | _candidates[_curr_length++] = e; |
---|
| 586 | } |
---|
| 587 | if (--cnt == 0) { |
---|
[774] | 588 | if (_curr_length > limit) goto search_end; |
---|
[648] | 589 | limit = 0; |
---|
| 590 | cnt = _block_size; |
---|
| 591 | } |
---|
| 592 | } |
---|
[910] | 593 | for (e = 0; e != _next_arc; ++e) { |
---|
[774] | 594 | _cand_cost[e] = _state[e] * |
---|
| 595 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 596 | if (_cand_cost[e] < 0) { |
---|
| 597 | _candidates[_curr_length++] = e; |
---|
| 598 | } |
---|
| 599 | if (--cnt == 0) { |
---|
| 600 | if (_curr_length > limit) goto search_end; |
---|
| 601 | limit = 0; |
---|
| 602 | cnt = _block_size; |
---|
[648] | 603 | } |
---|
| 604 | } |
---|
| 605 | if (_curr_length == 0) return false; |
---|
[774] | 606 | |
---|
| 607 | search_end: |
---|
[648] | 608 | |
---|
| 609 | // Make heap of the candidate list (approximating a partial sort) |
---|
| 610 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 611 | _sort_func ); |
---|
| 612 | |
---|
| 613 | // Pop the first element of the heap |
---|
| 614 | _in_arc = _candidates[0]; |
---|
[774] | 615 | _next_arc = e; |
---|
[648] | 616 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 617 | _sort_func ); |
---|
| 618 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
| 619 | return true; |
---|
| 620 | } |
---|
| 621 | |
---|
| 622 | }; //class AlteringListPivotRule |
---|
| 623 | |
---|
| 624 | public: |
---|
| 625 | |
---|
[652] | 626 | /// \brief Constructor. |
---|
[648] | 627 | /// |
---|
[656] | 628 | /// The constructor of the class. |
---|
[648] | 629 | /// |
---|
[650] | 630 | /// \param graph The digraph the algorithm runs on. |
---|
[775] | 631 | /// \param arc_mixing Indicate if the arcs have to be stored in a |
---|
| 632 | /// mixed order in the internal data structure. |
---|
| 633 | /// In special cases, it could lead to better overall performance, |
---|
| 634 | /// but it is usually slower. Therefore it is disabled by default. |
---|
| 635 | NetworkSimplex(const GR& graph, bool arc_mixing = false) : |
---|
[689] | 636 | _graph(graph), _node_id(graph), _arc_id(graph), |
---|
[877] | 637 | MAX(std::numeric_limits<Value>::max()), |
---|
[688] | 638 | INF(std::numeric_limits<Value>::has_infinity ? |
---|
[877] | 639 | std::numeric_limits<Value>::infinity() : MAX) |
---|
[652] | 640 | { |
---|
[878] | 641 | // Check the number types |
---|
[688] | 642 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
---|
[687] | 643 | "The flow type of NetworkSimplex must be signed"); |
---|
| 644 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
---|
| 645 | "The cost type of NetworkSimplex must be signed"); |
---|
[689] | 646 | |
---|
| 647 | // Resize vectors |
---|
| 648 | _node_num = countNodes(_graph); |
---|
| 649 | _arc_num = countArcs(_graph); |
---|
| 650 | int all_node_num = _node_num + 1; |
---|
[710] | 651 | int max_arc_num = _arc_num + 2 * _node_num; |
---|
[648] | 652 | |
---|
[710] | 653 | _source.resize(max_arc_num); |
---|
| 654 | _target.resize(max_arc_num); |
---|
[689] | 655 | |
---|
[710] | 656 | _lower.resize(_arc_num); |
---|
| 657 | _upper.resize(_arc_num); |
---|
| 658 | _cap.resize(max_arc_num); |
---|
| 659 | _cost.resize(max_arc_num); |
---|
[689] | 660 | _supply.resize(all_node_num); |
---|
[710] | 661 | _flow.resize(max_arc_num); |
---|
[689] | 662 | _pi.resize(all_node_num); |
---|
| 663 | |
---|
| 664 | _parent.resize(all_node_num); |
---|
| 665 | _pred.resize(all_node_num); |
---|
| 666 | _forward.resize(all_node_num); |
---|
| 667 | _thread.resize(all_node_num); |
---|
| 668 | _rev_thread.resize(all_node_num); |
---|
| 669 | _succ_num.resize(all_node_num); |
---|
| 670 | _last_succ.resize(all_node_num); |
---|
[710] | 671 | _state.resize(max_arc_num); |
---|
[689] | 672 | |
---|
[775] | 673 | // Copy the graph |
---|
[689] | 674 | int i = 0; |
---|
| 675 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 676 | _node_id[n] = i; |
---|
| 677 | } |
---|
[775] | 678 | if (arc_mixing) { |
---|
| 679 | // Store the arcs in a mixed order |
---|
| 680 | int k = std::max(int(std::sqrt(double(_arc_num))), 10); |
---|
| 681 | int i = 0, j = 0; |
---|
| 682 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 683 | _arc_id[a] = i; |
---|
| 684 | _source[i] = _node_id[_graph.source(a)]; |
---|
| 685 | _target[i] = _node_id[_graph.target(a)]; |
---|
| 686 | if ((i += k) >= _arc_num) i = ++j; |
---|
| 687 | } |
---|
| 688 | } else { |
---|
| 689 | // Store the arcs in the original order |
---|
| 690 | int i = 0; |
---|
| 691 | for (ArcIt a(_graph); a != INVALID; ++a, ++i) { |
---|
| 692 | _arc_id[a] = i; |
---|
| 693 | _source[i] = _node_id[_graph.source(a)]; |
---|
| 694 | _target[i] = _node_id[_graph.target(a)]; |
---|
| 695 | } |
---|
[689] | 696 | } |
---|
| 697 | |
---|
[776] | 698 | // Reset parameters |
---|
| 699 | reset(); |
---|
[648] | 700 | } |
---|
| 701 | |
---|
[656] | 702 | /// \name Parameters |
---|
| 703 | /// The parameters of the algorithm can be specified using these |
---|
| 704 | /// functions. |
---|
| 705 | |
---|
| 706 | /// @{ |
---|
| 707 | |
---|
[652] | 708 | /// \brief Set the lower bounds on the arcs. |
---|
| 709 | /// |
---|
| 710 | /// This function sets the lower bounds on the arcs. |
---|
[687] | 711 | /// If it is not used before calling \ref run(), the lower bounds |
---|
| 712 | /// will be set to zero on all arcs. |
---|
[652] | 713 | /// |
---|
| 714 | /// \param map An arc map storing the lower bounds. |
---|
[688] | 715 | /// Its \c Value type must be convertible to the \c Value type |
---|
[652] | 716 | /// of the algorithm. |
---|
| 717 | /// |
---|
| 718 | /// \return <tt>(*this)</tt> |
---|
[687] | 719 | template <typename LowerMap> |
---|
| 720 | NetworkSimplex& lowerMap(const LowerMap& map) { |
---|
[689] | 721 | _have_lower = true; |
---|
[652] | 722 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[689] | 723 | _lower[_arc_id[a]] = map[a]; |
---|
[652] | 724 | } |
---|
| 725 | return *this; |
---|
| 726 | } |
---|
| 727 | |
---|
| 728 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
| 729 | /// |
---|
| 730 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
[687] | 731 | /// If it is not used before calling \ref run(), the upper bounds |
---|
| 732 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
---|
[878] | 733 | /// unbounded from above). |
---|
[652] | 734 | /// |
---|
| 735 | /// \param map An arc map storing the upper bounds. |
---|
[688] | 736 | /// Its \c Value type must be convertible to the \c Value type |
---|
[652] | 737 | /// of the algorithm. |
---|
| 738 | /// |
---|
| 739 | /// \return <tt>(*this)</tt> |
---|
[687] | 740 | template<typename UpperMap> |
---|
| 741 | NetworkSimplex& upperMap(const UpperMap& map) { |
---|
[652] | 742 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[689] | 743 | _upper[_arc_id[a]] = map[a]; |
---|
[652] | 744 | } |
---|
| 745 | return *this; |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | /// \brief Set the costs of the arcs. |
---|
| 749 | /// |
---|
| 750 | /// This function sets the costs of the arcs. |
---|
| 751 | /// If it is not used before calling \ref run(), the costs |
---|
| 752 | /// will be set to \c 1 on all arcs. |
---|
| 753 | /// |
---|
| 754 | /// \param map An arc map storing the costs. |
---|
[654] | 755 | /// Its \c Value type must be convertible to the \c Cost type |
---|
[652] | 756 | /// of the algorithm. |
---|
| 757 | /// |
---|
| 758 | /// \return <tt>(*this)</tt> |
---|
[687] | 759 | template<typename CostMap> |
---|
| 760 | NetworkSimplex& costMap(const CostMap& map) { |
---|
[652] | 761 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[689] | 762 | _cost[_arc_id[a]] = map[a]; |
---|
[652] | 763 | } |
---|
| 764 | return *this; |
---|
| 765 | } |
---|
| 766 | |
---|
| 767 | /// \brief Set the supply values of the nodes. |
---|
| 768 | /// |
---|
| 769 | /// This function sets the supply values of the nodes. |
---|
| 770 | /// If neither this function nor \ref stSupply() is used before |
---|
| 771 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 772 | /// |
---|
| 773 | /// \param map A node map storing the supply values. |
---|
[688] | 774 | /// Its \c Value type must be convertible to the \c Value type |
---|
[652] | 775 | /// of the algorithm. |
---|
| 776 | /// |
---|
| 777 | /// \return <tt>(*this)</tt> |
---|
[687] | 778 | template<typename SupplyMap> |
---|
| 779 | NetworkSimplex& supplyMap(const SupplyMap& map) { |
---|
[652] | 780 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[689] | 781 | _supply[_node_id[n]] = map[n]; |
---|
[652] | 782 | } |
---|
| 783 | return *this; |
---|
| 784 | } |
---|
| 785 | |
---|
| 786 | /// \brief Set single source and target nodes and a supply value. |
---|
| 787 | /// |
---|
| 788 | /// This function sets a single source node and a single target node |
---|
| 789 | /// and the required flow value. |
---|
| 790 | /// If neither this function nor \ref supplyMap() is used before |
---|
| 791 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 792 | /// |
---|
[687] | 793 | /// Using this function has the same effect as using \ref supplyMap() |
---|
| 794 | /// with such a map in which \c k is assigned to \c s, \c -k is |
---|
| 795 | /// assigned to \c t and all other nodes have zero supply value. |
---|
| 796 | /// |
---|
[652] | 797 | /// \param s The source node. |
---|
| 798 | /// \param t The target node. |
---|
| 799 | /// \param k The required amount of flow from node \c s to node \c t |
---|
| 800 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
| 801 | /// |
---|
| 802 | /// \return <tt>(*this)</tt> |
---|
[688] | 803 | NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) { |
---|
[689] | 804 | for (int i = 0; i != _node_num; ++i) { |
---|
| 805 | _supply[i] = 0; |
---|
| 806 | } |
---|
| 807 | _supply[_node_id[s]] = k; |
---|
| 808 | _supply[_node_id[t]] = -k; |
---|
[652] | 809 | return *this; |
---|
| 810 | } |
---|
[656] | 811 | |
---|
[687] | 812 | /// \brief Set the type of the supply constraints. |
---|
[656] | 813 | /// |
---|
[687] | 814 | /// This function sets the type of the supply/demand constraints. |
---|
| 815 | /// If it is not used before calling \ref run(), the \ref GEQ supply |
---|
[656] | 816 | /// type will be used. |
---|
| 817 | /// |
---|
[833] | 818 | /// For more information, see \ref SupplyType. |
---|
[656] | 819 | /// |
---|
| 820 | /// \return <tt>(*this)</tt> |
---|
[687] | 821 | NetworkSimplex& supplyType(SupplyType supply_type) { |
---|
| 822 | _stype = supply_type; |
---|
[656] | 823 | return *this; |
---|
| 824 | } |
---|
[652] | 825 | |
---|
[656] | 826 | /// @} |
---|
[648] | 827 | |
---|
[652] | 828 | /// \name Execution Control |
---|
| 829 | /// The algorithm can be executed using \ref run(). |
---|
| 830 | |
---|
[648] | 831 | /// @{ |
---|
| 832 | |
---|
| 833 | /// \brief Run the algorithm. |
---|
| 834 | /// |
---|
| 835 | /// This function runs the algorithm. |
---|
[656] | 836 | /// The paramters can be specified using functions \ref lowerMap(), |
---|
[687] | 837 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), |
---|
[689] | 838 | /// \ref supplyType(). |
---|
[656] | 839 | /// For example, |
---|
[652] | 840 | /// \code |
---|
| 841 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
[687] | 842 | /// ns.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
[652] | 843 | /// .supplyMap(sup).run(); |
---|
| 844 | /// \endcode |
---|
[648] | 845 | /// |
---|
[653] | 846 | /// This function can be called more than once. All the parameters |
---|
| 847 | /// that have been given are kept for the next call, unless |
---|
| 848 | /// \ref reset() is called, thus only the modified parameters |
---|
| 849 | /// have to be set again. See \ref reset() for examples. |
---|
[833] | 850 | /// However, the underlying digraph must not be modified after this |
---|
[689] | 851 | /// class have been constructed, since it copies and extends the graph. |
---|
[653] | 852 | /// |
---|
[652] | 853 | /// \param pivot_rule The pivot rule that will be used during the |
---|
[833] | 854 | /// algorithm. For more information, see \ref PivotRule. |
---|
[648] | 855 | /// |
---|
[687] | 856 | /// \return \c INFEASIBLE if no feasible flow exists, |
---|
| 857 | /// \n \c OPTIMAL if the problem has optimal solution |
---|
| 858 | /// (i.e. it is feasible and bounded), and the algorithm has found |
---|
| 859 | /// optimal flow and node potentials (primal and dual solutions), |
---|
| 860 | /// \n \c UNBOUNDED if the objective function of the problem is |
---|
| 861 | /// unbounded, i.e. there is a directed cycle having negative total |
---|
| 862 | /// cost and infinite upper bound. |
---|
| 863 | /// |
---|
| 864 | /// \see ProblemType, PivotRule |
---|
| 865 | ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) { |
---|
| 866 | if (!init()) return INFEASIBLE; |
---|
| 867 | return start(pivot_rule); |
---|
[648] | 868 | } |
---|
| 869 | |
---|
[653] | 870 | /// \brief Reset all the parameters that have been given before. |
---|
| 871 | /// |
---|
| 872 | /// This function resets all the paramaters that have been given |
---|
[656] | 873 | /// before using functions \ref lowerMap(), \ref upperMap(), |
---|
[689] | 874 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). |
---|
[653] | 875 | /// |
---|
| 876 | /// It is useful for multiple run() calls. If this function is not |
---|
| 877 | /// used, all the parameters given before are kept for the next |
---|
| 878 | /// \ref run() call. |
---|
[833] | 879 | /// However, the underlying digraph must not be modified after this |
---|
[689] | 880 | /// class have been constructed, since it copies and extends the graph. |
---|
[653] | 881 | /// |
---|
| 882 | /// For example, |
---|
| 883 | /// \code |
---|
| 884 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
| 885 | /// |
---|
| 886 | /// // First run |
---|
[687] | 887 | /// ns.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
[653] | 888 | /// .supplyMap(sup).run(); |
---|
| 889 | /// |
---|
| 890 | /// // Run again with modified cost map (reset() is not called, |
---|
| 891 | /// // so only the cost map have to be set again) |
---|
| 892 | /// cost[e] += 100; |
---|
| 893 | /// ns.costMap(cost).run(); |
---|
| 894 | /// |
---|
| 895 | /// // Run again from scratch using reset() |
---|
| 896 | /// // (the lower bounds will be set to zero on all arcs) |
---|
| 897 | /// ns.reset(); |
---|
[687] | 898 | /// ns.upperMap(capacity).costMap(cost) |
---|
[653] | 899 | /// .supplyMap(sup).run(); |
---|
| 900 | /// \endcode |
---|
| 901 | /// |
---|
| 902 | /// \return <tt>(*this)</tt> |
---|
| 903 | NetworkSimplex& reset() { |
---|
[689] | 904 | for (int i = 0; i != _node_num; ++i) { |
---|
| 905 | _supply[i] = 0; |
---|
| 906 | } |
---|
| 907 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 908 | _lower[i] = 0; |
---|
| 909 | _upper[i] = INF; |
---|
| 910 | _cost[i] = 1; |
---|
| 911 | } |
---|
| 912 | _have_lower = false; |
---|
[687] | 913 | _stype = GEQ; |
---|
[653] | 914 | return *this; |
---|
| 915 | } |
---|
| 916 | |
---|
[648] | 917 | /// @} |
---|
| 918 | |
---|
| 919 | /// \name Query Functions |
---|
| 920 | /// The results of the algorithm can be obtained using these |
---|
| 921 | /// functions.\n |
---|
[652] | 922 | /// The \ref run() function must be called before using them. |
---|
| 923 | |
---|
[648] | 924 | /// @{ |
---|
| 925 | |
---|
[652] | 926 | /// \brief Return the total cost of the found flow. |
---|
| 927 | /// |
---|
| 928 | /// This function returns the total cost of the found flow. |
---|
[687] | 929 | /// Its complexity is O(e). |
---|
[652] | 930 | /// |
---|
| 931 | /// \note The return type of the function can be specified as a |
---|
| 932 | /// template parameter. For example, |
---|
| 933 | /// \code |
---|
| 934 | /// ns.totalCost<double>(); |
---|
| 935 | /// \endcode |
---|
[654] | 936 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
[652] | 937 | /// type of the algorithm, which is the default return type of the |
---|
| 938 | /// function. |
---|
| 939 | /// |
---|
| 940 | /// \pre \ref run() must be called before using this function. |
---|
[689] | 941 | template <typename Number> |
---|
| 942 | Number totalCost() const { |
---|
| 943 | Number c = 0; |
---|
| 944 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 945 | int i = _arc_id[a]; |
---|
| 946 | c += Number(_flow[i]) * Number(_cost[i]); |
---|
[652] | 947 | } |
---|
| 948 | return c; |
---|
| 949 | } |
---|
| 950 | |
---|
| 951 | #ifndef DOXYGEN |
---|
[654] | 952 | Cost totalCost() const { |
---|
| 953 | return totalCost<Cost>(); |
---|
[652] | 954 | } |
---|
| 955 | #endif |
---|
| 956 | |
---|
| 957 | /// \brief Return the flow on the given arc. |
---|
| 958 | /// |
---|
| 959 | /// This function returns the flow on the given arc. |
---|
| 960 | /// |
---|
| 961 | /// \pre \ref run() must be called before using this function. |
---|
[688] | 962 | Value flow(const Arc& a) const { |
---|
[689] | 963 | return _flow[_arc_id[a]]; |
---|
[652] | 964 | } |
---|
| 965 | |
---|
[689] | 966 | /// \brief Return the flow map (the primal solution). |
---|
[648] | 967 | /// |
---|
[689] | 968 | /// This function copies the flow value on each arc into the given |
---|
| 969 | /// map. The \c Value type of the algorithm must be convertible to |
---|
| 970 | /// the \c Value type of the map. |
---|
[648] | 971 | /// |
---|
| 972 | /// \pre \ref run() must be called before using this function. |
---|
[689] | 973 | template <typename FlowMap> |
---|
| 974 | void flowMap(FlowMap &map) const { |
---|
| 975 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 976 | map.set(a, _flow[_arc_id[a]]); |
---|
| 977 | } |
---|
[648] | 978 | } |
---|
| 979 | |
---|
[652] | 980 | /// \brief Return the potential (dual value) of the given node. |
---|
| 981 | /// |
---|
| 982 | /// This function returns the potential (dual value) of the |
---|
| 983 | /// given node. |
---|
| 984 | /// |
---|
| 985 | /// \pre \ref run() must be called before using this function. |
---|
[654] | 986 | Cost potential(const Node& n) const { |
---|
[689] | 987 | return _pi[_node_id[n]]; |
---|
[652] | 988 | } |
---|
| 989 | |
---|
[689] | 990 | /// \brief Return the potential map (the dual solution). |
---|
[648] | 991 | /// |
---|
[689] | 992 | /// This function copies the potential (dual value) of each node |
---|
| 993 | /// into the given map. |
---|
| 994 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 995 | /// \c Value type of the map. |
---|
[648] | 996 | /// |
---|
| 997 | /// \pre \ref run() must be called before using this function. |
---|
[689] | 998 | template <typename PotentialMap> |
---|
| 999 | void potentialMap(PotentialMap &map) const { |
---|
| 1000 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1001 | map.set(n, _pi[_node_id[n]]); |
---|
| 1002 | } |
---|
[648] | 1003 | } |
---|
| 1004 | |
---|
| 1005 | /// @} |
---|
| 1006 | |
---|
| 1007 | private: |
---|
| 1008 | |
---|
| 1009 | // Initialize internal data structures |
---|
| 1010 | bool init() { |
---|
[652] | 1011 | if (_node_num == 0) return false; |
---|
[648] | 1012 | |
---|
[689] | 1013 | // Check the sum of supply values |
---|
| 1014 | _sum_supply = 0; |
---|
| 1015 | for (int i = 0; i != _node_num; ++i) { |
---|
| 1016 | _sum_supply += _supply[i]; |
---|
| 1017 | } |
---|
[690] | 1018 | if ( !((_stype == GEQ && _sum_supply <= 0) || |
---|
| 1019 | (_stype == LEQ && _sum_supply >= 0)) ) return false; |
---|
[648] | 1020 | |
---|
[689] | 1021 | // Remove non-zero lower bounds |
---|
| 1022 | if (_have_lower) { |
---|
| 1023 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1024 | Value c = _lower[i]; |
---|
| 1025 | if (c >= 0) { |
---|
[877] | 1026 | _cap[i] = _upper[i] < MAX ? _upper[i] - c : INF; |
---|
[689] | 1027 | } else { |
---|
[877] | 1028 | _cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF; |
---|
[689] | 1029 | } |
---|
| 1030 | _supply[_source[i]] -= c; |
---|
| 1031 | _supply[_target[i]] += c; |
---|
| 1032 | } |
---|
| 1033 | } else { |
---|
| 1034 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1035 | _cap[i] = _upper[i]; |
---|
| 1036 | } |
---|
[652] | 1037 | } |
---|
[648] | 1038 | |
---|
[656] | 1039 | // Initialize artifical cost |
---|
[687] | 1040 | Cost ART_COST; |
---|
[656] | 1041 | if (std::numeric_limits<Cost>::is_exact) { |
---|
[710] | 1042 | ART_COST = std::numeric_limits<Cost>::max() / 2 + 1; |
---|
[656] | 1043 | } else { |
---|
[687] | 1044 | ART_COST = std::numeric_limits<Cost>::min(); |
---|
[656] | 1045 | for (int i = 0; i != _arc_num; ++i) { |
---|
[687] | 1046 | if (_cost[i] > ART_COST) ART_COST = _cost[i]; |
---|
[656] | 1047 | } |
---|
[687] | 1048 | ART_COST = (ART_COST + 1) * _node_num; |
---|
[656] | 1049 | } |
---|
| 1050 | |
---|
[689] | 1051 | // Initialize arc maps |
---|
| 1052 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1053 | _flow[i] = 0; |
---|
| 1054 | _state[i] = STATE_LOWER; |
---|
| 1055 | } |
---|
| 1056 | |
---|
[648] | 1057 | // Set data for the artificial root node |
---|
| 1058 | _root = _node_num; |
---|
| 1059 | _parent[_root] = -1; |
---|
| 1060 | _pred[_root] = -1; |
---|
| 1061 | _thread[_root] = 0; |
---|
[651] | 1062 | _rev_thread[0] = _root; |
---|
[689] | 1063 | _succ_num[_root] = _node_num + 1; |
---|
[651] | 1064 | _last_succ[_root] = _root - 1; |
---|
[687] | 1065 | _supply[_root] = -_sum_supply; |
---|
[710] | 1066 | _pi[_root] = 0; |
---|
[648] | 1067 | |
---|
| 1068 | // Add artificial arcs and initialize the spanning tree data structure |
---|
[710] | 1069 | if (_sum_supply == 0) { |
---|
| 1070 | // EQ supply constraints |
---|
| 1071 | _search_arc_num = _arc_num; |
---|
| 1072 | _all_arc_num = _arc_num + _node_num; |
---|
| 1073 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1074 | _parent[u] = _root; |
---|
| 1075 | _pred[u] = e; |
---|
| 1076 | _thread[u] = u + 1; |
---|
| 1077 | _rev_thread[u + 1] = u; |
---|
| 1078 | _succ_num[u] = 1; |
---|
| 1079 | _last_succ[u] = u; |
---|
| 1080 | _cap[e] = INF; |
---|
| 1081 | _state[e] = STATE_TREE; |
---|
| 1082 | if (_supply[u] >= 0) { |
---|
| 1083 | _forward[u] = true; |
---|
| 1084 | _pi[u] = 0; |
---|
| 1085 | _source[e] = u; |
---|
| 1086 | _target[e] = _root; |
---|
| 1087 | _flow[e] = _supply[u]; |
---|
| 1088 | _cost[e] = 0; |
---|
| 1089 | } else { |
---|
| 1090 | _forward[u] = false; |
---|
| 1091 | _pi[u] = ART_COST; |
---|
| 1092 | _source[e] = _root; |
---|
| 1093 | _target[e] = u; |
---|
| 1094 | _flow[e] = -_supply[u]; |
---|
| 1095 | _cost[e] = ART_COST; |
---|
| 1096 | } |
---|
[648] | 1097 | } |
---|
| 1098 | } |
---|
[710] | 1099 | else if (_sum_supply > 0) { |
---|
| 1100 | // LEQ supply constraints |
---|
| 1101 | _search_arc_num = _arc_num + _node_num; |
---|
| 1102 | int f = _arc_num + _node_num; |
---|
| 1103 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1104 | _parent[u] = _root; |
---|
| 1105 | _thread[u] = u + 1; |
---|
| 1106 | _rev_thread[u + 1] = u; |
---|
| 1107 | _succ_num[u] = 1; |
---|
| 1108 | _last_succ[u] = u; |
---|
| 1109 | if (_supply[u] >= 0) { |
---|
| 1110 | _forward[u] = true; |
---|
| 1111 | _pi[u] = 0; |
---|
| 1112 | _pred[u] = e; |
---|
| 1113 | _source[e] = u; |
---|
| 1114 | _target[e] = _root; |
---|
| 1115 | _cap[e] = INF; |
---|
| 1116 | _flow[e] = _supply[u]; |
---|
| 1117 | _cost[e] = 0; |
---|
| 1118 | _state[e] = STATE_TREE; |
---|
| 1119 | } else { |
---|
| 1120 | _forward[u] = false; |
---|
| 1121 | _pi[u] = ART_COST; |
---|
| 1122 | _pred[u] = f; |
---|
| 1123 | _source[f] = _root; |
---|
| 1124 | _target[f] = u; |
---|
| 1125 | _cap[f] = INF; |
---|
| 1126 | _flow[f] = -_supply[u]; |
---|
| 1127 | _cost[f] = ART_COST; |
---|
| 1128 | _state[f] = STATE_TREE; |
---|
| 1129 | _source[e] = u; |
---|
| 1130 | _target[e] = _root; |
---|
| 1131 | _cap[e] = INF; |
---|
| 1132 | _flow[e] = 0; |
---|
| 1133 | _cost[e] = 0; |
---|
| 1134 | _state[e] = STATE_LOWER; |
---|
| 1135 | ++f; |
---|
| 1136 | } |
---|
| 1137 | } |
---|
| 1138 | _all_arc_num = f; |
---|
| 1139 | } |
---|
| 1140 | else { |
---|
| 1141 | // GEQ supply constraints |
---|
| 1142 | _search_arc_num = _arc_num + _node_num; |
---|
| 1143 | int f = _arc_num + _node_num; |
---|
| 1144 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1145 | _parent[u] = _root; |
---|
| 1146 | _thread[u] = u + 1; |
---|
| 1147 | _rev_thread[u + 1] = u; |
---|
| 1148 | _succ_num[u] = 1; |
---|
| 1149 | _last_succ[u] = u; |
---|
| 1150 | if (_supply[u] <= 0) { |
---|
| 1151 | _forward[u] = false; |
---|
| 1152 | _pi[u] = 0; |
---|
| 1153 | _pred[u] = e; |
---|
| 1154 | _source[e] = _root; |
---|
| 1155 | _target[e] = u; |
---|
| 1156 | _cap[e] = INF; |
---|
| 1157 | _flow[e] = -_supply[u]; |
---|
| 1158 | _cost[e] = 0; |
---|
| 1159 | _state[e] = STATE_TREE; |
---|
| 1160 | } else { |
---|
| 1161 | _forward[u] = true; |
---|
| 1162 | _pi[u] = -ART_COST; |
---|
| 1163 | _pred[u] = f; |
---|
| 1164 | _source[f] = u; |
---|
| 1165 | _target[f] = _root; |
---|
| 1166 | _cap[f] = INF; |
---|
| 1167 | _flow[f] = _supply[u]; |
---|
| 1168 | _state[f] = STATE_TREE; |
---|
| 1169 | _cost[f] = ART_COST; |
---|
| 1170 | _source[e] = _root; |
---|
| 1171 | _target[e] = u; |
---|
| 1172 | _cap[e] = INF; |
---|
| 1173 | _flow[e] = 0; |
---|
| 1174 | _cost[e] = 0; |
---|
| 1175 | _state[e] = STATE_LOWER; |
---|
| 1176 | ++f; |
---|
| 1177 | } |
---|
| 1178 | } |
---|
| 1179 | _all_arc_num = f; |
---|
| 1180 | } |
---|
[648] | 1181 | |
---|
| 1182 | return true; |
---|
| 1183 | } |
---|
| 1184 | |
---|
| 1185 | // Find the join node |
---|
| 1186 | void findJoinNode() { |
---|
[650] | 1187 | int u = _source[in_arc]; |
---|
| 1188 | int v = _target[in_arc]; |
---|
[648] | 1189 | while (u != v) { |
---|
[651] | 1190 | if (_succ_num[u] < _succ_num[v]) { |
---|
| 1191 | u = _parent[u]; |
---|
| 1192 | } else { |
---|
| 1193 | v = _parent[v]; |
---|
| 1194 | } |
---|
[648] | 1195 | } |
---|
| 1196 | join = u; |
---|
| 1197 | } |
---|
| 1198 | |
---|
| 1199 | // Find the leaving arc of the cycle and returns true if the |
---|
| 1200 | // leaving arc is not the same as the entering arc |
---|
| 1201 | bool findLeavingArc() { |
---|
| 1202 | // Initialize first and second nodes according to the direction |
---|
| 1203 | // of the cycle |
---|
[650] | 1204 | if (_state[in_arc] == STATE_LOWER) { |
---|
| 1205 | first = _source[in_arc]; |
---|
| 1206 | second = _target[in_arc]; |
---|
[648] | 1207 | } else { |
---|
[650] | 1208 | first = _target[in_arc]; |
---|
| 1209 | second = _source[in_arc]; |
---|
[648] | 1210 | } |
---|
[650] | 1211 | delta = _cap[in_arc]; |
---|
[648] | 1212 | int result = 0; |
---|
[688] | 1213 | Value d; |
---|
[648] | 1214 | int e; |
---|
| 1215 | |
---|
| 1216 | // Search the cycle along the path form the first node to the root |
---|
| 1217 | for (int u = first; u != join; u = _parent[u]) { |
---|
| 1218 | e = _pred[u]; |
---|
[687] | 1219 | d = _forward[u] ? |
---|
[877] | 1220 | _flow[e] : (_cap[e] >= MAX ? INF : _cap[e] - _flow[e]); |
---|
[648] | 1221 | if (d < delta) { |
---|
| 1222 | delta = d; |
---|
| 1223 | u_out = u; |
---|
| 1224 | result = 1; |
---|
| 1225 | } |
---|
| 1226 | } |
---|
| 1227 | // Search the cycle along the path form the second node to the root |
---|
| 1228 | for (int u = second; u != join; u = _parent[u]) { |
---|
| 1229 | e = _pred[u]; |
---|
[687] | 1230 | d = _forward[u] ? |
---|
[877] | 1231 | (_cap[e] >= MAX ? INF : _cap[e] - _flow[e]) : _flow[e]; |
---|
[648] | 1232 | if (d <= delta) { |
---|
| 1233 | delta = d; |
---|
| 1234 | u_out = u; |
---|
| 1235 | result = 2; |
---|
| 1236 | } |
---|
| 1237 | } |
---|
| 1238 | |
---|
| 1239 | if (result == 1) { |
---|
| 1240 | u_in = first; |
---|
| 1241 | v_in = second; |
---|
| 1242 | } else { |
---|
| 1243 | u_in = second; |
---|
| 1244 | v_in = first; |
---|
| 1245 | } |
---|
| 1246 | return result != 0; |
---|
| 1247 | } |
---|
| 1248 | |
---|
| 1249 | // Change _flow and _state vectors |
---|
| 1250 | void changeFlow(bool change) { |
---|
| 1251 | // Augment along the cycle |
---|
| 1252 | if (delta > 0) { |
---|
[688] | 1253 | Value val = _state[in_arc] * delta; |
---|
[650] | 1254 | _flow[in_arc] += val; |
---|
| 1255 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
[648] | 1256 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
| 1257 | } |
---|
[650] | 1258 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
[648] | 1259 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
| 1260 | } |
---|
| 1261 | } |
---|
| 1262 | // Update the state of the entering and leaving arcs |
---|
| 1263 | if (change) { |
---|
[650] | 1264 | _state[in_arc] = STATE_TREE; |
---|
[648] | 1265 | _state[_pred[u_out]] = |
---|
| 1266 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
| 1267 | } else { |
---|
[650] | 1268 | _state[in_arc] = -_state[in_arc]; |
---|
[648] | 1269 | } |
---|
| 1270 | } |
---|
| 1271 | |
---|
[651] | 1272 | // Update the tree structure |
---|
| 1273 | void updateTreeStructure() { |
---|
| 1274 | int u, w; |
---|
| 1275 | int old_rev_thread = _rev_thread[u_out]; |
---|
| 1276 | int old_succ_num = _succ_num[u_out]; |
---|
| 1277 | int old_last_succ = _last_succ[u_out]; |
---|
[648] | 1278 | v_out = _parent[u_out]; |
---|
| 1279 | |
---|
[651] | 1280 | u = _last_succ[u_in]; // the last successor of u_in |
---|
| 1281 | right = _thread[u]; // the node after it |
---|
| 1282 | |
---|
| 1283 | // Handle the case when old_rev_thread equals to v_in |
---|
| 1284 | // (it also means that join and v_out coincide) |
---|
| 1285 | if (old_rev_thread == v_in) { |
---|
| 1286 | last = _thread[_last_succ[u_out]]; |
---|
| 1287 | } else { |
---|
| 1288 | last = _thread[v_in]; |
---|
[648] | 1289 | } |
---|
| 1290 | |
---|
[651] | 1291 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
| 1292 | // between u_in and u_out, whose parent have to be changed) |
---|
[648] | 1293 | _thread[v_in] = stem = u_in; |
---|
[651] | 1294 | _dirty_revs.clear(); |
---|
| 1295 | _dirty_revs.push_back(v_in); |
---|
[648] | 1296 | par_stem = v_in; |
---|
| 1297 | while (stem != u_out) { |
---|
[651] | 1298 | // Insert the next stem node into the thread list |
---|
| 1299 | new_stem = _parent[stem]; |
---|
| 1300 | _thread[u] = new_stem; |
---|
| 1301 | _dirty_revs.push_back(u); |
---|
[648] | 1302 | |
---|
[651] | 1303 | // Remove the subtree of stem from the thread list |
---|
| 1304 | w = _rev_thread[stem]; |
---|
| 1305 | _thread[w] = right; |
---|
| 1306 | _rev_thread[right] = w; |
---|
[648] | 1307 | |
---|
[651] | 1308 | // Change the parent node and shift stem nodes |
---|
[648] | 1309 | _parent[stem] = par_stem; |
---|
| 1310 | par_stem = stem; |
---|
| 1311 | stem = new_stem; |
---|
| 1312 | |
---|
[651] | 1313 | // Update u and right |
---|
| 1314 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
| 1315 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
[648] | 1316 | right = _thread[u]; |
---|
| 1317 | } |
---|
| 1318 | _parent[u_out] = par_stem; |
---|
| 1319 | _thread[u] = last; |
---|
[651] | 1320 | _rev_thread[last] = u; |
---|
| 1321 | _last_succ[u_out] = u; |
---|
[648] | 1322 | |
---|
[651] | 1323 | // Remove the subtree of u_out from the thread list except for |
---|
| 1324 | // the case when old_rev_thread equals to v_in |
---|
| 1325 | // (it also means that join and v_out coincide) |
---|
| 1326 | if (old_rev_thread != v_in) { |
---|
| 1327 | _thread[old_rev_thread] = right; |
---|
| 1328 | _rev_thread[right] = old_rev_thread; |
---|
| 1329 | } |
---|
| 1330 | |
---|
| 1331 | // Update _rev_thread using the new _thread values |
---|
[910] | 1332 | for (int i = 0; i != int(_dirty_revs.size()); ++i) { |
---|
[651] | 1333 | u = _dirty_revs[i]; |
---|
| 1334 | _rev_thread[_thread[u]] = u; |
---|
| 1335 | } |
---|
| 1336 | |
---|
| 1337 | // Update _pred, _forward, _last_succ and _succ_num for the |
---|
| 1338 | // stem nodes from u_out to u_in |
---|
| 1339 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
| 1340 | u = u_out; |
---|
| 1341 | while (u != u_in) { |
---|
| 1342 | w = _parent[u]; |
---|
| 1343 | _pred[u] = _pred[w]; |
---|
| 1344 | _forward[u] = !_forward[w]; |
---|
| 1345 | tmp_sc += _succ_num[u] - _succ_num[w]; |
---|
| 1346 | _succ_num[u] = tmp_sc; |
---|
| 1347 | _last_succ[w] = tmp_ls; |
---|
| 1348 | u = w; |
---|
| 1349 | } |
---|
| 1350 | _pred[u_in] = in_arc; |
---|
| 1351 | _forward[u_in] = (u_in == _source[in_arc]); |
---|
| 1352 | _succ_num[u_in] = old_succ_num; |
---|
| 1353 | |
---|
| 1354 | // Set limits for updating _last_succ form v_in and v_out |
---|
| 1355 | // towards the root |
---|
| 1356 | int up_limit_in = -1; |
---|
| 1357 | int up_limit_out = -1; |
---|
| 1358 | if (_last_succ[join] == v_in) { |
---|
| 1359 | up_limit_out = join; |
---|
[648] | 1360 | } else { |
---|
[651] | 1361 | up_limit_in = join; |
---|
| 1362 | } |
---|
| 1363 | |
---|
| 1364 | // Update _last_succ from v_in towards the root |
---|
| 1365 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
| 1366 | u = _parent[u]) { |
---|
| 1367 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1368 | } |
---|
| 1369 | // Update _last_succ from v_out towards the root |
---|
| 1370 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
| 1371 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1372 | u = _parent[u]) { |
---|
| 1373 | _last_succ[u] = old_rev_thread; |
---|
| 1374 | } |
---|
| 1375 | } else { |
---|
| 1376 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1377 | u = _parent[u]) { |
---|
| 1378 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1379 | } |
---|
| 1380 | } |
---|
| 1381 | |
---|
| 1382 | // Update _succ_num from v_in to join |
---|
| 1383 | for (u = v_in; u != join; u = _parent[u]) { |
---|
| 1384 | _succ_num[u] += old_succ_num; |
---|
| 1385 | } |
---|
| 1386 | // Update _succ_num from v_out to join |
---|
| 1387 | for (u = v_out; u != join; u = _parent[u]) { |
---|
| 1388 | _succ_num[u] -= old_succ_num; |
---|
[648] | 1389 | } |
---|
| 1390 | } |
---|
| 1391 | |
---|
[651] | 1392 | // Update potentials |
---|
| 1393 | void updatePotential() { |
---|
[654] | 1394 | Cost sigma = _forward[u_in] ? |
---|
[648] | 1395 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
| 1396 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
[655] | 1397 | // Update potentials in the subtree, which has been moved |
---|
| 1398 | int end = _thread[_last_succ[u_in]]; |
---|
| 1399 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
| 1400 | _pi[u] += sigma; |
---|
[648] | 1401 | } |
---|
| 1402 | } |
---|
| 1403 | |
---|
[910] | 1404 | // Heuristic initial pivots |
---|
| 1405 | bool initialPivots() { |
---|
| 1406 | Value curr, total = 0; |
---|
| 1407 | std::vector<Node> supply_nodes, demand_nodes; |
---|
| 1408 | for (NodeIt u(_graph); u != INVALID; ++u) { |
---|
| 1409 | curr = _supply[_node_id[u]]; |
---|
| 1410 | if (curr > 0) { |
---|
| 1411 | total += curr; |
---|
| 1412 | supply_nodes.push_back(u); |
---|
| 1413 | } |
---|
| 1414 | else if (curr < 0) { |
---|
| 1415 | demand_nodes.push_back(u); |
---|
| 1416 | } |
---|
| 1417 | } |
---|
| 1418 | if (_sum_supply > 0) total -= _sum_supply; |
---|
| 1419 | if (total <= 0) return true; |
---|
| 1420 | |
---|
| 1421 | IntVector arc_vector; |
---|
| 1422 | if (_sum_supply >= 0) { |
---|
| 1423 | if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { |
---|
| 1424 | // Perform a reverse graph search from the sink to the source |
---|
| 1425 | typename GR::template NodeMap<bool> reached(_graph, false); |
---|
| 1426 | Node s = supply_nodes[0], t = demand_nodes[0]; |
---|
| 1427 | std::vector<Node> stack; |
---|
| 1428 | reached[t] = true; |
---|
| 1429 | stack.push_back(t); |
---|
| 1430 | while (!stack.empty()) { |
---|
| 1431 | Node u, v = stack.back(); |
---|
| 1432 | stack.pop_back(); |
---|
| 1433 | if (v == s) break; |
---|
| 1434 | for (InArcIt a(_graph, v); a != INVALID; ++a) { |
---|
| 1435 | if (reached[u = _graph.source(a)]) continue; |
---|
| 1436 | int j = _arc_id[a]; |
---|
| 1437 | if (_cap[j] >= total) { |
---|
| 1438 | arc_vector.push_back(j); |
---|
| 1439 | reached[u] = true; |
---|
| 1440 | stack.push_back(u); |
---|
| 1441 | } |
---|
| 1442 | } |
---|
| 1443 | } |
---|
| 1444 | } else { |
---|
| 1445 | // Find the min. cost incomming arc for each demand node |
---|
| 1446 | for (int i = 0; i != int(demand_nodes.size()); ++i) { |
---|
| 1447 | Node v = demand_nodes[i]; |
---|
| 1448 | Cost c, min_cost = std::numeric_limits<Cost>::max(); |
---|
| 1449 | Arc min_arc = INVALID; |
---|
| 1450 | for (InArcIt a(_graph, v); a != INVALID; ++a) { |
---|
| 1451 | c = _cost[_arc_id[a]]; |
---|
| 1452 | if (c < min_cost) { |
---|
| 1453 | min_cost = c; |
---|
| 1454 | min_arc = a; |
---|
| 1455 | } |
---|
| 1456 | } |
---|
| 1457 | if (min_arc != INVALID) { |
---|
| 1458 | arc_vector.push_back(_arc_id[min_arc]); |
---|
| 1459 | } |
---|
| 1460 | } |
---|
| 1461 | } |
---|
| 1462 | } else { |
---|
| 1463 | // Find the min. cost outgoing arc for each supply node |
---|
| 1464 | for (int i = 0; i != int(supply_nodes.size()); ++i) { |
---|
| 1465 | Node u = supply_nodes[i]; |
---|
| 1466 | Cost c, min_cost = std::numeric_limits<Cost>::max(); |
---|
| 1467 | Arc min_arc = INVALID; |
---|
| 1468 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
---|
| 1469 | c = _cost[_arc_id[a]]; |
---|
| 1470 | if (c < min_cost) { |
---|
| 1471 | min_cost = c; |
---|
| 1472 | min_arc = a; |
---|
| 1473 | } |
---|
| 1474 | } |
---|
| 1475 | if (min_arc != INVALID) { |
---|
| 1476 | arc_vector.push_back(_arc_id[min_arc]); |
---|
| 1477 | } |
---|
| 1478 | } |
---|
| 1479 | } |
---|
| 1480 | |
---|
| 1481 | // Perform heuristic initial pivots |
---|
| 1482 | for (int i = 0; i != int(arc_vector.size()); ++i) { |
---|
| 1483 | in_arc = arc_vector[i]; |
---|
| 1484 | if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - |
---|
| 1485 | _pi[_target[in_arc]]) >= 0) continue; |
---|
| 1486 | findJoinNode(); |
---|
| 1487 | bool change = findLeavingArc(); |
---|
| 1488 | if (delta >= MAX) return false; |
---|
| 1489 | changeFlow(change); |
---|
| 1490 | if (change) { |
---|
| 1491 | updateTreeStructure(); |
---|
| 1492 | updatePotential(); |
---|
| 1493 | } |
---|
| 1494 | } |
---|
| 1495 | return true; |
---|
| 1496 | } |
---|
| 1497 | |
---|
[648] | 1498 | // Execute the algorithm |
---|
[687] | 1499 | ProblemType start(PivotRule pivot_rule) { |
---|
[648] | 1500 | // Select the pivot rule implementation |
---|
| 1501 | switch (pivot_rule) { |
---|
[652] | 1502 | case FIRST_ELIGIBLE: |
---|
[648] | 1503 | return start<FirstEligiblePivotRule>(); |
---|
[652] | 1504 | case BEST_ELIGIBLE: |
---|
[648] | 1505 | return start<BestEligiblePivotRule>(); |
---|
[652] | 1506 | case BLOCK_SEARCH: |
---|
[648] | 1507 | return start<BlockSearchPivotRule>(); |
---|
[652] | 1508 | case CANDIDATE_LIST: |
---|
[648] | 1509 | return start<CandidateListPivotRule>(); |
---|
[652] | 1510 | case ALTERING_LIST: |
---|
[648] | 1511 | return start<AlteringListPivotRule>(); |
---|
| 1512 | } |
---|
[687] | 1513 | return INFEASIBLE; // avoid warning |
---|
[648] | 1514 | } |
---|
| 1515 | |
---|
[652] | 1516 | template <typename PivotRuleImpl> |
---|
[687] | 1517 | ProblemType start() { |
---|
[652] | 1518 | PivotRuleImpl pivot(*this); |
---|
[648] | 1519 | |
---|
[910] | 1520 | // Perform heuristic initial pivots |
---|
| 1521 | if (!initialPivots()) return UNBOUNDED; |
---|
| 1522 | |
---|
[652] | 1523 | // Execute the Network Simplex algorithm |
---|
[648] | 1524 | while (pivot.findEnteringArc()) { |
---|
| 1525 | findJoinNode(); |
---|
| 1526 | bool change = findLeavingArc(); |
---|
[877] | 1527 | if (delta >= MAX) return UNBOUNDED; |
---|
[648] | 1528 | changeFlow(change); |
---|
| 1529 | if (change) { |
---|
[651] | 1530 | updateTreeStructure(); |
---|
| 1531 | updatePotential(); |
---|
[648] | 1532 | } |
---|
| 1533 | } |
---|
[687] | 1534 | |
---|
| 1535 | // Check feasibility |
---|
[710] | 1536 | for (int e = _search_arc_num; e != _all_arc_num; ++e) { |
---|
| 1537 | if (_flow[e] != 0) return INFEASIBLE; |
---|
[687] | 1538 | } |
---|
[648] | 1539 | |
---|
[689] | 1540 | // Transform the solution and the supply map to the original form |
---|
| 1541 | if (_have_lower) { |
---|
[648] | 1542 | for (int i = 0; i != _arc_num; ++i) { |
---|
[689] | 1543 | Value c = _lower[i]; |
---|
| 1544 | if (c != 0) { |
---|
| 1545 | _flow[i] += c; |
---|
| 1546 | _supply[_source[i]] += c; |
---|
| 1547 | _supply[_target[i]] -= c; |
---|
| 1548 | } |
---|
[648] | 1549 | } |
---|
| 1550 | } |
---|
[710] | 1551 | |
---|
| 1552 | // Shift potentials to meet the requirements of the GEQ/LEQ type |
---|
| 1553 | // optimality conditions |
---|
| 1554 | if (_sum_supply == 0) { |
---|
| 1555 | if (_stype == GEQ) { |
---|
| 1556 | Cost max_pot = std::numeric_limits<Cost>::min(); |
---|
| 1557 | for (int i = 0; i != _node_num; ++i) { |
---|
| 1558 | if (_pi[i] > max_pot) max_pot = _pi[i]; |
---|
| 1559 | } |
---|
| 1560 | if (max_pot > 0) { |
---|
| 1561 | for (int i = 0; i != _node_num; ++i) |
---|
| 1562 | _pi[i] -= max_pot; |
---|
| 1563 | } |
---|
| 1564 | } else { |
---|
| 1565 | Cost min_pot = std::numeric_limits<Cost>::max(); |
---|
| 1566 | for (int i = 0; i != _node_num; ++i) { |
---|
| 1567 | if (_pi[i] < min_pot) min_pot = _pi[i]; |
---|
| 1568 | } |
---|
| 1569 | if (min_pot < 0) { |
---|
| 1570 | for (int i = 0; i != _node_num; ++i) |
---|
| 1571 | _pi[i] -= min_pot; |
---|
| 1572 | } |
---|
| 1573 | } |
---|
| 1574 | } |
---|
[648] | 1575 | |
---|
[687] | 1576 | return OPTIMAL; |
---|
[648] | 1577 | } |
---|
| 1578 | |
---|
| 1579 | }; //class NetworkSimplex |
---|
| 1580 | |
---|
| 1581 | ///@} |
---|
| 1582 | |
---|
| 1583 | } //namespace lemon |
---|
| 1584 | |
---|
| 1585 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|