[956] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[874] | 2 | * |
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[956] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[874] | 4 | * |
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[956] | 5 | * Copyright (C) 2003-2010 |
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[874] | 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_COST_SCALING_H |
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| 20 | #define LEMON_COST_SCALING_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow_algs |
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| 23 | /// \file |
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| 24 | /// \brief Cost scaling algorithm for finding a minimum cost flow. |
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| 25 | |
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| 26 | #include <vector> |
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| 27 | #include <deque> |
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| 28 | #include <limits> |
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| 29 | |
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| 30 | #include <lemon/core.h> |
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| 31 | #include <lemon/maps.h> |
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| 32 | #include <lemon/math.h> |
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[875] | 33 | #include <lemon/static_graph.h> |
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[874] | 34 | #include <lemon/circulation.h> |
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| 35 | #include <lemon/bellman_ford.h> |
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| 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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[875] | 39 | /// \brief Default traits class of CostScaling algorithm. |
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| 40 | /// |
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| 41 | /// Default traits class of CostScaling algorithm. |
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| 42 | /// \tparam GR Digraph type. |
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[878] | 43 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[875] | 44 | /// and supply values. By default it is \c int. |
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[878] | 45 | /// \tparam C The number type used for costs and potentials. |
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[875] | 46 | /// By default it is the same as \c V. |
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| 47 | #ifdef DOXYGEN |
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| 48 | template <typename GR, typename V = int, typename C = V> |
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| 49 | #else |
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| 50 | template < typename GR, typename V = int, typename C = V, |
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| 51 | bool integer = std::numeric_limits<C>::is_integer > |
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| 52 | #endif |
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| 53 | struct CostScalingDefaultTraits |
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| 54 | { |
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| 55 | /// The type of the digraph |
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| 56 | typedef GR Digraph; |
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| 57 | /// The type of the flow amounts, capacity bounds and supply values |
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| 58 | typedef V Value; |
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| 59 | /// The type of the arc costs |
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| 60 | typedef C Cost; |
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| 61 | |
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| 62 | /// \brief The large cost type used for internal computations |
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| 63 | /// |
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| 64 | /// The large cost type used for internal computations. |
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| 65 | /// It is \c long \c long if the \c Cost type is integer, |
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| 66 | /// otherwise it is \c double. |
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| 67 | /// \c Cost must be convertible to \c LargeCost. |
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| 68 | typedef double LargeCost; |
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| 69 | }; |
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| 70 | |
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| 71 | // Default traits class for integer cost types |
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| 72 | template <typename GR, typename V, typename C> |
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| 73 | struct CostScalingDefaultTraits<GR, V, C, true> |
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| 74 | { |
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| 75 | typedef GR Digraph; |
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| 76 | typedef V Value; |
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| 77 | typedef C Cost; |
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| 78 | #ifdef LEMON_HAVE_LONG_LONG |
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| 79 | typedef long long LargeCost; |
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| 80 | #else |
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| 81 | typedef long LargeCost; |
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| 82 | #endif |
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| 83 | }; |
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| 84 | |
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| 85 | |
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[874] | 86 | /// \addtogroup min_cost_flow_algs |
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| 87 | /// @{ |
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| 88 | |
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[875] | 89 | /// \brief Implementation of the Cost Scaling algorithm for |
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| 90 | /// finding a \ref min_cost_flow "minimum cost flow". |
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[874] | 91 | /// |
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[875] | 92 | /// \ref CostScaling implements a cost scaling algorithm that performs |
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[879] | 93 | /// push/augment and relabel operations for finding a \ref min_cost_flow |
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| 94 | /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation, |
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[956] | 95 | /// \ref goldberg97efficient, \ref bunnagel98efficient. |
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[879] | 96 | /// It is a highly efficient primal-dual solution method, which |
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[875] | 97 | /// can be viewed as the generalization of the \ref Preflow |
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| 98 | /// "preflow push-relabel" algorithm for the maximum flow problem. |
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[874] | 99 | /// |
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[1023] | 100 | /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest |
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[1165] | 101 | /// implementations available in LEMON for solving this problem. |
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| 102 | /// (For more information, see \ref min_cost_flow_algs "the module page".) |
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[1023] | 103 | /// |
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[875] | 104 | /// Most of the parameters of the problem (except for the digraph) |
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| 105 | /// can be given using separate functions, and the algorithm can be |
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| 106 | /// executed using the \ref run() function. If some parameters are not |
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| 107 | /// specified, then default values will be used. |
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[874] | 108 | /// |
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[875] | 109 | /// \tparam GR The digraph type the algorithm runs on. |
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[878] | 110 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[891] | 111 | /// and supply values in the algorithm. By default, it is \c int. |
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[878] | 112 | /// \tparam C The number type used for costs and potentials in the |
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[891] | 113 | /// algorithm. By default, it is the same as \c V. |
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| 114 | /// \tparam TR The traits class that defines various types used by the |
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| 115 | /// algorithm. By default, it is \ref CostScalingDefaultTraits |
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| 116 | /// "CostScalingDefaultTraits<GR, V, C>". |
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| 117 | /// In most cases, this parameter should not be set directly, |
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| 118 | /// consider to use the named template parameters instead. |
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[874] | 119 | /// |
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[1025] | 120 | /// \warning Both \c V and \c C must be signed number types. |
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| 121 | /// \warning All input data (capacities, supply values, and costs) must |
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[875] | 122 | /// be integer. |
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[1023] | 123 | /// \warning This algorithm does not support negative costs for |
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| 124 | /// arcs having infinite upper bound. |
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[876] | 125 | /// |
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| 126 | /// \note %CostScaling provides three different internal methods, |
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| 127 | /// from which the most efficient one is used by default. |
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| 128 | /// For more information, see \ref Method. |
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[875] | 129 | #ifdef DOXYGEN |
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| 130 | template <typename GR, typename V, typename C, typename TR> |
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| 131 | #else |
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| 132 | template < typename GR, typename V = int, typename C = V, |
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| 133 | typename TR = CostScalingDefaultTraits<GR, V, C> > |
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| 134 | #endif |
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[874] | 135 | class CostScaling |
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| 136 | { |
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[875] | 137 | public: |
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[874] | 138 | |
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[875] | 139 | /// The type of the digraph |
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| 140 | typedef typename TR::Digraph Digraph; |
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| 141 | /// The type of the flow amounts, capacity bounds and supply values |
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| 142 | typedef typename TR::Value Value; |
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| 143 | /// The type of the arc costs |
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| 144 | typedef typename TR::Cost Cost; |
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[874] | 145 | |
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[875] | 146 | /// \brief The large cost type |
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| 147 | /// |
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| 148 | /// The large cost type used for internal computations. |
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[891] | 149 | /// By default, it is \c long \c long if the \c Cost type is integer, |
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[875] | 150 | /// otherwise it is \c double. |
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| 151 | typedef typename TR::LargeCost LargeCost; |
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[874] | 152 | |
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[875] | 153 | /// The \ref CostScalingDefaultTraits "traits class" of the algorithm |
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| 154 | typedef TR Traits; |
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[874] | 155 | |
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| 156 | public: |
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| 157 | |
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[875] | 158 | /// \brief Problem type constants for the \c run() function. |
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| 159 | /// |
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| 160 | /// Enum type containing the problem type constants that can be |
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| 161 | /// returned by the \ref run() function of the algorithm. |
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| 162 | enum ProblemType { |
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| 163 | /// The problem has no feasible solution (flow). |
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| 164 | INFEASIBLE, |
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| 165 | /// The problem has optimal solution (i.e. it is feasible and |
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| 166 | /// bounded), and the algorithm has found optimal flow and node |
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| 167 | /// potentials (primal and dual solutions). |
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| 168 | OPTIMAL, |
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| 169 | /// The digraph contains an arc of negative cost and infinite |
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| 170 | /// upper bound. It means that the objective function is unbounded |
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[878] | 171 | /// on that arc, however, note that it could actually be bounded |
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[875] | 172 | /// over the feasible flows, but this algroithm cannot handle |
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| 173 | /// these cases. |
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| 174 | UNBOUNDED |
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| 175 | }; |
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[874] | 176 | |
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[876] | 177 | /// \brief Constants for selecting the internal method. |
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| 178 | /// |
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| 179 | /// Enum type containing constants for selecting the internal method |
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| 180 | /// for the \ref run() function. |
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| 181 | /// |
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| 182 | /// \ref CostScaling provides three internal methods that differ mainly |
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| 183 | /// in their base operations, which are used in conjunction with the |
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| 184 | /// relabel operation. |
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| 185 | /// By default, the so called \ref PARTIAL_AUGMENT |
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[1023] | 186 | /// "Partial Augment-Relabel" method is used, which turned out to be |
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[876] | 187 | /// the most efficient and the most robust on various test inputs. |
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| 188 | /// However, the other methods can be selected using the \ref run() |
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| 189 | /// function with the proper parameter. |
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| 190 | enum Method { |
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| 191 | /// Local push operations are used, i.e. flow is moved only on one |
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| 192 | /// admissible arc at once. |
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| 193 | PUSH, |
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| 194 | /// Augment operations are used, i.e. flow is moved on admissible |
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| 195 | /// paths from a node with excess to a node with deficit. |
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| 196 | AUGMENT, |
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[956] | 197 | /// Partial augment operations are used, i.e. flow is moved on |
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[876] | 198 | /// admissible paths started from a node with excess, but the |
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| 199 | /// lengths of these paths are limited. This method can be viewed |
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| 200 | /// as a combined version of the previous two operations. |
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| 201 | PARTIAL_AUGMENT |
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| 202 | }; |
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| 203 | |
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[874] | 204 | private: |
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| 205 | |
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[875] | 206 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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[874] | 207 | |
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[875] | 208 | typedef std::vector<int> IntVector; |
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| 209 | typedef std::vector<Value> ValueVector; |
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| 210 | typedef std::vector<Cost> CostVector; |
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| 211 | typedef std::vector<LargeCost> LargeCostVector; |
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[910] | 212 | typedef std::vector<char> BoolVector; |
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| 213 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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[874] | 214 | |
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[875] | 215 | private: |
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[956] | 216 | |
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[875] | 217 | template <typename KT, typename VT> |
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[886] | 218 | class StaticVectorMap { |
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[874] | 219 | public: |
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[875] | 220 | typedef KT Key; |
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| 221 | typedef VT Value; |
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[956] | 222 | |
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[886] | 223 | StaticVectorMap(std::vector<Value>& v) : _v(v) {} |
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[956] | 224 | |
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[875] | 225 | const Value& operator[](const Key& key) const { |
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| 226 | return _v[StaticDigraph::id(key)]; |
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[874] | 227 | } |
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| 228 | |
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[875] | 229 | Value& operator[](const Key& key) { |
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| 230 | return _v[StaticDigraph::id(key)]; |
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| 231 | } |
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[956] | 232 | |
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[875] | 233 | void set(const Key& key, const Value& val) { |
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| 234 | _v[StaticDigraph::id(key)] = val; |
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[874] | 235 | } |
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| 236 | |
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[875] | 237 | private: |
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| 238 | std::vector<Value>& _v; |
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| 239 | }; |
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| 240 | |
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[886] | 241 | typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap; |
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[874] | 242 | |
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| 243 | private: |
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| 244 | |
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[875] | 245 | // Data related to the underlying digraph |
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| 246 | const GR &_graph; |
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| 247 | int _node_num; |
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| 248 | int _arc_num; |
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| 249 | int _res_node_num; |
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| 250 | int _res_arc_num; |
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| 251 | int _root; |
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[874] | 252 | |
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[875] | 253 | // Parameters of the problem |
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| 254 | bool _have_lower; |
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| 255 | Value _sum_supply; |
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[910] | 256 | int _sup_node_num; |
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[874] | 257 | |
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[875] | 258 | // Data structures for storing the digraph |
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| 259 | IntNodeMap _node_id; |
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| 260 | IntArcMap _arc_idf; |
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| 261 | IntArcMap _arc_idb; |
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| 262 | IntVector _first_out; |
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| 263 | BoolVector _forward; |
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| 264 | IntVector _source; |
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| 265 | IntVector _target; |
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| 266 | IntVector _reverse; |
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| 267 | |
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| 268 | // Node and arc data |
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| 269 | ValueVector _lower; |
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| 270 | ValueVector _upper; |
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| 271 | CostVector _scost; |
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| 272 | ValueVector _supply; |
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| 273 | |
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| 274 | ValueVector _res_cap; |
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| 275 | LargeCostVector _cost; |
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| 276 | LargeCostVector _pi; |
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| 277 | ValueVector _excess; |
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| 278 | IntVector _next_out; |
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| 279 | std::deque<int> _active_nodes; |
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| 280 | |
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| 281 | // Data for scaling |
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| 282 | LargeCost _epsilon; |
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[874] | 283 | int _alpha; |
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| 284 | |
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[910] | 285 | IntVector _buckets; |
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| 286 | IntVector _bucket_next; |
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| 287 | IntVector _bucket_prev; |
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| 288 | IntVector _rank; |
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| 289 | int _max_rank; |
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[956] | 290 | |
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[875] | 291 | public: |
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[956] | 292 | |
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[875] | 293 | /// \brief Constant for infinite upper bounds (capacities). |
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| 294 | /// |
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| 295 | /// Constant for infinite upper bounds (capacities). |
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| 296 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 297 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 298 | const Value INF; |
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| 299 | |
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[874] | 300 | public: |
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| 301 | |
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[875] | 302 | /// \name Named Template Parameters |
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| 303 | /// @{ |
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| 304 | |
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| 305 | template <typename T> |
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| 306 | struct SetLargeCostTraits : public Traits { |
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| 307 | typedef T LargeCost; |
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| 308 | }; |
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| 309 | |
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| 310 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 311 | /// \c LargeCost type. |
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[874] | 312 | /// |
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[875] | 313 | /// \ref named-templ-param "Named parameter" for setting \c LargeCost |
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| 314 | /// type, which is used for internal computations in the algorithm. |
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| 315 | /// \c Cost must be convertible to \c LargeCost. |
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| 316 | template <typename T> |
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| 317 | struct SetLargeCost |
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| 318 | : public CostScaling<GR, V, C, SetLargeCostTraits<T> > { |
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| 319 | typedef CostScaling<GR, V, C, SetLargeCostTraits<T> > Create; |
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| 320 | }; |
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| 321 | |
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| 322 | /// @} |
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| 323 | |
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[941] | 324 | protected: |
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| 325 | |
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| 326 | CostScaling() {} |
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| 327 | |
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[875] | 328 | public: |
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| 329 | |
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| 330 | /// \brief Constructor. |
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[874] | 331 | /// |
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[875] | 332 | /// The constructor of the class. |
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| 333 | /// |
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| 334 | /// \param graph The digraph the algorithm runs on. |
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| 335 | CostScaling(const GR& graph) : |
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| 336 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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| 337 | INF(std::numeric_limits<Value>::has_infinity ? |
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| 338 | std::numeric_limits<Value>::infinity() : |
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| 339 | std::numeric_limits<Value>::max()) |
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[874] | 340 | { |
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[878] | 341 | // Check the number types |
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[875] | 342 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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| 343 | "The flow type of CostScaling must be signed"); |
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| 344 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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| 345 | "The cost type of CostScaling must be signed"); |
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[956] | 346 | |
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[898] | 347 | // Reset data structures |
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[875] | 348 | reset(); |
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[874] | 349 | } |
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| 350 | |
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[875] | 351 | /// \name Parameters |
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| 352 | /// The parameters of the algorithm can be specified using these |
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| 353 | /// functions. |
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| 354 | |
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| 355 | /// @{ |
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| 356 | |
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| 357 | /// \brief Set the lower bounds on the arcs. |
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[874] | 358 | /// |
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[875] | 359 | /// This function sets the lower bounds on the arcs. |
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| 360 | /// If it is not used before calling \ref run(), the lower bounds |
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| 361 | /// will be set to zero on all arcs. |
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[874] | 362 | /// |
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[875] | 363 | /// \param map An arc map storing the lower bounds. |
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| 364 | /// Its \c Value type must be convertible to the \c Value type |
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| 365 | /// of the algorithm. |
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| 366 | /// |
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| 367 | /// \return <tt>(*this)</tt> |
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| 368 | template <typename LowerMap> |
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| 369 | CostScaling& lowerMap(const LowerMap& map) { |
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| 370 | _have_lower = true; |
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| 371 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 372 | _lower[_arc_idf[a]] = map[a]; |
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| 373 | _lower[_arc_idb[a]] = map[a]; |
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[874] | 374 | } |
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| 375 | return *this; |
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| 376 | } |
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| 377 | |
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[875] | 378 | /// \brief Set the upper bounds (capacities) on the arcs. |
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[874] | 379 | /// |
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[875] | 380 | /// This function sets the upper bounds (capacities) on the arcs. |
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| 381 | /// If it is not used before calling \ref run(), the upper bounds |
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| 382 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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[878] | 383 | /// unbounded from above). |
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[874] | 384 | /// |
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[875] | 385 | /// \param map An arc map storing the upper bounds. |
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| 386 | /// Its \c Value type must be convertible to the \c Value type |
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| 387 | /// of the algorithm. |
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| 388 | /// |
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| 389 | /// \return <tt>(*this)</tt> |
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| 390 | template<typename UpperMap> |
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| 391 | CostScaling& upperMap(const UpperMap& map) { |
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| 392 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 393 | _upper[_arc_idf[a]] = map[a]; |
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[874] | 394 | } |
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| 395 | return *this; |
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| 396 | } |
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| 397 | |
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[875] | 398 | /// \brief Set the costs of the arcs. |
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| 399 | /// |
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| 400 | /// This function sets the costs of the arcs. |
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| 401 | /// If it is not used before calling \ref run(), the costs |
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| 402 | /// will be set to \c 1 on all arcs. |
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| 403 | /// |
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| 404 | /// \param map An arc map storing the costs. |
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| 405 | /// Its \c Value type must be convertible to the \c Cost type |
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| 406 | /// of the algorithm. |
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| 407 | /// |
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| 408 | /// \return <tt>(*this)</tt> |
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| 409 | template<typename CostMap> |
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| 410 | CostScaling& costMap(const CostMap& map) { |
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| 411 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 412 | _scost[_arc_idf[a]] = map[a]; |
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| 413 | _scost[_arc_idb[a]] = -map[a]; |
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| 414 | } |
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| 415 | return *this; |
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| 416 | } |
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| 417 | |
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| 418 | /// \brief Set the supply values of the nodes. |
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| 419 | /// |
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| 420 | /// This function sets the supply values of the nodes. |
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| 421 | /// If neither this function nor \ref stSupply() is used before |
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| 422 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 423 | /// |
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| 424 | /// \param map A node map storing the supply values. |
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| 425 | /// Its \c Value type must be convertible to the \c Value type |
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| 426 | /// of the algorithm. |
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| 427 | /// |
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| 428 | /// \return <tt>(*this)</tt> |
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| 429 | template<typename SupplyMap> |
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| 430 | CostScaling& supplyMap(const SupplyMap& map) { |
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| 431 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 432 | _supply[_node_id[n]] = map[n]; |
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| 433 | } |
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| 434 | return *this; |
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| 435 | } |
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| 436 | |
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| 437 | /// \brief Set single source and target nodes and a supply value. |
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| 438 | /// |
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| 439 | /// This function sets a single source node and a single target node |
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| 440 | /// and the required flow value. |
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| 441 | /// If neither this function nor \ref supplyMap() is used before |
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| 442 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 443 | /// |
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| 444 | /// Using this function has the same effect as using \ref supplyMap() |
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[1023] | 445 | /// with a map in which \c k is assigned to \c s, \c -k is |
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[875] | 446 | /// assigned to \c t and all other nodes have zero supply value. |
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| 447 | /// |
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| 448 | /// \param s The source node. |
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| 449 | /// \param t The target node. |
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| 450 | /// \param k The required amount of flow from node \c s to node \c t |
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| 451 | /// (i.e. the supply of \c s and the demand of \c t). |
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| 452 | /// |
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| 453 | /// \return <tt>(*this)</tt> |
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| 454 | CostScaling& stSupply(const Node& s, const Node& t, Value k) { |
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| 455 | for (int i = 0; i != _res_node_num; ++i) { |
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| 456 | _supply[i] = 0; |
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| 457 | } |
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| 458 | _supply[_node_id[s]] = k; |
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| 459 | _supply[_node_id[t]] = -k; |
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| 460 | return *this; |
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| 461 | } |
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[956] | 462 | |
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[875] | 463 | /// @} |
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| 464 | |
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[874] | 465 | /// \name Execution control |
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[875] | 466 | /// The algorithm can be executed using \ref run(). |
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[874] | 467 | |
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| 468 | /// @{ |
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| 469 | |
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| 470 | /// \brief Run the algorithm. |
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| 471 | /// |
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[875] | 472 | /// This function runs the algorithm. |
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| 473 | /// The paramters can be specified using functions \ref lowerMap(), |
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| 474 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 475 | /// For example, |
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| 476 | /// \code |
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| 477 | /// CostScaling<ListDigraph> cs(graph); |
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| 478 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 479 | /// .supplyMap(sup).run(); |
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| 480 | /// \endcode |
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| 481 | /// |
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[898] | 482 | /// This function can be called more than once. All the given parameters |
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| 483 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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| 484 | /// is used, thus only the modified parameters have to be set again. |
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| 485 | /// If the underlying digraph was also modified after the construction |
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| 486 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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| 487 | /// function must be called. |
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[874] | 488 | /// |
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[876] | 489 | /// \param method The internal method that will be used in the |
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| 490 | /// algorithm. For more information, see \ref Method. |
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[1049] | 491 | /// \param factor The cost scaling factor. It must be at least two. |
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[874] | 492 | /// |
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[875] | 493 | /// \return \c INFEASIBLE if no feasible flow exists, |
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| 494 | /// \n \c OPTIMAL if the problem has optimal solution |
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| 495 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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| 496 | /// optimal flow and node potentials (primal and dual solutions), |
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| 497 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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| 498 | /// and infinite upper bound. It means that the objective function |
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[878] | 499 | /// is unbounded on that arc, however, note that it could actually be |
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[875] | 500 | /// bounded over the feasible flows, but this algroithm cannot handle |
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| 501 | /// these cases. |
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| 502 | /// |
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[876] | 503 | /// \see ProblemType, Method |
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[898] | 504 | /// \see resetParams(), reset() |
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[1049] | 505 | ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 16) { |
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| 506 | LEMON_ASSERT(factor >= 2, "The scaling factor must be at least 2"); |
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[876] | 507 | _alpha = factor; |
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[875] | 508 | ProblemType pt = init(); |
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| 509 | if (pt != OPTIMAL) return pt; |
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[876] | 510 | start(method); |
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[875] | 511 | return OPTIMAL; |
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| 512 | } |
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| 513 | |
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| 514 | /// \brief Reset all the parameters that have been given before. |
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| 515 | /// |
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| 516 | /// This function resets all the paramaters that have been given |
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| 517 | /// before using functions \ref lowerMap(), \ref upperMap(), |
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| 518 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 519 | /// |
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[898] | 520 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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| 521 | /// parameters are kept for the next \ref run() call, unless |
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| 522 | /// \ref resetParams() or \ref reset() is used. |
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| 523 | /// If the underlying digraph was also modified after the construction |
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| 524 | /// of the class or the last \ref reset() call, then the \ref reset() |
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| 525 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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[875] | 526 | /// |
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| 527 | /// For example, |
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| 528 | /// \code |
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| 529 | /// CostScaling<ListDigraph> cs(graph); |
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| 530 | /// |
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| 531 | /// // First run |
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| 532 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 533 | /// .supplyMap(sup).run(); |
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| 534 | /// |
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[898] | 535 | /// // Run again with modified cost map (resetParams() is not called, |
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[875] | 536 | /// // so only the cost map have to be set again) |
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| 537 | /// cost[e] += 100; |
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| 538 | /// cs.costMap(cost).run(); |
---|
| 539 | /// |
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[898] | 540 | /// // Run again from scratch using resetParams() |
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[875] | 541 | /// // (the lower bounds will be set to zero on all arcs) |
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[898] | 542 | /// cs.resetParams(); |
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[875] | 543 | /// cs.upperMap(capacity).costMap(cost) |
---|
| 544 | /// .supplyMap(sup).run(); |
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| 545 | /// \endcode |
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| 546 | /// |
---|
| 547 | /// \return <tt>(*this)</tt> |
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[898] | 548 | /// |
---|
| 549 | /// \see reset(), run() |
---|
| 550 | CostScaling& resetParams() { |
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[875] | 551 | for (int i = 0; i != _res_node_num; ++i) { |
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| 552 | _supply[i] = 0; |
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[874] | 553 | } |
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[875] | 554 | int limit = _first_out[_root]; |
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| 555 | for (int j = 0; j != limit; ++j) { |
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| 556 | _lower[j] = 0; |
---|
| 557 | _upper[j] = INF; |
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| 558 | _scost[j] = _forward[j] ? 1 : -1; |
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| 559 | } |
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| 560 | for (int j = limit; j != _res_arc_num; ++j) { |
---|
| 561 | _lower[j] = 0; |
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| 562 | _upper[j] = INF; |
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| 563 | _scost[j] = 0; |
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| 564 | _scost[_reverse[j]] = 0; |
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[956] | 565 | } |
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[875] | 566 | _have_lower = false; |
---|
| 567 | return *this; |
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[874] | 568 | } |
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| 569 | |
---|
[1045] | 570 | /// \brief Reset the internal data structures and all the parameters |
---|
| 571 | /// that have been given before. |
---|
[898] | 572 | /// |
---|
[1045] | 573 | /// This function resets the internal data structures and all the |
---|
| 574 | /// paramaters that have been given before using functions \ref lowerMap(), |
---|
| 575 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
[898] | 576 | /// |
---|
[1045] | 577 | /// It is useful for multiple \ref run() calls. By default, all the given |
---|
| 578 | /// parameters are kept for the next \ref run() call, unless |
---|
| 579 | /// \ref resetParams() or \ref reset() is used. |
---|
| 580 | /// If the underlying digraph was also modified after the construction |
---|
| 581 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
| 582 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
| 583 | /// |
---|
| 584 | /// See \ref resetParams() for examples. |
---|
| 585 | /// |
---|
[898] | 586 | /// \return <tt>(*this)</tt> |
---|
[1045] | 587 | /// |
---|
| 588 | /// \see resetParams(), run() |
---|
[898] | 589 | CostScaling& reset() { |
---|
| 590 | // Resize vectors |
---|
| 591 | _node_num = countNodes(_graph); |
---|
| 592 | _arc_num = countArcs(_graph); |
---|
| 593 | _res_node_num = _node_num + 1; |
---|
| 594 | _res_arc_num = 2 * (_arc_num + _node_num); |
---|
| 595 | _root = _node_num; |
---|
| 596 | |
---|
| 597 | _first_out.resize(_res_node_num + 1); |
---|
| 598 | _forward.resize(_res_arc_num); |
---|
| 599 | _source.resize(_res_arc_num); |
---|
| 600 | _target.resize(_res_arc_num); |
---|
| 601 | _reverse.resize(_res_arc_num); |
---|
| 602 | |
---|
| 603 | _lower.resize(_res_arc_num); |
---|
| 604 | _upper.resize(_res_arc_num); |
---|
| 605 | _scost.resize(_res_arc_num); |
---|
| 606 | _supply.resize(_res_node_num); |
---|
[956] | 607 | |
---|
[898] | 608 | _res_cap.resize(_res_arc_num); |
---|
| 609 | _cost.resize(_res_arc_num); |
---|
| 610 | _pi.resize(_res_node_num); |
---|
| 611 | _excess.resize(_res_node_num); |
---|
| 612 | _next_out.resize(_res_node_num); |
---|
| 613 | |
---|
| 614 | // Copy the graph |
---|
| 615 | int i = 0, j = 0, k = 2 * _arc_num + _node_num; |
---|
| 616 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 617 | _node_id[n] = i; |
---|
| 618 | } |
---|
| 619 | i = 0; |
---|
| 620 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 621 | _first_out[i] = j; |
---|
| 622 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
| 623 | _arc_idf[a] = j; |
---|
| 624 | _forward[j] = true; |
---|
| 625 | _source[j] = i; |
---|
| 626 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
| 627 | } |
---|
| 628 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
| 629 | _arc_idb[a] = j; |
---|
| 630 | _forward[j] = false; |
---|
| 631 | _source[j] = i; |
---|
| 632 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
| 633 | } |
---|
| 634 | _forward[j] = false; |
---|
| 635 | _source[j] = i; |
---|
| 636 | _target[j] = _root; |
---|
| 637 | _reverse[j] = k; |
---|
| 638 | _forward[k] = true; |
---|
| 639 | _source[k] = _root; |
---|
| 640 | _target[k] = i; |
---|
| 641 | _reverse[k] = j; |
---|
| 642 | ++j; ++k; |
---|
| 643 | } |
---|
| 644 | _first_out[i] = j; |
---|
| 645 | _first_out[_res_node_num] = k; |
---|
| 646 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 647 | int fi = _arc_idf[a]; |
---|
| 648 | int bi = _arc_idb[a]; |
---|
| 649 | _reverse[fi] = bi; |
---|
| 650 | _reverse[bi] = fi; |
---|
| 651 | } |
---|
[956] | 652 | |
---|
[898] | 653 | // Reset parameters |
---|
| 654 | resetParams(); |
---|
| 655 | return *this; |
---|
| 656 | } |
---|
| 657 | |
---|
[874] | 658 | /// @} |
---|
| 659 | |
---|
| 660 | /// \name Query Functions |
---|
[875] | 661 | /// The results of the algorithm can be obtained using these |
---|
[874] | 662 | /// functions.\n |
---|
[875] | 663 | /// The \ref run() function must be called before using them. |
---|
[874] | 664 | |
---|
| 665 | /// @{ |
---|
| 666 | |
---|
[875] | 667 | /// \brief Return the total cost of the found flow. |
---|
[874] | 668 | /// |
---|
[875] | 669 | /// This function returns the total cost of the found flow. |
---|
| 670 | /// Its complexity is O(e). |
---|
| 671 | /// |
---|
| 672 | /// \note The return type of the function can be specified as a |
---|
| 673 | /// template parameter. For example, |
---|
| 674 | /// \code |
---|
| 675 | /// cs.totalCost<double>(); |
---|
| 676 | /// \endcode |
---|
| 677 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
| 678 | /// type of the algorithm, which is the default return type of the |
---|
| 679 | /// function. |
---|
[874] | 680 | /// |
---|
| 681 | /// \pre \ref run() must be called before using this function. |
---|
[875] | 682 | template <typename Number> |
---|
| 683 | Number totalCost() const { |
---|
| 684 | Number c = 0; |
---|
| 685 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 686 | int i = _arc_idb[a]; |
---|
| 687 | c += static_cast<Number>(_res_cap[i]) * |
---|
| 688 | (-static_cast<Number>(_scost[i])); |
---|
| 689 | } |
---|
| 690 | return c; |
---|
[874] | 691 | } |
---|
| 692 | |
---|
[875] | 693 | #ifndef DOXYGEN |
---|
| 694 | Cost totalCost() const { |
---|
| 695 | return totalCost<Cost>(); |
---|
[874] | 696 | } |
---|
[875] | 697 | #endif |
---|
[874] | 698 | |
---|
| 699 | /// \brief Return the flow on the given arc. |
---|
| 700 | /// |
---|
[875] | 701 | /// This function returns the flow on the given arc. |
---|
[874] | 702 | /// |
---|
| 703 | /// \pre \ref run() must be called before using this function. |
---|
[875] | 704 | Value flow(const Arc& a) const { |
---|
| 705 | return _res_cap[_arc_idb[a]]; |
---|
[874] | 706 | } |
---|
| 707 | |
---|
[1165] | 708 | /// \brief Copy the flow values (the primal solution) into the |
---|
| 709 | /// given map. |
---|
[874] | 710 | /// |
---|
[875] | 711 | /// This function copies the flow value on each arc into the given |
---|
| 712 | /// map. The \c Value type of the algorithm must be convertible to |
---|
| 713 | /// the \c Value type of the map. |
---|
[874] | 714 | /// |
---|
| 715 | /// \pre \ref run() must be called before using this function. |
---|
[875] | 716 | template <typename FlowMap> |
---|
| 717 | void flowMap(FlowMap &map) const { |
---|
| 718 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 719 | map.set(a, _res_cap[_arc_idb[a]]); |
---|
| 720 | } |
---|
[874] | 721 | } |
---|
| 722 | |
---|
[875] | 723 | /// \brief Return the potential (dual value) of the given node. |
---|
[874] | 724 | /// |
---|
[875] | 725 | /// This function returns the potential (dual value) of the |
---|
| 726 | /// given node. |
---|
[874] | 727 | /// |
---|
| 728 | /// \pre \ref run() must be called before using this function. |
---|
[875] | 729 | Cost potential(const Node& n) const { |
---|
| 730 | return static_cast<Cost>(_pi[_node_id[n]]); |
---|
| 731 | } |
---|
| 732 | |
---|
[1165] | 733 | /// \brief Copy the potential values (the dual solution) into the |
---|
| 734 | /// given map. |
---|
[875] | 735 | /// |
---|
| 736 | /// This function copies the potential (dual value) of each node |
---|
| 737 | /// into the given map. |
---|
| 738 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 739 | /// \c Value type of the map. |
---|
| 740 | /// |
---|
| 741 | /// \pre \ref run() must be called before using this function. |
---|
| 742 | template <typename PotentialMap> |
---|
| 743 | void potentialMap(PotentialMap &map) const { |
---|
| 744 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 745 | map.set(n, static_cast<Cost>(_pi[_node_id[n]])); |
---|
| 746 | } |
---|
[874] | 747 | } |
---|
| 748 | |
---|
| 749 | /// @} |
---|
| 750 | |
---|
| 751 | private: |
---|
| 752 | |
---|
[875] | 753 | // Initialize the algorithm |
---|
| 754 | ProblemType init() { |
---|
[887] | 755 | if (_res_node_num <= 1) return INFEASIBLE; |
---|
[875] | 756 | |
---|
| 757 | // Check the sum of supply values |
---|
| 758 | _sum_supply = 0; |
---|
| 759 | for (int i = 0; i != _root; ++i) { |
---|
| 760 | _sum_supply += _supply[i]; |
---|
[874] | 761 | } |
---|
[875] | 762 | if (_sum_supply > 0) return INFEASIBLE; |
---|
[956] | 763 | |
---|
[875] | 764 | |
---|
| 765 | // Initialize vectors |
---|
| 766 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 767 | _pi[i] = 0; |
---|
| 768 | _excess[i] = _supply[i]; |
---|
| 769 | } |
---|
[956] | 770 | |
---|
[875] | 771 | // Remove infinite upper bounds and check negative arcs |
---|
| 772 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
| 773 | int last_out; |
---|
| 774 | if (_have_lower) { |
---|
| 775 | for (int i = 0; i != _root; ++i) { |
---|
| 776 | last_out = _first_out[i+1]; |
---|
| 777 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 778 | if (_forward[j]) { |
---|
| 779 | Value c = _scost[j] < 0 ? _upper[j] : _lower[j]; |
---|
| 780 | if (c >= MAX) return UNBOUNDED; |
---|
| 781 | _excess[i] -= c; |
---|
| 782 | _excess[_target[j]] += c; |
---|
| 783 | } |
---|
| 784 | } |
---|
| 785 | } |
---|
| 786 | } else { |
---|
| 787 | for (int i = 0; i != _root; ++i) { |
---|
| 788 | last_out = _first_out[i+1]; |
---|
| 789 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 790 | if (_forward[j] && _scost[j] < 0) { |
---|
| 791 | Value c = _upper[j]; |
---|
| 792 | if (c >= MAX) return UNBOUNDED; |
---|
| 793 | _excess[i] -= c; |
---|
| 794 | _excess[_target[j]] += c; |
---|
| 795 | } |
---|
| 796 | } |
---|
| 797 | } |
---|
| 798 | } |
---|
| 799 | Value ex, max_cap = 0; |
---|
| 800 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 801 | ex = _excess[i]; |
---|
| 802 | _excess[i] = 0; |
---|
| 803 | if (ex < 0) max_cap -= ex; |
---|
| 804 | } |
---|
| 805 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 806 | if (_upper[j] >= MAX) _upper[j] = max_cap; |
---|
[874] | 807 | } |
---|
| 808 | |
---|
[875] | 809 | // Initialize the large cost vector and the epsilon parameter |
---|
| 810 | _epsilon = 0; |
---|
| 811 | LargeCost lc; |
---|
| 812 | for (int i = 0; i != _root; ++i) { |
---|
| 813 | last_out = _first_out[i+1]; |
---|
| 814 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 815 | lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha; |
---|
| 816 | _cost[j] = lc; |
---|
| 817 | if (lc > _epsilon) _epsilon = lc; |
---|
| 818 | } |
---|
| 819 | } |
---|
| 820 | _epsilon /= _alpha; |
---|
[874] | 821 | |
---|
[875] | 822 | // Initialize maps for Circulation and remove non-zero lower bounds |
---|
| 823 | ConstMap<Arc, Value> low(0); |
---|
| 824 | typedef typename Digraph::template ArcMap<Value> ValueArcMap; |
---|
| 825 | typedef typename Digraph::template NodeMap<Value> ValueNodeMap; |
---|
| 826 | ValueArcMap cap(_graph), flow(_graph); |
---|
| 827 | ValueNodeMap sup(_graph); |
---|
| 828 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 829 | sup[n] = _supply[_node_id[n]]; |
---|
[874] | 830 | } |
---|
[875] | 831 | if (_have_lower) { |
---|
| 832 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 833 | int j = _arc_idf[a]; |
---|
| 834 | Value c = _lower[j]; |
---|
| 835 | cap[a] = _upper[j] - c; |
---|
| 836 | sup[_graph.source(a)] -= c; |
---|
| 837 | sup[_graph.target(a)] += c; |
---|
| 838 | } |
---|
| 839 | } else { |
---|
| 840 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 841 | cap[a] = _upper[_arc_idf[a]]; |
---|
| 842 | } |
---|
| 843 | } |
---|
[874] | 844 | |
---|
[910] | 845 | _sup_node_num = 0; |
---|
| 846 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 847 | if (sup[n] > 0) ++_sup_node_num; |
---|
| 848 | } |
---|
| 849 | |
---|
[874] | 850 | // Find a feasible flow using Circulation |
---|
[875] | 851 | Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> |
---|
| 852 | circ(_graph, low, cap, sup); |
---|
| 853 | if (!circ.flowMap(flow).run()) return INFEASIBLE; |
---|
| 854 | |
---|
| 855 | // Set residual capacities and handle GEQ supply type |
---|
| 856 | if (_sum_supply < 0) { |
---|
| 857 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 858 | Value fa = flow[a]; |
---|
| 859 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
| 860 | _res_cap[_arc_idb[a]] = fa; |
---|
| 861 | sup[_graph.source(a)] -= fa; |
---|
| 862 | sup[_graph.target(a)] += fa; |
---|
| 863 | } |
---|
| 864 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 865 | _excess[_node_id[n]] = sup[n]; |
---|
| 866 | } |
---|
| 867 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
| 868 | int u = _target[a]; |
---|
| 869 | int ra = _reverse[a]; |
---|
| 870 | _res_cap[a] = -_sum_supply + 1; |
---|
| 871 | _res_cap[ra] = -_excess[u]; |
---|
| 872 | _cost[a] = 0; |
---|
| 873 | _cost[ra] = 0; |
---|
| 874 | _excess[u] = 0; |
---|
| 875 | } |
---|
| 876 | } else { |
---|
| 877 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 878 | Value fa = flow[a]; |
---|
| 879 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
| 880 | _res_cap[_arc_idb[a]] = fa; |
---|
| 881 | } |
---|
| 882 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
| 883 | int ra = _reverse[a]; |
---|
[910] | 884 | _res_cap[a] = 0; |
---|
[875] | 885 | _res_cap[ra] = 0; |
---|
| 886 | _cost[a] = 0; |
---|
| 887 | _cost[ra] = 0; |
---|
| 888 | } |
---|
| 889 | } |
---|
[956] | 890 | |
---|
| 891 | // Initialize data structures for buckets |
---|
[910] | 892 | _max_rank = _alpha * _res_node_num; |
---|
| 893 | _buckets.resize(_max_rank); |
---|
| 894 | _bucket_next.resize(_res_node_num + 1); |
---|
| 895 | _bucket_prev.resize(_res_node_num + 1); |
---|
| 896 | _rank.resize(_res_node_num + 1); |
---|
[956] | 897 | |
---|
[1045] | 898 | return OPTIMAL; |
---|
| 899 | } |
---|
| 900 | |
---|
| 901 | // Execute the algorithm and transform the results |
---|
| 902 | void start(Method method) { |
---|
| 903 | const int MAX_PARTIAL_PATH_LENGTH = 4; |
---|
| 904 | |
---|
[876] | 905 | switch (method) { |
---|
| 906 | case PUSH: |
---|
| 907 | startPush(); |
---|
| 908 | break; |
---|
| 909 | case AUGMENT: |
---|
[1041] | 910 | startAugment(_res_node_num - 1); |
---|
[876] | 911 | break; |
---|
| 912 | case PARTIAL_AUGMENT: |
---|
[1045] | 913 | startAugment(MAX_PARTIAL_PATH_LENGTH); |
---|
[876] | 914 | break; |
---|
[875] | 915 | } |
---|
| 916 | |
---|
[1048] | 917 | // Compute node potentials (dual solution) |
---|
| 918 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 919 | _pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha)); |
---|
| 920 | } |
---|
| 921 | bool optimal = true; |
---|
| 922 | for (int i = 0; optimal && i != _res_node_num; ++i) { |
---|
| 923 | LargeCost pi_i = _pi[i]; |
---|
| 924 | int last_out = _first_out[i+1]; |
---|
| 925 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 926 | if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) { |
---|
| 927 | optimal = false; |
---|
| 928 | break; |
---|
| 929 | } |
---|
[875] | 930 | } |
---|
| 931 | } |
---|
| 932 | |
---|
[1048] | 933 | if (!optimal) { |
---|
| 934 | // Compute node potentials for the original costs with BellmanFord |
---|
| 935 | // (if it is necessary) |
---|
| 936 | typedef std::pair<int, int> IntPair; |
---|
| 937 | StaticDigraph sgr; |
---|
| 938 | std::vector<IntPair> arc_vec; |
---|
| 939 | std::vector<LargeCost> cost_vec; |
---|
| 940 | LargeCostArcMap cost_map(cost_vec); |
---|
| 941 | |
---|
| 942 | arc_vec.clear(); |
---|
| 943 | cost_vec.clear(); |
---|
| 944 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 945 | if (_res_cap[j] > 0) { |
---|
| 946 | int u = _source[j], v = _target[j]; |
---|
| 947 | arc_vec.push_back(IntPair(u, v)); |
---|
| 948 | cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]); |
---|
| 949 | } |
---|
| 950 | } |
---|
| 951 | sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end()); |
---|
| 952 | |
---|
| 953 | typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create |
---|
| 954 | bf(sgr, cost_map); |
---|
| 955 | bf.init(0); |
---|
| 956 | bf.start(); |
---|
| 957 | |
---|
| 958 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 959 | _pi[i] += bf.dist(sgr.node(i)); |
---|
| 960 | } |
---|
| 961 | } |
---|
| 962 | |
---|
| 963 | // Shift potentials to meet the requirements of the GEQ type |
---|
| 964 | // optimality conditions |
---|
| 965 | LargeCost max_pot = _pi[_root]; |
---|
| 966 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 967 | if (_pi[i] > max_pot) max_pot = _pi[i]; |
---|
| 968 | } |
---|
| 969 | if (max_pot != 0) { |
---|
| 970 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 971 | _pi[i] -= max_pot; |
---|
| 972 | } |
---|
| 973 | } |
---|
[875] | 974 | |
---|
| 975 | // Handle non-zero lower bounds |
---|
| 976 | if (_have_lower) { |
---|
| 977 | int limit = _first_out[_root]; |
---|
| 978 | for (int j = 0; j != limit; ++j) { |
---|
| 979 | if (!_forward[j]) _res_cap[j] += _lower[j]; |
---|
| 980 | } |
---|
| 981 | } |
---|
[874] | 982 | } |
---|
[956] | 983 | |
---|
[910] | 984 | // Initialize a cost scaling phase |
---|
| 985 | void initPhase() { |
---|
| 986 | // Saturate arcs not satisfying the optimality condition |
---|
| 987 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 988 | int last_out = _first_out[u+1]; |
---|
| 989 | LargeCost pi_u = _pi[u]; |
---|
| 990 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
[1045] | 991 | Value delta = _res_cap[a]; |
---|
| 992 | if (delta > 0) { |
---|
| 993 | int v = _target[a]; |
---|
| 994 | if (_cost[a] + pi_u - _pi[v] < 0) { |
---|
| 995 | _excess[u] -= delta; |
---|
| 996 | _excess[v] += delta; |
---|
| 997 | _res_cap[a] = 0; |
---|
| 998 | _res_cap[_reverse[a]] += delta; |
---|
| 999 | } |
---|
[910] | 1000 | } |
---|
| 1001 | } |
---|
| 1002 | } |
---|
[956] | 1003 | |
---|
[910] | 1004 | // Find active nodes (i.e. nodes with positive excess) |
---|
| 1005 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1006 | if (_excess[u] > 0) _active_nodes.push_back(u); |
---|
| 1007 | } |
---|
| 1008 | |
---|
| 1009 | // Initialize the next arcs |
---|
| 1010 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1011 | _next_out[u] = _first_out[u]; |
---|
| 1012 | } |
---|
| 1013 | } |
---|
[956] | 1014 | |
---|
[1047] | 1015 | // Price (potential) refinement heuristic |
---|
| 1016 | bool priceRefinement() { |
---|
[910] | 1017 | |
---|
[1047] | 1018 | // Stack for stroing the topological order |
---|
| 1019 | IntVector stack(_res_node_num); |
---|
| 1020 | int stack_top; |
---|
| 1021 | |
---|
| 1022 | // Perform phases |
---|
| 1023 | while (topologicalSort(stack, stack_top)) { |
---|
| 1024 | |
---|
| 1025 | // Compute node ranks in the acyclic admissible network and |
---|
| 1026 | // store the nodes in buckets |
---|
| 1027 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 1028 | _rank[i] = 0; |
---|
[910] | 1029 | } |
---|
[1047] | 1030 | const int bucket_end = _root + 1; |
---|
| 1031 | for (int r = 0; r != _max_rank; ++r) { |
---|
| 1032 | _buckets[r] = bucket_end; |
---|
| 1033 | } |
---|
| 1034 | int top_rank = 0; |
---|
| 1035 | for ( ; stack_top >= 0; --stack_top) { |
---|
| 1036 | int u = stack[stack_top], v; |
---|
| 1037 | int rank_u = _rank[u]; |
---|
| 1038 | |
---|
| 1039 | LargeCost rc, pi_u = _pi[u]; |
---|
| 1040 | int last_out = _first_out[u+1]; |
---|
| 1041 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
| 1042 | if (_res_cap[a] > 0) { |
---|
| 1043 | v = _target[a]; |
---|
| 1044 | rc = _cost[a] + pi_u - _pi[v]; |
---|
| 1045 | if (rc < 0) { |
---|
| 1046 | LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon); |
---|
| 1047 | if (nrc < LargeCost(_max_rank)) { |
---|
| 1048 | int new_rank_v = rank_u + static_cast<int>(nrc); |
---|
| 1049 | if (new_rank_v > _rank[v]) { |
---|
| 1050 | _rank[v] = new_rank_v; |
---|
| 1051 | } |
---|
| 1052 | } |
---|
| 1053 | } |
---|
| 1054 | } |
---|
| 1055 | } |
---|
| 1056 | |
---|
| 1057 | if (rank_u > 0) { |
---|
| 1058 | top_rank = std::max(top_rank, rank_u); |
---|
| 1059 | int bfirst = _buckets[rank_u]; |
---|
| 1060 | _bucket_next[u] = bfirst; |
---|
| 1061 | _bucket_prev[bfirst] = u; |
---|
| 1062 | _buckets[rank_u] = u; |
---|
| 1063 | } |
---|
| 1064 | } |
---|
| 1065 | |
---|
| 1066 | // Check if the current flow is epsilon-optimal |
---|
| 1067 | if (top_rank == 0) { |
---|
| 1068 | return true; |
---|
| 1069 | } |
---|
| 1070 | |
---|
| 1071 | // Process buckets in top-down order |
---|
| 1072 | for (int rank = top_rank; rank > 0; --rank) { |
---|
| 1073 | while (_buckets[rank] != bucket_end) { |
---|
| 1074 | // Remove the first node from the current bucket |
---|
| 1075 | int u = _buckets[rank]; |
---|
| 1076 | _buckets[rank] = _bucket_next[u]; |
---|
| 1077 | |
---|
| 1078 | // Search the outgoing arcs of u |
---|
| 1079 | LargeCost rc, pi_u = _pi[u]; |
---|
| 1080 | int last_out = _first_out[u+1]; |
---|
| 1081 | int v, old_rank_v, new_rank_v; |
---|
| 1082 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
| 1083 | if (_res_cap[a] > 0) { |
---|
| 1084 | v = _target[a]; |
---|
| 1085 | old_rank_v = _rank[v]; |
---|
| 1086 | |
---|
| 1087 | if (old_rank_v < rank) { |
---|
| 1088 | |
---|
| 1089 | // Compute the new rank of node v |
---|
| 1090 | rc = _cost[a] + pi_u - _pi[v]; |
---|
| 1091 | if (rc < 0) { |
---|
| 1092 | new_rank_v = rank; |
---|
| 1093 | } else { |
---|
| 1094 | LargeCost nrc = rc / _epsilon; |
---|
| 1095 | new_rank_v = 0; |
---|
| 1096 | if (nrc < LargeCost(_max_rank)) { |
---|
| 1097 | new_rank_v = rank - 1 - static_cast<int>(nrc); |
---|
| 1098 | } |
---|
| 1099 | } |
---|
| 1100 | |
---|
| 1101 | // Change the rank of node v |
---|
| 1102 | if (new_rank_v > old_rank_v) { |
---|
| 1103 | _rank[v] = new_rank_v; |
---|
| 1104 | |
---|
| 1105 | // Remove v from its old bucket |
---|
| 1106 | if (old_rank_v > 0) { |
---|
| 1107 | if (_buckets[old_rank_v] == v) { |
---|
| 1108 | _buckets[old_rank_v] = _bucket_next[v]; |
---|
| 1109 | } else { |
---|
| 1110 | int pv = _bucket_prev[v], nv = _bucket_next[v]; |
---|
| 1111 | _bucket_next[pv] = nv; |
---|
| 1112 | _bucket_prev[nv] = pv; |
---|
| 1113 | } |
---|
| 1114 | } |
---|
| 1115 | |
---|
| 1116 | // Insert v into its new bucket |
---|
| 1117 | int nv = _buckets[new_rank_v]; |
---|
| 1118 | _bucket_next[v] = nv; |
---|
| 1119 | _bucket_prev[nv] = v; |
---|
| 1120 | _buckets[new_rank_v] = v; |
---|
| 1121 | } |
---|
| 1122 | } |
---|
| 1123 | } |
---|
| 1124 | } |
---|
| 1125 | |
---|
| 1126 | // Refine potential of node u |
---|
| 1127 | _pi[u] -= rank * _epsilon; |
---|
| 1128 | } |
---|
| 1129 | } |
---|
| 1130 | |
---|
[910] | 1131 | } |
---|
| 1132 | |
---|
[1047] | 1133 | return false; |
---|
| 1134 | } |
---|
| 1135 | |
---|
| 1136 | // Find and cancel cycles in the admissible network and |
---|
| 1137 | // determine topological order using DFS |
---|
| 1138 | bool topologicalSort(IntVector &stack, int &stack_top) { |
---|
| 1139 | const int MAX_CYCLE_CANCEL = 1; |
---|
| 1140 | |
---|
| 1141 | BoolVector reached(_res_node_num, false); |
---|
| 1142 | BoolVector processed(_res_node_num, false); |
---|
| 1143 | IntVector pred(_res_node_num); |
---|
| 1144 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 1145 | _next_out[i] = _first_out[i]; |
---|
[910] | 1146 | } |
---|
[1047] | 1147 | stack_top = -1; |
---|
| 1148 | |
---|
| 1149 | int cycle_cnt = 0; |
---|
| 1150 | for (int start = 0; start != _res_node_num; ++start) { |
---|
| 1151 | if (reached[start]) continue; |
---|
| 1152 | |
---|
| 1153 | // Start DFS search from this start node |
---|
| 1154 | pred[start] = -1; |
---|
| 1155 | int tip = start, v; |
---|
| 1156 | while (true) { |
---|
| 1157 | // Check the outgoing arcs of the current tip node |
---|
| 1158 | reached[tip] = true; |
---|
| 1159 | LargeCost pi_tip = _pi[tip]; |
---|
| 1160 | int a, last_out = _first_out[tip+1]; |
---|
| 1161 | for (a = _next_out[tip]; a != last_out; ++a) { |
---|
| 1162 | if (_res_cap[a] > 0) { |
---|
| 1163 | v = _target[a]; |
---|
| 1164 | if (_cost[a] + pi_tip - _pi[v] < 0) { |
---|
| 1165 | if (!reached[v]) { |
---|
| 1166 | // A new node is reached |
---|
| 1167 | reached[v] = true; |
---|
| 1168 | pred[v] = tip; |
---|
| 1169 | _next_out[tip] = a; |
---|
| 1170 | tip = v; |
---|
| 1171 | a = _next_out[tip]; |
---|
| 1172 | last_out = _first_out[tip+1]; |
---|
| 1173 | break; |
---|
| 1174 | } |
---|
| 1175 | else if (!processed[v]) { |
---|
| 1176 | // A cycle is found |
---|
| 1177 | ++cycle_cnt; |
---|
| 1178 | _next_out[tip] = a; |
---|
| 1179 | |
---|
| 1180 | // Find the minimum residual capacity along the cycle |
---|
| 1181 | Value d, delta = _res_cap[a]; |
---|
| 1182 | int u, delta_node = tip; |
---|
| 1183 | for (u = tip; u != v; ) { |
---|
| 1184 | u = pred[u]; |
---|
| 1185 | d = _res_cap[_next_out[u]]; |
---|
| 1186 | if (d <= delta) { |
---|
| 1187 | delta = d; |
---|
| 1188 | delta_node = u; |
---|
| 1189 | } |
---|
| 1190 | } |
---|
| 1191 | |
---|
| 1192 | // Augment along the cycle |
---|
| 1193 | _res_cap[a] -= delta; |
---|
| 1194 | _res_cap[_reverse[a]] += delta; |
---|
| 1195 | for (u = tip; u != v; ) { |
---|
| 1196 | u = pred[u]; |
---|
| 1197 | int ca = _next_out[u]; |
---|
| 1198 | _res_cap[ca] -= delta; |
---|
| 1199 | _res_cap[_reverse[ca]] += delta; |
---|
| 1200 | } |
---|
| 1201 | |
---|
| 1202 | // Check the maximum number of cycle canceling |
---|
| 1203 | if (cycle_cnt >= MAX_CYCLE_CANCEL) { |
---|
| 1204 | return false; |
---|
| 1205 | } |
---|
| 1206 | |
---|
| 1207 | // Roll back search to delta_node |
---|
| 1208 | if (delta_node != tip) { |
---|
| 1209 | for (u = tip; u != delta_node; u = pred[u]) { |
---|
| 1210 | reached[u] = false; |
---|
| 1211 | } |
---|
| 1212 | tip = delta_node; |
---|
| 1213 | a = _next_out[tip] + 1; |
---|
| 1214 | last_out = _first_out[tip+1]; |
---|
| 1215 | break; |
---|
| 1216 | } |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | } |
---|
| 1220 | } |
---|
| 1221 | |
---|
| 1222 | // Step back to the previous node |
---|
| 1223 | if (a == last_out) { |
---|
| 1224 | processed[tip] = true; |
---|
| 1225 | stack[++stack_top] = tip; |
---|
| 1226 | tip = pred[tip]; |
---|
| 1227 | if (tip < 0) { |
---|
| 1228 | // Finish DFS from the current start node |
---|
| 1229 | break; |
---|
| 1230 | } |
---|
| 1231 | ++_next_out[tip]; |
---|
| 1232 | } |
---|
| 1233 | } |
---|
| 1234 | |
---|
| 1235 | } |
---|
| 1236 | |
---|
| 1237 | return (cycle_cnt == 0); |
---|
[910] | 1238 | } |
---|
| 1239 | |
---|
| 1240 | // Global potential update heuristic |
---|
| 1241 | void globalUpdate() { |
---|
[1045] | 1242 | const int bucket_end = _root + 1; |
---|
[956] | 1243 | |
---|
[910] | 1244 | // Initialize buckets |
---|
| 1245 | for (int r = 0; r != _max_rank; ++r) { |
---|
| 1246 | _buckets[r] = bucket_end; |
---|
| 1247 | } |
---|
| 1248 | Value total_excess = 0; |
---|
[1045] | 1249 | int b0 = bucket_end; |
---|
[910] | 1250 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 1251 | if (_excess[i] < 0) { |
---|
| 1252 | _rank[i] = 0; |
---|
[1045] | 1253 | _bucket_next[i] = b0; |
---|
| 1254 | _bucket_prev[b0] = i; |
---|
| 1255 | b0 = i; |
---|
[910] | 1256 | } else { |
---|
| 1257 | total_excess += _excess[i]; |
---|
| 1258 | _rank[i] = _max_rank; |
---|
| 1259 | } |
---|
| 1260 | } |
---|
| 1261 | if (total_excess == 0) return; |
---|
[1045] | 1262 | _buckets[0] = b0; |
---|
[910] | 1263 | |
---|
| 1264 | // Search the buckets |
---|
| 1265 | int r = 0; |
---|
| 1266 | for ( ; r != _max_rank; ++r) { |
---|
| 1267 | while (_buckets[r] != bucket_end) { |
---|
| 1268 | // Remove the first node from the current bucket |
---|
| 1269 | int u = _buckets[r]; |
---|
| 1270 | _buckets[r] = _bucket_next[u]; |
---|
[956] | 1271 | |
---|
[910] | 1272 | // Search the incomming arcs of u |
---|
| 1273 | LargeCost pi_u = _pi[u]; |
---|
| 1274 | int last_out = _first_out[u+1]; |
---|
| 1275 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
| 1276 | int ra = _reverse[a]; |
---|
| 1277 | if (_res_cap[ra] > 0) { |
---|
| 1278 | int v = _source[ra]; |
---|
| 1279 | int old_rank_v = _rank[v]; |
---|
| 1280 | if (r < old_rank_v) { |
---|
| 1281 | // Compute the new rank of v |
---|
| 1282 | LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon; |
---|
| 1283 | int new_rank_v = old_rank_v; |
---|
[1045] | 1284 | if (nrc < LargeCost(_max_rank)) { |
---|
| 1285 | new_rank_v = r + 1 + static_cast<int>(nrc); |
---|
| 1286 | } |
---|
[956] | 1287 | |
---|
[910] | 1288 | // Change the rank of v |
---|
| 1289 | if (new_rank_v < old_rank_v) { |
---|
| 1290 | _rank[v] = new_rank_v; |
---|
| 1291 | _next_out[v] = _first_out[v]; |
---|
[956] | 1292 | |
---|
[910] | 1293 | // Remove v from its old bucket |
---|
| 1294 | if (old_rank_v < _max_rank) { |
---|
| 1295 | if (_buckets[old_rank_v] == v) { |
---|
| 1296 | _buckets[old_rank_v] = _bucket_next[v]; |
---|
| 1297 | } else { |
---|
[1045] | 1298 | int pv = _bucket_prev[v], nv = _bucket_next[v]; |
---|
| 1299 | _bucket_next[pv] = nv; |
---|
| 1300 | _bucket_prev[nv] = pv; |
---|
[910] | 1301 | } |
---|
| 1302 | } |
---|
[956] | 1303 | |
---|
[1045] | 1304 | // Insert v into its new bucket |
---|
| 1305 | int nv = _buckets[new_rank_v]; |
---|
| 1306 | _bucket_next[v] = nv; |
---|
| 1307 | _bucket_prev[nv] = v; |
---|
[910] | 1308 | _buckets[new_rank_v] = v; |
---|
| 1309 | } |
---|
| 1310 | } |
---|
| 1311 | } |
---|
| 1312 | } |
---|
| 1313 | |
---|
| 1314 | // Finish search if there are no more active nodes |
---|
| 1315 | if (_excess[u] > 0) { |
---|
| 1316 | total_excess -= _excess[u]; |
---|
| 1317 | if (total_excess <= 0) break; |
---|
| 1318 | } |
---|
| 1319 | } |
---|
| 1320 | if (total_excess <= 0) break; |
---|
| 1321 | } |
---|
[956] | 1322 | |
---|
[910] | 1323 | // Relabel nodes |
---|
| 1324 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1325 | int k = std::min(_rank[u], r); |
---|
| 1326 | if (k > 0) { |
---|
| 1327 | _pi[u] -= _epsilon * k; |
---|
| 1328 | _next_out[u] = _first_out[u]; |
---|
| 1329 | } |
---|
| 1330 | } |
---|
| 1331 | } |
---|
[874] | 1332 | |
---|
[876] | 1333 | /// Execute the algorithm performing augment and relabel operations |
---|
[1041] | 1334 | void startAugment(int max_length) { |
---|
[874] | 1335 | // Paramters for heuristics |
---|
[1047] | 1336 | const int PRICE_REFINEMENT_LIMIT = 2; |
---|
[1046] | 1337 | const double GLOBAL_UPDATE_FACTOR = 1.0; |
---|
| 1338 | const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR * |
---|
[910] | 1339 | (_res_node_num + _sup_node_num * _sup_node_num)); |
---|
[1046] | 1340 | int next_global_update_limit = global_update_skip; |
---|
[956] | 1341 | |
---|
[875] | 1342 | // Perform cost scaling phases |
---|
[1046] | 1343 | IntVector path; |
---|
| 1344 | BoolVector path_arc(_res_arc_num, false); |
---|
| 1345 | int relabel_cnt = 0; |
---|
[1047] | 1346 | int eps_phase_cnt = 0; |
---|
[874] | 1347 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
| 1348 | 1 : _epsilon / _alpha ) |
---|
| 1349 | { |
---|
[1047] | 1350 | ++eps_phase_cnt; |
---|
| 1351 | |
---|
| 1352 | // Price refinement heuristic |
---|
| 1353 | if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) { |
---|
| 1354 | if (priceRefinement()) continue; |
---|
[874] | 1355 | } |
---|
[956] | 1356 | |
---|
[910] | 1357 | // Initialize current phase |
---|
| 1358 | initPhase(); |
---|
[956] | 1359 | |
---|
[874] | 1360 | // Perform partial augment and relabel operations |
---|
[875] | 1361 | while (true) { |
---|
[874] | 1362 | // Select an active node (FIFO selection) |
---|
[875] | 1363 | while (_active_nodes.size() > 0 && |
---|
| 1364 | _excess[_active_nodes.front()] <= 0) { |
---|
| 1365 | _active_nodes.pop_front(); |
---|
[874] | 1366 | } |
---|
[875] | 1367 | if (_active_nodes.size() == 0) break; |
---|
| 1368 | int start = _active_nodes.front(); |
---|
[874] | 1369 | |
---|
| 1370 | // Find an augmenting path from the start node |
---|
[875] | 1371 | int tip = start; |
---|
[1046] | 1372 | while (int(path.size()) < max_length && _excess[tip] >= 0) { |
---|
[875] | 1373 | int u; |
---|
[1046] | 1374 | LargeCost rc, min_red_cost = std::numeric_limits<LargeCost>::max(); |
---|
| 1375 | LargeCost pi_tip = _pi[tip]; |
---|
[910] | 1376 | int last_out = _first_out[tip+1]; |
---|
[875] | 1377 | for (int a = _next_out[tip]; a != last_out; ++a) { |
---|
[1046] | 1378 | if (_res_cap[a] > 0) { |
---|
| 1379 | u = _target[a]; |
---|
| 1380 | rc = _cost[a] + pi_tip - _pi[u]; |
---|
| 1381 | if (rc < 0) { |
---|
| 1382 | path.push_back(a); |
---|
| 1383 | _next_out[tip] = a; |
---|
| 1384 | if (path_arc[a]) { |
---|
| 1385 | goto augment; // a cycle is found, stop path search |
---|
| 1386 | } |
---|
| 1387 | tip = u; |
---|
| 1388 | path_arc[a] = true; |
---|
| 1389 | goto next_step; |
---|
| 1390 | } |
---|
| 1391 | else if (rc < min_red_cost) { |
---|
| 1392 | min_red_cost = rc; |
---|
| 1393 | } |
---|
[874] | 1394 | } |
---|
| 1395 | } |
---|
| 1396 | |
---|
| 1397 | // Relabel tip node |
---|
[910] | 1398 | if (tip != start) { |
---|
| 1399 | int ra = _reverse[path.back()]; |
---|
[1046] | 1400 | min_red_cost = |
---|
| 1401 | std::min(min_red_cost, _cost[ra] + pi_tip - _pi[_target[ra]]); |
---|
[910] | 1402 | } |
---|
[1046] | 1403 | last_out = _next_out[tip]; |
---|
[875] | 1404 | for (int a = _first_out[tip]; a != last_out; ++a) { |
---|
[1046] | 1405 | if (_res_cap[a] > 0) { |
---|
| 1406 | rc = _cost[a] + pi_tip - _pi[_target[a]]; |
---|
| 1407 | if (rc < min_red_cost) { |
---|
| 1408 | min_red_cost = rc; |
---|
| 1409 | } |
---|
[875] | 1410 | } |
---|
[874] | 1411 | } |
---|
[875] | 1412 | _pi[tip] -= min_red_cost + _epsilon; |
---|
| 1413 | _next_out[tip] = _first_out[tip]; |
---|
[910] | 1414 | ++relabel_cnt; |
---|
[874] | 1415 | |
---|
| 1416 | // Step back |
---|
| 1417 | if (tip != start) { |
---|
[1046] | 1418 | int pa = path.back(); |
---|
| 1419 | path_arc[pa] = false; |
---|
| 1420 | tip = _source[pa]; |
---|
[910] | 1421 | path.pop_back(); |
---|
[874] | 1422 | } |
---|
| 1423 | |
---|
[875] | 1424 | next_step: ; |
---|
[874] | 1425 | } |
---|
| 1426 | |
---|
| 1427 | // Augment along the found path (as much flow as possible) |
---|
[1046] | 1428 | augment: |
---|
[875] | 1429 | Value delta; |
---|
[910] | 1430 | int pa, u, v = start; |
---|
| 1431 | for (int i = 0; i != int(path.size()); ++i) { |
---|
| 1432 | pa = path[i]; |
---|
[875] | 1433 | u = v; |
---|
[910] | 1434 | v = _target[pa]; |
---|
[1046] | 1435 | path_arc[pa] = false; |
---|
[875] | 1436 | delta = std::min(_res_cap[pa], _excess[u]); |
---|
| 1437 | _res_cap[pa] -= delta; |
---|
| 1438 | _res_cap[_reverse[pa]] += delta; |
---|
| 1439 | _excess[u] -= delta; |
---|
| 1440 | _excess[v] += delta; |
---|
[1046] | 1441 | if (_excess[v] > 0 && _excess[v] <= delta) { |
---|
[875] | 1442 | _active_nodes.push_back(v); |
---|
[1046] | 1443 | } |
---|
[874] | 1444 | } |
---|
[1046] | 1445 | path.clear(); |
---|
[910] | 1446 | |
---|
| 1447 | // Global update heuristic |
---|
[1046] | 1448 | if (relabel_cnt >= next_global_update_limit) { |
---|
[910] | 1449 | globalUpdate(); |
---|
[1046] | 1450 | next_global_update_limit += global_update_skip; |
---|
[910] | 1451 | } |
---|
[874] | 1452 | } |
---|
[1046] | 1453 | |
---|
[874] | 1454 | } |
---|
[1046] | 1455 | |
---|
[874] | 1456 | } |
---|
| 1457 | |
---|
[875] | 1458 | /// Execute the algorithm performing push and relabel operations |
---|
[876] | 1459 | void startPush() { |
---|
[874] | 1460 | // Paramters for heuristics |
---|
[1047] | 1461 | const int PRICE_REFINEMENT_LIMIT = 2; |
---|
[910] | 1462 | const double GLOBAL_UPDATE_FACTOR = 2.0; |
---|
[874] | 1463 | |
---|
[1046] | 1464 | const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR * |
---|
[910] | 1465 | (_res_node_num + _sup_node_num * _sup_node_num)); |
---|
[1046] | 1466 | int next_global_update_limit = global_update_skip; |
---|
[956] | 1467 | |
---|
[875] | 1468 | // Perform cost scaling phases |
---|
| 1469 | BoolVector hyper(_res_node_num, false); |
---|
[910] | 1470 | LargeCostVector hyper_cost(_res_node_num); |
---|
[1046] | 1471 | int relabel_cnt = 0; |
---|
[1047] | 1472 | int eps_phase_cnt = 0; |
---|
[874] | 1473 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
| 1474 | 1 : _epsilon / _alpha ) |
---|
| 1475 | { |
---|
[1047] | 1476 | ++eps_phase_cnt; |
---|
| 1477 | |
---|
| 1478 | // Price refinement heuristic |
---|
| 1479 | if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) { |
---|
| 1480 | if (priceRefinement()) continue; |
---|
[874] | 1481 | } |
---|
[956] | 1482 | |
---|
[910] | 1483 | // Initialize current phase |
---|
| 1484 | initPhase(); |
---|
[874] | 1485 | |
---|
| 1486 | // Perform push and relabel operations |
---|
[875] | 1487 | while (_active_nodes.size() > 0) { |
---|
[910] | 1488 | LargeCost min_red_cost, rc, pi_n; |
---|
[875] | 1489 | Value delta; |
---|
| 1490 | int n, t, a, last_out = _res_arc_num; |
---|
| 1491 | |
---|
[910] | 1492 | next_node: |
---|
[874] | 1493 | // Select an active node (FIFO selection) |
---|
[875] | 1494 | n = _active_nodes.front(); |
---|
[910] | 1495 | last_out = _first_out[n+1]; |
---|
| 1496 | pi_n = _pi[n]; |
---|
[956] | 1497 | |
---|
[874] | 1498 | // Perform push operations if there are admissible arcs |
---|
[875] | 1499 | if (_excess[n] > 0) { |
---|
| 1500 | for (a = _next_out[n]; a != last_out; ++a) { |
---|
| 1501 | if (_res_cap[a] > 0 && |
---|
[910] | 1502 | _cost[a] + pi_n - _pi[_target[a]] < 0) { |
---|
[875] | 1503 | delta = std::min(_res_cap[a], _excess[n]); |
---|
| 1504 | t = _target[a]; |
---|
[874] | 1505 | |
---|
| 1506 | // Push-look-ahead heuristic |
---|
[875] | 1507 | Value ahead = -_excess[t]; |
---|
[910] | 1508 | int last_out_t = _first_out[t+1]; |
---|
| 1509 | LargeCost pi_t = _pi[t]; |
---|
[875] | 1510 | for (int ta = _next_out[t]; ta != last_out_t; ++ta) { |
---|
[956] | 1511 | if (_res_cap[ta] > 0 && |
---|
[910] | 1512 | _cost[ta] + pi_t - _pi[_target[ta]] < 0) |
---|
[875] | 1513 | ahead += _res_cap[ta]; |
---|
| 1514 | if (ahead >= delta) break; |
---|
[874] | 1515 | } |
---|
| 1516 | if (ahead < 0) ahead = 0; |
---|
| 1517 | |
---|
| 1518 | // Push flow along the arc |
---|
[910] | 1519 | if (ahead < delta && !hyper[t]) { |
---|
[875] | 1520 | _res_cap[a] -= ahead; |
---|
| 1521 | _res_cap[_reverse[a]] += ahead; |
---|
[874] | 1522 | _excess[n] -= ahead; |
---|
| 1523 | _excess[t] += ahead; |
---|
[875] | 1524 | _active_nodes.push_front(t); |
---|
[874] | 1525 | hyper[t] = true; |
---|
[910] | 1526 | hyper_cost[t] = _cost[a] + pi_n - pi_t; |
---|
[875] | 1527 | _next_out[n] = a; |
---|
| 1528 | goto next_node; |
---|
[874] | 1529 | } else { |
---|
[875] | 1530 | _res_cap[a] -= delta; |
---|
| 1531 | _res_cap[_reverse[a]] += delta; |
---|
[874] | 1532 | _excess[n] -= delta; |
---|
| 1533 | _excess[t] += delta; |
---|
| 1534 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
[875] | 1535 | _active_nodes.push_back(t); |
---|
[874] | 1536 | } |
---|
| 1537 | |
---|
[875] | 1538 | if (_excess[n] == 0) { |
---|
| 1539 | _next_out[n] = a; |
---|
| 1540 | goto remove_nodes; |
---|
| 1541 | } |
---|
[874] | 1542 | } |
---|
| 1543 | } |
---|
[875] | 1544 | _next_out[n] = a; |
---|
[874] | 1545 | } |
---|
| 1546 | |
---|
| 1547 | // Relabel the node if it is still active (or hyper) |
---|
[875] | 1548 | if (_excess[n] > 0 || hyper[n]) { |
---|
[910] | 1549 | min_red_cost = hyper[n] ? -hyper_cost[n] : |
---|
| 1550 | std::numeric_limits<LargeCost>::max(); |
---|
[875] | 1551 | for (int a = _first_out[n]; a != last_out; ++a) { |
---|
[1046] | 1552 | if (_res_cap[a] > 0) { |
---|
| 1553 | rc = _cost[a] + pi_n - _pi[_target[a]]; |
---|
| 1554 | if (rc < min_red_cost) { |
---|
| 1555 | min_red_cost = rc; |
---|
| 1556 | } |
---|
[875] | 1557 | } |
---|
[874] | 1558 | } |
---|
[875] | 1559 | _pi[n] -= min_red_cost + _epsilon; |
---|
[910] | 1560 | _next_out[n] = _first_out[n]; |
---|
[874] | 1561 | hyper[n] = false; |
---|
[910] | 1562 | ++relabel_cnt; |
---|
[874] | 1563 | } |
---|
[956] | 1564 | |
---|
[874] | 1565 | // Remove nodes that are not active nor hyper |
---|
[875] | 1566 | remove_nodes: |
---|
| 1567 | while ( _active_nodes.size() > 0 && |
---|
| 1568 | _excess[_active_nodes.front()] <= 0 && |
---|
| 1569 | !hyper[_active_nodes.front()] ) { |
---|
| 1570 | _active_nodes.pop_front(); |
---|
[874] | 1571 | } |
---|
[956] | 1572 | |
---|
[910] | 1573 | // Global update heuristic |
---|
[1046] | 1574 | if (relabel_cnt >= next_global_update_limit) { |
---|
[910] | 1575 | globalUpdate(); |
---|
| 1576 | for (int u = 0; u != _res_node_num; ++u) |
---|
| 1577 | hyper[u] = false; |
---|
[1046] | 1578 | next_global_update_limit += global_update_skip; |
---|
[910] | 1579 | } |
---|
[874] | 1580 | } |
---|
| 1581 | } |
---|
| 1582 | } |
---|
| 1583 | |
---|
| 1584 | }; //class CostScaling |
---|
| 1585 | |
---|
| 1586 | ///@} |
---|
| 1587 | |
---|
| 1588 | } //namespace lemon |
---|
| 1589 | |
---|
| 1590 | #endif //LEMON_COST_SCALING_H |
---|