[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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[1270] | 5 | * Copyright (C) 2003-2013 |
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[648] | 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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[1221] | 44 | /// \cite amo93networkflows, \cite dantzig63linearprog, |
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| 45 | /// \cite 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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[1023] | 50 | /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest |
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[1165] | 51 | /// implementations available in LEMON for solving this problem. |
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| 52 | /// (For more information, see \ref min_cost_flow_algs "the module page".) |
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[1023] | 53 | /// Furthermore, this class supports both directions of the supply/demand |
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| 54 | /// inequality constraints. For more information, see \ref SupplyType. |
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[687] | 55 | /// |
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| 56 | /// Most of the parameters of the problem (except for the digraph) |
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| 57 | /// can be given using separate functions, and the algorithm can be |
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| 58 | /// executed using the \ref run() function. If some parameters are not |
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| 59 | /// specified, then default values will be used. |
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[648] | 60 | /// |
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[652] | 61 | /// \tparam GR The digraph type the algorithm runs on. |
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[878] | 62 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[833] | 63 | /// and supply values in the algorithm. By default, it is \c int. |
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[878] | 64 | /// \tparam C The number type used for costs and potentials in the |
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[833] | 65 | /// algorithm. By default, it is the same as \c V. |
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[648] | 66 | /// |
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[1025] | 67 | /// \warning Both \c V and \c C must be signed number types. |
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| 68 | /// \warning All input data (capacities, supply values, and costs) must |
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[655] | 69 | /// be integer. |
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[648] | 70 | /// |
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[652] | 71 | /// \note %NetworkSimplex provides five different pivot rule |
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[656] | 72 | /// implementations, from which the most efficient one is used |
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[833] | 73 | /// by default. For more information, see \ref PivotRule. |
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[688] | 74 | template <typename GR, typename V = int, typename C = V> |
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[648] | 75 | class NetworkSimplex |
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| 76 | { |
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[652] | 77 | public: |
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[648] | 78 | |
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[689] | 79 | /// The type of the flow amounts, capacity bounds and supply values |
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[688] | 80 | typedef V Value; |
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[689] | 81 | /// The type of the arc costs |
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[654] | 82 | typedef C Cost; |
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[652] | 83 | |
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| 84 | public: |
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| 85 | |
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[687] | 86 | /// \brief Problem type constants for the \c run() function. |
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[652] | 87 | /// |
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[687] | 88 | /// Enum type containing the problem type constants that can be |
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| 89 | /// returned by the \ref run() function of the algorithm. |
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| 90 | enum ProblemType { |
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| 91 | /// The problem has no feasible solution (flow). |
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| 92 | INFEASIBLE, |
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| 93 | /// The problem has optimal solution (i.e. it is feasible and |
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| 94 | /// bounded), and the algorithm has found optimal flow and node |
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| 95 | /// potentials (primal and dual solutions). |
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| 96 | OPTIMAL, |
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| 97 | /// The objective function of the problem is unbounded, i.e. |
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| 98 | /// there is a directed cycle having negative total cost and |
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| 99 | /// infinite upper bound. |
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| 100 | UNBOUNDED |
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| 101 | }; |
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[956] | 102 | |
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[687] | 103 | /// \brief Constants for selecting the type of the supply constraints. |
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| 104 | /// |
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| 105 | /// Enum type containing constants for selecting the supply type, |
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| 106 | /// i.e. the direction of the inequalities in the supply/demand |
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| 107 | /// constraints of the \ref min_cost_flow "minimum cost flow problem". |
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| 108 | /// |
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[710] | 109 | /// The default supply type is \c GEQ, the \c LEQ type can be |
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| 110 | /// selected using \ref supplyType(). |
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| 111 | /// The equality form is a special case of both supply types. |
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[687] | 112 | enum SupplyType { |
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| 113 | /// This option means that there are <em>"greater or equal"</em> |
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[710] | 114 | /// supply/demand constraints in the definition of the problem. |
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[687] | 115 | GEQ, |
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| 116 | /// This option means that there are <em>"less or equal"</em> |
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[710] | 117 | /// supply/demand constraints in the definition of the problem. |
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| 118 | LEQ |
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[687] | 119 | }; |
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[956] | 120 | |
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[687] | 121 | /// \brief Constants for selecting the pivot rule. |
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| 122 | /// |
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| 123 | /// Enum type containing constants for selecting the pivot rule for |
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| 124 | /// the \ref run() function. |
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| 125 | /// |
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[1136] | 126 | /// \ref NetworkSimplex provides five different implementations for |
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| 127 | /// the pivot strategy that significantly affects the running time |
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[652] | 128 | /// of the algorithm. |
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[1136] | 129 | /// According to experimental tests conducted on various problem |
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| 130 | /// instances, \ref BLOCK_SEARCH "Block Search" and |
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| 131 | /// \ref ALTERING_LIST "Altering Candidate List" rules turned out |
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| 132 | /// to be the most efficient. |
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| 133 | /// Since \ref BLOCK_SEARCH "Block Search" is a simpler strategy that |
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| 134 | /// seemed to be slightly more robust, it is used by default. |
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| 135 | /// However, another pivot rule can easily be selected using the |
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| 136 | /// \ref run() function with the proper parameter. |
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[652] | 137 | enum PivotRule { |
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| 138 | |
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[833] | 139 | /// The \e First \e Eligible pivot rule. |
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[652] | 140 | /// The next eligible arc is selected in a wraparound fashion |
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| 141 | /// in every iteration. |
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| 142 | FIRST_ELIGIBLE, |
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| 143 | |
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[833] | 144 | /// The \e Best \e Eligible pivot rule. |
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[652] | 145 | /// The best eligible arc is selected in every iteration. |
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| 146 | BEST_ELIGIBLE, |
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| 147 | |
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[833] | 148 | /// The \e Block \e Search pivot rule. |
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[652] | 149 | /// A specified number of arcs are examined in every iteration |
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| 150 | /// in a wraparound fashion and the best eligible arc is selected |
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| 151 | /// from this block. |
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| 152 | BLOCK_SEARCH, |
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| 153 | |
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[833] | 154 | /// The \e Candidate \e List pivot rule. |
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[652] | 155 | /// In a major iteration a candidate list is built from eligible arcs |
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| 156 | /// in a wraparound fashion and in the following minor iterations |
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| 157 | /// the best eligible arc is selected from this list. |
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| 158 | CANDIDATE_LIST, |
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| 159 | |
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[833] | 160 | /// The \e Altering \e Candidate \e List pivot rule. |
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[652] | 161 | /// It is a modified version of the Candidate List method. |
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[1136] | 162 | /// It keeps only a few of the best eligible arcs from the former |
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[652] | 163 | /// candidate list and extends this list in every iteration. |
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| 164 | ALTERING_LIST |
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| 165 | }; |
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[956] | 166 | |
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[652] | 167 | private: |
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| 168 | |
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| 169 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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| 170 | |
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[648] | 171 | typedef std::vector<int> IntVector; |
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[689] | 172 | typedef std::vector<Value> ValueVector; |
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[654] | 173 | typedef std::vector<Cost> CostVector; |
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[990] | 174 | typedef std::vector<signed char> CharVector; |
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[1023] | 175 | // Note: vector<signed char> is used instead of vector<ArcState> and |
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[990] | 176 | // vector<ArcDirection> for efficiency reasons |
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[648] | 177 | |
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| 178 | // State constants for arcs |
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[936] | 179 | enum ArcState { |
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[648] | 180 | STATE_UPPER = -1, |
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| 181 | STATE_TREE = 0, |
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| 182 | STATE_LOWER = 1 |
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| 183 | }; |
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| 184 | |
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[990] | 185 | // Direction constants for tree arcs |
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| 186 | enum ArcDirection { |
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| 187 | DIR_DOWN = -1, |
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| 188 | DIR_UP = 1 |
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| 189 | }; |
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[936] | 190 | |
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[648] | 191 | private: |
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| 192 | |
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[652] | 193 | // Data related to the underlying digraph |
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| 194 | const GR &_graph; |
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| 195 | int _node_num; |
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| 196 | int _arc_num; |
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[710] | 197 | int _all_arc_num; |
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| 198 | int _search_arc_num; |
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[652] | 199 | |
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| 200 | // Parameters of the problem |
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[689] | 201 | bool _have_lower; |
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[687] | 202 | SupplyType _stype; |
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[688] | 203 | Value _sum_supply; |
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[648] | 204 | |
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[652] | 205 | // Data structures for storing the digraph |
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[650] | 206 | IntNodeMap _node_id; |
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[689] | 207 | IntArcMap _arc_id; |
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[650] | 208 | IntVector _source; |
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| 209 | IntVector _target; |
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[898] | 210 | bool _arc_mixing; |
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[650] | 211 | |
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[652] | 212 | // Node and arc data |
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[689] | 213 | ValueVector _lower; |
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| 214 | ValueVector _upper; |
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| 215 | ValueVector _cap; |
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[654] | 216 | CostVector _cost; |
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[689] | 217 | ValueVector _supply; |
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| 218 | ValueVector _flow; |
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[654] | 219 | CostVector _pi; |
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[648] | 220 | |
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[650] | 221 | // Data for storing the spanning tree structure |
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[648] | 222 | IntVector _parent; |
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| 223 | IntVector _pred; |
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| 224 | IntVector _thread; |
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[651] | 225 | IntVector _rev_thread; |
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| 226 | IntVector _succ_num; |
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| 227 | IntVector _last_succ; |
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[990] | 228 | CharVector _pred_dir; |
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| 229 | CharVector _state; |
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[651] | 230 | IntVector _dirty_revs; |
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[648] | 231 | int _root; |
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| 232 | |
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| 233 | // Temporary data used in the current pivot iteration |
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[650] | 234 | int in_arc, join, u_in, v_in, u_out, v_out; |
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[688] | 235 | Value delta; |
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[648] | 236 | |
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[877] | 237 | const Value MAX; |
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[710] | 238 | |
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[687] | 239 | public: |
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[956] | 240 | |
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[687] | 241 | /// \brief Constant for infinite upper bounds (capacities). |
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| 242 | /// |
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| 243 | /// Constant for infinite upper bounds (capacities). |
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[688] | 244 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 245 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 246 | const Value INF; |
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[687] | 247 | |
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[648] | 248 | private: |
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| 249 | |
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[652] | 250 | // Implementation of the First Eligible pivot rule |
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[648] | 251 | class FirstEligiblePivotRule |
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| 252 | { |
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| 253 | private: |
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| 254 | |
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| 255 | // References to the NetworkSimplex class |
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| 256 | const IntVector &_source; |
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| 257 | const IntVector &_target; |
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[654] | 258 | const CostVector &_cost; |
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[990] | 259 | const CharVector &_state; |
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[654] | 260 | const CostVector &_pi; |
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[648] | 261 | int &_in_arc; |
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[710] | 262 | int _search_arc_num; |
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[648] | 263 | |
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| 264 | // Pivot rule data |
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| 265 | int _next_arc; |
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| 266 | |
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| 267 | public: |
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| 268 | |
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[652] | 269 | // Constructor |
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[648] | 270 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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[650] | 271 | _source(ns._source), _target(ns._target), |
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[648] | 272 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 273 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
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| 274 | _next_arc(0) |
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[648] | 275 | {} |
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| 276 | |
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[652] | 277 | // Find next entering arc |
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[648] | 278 | bool findEnteringArc() { |
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[654] | 279 | Cost c; |
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[910] | 280 | for (int e = _next_arc; e != _search_arc_num; ++e) { |
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[648] | 281 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 282 | if (c < 0) { |
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| 283 | _in_arc = e; |
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| 284 | _next_arc = e + 1; |
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| 285 | return true; |
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| 286 | } |
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| 287 | } |
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[910] | 288 | for (int e = 0; e != _next_arc; ++e) { |
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[648] | 289 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 290 | if (c < 0) { |
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| 291 | _in_arc = e; |
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| 292 | _next_arc = e + 1; |
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| 293 | return true; |
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| 294 | } |
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| 295 | } |
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| 296 | return false; |
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| 297 | } |
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| 298 | |
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| 299 | }; //class FirstEligiblePivotRule |
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| 300 | |
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| 301 | |
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[652] | 302 | // Implementation of the Best Eligible pivot rule |
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[648] | 303 | class BestEligiblePivotRule |
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| 304 | { |
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| 305 | private: |
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| 306 | |
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| 307 | // References to the NetworkSimplex class |
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| 308 | const IntVector &_source; |
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| 309 | const IntVector &_target; |
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[654] | 310 | const CostVector &_cost; |
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[990] | 311 | const CharVector &_state; |
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[654] | 312 | const CostVector &_pi; |
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[648] | 313 | int &_in_arc; |
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[710] | 314 | int _search_arc_num; |
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[648] | 315 | |
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| 316 | public: |
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| 317 | |
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[652] | 318 | // Constructor |
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[648] | 319 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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[650] | 320 | _source(ns._source), _target(ns._target), |
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[648] | 321 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 322 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num) |
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[648] | 323 | {} |
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| 324 | |
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[652] | 325 | // Find next entering arc |
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[648] | 326 | bool findEnteringArc() { |
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[654] | 327 | Cost c, min = 0; |
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[910] | 328 | for (int e = 0; e != _search_arc_num; ++e) { |
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[648] | 329 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 330 | if (c < min) { |
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| 331 | min = c; |
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| 332 | _in_arc = e; |
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| 333 | } |
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| 334 | } |
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| 335 | return min < 0; |
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| 336 | } |
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| 337 | |
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| 338 | }; //class BestEligiblePivotRule |
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| 339 | |
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| 340 | |
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[652] | 341 | // Implementation of the Block Search pivot rule |
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[648] | 342 | class BlockSearchPivotRule |
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| 343 | { |
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| 344 | private: |
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| 345 | |
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| 346 | // References to the NetworkSimplex class |
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| 347 | const IntVector &_source; |
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| 348 | const IntVector &_target; |
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[654] | 349 | const CostVector &_cost; |
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[990] | 350 | const CharVector &_state; |
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[654] | 351 | const CostVector &_pi; |
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[648] | 352 | int &_in_arc; |
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[710] | 353 | int _search_arc_num; |
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[648] | 354 | |
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| 355 | // Pivot rule data |
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| 356 | int _block_size; |
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| 357 | int _next_arc; |
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| 358 | |
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| 359 | public: |
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| 360 | |
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[652] | 361 | // Constructor |
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[648] | 362 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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[650] | 363 | _source(ns._source), _target(ns._target), |
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[648] | 364 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 365 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
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| 366 | _next_arc(0) |
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[648] | 367 | { |
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| 368 | // The main parameters of the pivot rule |
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[910] | 369 | const double BLOCK_SIZE_FACTOR = 1.0; |
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[648] | 370 | const int MIN_BLOCK_SIZE = 10; |
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| 371 | |
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[659] | 372 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
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[710] | 373 | std::sqrt(double(_search_arc_num))), |
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[648] | 374 | MIN_BLOCK_SIZE ); |
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| 375 | } |
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| 376 | |
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[652] | 377 | // Find next entering arc |
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[648] | 378 | bool findEnteringArc() { |
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[654] | 379 | Cost c, min = 0; |
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[648] | 380 | int cnt = _block_size; |
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[774] | 381 | int e; |
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[910] | 382 | for (e = _next_arc; e != _search_arc_num; ++e) { |
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[648] | 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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[774] | 386 | _in_arc = e; |
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[648] | 387 | } |
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| 388 | if (--cnt == 0) { |
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[774] | 389 | if (min < 0) goto search_end; |
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[648] | 390 | cnt = _block_size; |
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| 391 | } |
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| 392 | } |
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[910] | 393 | for (e = 0; e != _next_arc; ++e) { |
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[774] | 394 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 395 | if (c < min) { |
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| 396 | min = c; |
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| 397 | _in_arc = e; |
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| 398 | } |
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| 399 | if (--cnt == 0) { |
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| 400 | if (min < 0) goto search_end; |
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| 401 | cnt = _block_size; |
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[648] | 402 | } |
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| 403 | } |
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| 404 | if (min >= 0) return false; |
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[774] | 405 | |
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| 406 | search_end: |
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[648] | 407 | _next_arc = e; |
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| 408 | return true; |
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| 409 | } |
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| 410 | |
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| 411 | }; //class BlockSearchPivotRule |
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| 412 | |
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| 413 | |
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[652] | 414 | // Implementation of the Candidate List pivot rule |
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[648] | 415 | class CandidateListPivotRule |
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| 416 | { |
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| 417 | private: |
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| 418 | |
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| 419 | // References to the NetworkSimplex class |
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| 420 | const IntVector &_source; |
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| 421 | const IntVector &_target; |
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[654] | 422 | const CostVector &_cost; |
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[990] | 423 | const CharVector &_state; |
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[654] | 424 | const CostVector &_pi; |
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[648] | 425 | int &_in_arc; |
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[710] | 426 | int _search_arc_num; |
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[648] | 427 | |
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| 428 | // Pivot rule data |
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| 429 | IntVector _candidates; |
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| 430 | int _list_length, _minor_limit; |
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| 431 | int _curr_length, _minor_count; |
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| 432 | int _next_arc; |
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| 433 | |
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| 434 | public: |
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| 435 | |
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| 436 | /// Constructor |
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| 437 | CandidateListPivotRule(NetworkSimplex &ns) : |
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[650] | 438 | _source(ns._source), _target(ns._target), |
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[648] | 439 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[710] | 440 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
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| 441 | _next_arc(0) |
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[648] | 442 | { |
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| 443 | // The main parameters of the pivot rule |
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[774] | 444 | const double LIST_LENGTH_FACTOR = 0.25; |
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[648] | 445 | const int MIN_LIST_LENGTH = 10; |
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| 446 | const double MINOR_LIMIT_FACTOR = 0.1; |
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| 447 | const int MIN_MINOR_LIMIT = 3; |
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| 448 | |
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[659] | 449 | _list_length = std::max( int(LIST_LENGTH_FACTOR * |
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[710] | 450 | std::sqrt(double(_search_arc_num))), |
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[648] | 451 | MIN_LIST_LENGTH ); |
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| 452 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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| 453 | MIN_MINOR_LIMIT ); |
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| 454 | _curr_length = _minor_count = 0; |
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| 455 | _candidates.resize(_list_length); |
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| 456 | } |
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| 457 | |
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| 458 | /// Find next entering arc |
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| 459 | bool findEnteringArc() { |
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[654] | 460 | Cost min, c; |
---|
[774] | 461 | int e; |
---|
[648] | 462 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
---|
| 463 | // Minor iteration: select the best eligible arc from the |
---|
| 464 | // current candidate list |
---|
| 465 | ++_minor_count; |
---|
| 466 | min = 0; |
---|
| 467 | for (int i = 0; i < _curr_length; ++i) { |
---|
| 468 | e = _candidates[i]; |
---|
| 469 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 470 | if (c < min) { |
---|
| 471 | min = c; |
---|
[774] | 472 | _in_arc = e; |
---|
[648] | 473 | } |
---|
[774] | 474 | else if (c >= 0) { |
---|
[648] | 475 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 476 | } |
---|
| 477 | } |
---|
[774] | 478 | if (min < 0) return true; |
---|
[648] | 479 | } |
---|
| 480 | |
---|
| 481 | // Major iteration: build a new candidate list |
---|
| 482 | min = 0; |
---|
| 483 | _curr_length = 0; |
---|
[910] | 484 | for (e = _next_arc; e != _search_arc_num; ++e) { |
---|
[648] | 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; |
---|
[774] | 490 | _in_arc = e; |
---|
[648] | 491 | } |
---|
[774] | 492 | if (_curr_length == _list_length) goto search_end; |
---|
[648] | 493 | } |
---|
| 494 | } |
---|
[910] | 495 | for (e = 0; e != _next_arc; ++e) { |
---|
[774] | 496 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 497 | if (c < 0) { |
---|
| 498 | _candidates[_curr_length++] = e; |
---|
| 499 | if (c < min) { |
---|
| 500 | min = c; |
---|
| 501 | _in_arc = e; |
---|
[648] | 502 | } |
---|
[774] | 503 | if (_curr_length == _list_length) goto search_end; |
---|
[648] | 504 | } |
---|
| 505 | } |
---|
| 506 | if (_curr_length == 0) return false; |
---|
[956] | 507 | |
---|
| 508 | search_end: |
---|
[648] | 509 | _minor_count = 1; |
---|
| 510 | _next_arc = e; |
---|
| 511 | return true; |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | }; //class CandidateListPivotRule |
---|
| 515 | |
---|
| 516 | |
---|
[652] | 517 | // Implementation of the Altering Candidate List pivot rule |
---|
[648] | 518 | class AlteringListPivotRule |
---|
| 519 | { |
---|
| 520 | private: |
---|
| 521 | |
---|
| 522 | // References to the NetworkSimplex class |
---|
| 523 | const IntVector &_source; |
---|
| 524 | const IntVector &_target; |
---|
[654] | 525 | const CostVector &_cost; |
---|
[990] | 526 | const CharVector &_state; |
---|
[654] | 527 | const CostVector &_pi; |
---|
[648] | 528 | int &_in_arc; |
---|
[710] | 529 | int _search_arc_num; |
---|
[648] | 530 | |
---|
| 531 | // Pivot rule data |
---|
| 532 | int _block_size, _head_length, _curr_length; |
---|
| 533 | int _next_arc; |
---|
| 534 | IntVector _candidates; |
---|
[654] | 535 | CostVector _cand_cost; |
---|
[648] | 536 | |
---|
| 537 | // Functor class to compare arcs during sort of the candidate list |
---|
| 538 | class SortFunc |
---|
| 539 | { |
---|
| 540 | private: |
---|
[654] | 541 | const CostVector &_map; |
---|
[648] | 542 | public: |
---|
[654] | 543 | SortFunc(const CostVector &map) : _map(map) {} |
---|
[648] | 544 | bool operator()(int left, int right) { |
---|
[1136] | 545 | return _map[left] < _map[right]; |
---|
[648] | 546 | } |
---|
| 547 | }; |
---|
| 548 | |
---|
| 549 | SortFunc _sort_func; |
---|
| 550 | |
---|
| 551 | public: |
---|
| 552 | |
---|
[652] | 553 | // Constructor |
---|
[648] | 554 | AlteringListPivotRule(NetworkSimplex &ns) : |
---|
[650] | 555 | _source(ns._source), _target(ns._target), |
---|
[648] | 556 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
[710] | 557 | _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), |
---|
| 558 | _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost) |
---|
[648] | 559 | { |
---|
| 560 | // The main parameters of the pivot rule |
---|
[774] | 561 | const double BLOCK_SIZE_FACTOR = 1.0; |
---|
[648] | 562 | const int MIN_BLOCK_SIZE = 10; |
---|
[1136] | 563 | const double HEAD_LENGTH_FACTOR = 0.01; |
---|
[648] | 564 | const int MIN_HEAD_LENGTH = 3; |
---|
| 565 | |
---|
[659] | 566 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
---|
[710] | 567 | std::sqrt(double(_search_arc_num))), |
---|
[648] | 568 | MIN_BLOCK_SIZE ); |
---|
| 569 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
---|
| 570 | MIN_HEAD_LENGTH ); |
---|
| 571 | _candidates.resize(_head_length + _block_size); |
---|
| 572 | _curr_length = 0; |
---|
| 573 | } |
---|
| 574 | |
---|
[652] | 575 | // Find next entering arc |
---|
[648] | 576 | bool findEnteringArc() { |
---|
| 577 | // Check the current candidate list |
---|
| 578 | int e; |
---|
[990] | 579 | Cost c; |
---|
[910] | 580 | for (int i = 0; i != _curr_length; ++i) { |
---|
[648] | 581 | e = _candidates[i]; |
---|
[990] | 582 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 583 | if (c < 0) { |
---|
| 584 | _cand_cost[e] = c; |
---|
| 585 | } else { |
---|
[648] | 586 | _candidates[i--] = _candidates[--_curr_length]; |
---|
| 587 | } |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | // Extend the list |
---|
| 591 | int cnt = _block_size; |
---|
| 592 | int limit = _head_length; |
---|
| 593 | |
---|
[910] | 594 | for (e = _next_arc; e != _search_arc_num; ++e) { |
---|
[990] | 595 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 596 | if (c < 0) { |
---|
| 597 | _cand_cost[e] = c; |
---|
[648] | 598 | _candidates[_curr_length++] = e; |
---|
| 599 | } |
---|
| 600 | if (--cnt == 0) { |
---|
[774] | 601 | if (_curr_length > limit) goto search_end; |
---|
[648] | 602 | limit = 0; |
---|
| 603 | cnt = _block_size; |
---|
| 604 | } |
---|
| 605 | } |
---|
[910] | 606 | for (e = 0; e != _next_arc; ++e) { |
---|
[1136] | 607 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
| 608 | if (c < 0) { |
---|
| 609 | _cand_cost[e] = c; |
---|
[774] | 610 | _candidates[_curr_length++] = e; |
---|
| 611 | } |
---|
| 612 | if (--cnt == 0) { |
---|
| 613 | if (_curr_length > limit) goto search_end; |
---|
| 614 | limit = 0; |
---|
| 615 | cnt = _block_size; |
---|
[648] | 616 | } |
---|
| 617 | } |
---|
| 618 | if (_curr_length == 0) return false; |
---|
[956] | 619 | |
---|
[774] | 620 | search_end: |
---|
[648] | 621 | |
---|
[1136] | 622 | // Perform partial sort operation on the candidate list |
---|
| 623 | int new_length = std::min(_head_length + 1, _curr_length); |
---|
| 624 | std::partial_sort(_candidates.begin(), _candidates.begin() + new_length, |
---|
| 625 | _candidates.begin() + _curr_length, _sort_func); |
---|
[648] | 626 | |
---|
[1136] | 627 | // Select the entering arc and remove it from the list |
---|
[648] | 628 | _in_arc = _candidates[0]; |
---|
[774] | 629 | _next_arc = e; |
---|
[1136] | 630 | _candidates[0] = _candidates[new_length - 1]; |
---|
| 631 | _curr_length = new_length - 1; |
---|
[648] | 632 | return true; |
---|
| 633 | } |
---|
| 634 | |
---|
| 635 | }; //class AlteringListPivotRule |
---|
| 636 | |
---|
| 637 | public: |
---|
| 638 | |
---|
[652] | 639 | /// \brief Constructor. |
---|
[648] | 640 | /// |
---|
[656] | 641 | /// The constructor of the class. |
---|
[648] | 642 | /// |
---|
[650] | 643 | /// \param graph The digraph the algorithm runs on. |
---|
[991] | 644 | /// \param arc_mixing Indicate if the arcs will be stored in a |
---|
[956] | 645 | /// mixed order in the internal data structure. |
---|
[991] | 646 | /// In general, it leads to similar performance as using the original |
---|
| 647 | /// arc order, but it makes the algorithm more robust and in special |
---|
| 648 | /// cases, even significantly faster. Therefore, it is enabled by default. |
---|
| 649 | NetworkSimplex(const GR& graph, bool arc_mixing = true) : |
---|
[689] | 650 | _graph(graph), _node_id(graph), _arc_id(graph), |
---|
[898] | 651 | _arc_mixing(arc_mixing), |
---|
[877] | 652 | MAX(std::numeric_limits<Value>::max()), |
---|
[688] | 653 | INF(std::numeric_limits<Value>::has_infinity ? |
---|
[877] | 654 | std::numeric_limits<Value>::infinity() : MAX) |
---|
[652] | 655 | { |
---|
[878] | 656 | // Check the number types |
---|
[688] | 657 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
---|
[687] | 658 | "The flow type of NetworkSimplex must be signed"); |
---|
| 659 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
---|
| 660 | "The cost type of NetworkSimplex must be signed"); |
---|
[648] | 661 | |
---|
[898] | 662 | // Reset data structures |
---|
[776] | 663 | reset(); |
---|
[648] | 664 | } |
---|
| 665 | |
---|
[656] | 666 | /// \name Parameters |
---|
| 667 | /// The parameters of the algorithm can be specified using these |
---|
| 668 | /// functions. |
---|
| 669 | |
---|
| 670 | /// @{ |
---|
| 671 | |
---|
[652] | 672 | /// \brief Set the lower bounds on the arcs. |
---|
| 673 | /// |
---|
| 674 | /// This function sets the lower bounds on the arcs. |
---|
[687] | 675 | /// If it is not used before calling \ref run(), the lower bounds |
---|
| 676 | /// will be set to zero on all arcs. |
---|
[652] | 677 | /// |
---|
| 678 | /// \param map An arc map storing the lower bounds. |
---|
[688] | 679 | /// Its \c Value type must be convertible to the \c Value type |
---|
[652] | 680 | /// of the algorithm. |
---|
| 681 | /// |
---|
| 682 | /// \return <tt>(*this)</tt> |
---|
[687] | 683 | template <typename LowerMap> |
---|
| 684 | NetworkSimplex& lowerMap(const LowerMap& map) { |
---|
[689] | 685 | _have_lower = true; |
---|
[652] | 686 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[689] | 687 | _lower[_arc_id[a]] = map[a]; |
---|
[652] | 688 | } |
---|
| 689 | return *this; |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
| 693 | /// |
---|
| 694 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
[687] | 695 | /// If it is not used before calling \ref run(), the upper bounds |
---|
| 696 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
---|
[878] | 697 | /// unbounded from above). |
---|
[652] | 698 | /// |
---|
| 699 | /// \param map An arc map storing the upper bounds. |
---|
[688] | 700 | /// Its \c Value type must be convertible to the \c Value type |
---|
[652] | 701 | /// of the algorithm. |
---|
| 702 | /// |
---|
| 703 | /// \return <tt>(*this)</tt> |
---|
[687] | 704 | template<typename UpperMap> |
---|
| 705 | NetworkSimplex& upperMap(const UpperMap& map) { |
---|
[652] | 706 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[689] | 707 | _upper[_arc_id[a]] = map[a]; |
---|
[652] | 708 | } |
---|
| 709 | return *this; |
---|
| 710 | } |
---|
| 711 | |
---|
| 712 | /// \brief Set the costs of the arcs. |
---|
| 713 | /// |
---|
| 714 | /// This function sets the costs of the arcs. |
---|
| 715 | /// If it is not used before calling \ref run(), the costs |
---|
| 716 | /// will be set to \c 1 on all arcs. |
---|
| 717 | /// |
---|
| 718 | /// \param map An arc map storing the costs. |
---|
[654] | 719 | /// Its \c Value type must be convertible to the \c Cost type |
---|
[652] | 720 | /// of the algorithm. |
---|
| 721 | /// |
---|
| 722 | /// \return <tt>(*this)</tt> |
---|
[687] | 723 | template<typename CostMap> |
---|
| 724 | NetworkSimplex& costMap(const CostMap& map) { |
---|
[652] | 725 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
[689] | 726 | _cost[_arc_id[a]] = map[a]; |
---|
[652] | 727 | } |
---|
| 728 | return *this; |
---|
| 729 | } |
---|
| 730 | |
---|
| 731 | /// \brief Set the supply values of the nodes. |
---|
| 732 | /// |
---|
| 733 | /// This function sets the supply values of the nodes. |
---|
| 734 | /// If neither this function nor \ref stSupply() is used before |
---|
| 735 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 736 | /// |
---|
| 737 | /// \param map A node map storing the supply values. |
---|
[688] | 738 | /// Its \c Value type must be convertible to the \c Value type |
---|
[652] | 739 | /// of the algorithm. |
---|
| 740 | /// |
---|
| 741 | /// \return <tt>(*this)</tt> |
---|
[1023] | 742 | /// |
---|
| 743 | /// \sa supplyType() |
---|
[687] | 744 | template<typename SupplyMap> |
---|
| 745 | NetworkSimplex& supplyMap(const SupplyMap& map) { |
---|
[652] | 746 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[689] | 747 | _supply[_node_id[n]] = map[n]; |
---|
[652] | 748 | } |
---|
| 749 | return *this; |
---|
| 750 | } |
---|
| 751 | |
---|
| 752 | /// \brief Set single source and target nodes and a supply value. |
---|
| 753 | /// |
---|
| 754 | /// This function sets a single source node and a single target node |
---|
| 755 | /// and the required flow value. |
---|
| 756 | /// If neither this function nor \ref supplyMap() is used before |
---|
| 757 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 758 | /// |
---|
[687] | 759 | /// Using this function has the same effect as using \ref supplyMap() |
---|
[1023] | 760 | /// with a map in which \c k is assigned to \c s, \c -k is |
---|
[687] | 761 | /// assigned to \c t and all other nodes have zero supply value. |
---|
| 762 | /// |
---|
[652] | 763 | /// \param s The source node. |
---|
| 764 | /// \param t The target node. |
---|
| 765 | /// \param k The required amount of flow from node \c s to node \c t |
---|
| 766 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
| 767 | /// |
---|
| 768 | /// \return <tt>(*this)</tt> |
---|
[688] | 769 | NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) { |
---|
[689] | 770 | for (int i = 0; i != _node_num; ++i) { |
---|
| 771 | _supply[i] = 0; |
---|
| 772 | } |
---|
| 773 | _supply[_node_id[s]] = k; |
---|
| 774 | _supply[_node_id[t]] = -k; |
---|
[652] | 775 | return *this; |
---|
| 776 | } |
---|
[956] | 777 | |
---|
[687] | 778 | /// \brief Set the type of the supply constraints. |
---|
[656] | 779 | /// |
---|
[687] | 780 | /// This function sets the type of the supply/demand constraints. |
---|
| 781 | /// If it is not used before calling \ref run(), the \ref GEQ supply |
---|
[656] | 782 | /// type will be used. |
---|
| 783 | /// |
---|
[833] | 784 | /// For more information, see \ref SupplyType. |
---|
[656] | 785 | /// |
---|
| 786 | /// \return <tt>(*this)</tt> |
---|
[687] | 787 | NetworkSimplex& supplyType(SupplyType supply_type) { |
---|
| 788 | _stype = supply_type; |
---|
[656] | 789 | return *this; |
---|
| 790 | } |
---|
[652] | 791 | |
---|
[656] | 792 | /// @} |
---|
[648] | 793 | |
---|
[652] | 794 | /// \name Execution Control |
---|
| 795 | /// The algorithm can be executed using \ref run(). |
---|
| 796 | |
---|
[648] | 797 | /// @{ |
---|
| 798 | |
---|
| 799 | /// \brief Run the algorithm. |
---|
| 800 | /// |
---|
| 801 | /// This function runs the algorithm. |
---|
[656] | 802 | /// The paramters can be specified using functions \ref lowerMap(), |
---|
[956] | 803 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), |
---|
[689] | 804 | /// \ref supplyType(). |
---|
[656] | 805 | /// For example, |
---|
[652] | 806 | /// \code |
---|
| 807 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
[687] | 808 | /// ns.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
[652] | 809 | /// .supplyMap(sup).run(); |
---|
| 810 | /// \endcode |
---|
[648] | 811 | /// |
---|
[898] | 812 | /// This function can be called more than once. All the given parameters |
---|
| 813 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
---|
| 814 | /// is used, thus only the modified parameters have to be set again. |
---|
| 815 | /// If the underlying digraph was also modified after the construction |
---|
| 816 | /// of the class (or the last \ref reset() call), then the \ref reset() |
---|
| 817 | /// function must be called. |
---|
[653] | 818 | /// |
---|
[652] | 819 | /// \param pivot_rule The pivot rule that will be used during the |
---|
[833] | 820 | /// algorithm. For more information, see \ref PivotRule. |
---|
[648] | 821 | /// |
---|
[687] | 822 | /// \return \c INFEASIBLE if no feasible flow exists, |
---|
| 823 | /// \n \c OPTIMAL if the problem has optimal solution |
---|
| 824 | /// (i.e. it is feasible and bounded), and the algorithm has found |
---|
| 825 | /// optimal flow and node potentials (primal and dual solutions), |
---|
| 826 | /// \n \c UNBOUNDED if the objective function of the problem is |
---|
| 827 | /// unbounded, i.e. there is a directed cycle having negative total |
---|
| 828 | /// cost and infinite upper bound. |
---|
| 829 | /// |
---|
| 830 | /// \see ProblemType, PivotRule |
---|
[898] | 831 | /// \see resetParams(), reset() |
---|
[687] | 832 | ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) { |
---|
| 833 | if (!init()) return INFEASIBLE; |
---|
| 834 | return start(pivot_rule); |
---|
[648] | 835 | } |
---|
| 836 | |
---|
[653] | 837 | /// \brief Reset all the parameters that have been given before. |
---|
| 838 | /// |
---|
| 839 | /// This function resets all the paramaters that have been given |
---|
[656] | 840 | /// before using functions \ref lowerMap(), \ref upperMap(), |
---|
[689] | 841 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). |
---|
[653] | 842 | /// |
---|
[898] | 843 | /// It is useful for multiple \ref run() calls. Basically, all the given |
---|
| 844 | /// parameters are kept for the next \ref run() call, unless |
---|
| 845 | /// \ref resetParams() or \ref reset() is used. |
---|
| 846 | /// If the underlying digraph was also modified after the construction |
---|
| 847 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
| 848 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
[653] | 849 | /// |
---|
| 850 | /// For example, |
---|
| 851 | /// \code |
---|
| 852 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
| 853 | /// |
---|
| 854 | /// // First run |
---|
[687] | 855 | /// ns.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
[653] | 856 | /// .supplyMap(sup).run(); |
---|
| 857 | /// |
---|
[898] | 858 | /// // Run again with modified cost map (resetParams() is not called, |
---|
[653] | 859 | /// // so only the cost map have to be set again) |
---|
| 860 | /// cost[e] += 100; |
---|
| 861 | /// ns.costMap(cost).run(); |
---|
| 862 | /// |
---|
[898] | 863 | /// // Run again from scratch using resetParams() |
---|
[653] | 864 | /// // (the lower bounds will be set to zero on all arcs) |
---|
[898] | 865 | /// ns.resetParams(); |
---|
[687] | 866 | /// ns.upperMap(capacity).costMap(cost) |
---|
[653] | 867 | /// .supplyMap(sup).run(); |
---|
| 868 | /// \endcode |
---|
| 869 | /// |
---|
| 870 | /// \return <tt>(*this)</tt> |
---|
[898] | 871 | /// |
---|
| 872 | /// \see reset(), run() |
---|
| 873 | NetworkSimplex& resetParams() { |
---|
[689] | 874 | for (int i = 0; i != _node_num; ++i) { |
---|
| 875 | _supply[i] = 0; |
---|
| 876 | } |
---|
| 877 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 878 | _lower[i] = 0; |
---|
| 879 | _upper[i] = INF; |
---|
| 880 | _cost[i] = 1; |
---|
| 881 | } |
---|
| 882 | _have_lower = false; |
---|
[687] | 883 | _stype = GEQ; |
---|
[653] | 884 | return *this; |
---|
| 885 | } |
---|
| 886 | |
---|
[898] | 887 | /// \brief Reset the internal data structures and all the parameters |
---|
| 888 | /// that have been given before. |
---|
| 889 | /// |
---|
| 890 | /// This function resets the internal data structures and all the |
---|
| 891 | /// paramaters that have been given before using functions \ref lowerMap(), |
---|
| 892 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), |
---|
| 893 | /// \ref supplyType(). |
---|
| 894 | /// |
---|
| 895 | /// It is useful for multiple \ref run() calls. Basically, all the given |
---|
| 896 | /// parameters are kept for the next \ref run() call, unless |
---|
| 897 | /// \ref resetParams() or \ref reset() is used. |
---|
| 898 | /// If the underlying digraph was also modified after the construction |
---|
| 899 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
| 900 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
| 901 | /// |
---|
| 902 | /// See \ref resetParams() for examples. |
---|
| 903 | /// |
---|
| 904 | /// \return <tt>(*this)</tt> |
---|
| 905 | /// |
---|
| 906 | /// \see resetParams(), run() |
---|
| 907 | NetworkSimplex& reset() { |
---|
| 908 | // Resize vectors |
---|
| 909 | _node_num = countNodes(_graph); |
---|
| 910 | _arc_num = countArcs(_graph); |
---|
| 911 | int all_node_num = _node_num + 1; |
---|
| 912 | int max_arc_num = _arc_num + 2 * _node_num; |
---|
| 913 | |
---|
| 914 | _source.resize(max_arc_num); |
---|
| 915 | _target.resize(max_arc_num); |
---|
| 916 | |
---|
| 917 | _lower.resize(_arc_num); |
---|
| 918 | _upper.resize(_arc_num); |
---|
| 919 | _cap.resize(max_arc_num); |
---|
| 920 | _cost.resize(max_arc_num); |
---|
| 921 | _supply.resize(all_node_num); |
---|
| 922 | _flow.resize(max_arc_num); |
---|
| 923 | _pi.resize(all_node_num); |
---|
| 924 | |
---|
| 925 | _parent.resize(all_node_num); |
---|
| 926 | _pred.resize(all_node_num); |
---|
[990] | 927 | _pred_dir.resize(all_node_num); |
---|
[898] | 928 | _thread.resize(all_node_num); |
---|
| 929 | _rev_thread.resize(all_node_num); |
---|
| 930 | _succ_num.resize(all_node_num); |
---|
| 931 | _last_succ.resize(all_node_num); |
---|
| 932 | _state.resize(max_arc_num); |
---|
| 933 | |
---|
| 934 | // Copy the graph |
---|
| 935 | int i = 0; |
---|
| 936 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 937 | _node_id[n] = i; |
---|
| 938 | } |
---|
| 939 | if (_arc_mixing) { |
---|
| 940 | // Store the arcs in a mixed order |
---|
[991] | 941 | const int skip = std::max(_arc_num / _node_num, 3); |
---|
[898] | 942 | int i = 0, j = 0; |
---|
| 943 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 944 | _arc_id[a] = i; |
---|
| 945 | _source[i] = _node_id[_graph.source(a)]; |
---|
| 946 | _target[i] = _node_id[_graph.target(a)]; |
---|
[991] | 947 | if ((i += skip) >= _arc_num) i = ++j; |
---|
[898] | 948 | } |
---|
| 949 | } else { |
---|
| 950 | // Store the arcs in the original order |
---|
| 951 | int i = 0; |
---|
| 952 | for (ArcIt a(_graph); a != INVALID; ++a, ++i) { |
---|
| 953 | _arc_id[a] = i; |
---|
| 954 | _source[i] = _node_id[_graph.source(a)]; |
---|
| 955 | _target[i] = _node_id[_graph.target(a)]; |
---|
| 956 | } |
---|
| 957 | } |
---|
[956] | 958 | |
---|
[898] | 959 | // Reset parameters |
---|
| 960 | resetParams(); |
---|
| 961 | return *this; |
---|
| 962 | } |
---|
[956] | 963 | |
---|
[648] | 964 | /// @} |
---|
| 965 | |
---|
| 966 | /// \name Query Functions |
---|
| 967 | /// The results of the algorithm can be obtained using these |
---|
| 968 | /// functions.\n |
---|
[652] | 969 | /// The \ref run() function must be called before using them. |
---|
| 970 | |
---|
[648] | 971 | /// @{ |
---|
| 972 | |
---|
[652] | 973 | /// \brief Return the total cost of the found flow. |
---|
| 974 | /// |
---|
| 975 | /// This function returns the total cost of the found flow. |
---|
[1254] | 976 | /// Its complexity is O(m). |
---|
[652] | 977 | /// |
---|
| 978 | /// \note The return type of the function can be specified as a |
---|
| 979 | /// template parameter. For example, |
---|
| 980 | /// \code |
---|
| 981 | /// ns.totalCost<double>(); |
---|
| 982 | /// \endcode |
---|
[654] | 983 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
[652] | 984 | /// type of the algorithm, which is the default return type of the |
---|
| 985 | /// function. |
---|
| 986 | /// |
---|
| 987 | /// \pre \ref run() must be called before using this function. |
---|
[689] | 988 | template <typename Number> |
---|
| 989 | Number totalCost() const { |
---|
| 990 | Number c = 0; |
---|
| 991 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 992 | int i = _arc_id[a]; |
---|
| 993 | c += Number(_flow[i]) * Number(_cost[i]); |
---|
[652] | 994 | } |
---|
| 995 | return c; |
---|
| 996 | } |
---|
| 997 | |
---|
| 998 | #ifndef DOXYGEN |
---|
[654] | 999 | Cost totalCost() const { |
---|
| 1000 | return totalCost<Cost>(); |
---|
[652] | 1001 | } |
---|
| 1002 | #endif |
---|
| 1003 | |
---|
| 1004 | /// \brief Return the flow on the given arc. |
---|
| 1005 | /// |
---|
| 1006 | /// This function returns the flow on the given arc. |
---|
| 1007 | /// |
---|
| 1008 | /// \pre \ref run() must be called before using this function. |
---|
[688] | 1009 | Value flow(const Arc& a) const { |
---|
[689] | 1010 | return _flow[_arc_id[a]]; |
---|
[652] | 1011 | } |
---|
| 1012 | |
---|
[1165] | 1013 | /// \brief Copy the flow values (the primal solution) into the |
---|
| 1014 | /// given map. |
---|
[648] | 1015 | /// |
---|
[689] | 1016 | /// This function copies the flow value on each arc into the given |
---|
| 1017 | /// map. The \c Value type of the algorithm must be convertible to |
---|
| 1018 | /// the \c Value type of the map. |
---|
[648] | 1019 | /// |
---|
| 1020 | /// \pre \ref run() must be called before using this function. |
---|
[689] | 1021 | template <typename FlowMap> |
---|
| 1022 | void flowMap(FlowMap &map) const { |
---|
| 1023 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 1024 | map.set(a, _flow[_arc_id[a]]); |
---|
| 1025 | } |
---|
[648] | 1026 | } |
---|
| 1027 | |
---|
[652] | 1028 | /// \brief Return the potential (dual value) of the given node. |
---|
| 1029 | /// |
---|
| 1030 | /// This function returns the potential (dual value) of the |
---|
| 1031 | /// given node. |
---|
| 1032 | /// |
---|
| 1033 | /// \pre \ref run() must be called before using this function. |
---|
[654] | 1034 | Cost potential(const Node& n) const { |
---|
[689] | 1035 | return _pi[_node_id[n]]; |
---|
[652] | 1036 | } |
---|
| 1037 | |
---|
[1165] | 1038 | /// \brief Copy the potential values (the dual solution) into the |
---|
| 1039 | /// given map. |
---|
[648] | 1040 | /// |
---|
[689] | 1041 | /// This function copies the potential (dual value) of each node |
---|
| 1042 | /// into the given map. |
---|
| 1043 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 1044 | /// \c Value type of the map. |
---|
[648] | 1045 | /// |
---|
| 1046 | /// \pre \ref run() must be called before using this function. |
---|
[689] | 1047 | template <typename PotentialMap> |
---|
| 1048 | void potentialMap(PotentialMap &map) const { |
---|
| 1049 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1050 | map.set(n, _pi[_node_id[n]]); |
---|
| 1051 | } |
---|
[648] | 1052 | } |
---|
| 1053 | |
---|
| 1054 | /// @} |
---|
| 1055 | |
---|
| 1056 | private: |
---|
| 1057 | |
---|
| 1058 | // Initialize internal data structures |
---|
| 1059 | bool init() { |
---|
[652] | 1060 | if (_node_num == 0) return false; |
---|
[648] | 1061 | |
---|
[689] | 1062 | // Check the sum of supply values |
---|
| 1063 | _sum_supply = 0; |
---|
| 1064 | for (int i = 0; i != _node_num; ++i) { |
---|
| 1065 | _sum_supply += _supply[i]; |
---|
| 1066 | } |
---|
[690] | 1067 | if ( !((_stype == GEQ && _sum_supply <= 0) || |
---|
| 1068 | (_stype == LEQ && _sum_supply >= 0)) ) return false; |
---|
[648] | 1069 | |
---|
[1240] | 1070 | // Check lower and upper bounds |
---|
| 1071 | LEMON_DEBUG(checkBoundMaps(), |
---|
| 1072 | "Upper bounds must be greater or equal to the lower bounds"); |
---|
| 1073 | |
---|
[689] | 1074 | // Remove non-zero lower bounds |
---|
| 1075 | if (_have_lower) { |
---|
| 1076 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1077 | Value c = _lower[i]; |
---|
| 1078 | if (c >= 0) { |
---|
[877] | 1079 | _cap[i] = _upper[i] < MAX ? _upper[i] - c : INF; |
---|
[689] | 1080 | } else { |
---|
[877] | 1081 | _cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF; |
---|
[689] | 1082 | } |
---|
| 1083 | _supply[_source[i]] -= c; |
---|
| 1084 | _supply[_target[i]] += c; |
---|
| 1085 | } |
---|
| 1086 | } else { |
---|
| 1087 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1088 | _cap[i] = _upper[i]; |
---|
| 1089 | } |
---|
[652] | 1090 | } |
---|
[648] | 1091 | |
---|
[656] | 1092 | // Initialize artifical cost |
---|
[687] | 1093 | Cost ART_COST; |
---|
[656] | 1094 | if (std::numeric_limits<Cost>::is_exact) { |
---|
[710] | 1095 | ART_COST = std::numeric_limits<Cost>::max() / 2 + 1; |
---|
[656] | 1096 | } else { |
---|
[976] | 1097 | ART_COST = 0; |
---|
[656] | 1098 | for (int i = 0; i != _arc_num; ++i) { |
---|
[687] | 1099 | if (_cost[i] > ART_COST) ART_COST = _cost[i]; |
---|
[656] | 1100 | } |
---|
[687] | 1101 | ART_COST = (ART_COST + 1) * _node_num; |
---|
[656] | 1102 | } |
---|
| 1103 | |
---|
[689] | 1104 | // Initialize arc maps |
---|
| 1105 | for (int i = 0; i != _arc_num; ++i) { |
---|
| 1106 | _flow[i] = 0; |
---|
| 1107 | _state[i] = STATE_LOWER; |
---|
| 1108 | } |
---|
[956] | 1109 | |
---|
[648] | 1110 | // Set data for the artificial root node |
---|
| 1111 | _root = _node_num; |
---|
| 1112 | _parent[_root] = -1; |
---|
| 1113 | _pred[_root] = -1; |
---|
| 1114 | _thread[_root] = 0; |
---|
[651] | 1115 | _rev_thread[0] = _root; |
---|
[689] | 1116 | _succ_num[_root] = _node_num + 1; |
---|
[651] | 1117 | _last_succ[_root] = _root - 1; |
---|
[687] | 1118 | _supply[_root] = -_sum_supply; |
---|
[710] | 1119 | _pi[_root] = 0; |
---|
[648] | 1120 | |
---|
| 1121 | // Add artificial arcs and initialize the spanning tree data structure |
---|
[710] | 1122 | if (_sum_supply == 0) { |
---|
| 1123 | // EQ supply constraints |
---|
| 1124 | _search_arc_num = _arc_num; |
---|
| 1125 | _all_arc_num = _arc_num + _node_num; |
---|
| 1126 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1127 | _parent[u] = _root; |
---|
| 1128 | _pred[u] = e; |
---|
| 1129 | _thread[u] = u + 1; |
---|
| 1130 | _rev_thread[u + 1] = u; |
---|
| 1131 | _succ_num[u] = 1; |
---|
| 1132 | _last_succ[u] = u; |
---|
| 1133 | _cap[e] = INF; |
---|
| 1134 | _state[e] = STATE_TREE; |
---|
| 1135 | if (_supply[u] >= 0) { |
---|
[990] | 1136 | _pred_dir[u] = DIR_UP; |
---|
[710] | 1137 | _pi[u] = 0; |
---|
| 1138 | _source[e] = u; |
---|
| 1139 | _target[e] = _root; |
---|
| 1140 | _flow[e] = _supply[u]; |
---|
| 1141 | _cost[e] = 0; |
---|
| 1142 | } else { |
---|
[990] | 1143 | _pred_dir[u] = DIR_DOWN; |
---|
[710] | 1144 | _pi[u] = ART_COST; |
---|
| 1145 | _source[e] = _root; |
---|
| 1146 | _target[e] = u; |
---|
| 1147 | _flow[e] = -_supply[u]; |
---|
| 1148 | _cost[e] = ART_COST; |
---|
| 1149 | } |
---|
[648] | 1150 | } |
---|
| 1151 | } |
---|
[710] | 1152 | else if (_sum_supply > 0) { |
---|
| 1153 | // LEQ supply constraints |
---|
| 1154 | _search_arc_num = _arc_num + _node_num; |
---|
| 1155 | int f = _arc_num + _node_num; |
---|
| 1156 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1157 | _parent[u] = _root; |
---|
| 1158 | _thread[u] = u + 1; |
---|
| 1159 | _rev_thread[u + 1] = u; |
---|
| 1160 | _succ_num[u] = 1; |
---|
| 1161 | _last_succ[u] = u; |
---|
| 1162 | if (_supply[u] >= 0) { |
---|
[990] | 1163 | _pred_dir[u] = DIR_UP; |
---|
[710] | 1164 | _pi[u] = 0; |
---|
| 1165 | _pred[u] = e; |
---|
| 1166 | _source[e] = u; |
---|
| 1167 | _target[e] = _root; |
---|
| 1168 | _cap[e] = INF; |
---|
| 1169 | _flow[e] = _supply[u]; |
---|
| 1170 | _cost[e] = 0; |
---|
| 1171 | _state[e] = STATE_TREE; |
---|
| 1172 | } else { |
---|
[990] | 1173 | _pred_dir[u] = DIR_DOWN; |
---|
[710] | 1174 | _pi[u] = ART_COST; |
---|
| 1175 | _pred[u] = f; |
---|
| 1176 | _source[f] = _root; |
---|
| 1177 | _target[f] = u; |
---|
| 1178 | _cap[f] = INF; |
---|
| 1179 | _flow[f] = -_supply[u]; |
---|
| 1180 | _cost[f] = ART_COST; |
---|
| 1181 | _state[f] = STATE_TREE; |
---|
| 1182 | _source[e] = u; |
---|
| 1183 | _target[e] = _root; |
---|
| 1184 | _cap[e] = INF; |
---|
| 1185 | _flow[e] = 0; |
---|
| 1186 | _cost[e] = 0; |
---|
| 1187 | _state[e] = STATE_LOWER; |
---|
| 1188 | ++f; |
---|
| 1189 | } |
---|
| 1190 | } |
---|
| 1191 | _all_arc_num = f; |
---|
| 1192 | } |
---|
| 1193 | else { |
---|
| 1194 | // GEQ supply constraints |
---|
| 1195 | _search_arc_num = _arc_num + _node_num; |
---|
| 1196 | int f = _arc_num + _node_num; |
---|
| 1197 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 1198 | _parent[u] = _root; |
---|
| 1199 | _thread[u] = u + 1; |
---|
| 1200 | _rev_thread[u + 1] = u; |
---|
| 1201 | _succ_num[u] = 1; |
---|
| 1202 | _last_succ[u] = u; |
---|
| 1203 | if (_supply[u] <= 0) { |
---|
[990] | 1204 | _pred_dir[u] = DIR_DOWN; |
---|
[710] | 1205 | _pi[u] = 0; |
---|
| 1206 | _pred[u] = e; |
---|
| 1207 | _source[e] = _root; |
---|
| 1208 | _target[e] = u; |
---|
| 1209 | _cap[e] = INF; |
---|
| 1210 | _flow[e] = -_supply[u]; |
---|
| 1211 | _cost[e] = 0; |
---|
| 1212 | _state[e] = STATE_TREE; |
---|
| 1213 | } else { |
---|
[990] | 1214 | _pred_dir[u] = DIR_UP; |
---|
[710] | 1215 | _pi[u] = -ART_COST; |
---|
| 1216 | _pred[u] = f; |
---|
| 1217 | _source[f] = u; |
---|
| 1218 | _target[f] = _root; |
---|
| 1219 | _cap[f] = INF; |
---|
| 1220 | _flow[f] = _supply[u]; |
---|
| 1221 | _state[f] = STATE_TREE; |
---|
| 1222 | _cost[f] = ART_COST; |
---|
| 1223 | _source[e] = _root; |
---|
| 1224 | _target[e] = u; |
---|
| 1225 | _cap[e] = INF; |
---|
| 1226 | _flow[e] = 0; |
---|
| 1227 | _cost[e] = 0; |
---|
| 1228 | _state[e] = STATE_LOWER; |
---|
| 1229 | ++f; |
---|
| 1230 | } |
---|
| 1231 | } |
---|
| 1232 | _all_arc_num = f; |
---|
| 1233 | } |
---|
[648] | 1234 | |
---|
| 1235 | return true; |
---|
| 1236 | } |
---|
[1270] | 1237 | |
---|
[1240] | 1238 | // Check if the upper bound is greater or equal to the lower bound |
---|
| 1239 | // on each arc. |
---|
| 1240 | bool checkBoundMaps() { |
---|
| 1241 | for (int j = 0; j != _arc_num; ++j) { |
---|
| 1242 | if (_upper[j] < _lower[j]) return false; |
---|
| 1243 | } |
---|
| 1244 | return true; |
---|
| 1245 | } |
---|
[648] | 1246 | |
---|
| 1247 | // Find the join node |
---|
| 1248 | void findJoinNode() { |
---|
[650] | 1249 | int u = _source[in_arc]; |
---|
| 1250 | int v = _target[in_arc]; |
---|
[648] | 1251 | while (u != v) { |
---|
[651] | 1252 | if (_succ_num[u] < _succ_num[v]) { |
---|
| 1253 | u = _parent[u]; |
---|
| 1254 | } else { |
---|
| 1255 | v = _parent[v]; |
---|
| 1256 | } |
---|
[648] | 1257 | } |
---|
| 1258 | join = u; |
---|
| 1259 | } |
---|
| 1260 | |
---|
| 1261 | // Find the leaving arc of the cycle and returns true if the |
---|
| 1262 | // leaving arc is not the same as the entering arc |
---|
| 1263 | bool findLeavingArc() { |
---|
| 1264 | // Initialize first and second nodes according to the direction |
---|
| 1265 | // of the cycle |
---|
[990] | 1266 | int first, second; |
---|
[650] | 1267 | if (_state[in_arc] == STATE_LOWER) { |
---|
| 1268 | first = _source[in_arc]; |
---|
| 1269 | second = _target[in_arc]; |
---|
[648] | 1270 | } else { |
---|
[650] | 1271 | first = _target[in_arc]; |
---|
| 1272 | second = _source[in_arc]; |
---|
[648] | 1273 | } |
---|
[650] | 1274 | delta = _cap[in_arc]; |
---|
[648] | 1275 | int result = 0; |
---|
[990] | 1276 | Value c, d; |
---|
[648] | 1277 | int e; |
---|
| 1278 | |
---|
[990] | 1279 | // Search the cycle form the first node to the join node |
---|
[648] | 1280 | for (int u = first; u != join; u = _parent[u]) { |
---|
| 1281 | e = _pred[u]; |
---|
[990] | 1282 | d = _flow[e]; |
---|
| 1283 | if (_pred_dir[u] == DIR_DOWN) { |
---|
| 1284 | c = _cap[e]; |
---|
| 1285 | d = c >= MAX ? INF : c - d; |
---|
| 1286 | } |
---|
[648] | 1287 | if (d < delta) { |
---|
| 1288 | delta = d; |
---|
| 1289 | u_out = u; |
---|
| 1290 | result = 1; |
---|
| 1291 | } |
---|
| 1292 | } |
---|
[990] | 1293 | |
---|
| 1294 | // Search the cycle form the second node to the join node |
---|
[648] | 1295 | for (int u = second; u != join; u = _parent[u]) { |
---|
| 1296 | e = _pred[u]; |
---|
[990] | 1297 | d = _flow[e]; |
---|
| 1298 | if (_pred_dir[u] == DIR_UP) { |
---|
| 1299 | c = _cap[e]; |
---|
| 1300 | d = c >= MAX ? INF : c - d; |
---|
| 1301 | } |
---|
[648] | 1302 | if (d <= delta) { |
---|
| 1303 | delta = d; |
---|
| 1304 | u_out = u; |
---|
| 1305 | result = 2; |
---|
| 1306 | } |
---|
| 1307 | } |
---|
| 1308 | |
---|
| 1309 | if (result == 1) { |
---|
| 1310 | u_in = first; |
---|
| 1311 | v_in = second; |
---|
| 1312 | } else { |
---|
| 1313 | u_in = second; |
---|
| 1314 | v_in = first; |
---|
| 1315 | } |
---|
| 1316 | return result != 0; |
---|
| 1317 | } |
---|
| 1318 | |
---|
| 1319 | // Change _flow and _state vectors |
---|
| 1320 | void changeFlow(bool change) { |
---|
| 1321 | // Augment along the cycle |
---|
| 1322 | if (delta > 0) { |
---|
[688] | 1323 | Value val = _state[in_arc] * delta; |
---|
[650] | 1324 | _flow[in_arc] += val; |
---|
| 1325 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
[990] | 1326 | _flow[_pred[u]] -= _pred_dir[u] * val; |
---|
[648] | 1327 | } |
---|
[650] | 1328 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
[990] | 1329 | _flow[_pred[u]] += _pred_dir[u] * val; |
---|
[648] | 1330 | } |
---|
| 1331 | } |
---|
| 1332 | // Update the state of the entering and leaving arcs |
---|
| 1333 | if (change) { |
---|
[650] | 1334 | _state[in_arc] = STATE_TREE; |
---|
[648] | 1335 | _state[_pred[u_out]] = |
---|
| 1336 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
| 1337 | } else { |
---|
[650] | 1338 | _state[in_arc] = -_state[in_arc]; |
---|
[648] | 1339 | } |
---|
| 1340 | } |
---|
| 1341 | |
---|
[651] | 1342 | // Update the tree structure |
---|
| 1343 | void updateTreeStructure() { |
---|
| 1344 | int old_rev_thread = _rev_thread[u_out]; |
---|
| 1345 | int old_succ_num = _succ_num[u_out]; |
---|
| 1346 | int old_last_succ = _last_succ[u_out]; |
---|
[648] | 1347 | v_out = _parent[u_out]; |
---|
| 1348 | |
---|
[990] | 1349 | // Check if u_in and u_out coincide |
---|
| 1350 | if (u_in == u_out) { |
---|
| 1351 | // Update _parent, _pred, _pred_dir |
---|
| 1352 | _parent[u_in] = v_in; |
---|
| 1353 | _pred[u_in] = in_arc; |
---|
| 1354 | _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN; |
---|
[651] | 1355 | |
---|
[990] | 1356 | // Update _thread and _rev_thread |
---|
| 1357 | if (_thread[v_in] != u_out) { |
---|
| 1358 | int after = _thread[old_last_succ]; |
---|
| 1359 | _thread[old_rev_thread] = after; |
---|
| 1360 | _rev_thread[after] = old_rev_thread; |
---|
| 1361 | after = _thread[v_in]; |
---|
| 1362 | _thread[v_in] = u_out; |
---|
| 1363 | _rev_thread[u_out] = v_in; |
---|
| 1364 | _thread[old_last_succ] = after; |
---|
| 1365 | _rev_thread[after] = old_last_succ; |
---|
| 1366 | } |
---|
[651] | 1367 | } else { |
---|
[990] | 1368 | // Handle the case when old_rev_thread equals to v_in |
---|
| 1369 | // (it also means that join and v_out coincide) |
---|
| 1370 | int thread_continue = old_rev_thread == v_in ? |
---|
| 1371 | _thread[old_last_succ] : _thread[v_in]; |
---|
[648] | 1372 | |
---|
[990] | 1373 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
| 1374 | // between u_in and u_out, whose parent have to be changed) |
---|
| 1375 | int stem = u_in; // the current stem node |
---|
| 1376 | int par_stem = v_in; // the new parent of stem |
---|
| 1377 | int next_stem; // the next stem node |
---|
| 1378 | int last = _last_succ[u_in]; // the last successor of stem |
---|
| 1379 | int before, after = _thread[last]; |
---|
| 1380 | _thread[v_in] = u_in; |
---|
| 1381 | _dirty_revs.clear(); |
---|
| 1382 | _dirty_revs.push_back(v_in); |
---|
| 1383 | while (stem != u_out) { |
---|
| 1384 | // Insert the next stem node into the thread list |
---|
| 1385 | next_stem = _parent[stem]; |
---|
| 1386 | _thread[last] = next_stem; |
---|
| 1387 | _dirty_revs.push_back(last); |
---|
[648] | 1388 | |
---|
[990] | 1389 | // Remove the subtree of stem from the thread list |
---|
| 1390 | before = _rev_thread[stem]; |
---|
| 1391 | _thread[before] = after; |
---|
| 1392 | _rev_thread[after] = before; |
---|
[648] | 1393 | |
---|
[990] | 1394 | // Change the parent node and shift stem nodes |
---|
| 1395 | _parent[stem] = par_stem; |
---|
| 1396 | par_stem = stem; |
---|
| 1397 | stem = next_stem; |
---|
[648] | 1398 | |
---|
[990] | 1399 | // Update last and after |
---|
| 1400 | last = _last_succ[stem] == _last_succ[par_stem] ? |
---|
| 1401 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
| 1402 | after = _thread[last]; |
---|
| 1403 | } |
---|
| 1404 | _parent[u_out] = par_stem; |
---|
| 1405 | _thread[last] = thread_continue; |
---|
| 1406 | _rev_thread[thread_continue] = last; |
---|
| 1407 | _last_succ[u_out] = last; |
---|
[648] | 1408 | |
---|
[990] | 1409 | // Remove the subtree of u_out from the thread list except for |
---|
| 1410 | // the case when old_rev_thread equals to v_in |
---|
| 1411 | if (old_rev_thread != v_in) { |
---|
| 1412 | _thread[old_rev_thread] = after; |
---|
| 1413 | _rev_thread[after] = old_rev_thread; |
---|
| 1414 | } |
---|
[651] | 1415 | |
---|
[990] | 1416 | // Update _rev_thread using the new _thread values |
---|
| 1417 | for (int i = 0; i != int(_dirty_revs.size()); ++i) { |
---|
| 1418 | int u = _dirty_revs[i]; |
---|
| 1419 | _rev_thread[_thread[u]] = u; |
---|
| 1420 | } |
---|
[651] | 1421 | |
---|
[990] | 1422 | // Update _pred, _pred_dir, _last_succ and _succ_num for the |
---|
| 1423 | // stem nodes from u_out to u_in |
---|
| 1424 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
| 1425 | for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) { |
---|
| 1426 | _pred[u] = _pred[p]; |
---|
| 1427 | _pred_dir[u] = -_pred_dir[p]; |
---|
| 1428 | tmp_sc += _succ_num[u] - _succ_num[p]; |
---|
| 1429 | _succ_num[u] = tmp_sc; |
---|
| 1430 | _last_succ[p] = tmp_ls; |
---|
| 1431 | } |
---|
| 1432 | _pred[u_in] = in_arc; |
---|
| 1433 | _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN; |
---|
| 1434 | _succ_num[u_in] = old_succ_num; |
---|
[651] | 1435 | } |
---|
| 1436 | |
---|
| 1437 | // Update _last_succ from v_in towards the root |
---|
[990] | 1438 | int up_limit_out = _last_succ[join] == v_in ? join : -1; |
---|
| 1439 | int last_succ_out = _last_succ[u_out]; |
---|
| 1440 | for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) { |
---|
| 1441 | _last_succ[u] = last_succ_out; |
---|
[651] | 1442 | } |
---|
[990] | 1443 | |
---|
[651] | 1444 | // Update _last_succ from v_out towards the root |
---|
| 1445 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
[990] | 1446 | for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
[651] | 1447 | u = _parent[u]) { |
---|
| 1448 | _last_succ[u] = old_rev_thread; |
---|
| 1449 | } |
---|
[990] | 1450 | } |
---|
| 1451 | else if (last_succ_out != old_last_succ) { |
---|
| 1452 | for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
[651] | 1453 | u = _parent[u]) { |
---|
[990] | 1454 | _last_succ[u] = last_succ_out; |
---|
[651] | 1455 | } |
---|
| 1456 | } |
---|
| 1457 | |
---|
| 1458 | // Update _succ_num from v_in to join |
---|
[990] | 1459 | for (int u = v_in; u != join; u = _parent[u]) { |
---|
[651] | 1460 | _succ_num[u] += old_succ_num; |
---|
| 1461 | } |
---|
| 1462 | // Update _succ_num from v_out to join |
---|
[990] | 1463 | for (int u = v_out; u != join; u = _parent[u]) { |
---|
[651] | 1464 | _succ_num[u] -= old_succ_num; |
---|
[648] | 1465 | } |
---|
| 1466 | } |
---|
| 1467 | |
---|
[990] | 1468 | // Update potentials in the subtree that has been moved |
---|
[651] | 1469 | void updatePotential() { |
---|
[990] | 1470 | Cost sigma = _pi[v_in] - _pi[u_in] - |
---|
| 1471 | _pred_dir[u_in] * _cost[in_arc]; |
---|
[655] | 1472 | int end = _thread[_last_succ[u_in]]; |
---|
| 1473 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
| 1474 | _pi[u] += sigma; |
---|
[648] | 1475 | } |
---|
| 1476 | } |
---|
| 1477 | |
---|
[910] | 1478 | // Heuristic initial pivots |
---|
| 1479 | bool initialPivots() { |
---|
| 1480 | Value curr, total = 0; |
---|
| 1481 | std::vector<Node> supply_nodes, demand_nodes; |
---|
| 1482 | for (NodeIt u(_graph); u != INVALID; ++u) { |
---|
| 1483 | curr = _supply[_node_id[u]]; |
---|
| 1484 | if (curr > 0) { |
---|
| 1485 | total += curr; |
---|
| 1486 | supply_nodes.push_back(u); |
---|
| 1487 | } |
---|
| 1488 | else if (curr < 0) { |
---|
| 1489 | demand_nodes.push_back(u); |
---|
| 1490 | } |
---|
| 1491 | } |
---|
| 1492 | if (_sum_supply > 0) total -= _sum_supply; |
---|
| 1493 | if (total <= 0) return true; |
---|
| 1494 | |
---|
| 1495 | IntVector arc_vector; |
---|
| 1496 | if (_sum_supply >= 0) { |
---|
| 1497 | if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { |
---|
| 1498 | // Perform a reverse graph search from the sink to the source |
---|
| 1499 | typename GR::template NodeMap<bool> reached(_graph, false); |
---|
| 1500 | Node s = supply_nodes[0], t = demand_nodes[0]; |
---|
| 1501 | std::vector<Node> stack; |
---|
| 1502 | reached[t] = true; |
---|
| 1503 | stack.push_back(t); |
---|
| 1504 | while (!stack.empty()) { |
---|
| 1505 | Node u, v = stack.back(); |
---|
| 1506 | stack.pop_back(); |
---|
| 1507 | if (v == s) break; |
---|
| 1508 | for (InArcIt a(_graph, v); a != INVALID; ++a) { |
---|
| 1509 | if (reached[u = _graph.source(a)]) continue; |
---|
| 1510 | int j = _arc_id[a]; |
---|
| 1511 | if (_cap[j] >= total) { |
---|
| 1512 | arc_vector.push_back(j); |
---|
| 1513 | reached[u] = true; |
---|
| 1514 | stack.push_back(u); |
---|
| 1515 | } |
---|
| 1516 | } |
---|
| 1517 | } |
---|
| 1518 | } else { |
---|
[1217] | 1519 | // Find the min. cost incoming arc for each demand node |
---|
[910] | 1520 | for (int i = 0; i != int(demand_nodes.size()); ++i) { |
---|
| 1521 | Node v = demand_nodes[i]; |
---|
| 1522 | Cost c, min_cost = std::numeric_limits<Cost>::max(); |
---|
| 1523 | Arc min_arc = INVALID; |
---|
| 1524 | for (InArcIt a(_graph, v); a != INVALID; ++a) { |
---|
| 1525 | c = _cost[_arc_id[a]]; |
---|
| 1526 | if (c < min_cost) { |
---|
| 1527 | min_cost = c; |
---|
| 1528 | min_arc = a; |
---|
| 1529 | } |
---|
| 1530 | } |
---|
| 1531 | if (min_arc != INVALID) { |
---|
| 1532 | arc_vector.push_back(_arc_id[min_arc]); |
---|
| 1533 | } |
---|
| 1534 | } |
---|
| 1535 | } |
---|
| 1536 | } else { |
---|
| 1537 | // Find the min. cost outgoing arc for each supply node |
---|
| 1538 | for (int i = 0; i != int(supply_nodes.size()); ++i) { |
---|
| 1539 | Node u = supply_nodes[i]; |
---|
| 1540 | Cost c, min_cost = std::numeric_limits<Cost>::max(); |
---|
| 1541 | Arc min_arc = INVALID; |
---|
| 1542 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
---|
| 1543 | c = _cost[_arc_id[a]]; |
---|
| 1544 | if (c < min_cost) { |
---|
| 1545 | min_cost = c; |
---|
| 1546 | min_arc = a; |
---|
| 1547 | } |
---|
| 1548 | } |
---|
| 1549 | if (min_arc != INVALID) { |
---|
| 1550 | arc_vector.push_back(_arc_id[min_arc]); |
---|
| 1551 | } |
---|
| 1552 | } |
---|
| 1553 | } |
---|
| 1554 | |
---|
| 1555 | // Perform heuristic initial pivots |
---|
| 1556 | for (int i = 0; i != int(arc_vector.size()); ++i) { |
---|
| 1557 | in_arc = arc_vector[i]; |
---|
| 1558 | if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - |
---|
| 1559 | _pi[_target[in_arc]]) >= 0) continue; |
---|
| 1560 | findJoinNode(); |
---|
| 1561 | bool change = findLeavingArc(); |
---|
| 1562 | if (delta >= MAX) return false; |
---|
| 1563 | changeFlow(change); |
---|
| 1564 | if (change) { |
---|
| 1565 | updateTreeStructure(); |
---|
| 1566 | updatePotential(); |
---|
| 1567 | } |
---|
| 1568 | } |
---|
| 1569 | return true; |
---|
| 1570 | } |
---|
| 1571 | |
---|
[648] | 1572 | // Execute the algorithm |
---|
[687] | 1573 | ProblemType start(PivotRule pivot_rule) { |
---|
[648] | 1574 | // Select the pivot rule implementation |
---|
| 1575 | switch (pivot_rule) { |
---|
[652] | 1576 | case FIRST_ELIGIBLE: |
---|
[648] | 1577 | return start<FirstEligiblePivotRule>(); |
---|
[652] | 1578 | case BEST_ELIGIBLE: |
---|
[648] | 1579 | return start<BestEligiblePivotRule>(); |
---|
[652] | 1580 | case BLOCK_SEARCH: |
---|
[648] | 1581 | return start<BlockSearchPivotRule>(); |
---|
[652] | 1582 | case CANDIDATE_LIST: |
---|
[648] | 1583 | return start<CandidateListPivotRule>(); |
---|
[652] | 1584 | case ALTERING_LIST: |
---|
[648] | 1585 | return start<AlteringListPivotRule>(); |
---|
| 1586 | } |
---|
[687] | 1587 | return INFEASIBLE; // avoid warning |
---|
[648] | 1588 | } |
---|
| 1589 | |
---|
[652] | 1590 | template <typename PivotRuleImpl> |
---|
[687] | 1591 | ProblemType start() { |
---|
[652] | 1592 | PivotRuleImpl pivot(*this); |
---|
[648] | 1593 | |
---|
[910] | 1594 | // Perform heuristic initial pivots |
---|
| 1595 | if (!initialPivots()) return UNBOUNDED; |
---|
| 1596 | |
---|
[652] | 1597 | // Execute the Network Simplex algorithm |
---|
[648] | 1598 | while (pivot.findEnteringArc()) { |
---|
| 1599 | findJoinNode(); |
---|
| 1600 | bool change = findLeavingArc(); |
---|
[877] | 1601 | if (delta >= MAX) return UNBOUNDED; |
---|
[648] | 1602 | changeFlow(change); |
---|
| 1603 | if (change) { |
---|
[651] | 1604 | updateTreeStructure(); |
---|
| 1605 | updatePotential(); |
---|
[648] | 1606 | } |
---|
| 1607 | } |
---|
[956] | 1608 | |
---|
[687] | 1609 | // Check feasibility |
---|
[710] | 1610 | for (int e = _search_arc_num; e != _all_arc_num; ++e) { |
---|
| 1611 | if (_flow[e] != 0) return INFEASIBLE; |
---|
[687] | 1612 | } |
---|
[648] | 1613 | |
---|
[689] | 1614 | // Transform the solution and the supply map to the original form |
---|
| 1615 | if (_have_lower) { |
---|
[648] | 1616 | for (int i = 0; i != _arc_num; ++i) { |
---|
[689] | 1617 | Value c = _lower[i]; |
---|
| 1618 | if (c != 0) { |
---|
| 1619 | _flow[i] += c; |
---|
| 1620 | _supply[_source[i]] += c; |
---|
| 1621 | _supply[_target[i]] -= c; |
---|
| 1622 | } |
---|
[648] | 1623 | } |
---|
| 1624 | } |
---|
[956] | 1625 | |
---|
[710] | 1626 | // Shift potentials to meet the requirements of the GEQ/LEQ type |
---|
| 1627 | // optimality conditions |
---|
| 1628 | if (_sum_supply == 0) { |
---|
| 1629 | if (_stype == GEQ) { |
---|
[976] | 1630 | Cost max_pot = -std::numeric_limits<Cost>::max(); |
---|
[710] | 1631 | for (int i = 0; i != _node_num; ++i) { |
---|
| 1632 | if (_pi[i] > max_pot) max_pot = _pi[i]; |
---|
| 1633 | } |
---|
| 1634 | if (max_pot > 0) { |
---|
| 1635 | for (int i = 0; i != _node_num; ++i) |
---|
| 1636 | _pi[i] -= max_pot; |
---|
| 1637 | } |
---|
| 1638 | } else { |
---|
| 1639 | Cost min_pot = std::numeric_limits<Cost>::max(); |
---|
| 1640 | for (int i = 0; i != _node_num; ++i) { |
---|
| 1641 | if (_pi[i] < min_pot) min_pot = _pi[i]; |
---|
| 1642 | } |
---|
| 1643 | if (min_pot < 0) { |
---|
| 1644 | for (int i = 0; i != _node_num; ++i) |
---|
| 1645 | _pi[i] -= min_pot; |
---|
| 1646 | } |
---|
| 1647 | } |
---|
| 1648 | } |
---|
[648] | 1649 | |
---|
[687] | 1650 | return OPTIMAL; |
---|
[648] | 1651 | } |
---|
| 1652 | |
---|
| 1653 | }; //class NetworkSimplex |
---|
| 1654 | |
---|
| 1655 | ///@} |
---|
| 1656 | |
---|
| 1657 | } //namespace lemon |
---|
| 1658 | |
---|
| 1659 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|