[808] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_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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[809] | 33 | #include <lemon/static_graph.h> |
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[808] | 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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[809] | 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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| 43 | /// \tparam V The value type used for flow amounts, capacity bounds |
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| 44 | /// and supply values. By default it is \c int. |
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| 45 | /// \tparam C The value type used for costs and potentials. |
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| 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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[808] | 86 | /// \addtogroup min_cost_flow_algs |
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| 87 | /// @{ |
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| 88 | |
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[809] | 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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[808] | 91 | /// |
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[809] | 92 | /// \ref CostScaling implements a cost scaling algorithm that performs |
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| 93 | /// push/augment and relabel operations for finding a minimum cost |
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| 94 | /// flow. It is an efficient primal-dual solution method, which |
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| 95 | /// can be viewed as the generalization of the \ref Preflow |
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| 96 | /// "preflow push-relabel" algorithm for the maximum flow problem. |
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[808] | 97 | /// |
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[809] | 98 | /// Most of the parameters of the problem (except for the digraph) |
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| 99 | /// can be given using separate functions, and the algorithm can be |
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| 100 | /// executed using the \ref run() function. If some parameters are not |
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| 101 | /// specified, then default values will be used. |
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[808] | 102 | /// |
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[809] | 103 | /// \tparam GR The digraph type the algorithm runs on. |
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| 104 | /// \tparam V The value type used for flow amounts, capacity bounds |
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| 105 | /// and supply values in the algorithm. By default it is \c int. |
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| 106 | /// \tparam C The value type used for costs and potentials in the |
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| 107 | /// algorithm. By default it is the same as \c V. |
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[808] | 108 | /// |
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[809] | 109 | /// \warning Both value types must be signed and all input data must |
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| 110 | /// be integer. |
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| 111 | /// \warning This algorithm does not support negative costs for such |
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| 112 | /// arcs that have infinite upper bound. |
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[810] | 113 | /// |
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| 114 | /// \note %CostScaling provides three different internal methods, |
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| 115 | /// from which the most efficient one is used by default. |
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| 116 | /// For more information, see \ref Method. |
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[809] | 117 | #ifdef DOXYGEN |
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| 118 | template <typename GR, typename V, typename C, typename TR> |
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| 119 | #else |
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| 120 | template < typename GR, typename V = int, typename C = V, |
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| 121 | typename TR = CostScalingDefaultTraits<GR, V, C> > |
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| 122 | #endif |
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[808] | 123 | class CostScaling |
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| 124 | { |
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[809] | 125 | public: |
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[808] | 126 | |
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[809] | 127 | /// The type of the digraph |
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| 128 | typedef typename TR::Digraph Digraph; |
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| 129 | /// The type of the flow amounts, capacity bounds and supply values |
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| 130 | typedef typename TR::Value Value; |
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| 131 | /// The type of the arc costs |
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| 132 | typedef typename TR::Cost Cost; |
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[808] | 133 | |
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[809] | 134 | /// \brief The large cost type |
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| 135 | /// |
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| 136 | /// The large cost type used for internal computations. |
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| 137 | /// Using the \ref CostScalingDefaultTraits "default traits class", |
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| 138 | /// it is \c long \c long if the \c Cost type is integer, |
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| 139 | /// otherwise it is \c double. |
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| 140 | typedef typename TR::LargeCost LargeCost; |
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[808] | 141 | |
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[809] | 142 | /// The \ref CostScalingDefaultTraits "traits class" of the algorithm |
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| 143 | typedef TR Traits; |
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[808] | 144 | |
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| 145 | public: |
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| 146 | |
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[809] | 147 | /// \brief Problem type constants for the \c run() function. |
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| 148 | /// |
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| 149 | /// Enum type containing the problem type constants that can be |
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| 150 | /// returned by the \ref run() function of the algorithm. |
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| 151 | enum ProblemType { |
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| 152 | /// The problem has no feasible solution (flow). |
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| 153 | INFEASIBLE, |
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| 154 | /// The problem has optimal solution (i.e. it is feasible and |
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| 155 | /// bounded), and the algorithm has found optimal flow and node |
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| 156 | /// potentials (primal and dual solutions). |
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| 157 | OPTIMAL, |
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| 158 | /// The digraph contains an arc of negative cost and infinite |
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| 159 | /// upper bound. It means that the objective function is unbounded |
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| 160 | /// on that arc, however note that it could actually be bounded |
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| 161 | /// over the feasible flows, but this algroithm cannot handle |
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| 162 | /// these cases. |
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| 163 | UNBOUNDED |
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| 164 | }; |
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[808] | 165 | |
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[810] | 166 | /// \brief Constants for selecting the internal method. |
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| 167 | /// |
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| 168 | /// Enum type containing constants for selecting the internal method |
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| 169 | /// for the \ref run() function. |
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| 170 | /// |
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| 171 | /// \ref CostScaling provides three internal methods that differ mainly |
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| 172 | /// in their base operations, which are used in conjunction with the |
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| 173 | /// relabel operation. |
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| 174 | /// By default, the so called \ref PARTIAL_AUGMENT |
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| 175 | /// "Partial Augment-Relabel" method is used, which proved to be |
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| 176 | /// the most efficient and the most robust on various test inputs. |
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| 177 | /// However, the other methods can be selected using the \ref run() |
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| 178 | /// function with the proper parameter. |
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| 179 | enum Method { |
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| 180 | /// Local push operations are used, i.e. flow is moved only on one |
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| 181 | /// admissible arc at once. |
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| 182 | PUSH, |
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| 183 | /// Augment operations are used, i.e. flow is moved on admissible |
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| 184 | /// paths from a node with excess to a node with deficit. |
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| 185 | AUGMENT, |
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| 186 | /// Partial augment operations are used, i.e. flow is moved on |
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| 187 | /// admissible paths started from a node with excess, but the |
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| 188 | /// lengths of these paths are limited. This method can be viewed |
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| 189 | /// as a combined version of the previous two operations. |
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| 190 | PARTIAL_AUGMENT |
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| 191 | }; |
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| 192 | |
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[808] | 193 | private: |
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| 194 | |
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[809] | 195 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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[808] | 196 | |
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[809] | 197 | typedef std::vector<int> IntVector; |
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| 198 | typedef std::vector<char> BoolVector; |
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| 199 | typedef std::vector<Value> ValueVector; |
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| 200 | typedef std::vector<Cost> CostVector; |
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| 201 | typedef std::vector<LargeCost> LargeCostVector; |
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[808] | 202 | |
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[809] | 203 | private: |
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| 204 | |
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| 205 | template <typename KT, typename VT> |
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| 206 | class VectorMap { |
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[808] | 207 | public: |
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[809] | 208 | typedef KT Key; |
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| 209 | typedef VT Value; |
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| 210 | |
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| 211 | VectorMap(std::vector<Value>& v) : _v(v) {} |
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| 212 | |
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| 213 | const Value& operator[](const Key& key) const { |
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| 214 | return _v[StaticDigraph::id(key)]; |
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[808] | 215 | } |
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| 216 | |
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[809] | 217 | Value& operator[](const Key& key) { |
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| 218 | return _v[StaticDigraph::id(key)]; |
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| 219 | } |
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| 220 | |
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| 221 | void set(const Key& key, const Value& val) { |
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| 222 | _v[StaticDigraph::id(key)] = val; |
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[808] | 223 | } |
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| 224 | |
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[809] | 225 | private: |
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| 226 | std::vector<Value>& _v; |
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| 227 | }; |
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| 228 | |
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| 229 | typedef VectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap; |
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| 230 | typedef VectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap; |
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[808] | 231 | |
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| 232 | private: |
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| 233 | |
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[809] | 234 | // Data related to the underlying digraph |
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| 235 | const GR &_graph; |
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| 236 | int _node_num; |
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| 237 | int _arc_num; |
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| 238 | int _res_node_num; |
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| 239 | int _res_arc_num; |
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| 240 | int _root; |
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[808] | 241 | |
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[809] | 242 | // Parameters of the problem |
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| 243 | bool _have_lower; |
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| 244 | Value _sum_supply; |
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[808] | 245 | |
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[809] | 246 | // Data structures for storing the digraph |
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| 247 | IntNodeMap _node_id; |
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| 248 | IntArcMap _arc_idf; |
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| 249 | IntArcMap _arc_idb; |
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| 250 | IntVector _first_out; |
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| 251 | BoolVector _forward; |
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| 252 | IntVector _source; |
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| 253 | IntVector _target; |
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| 254 | IntVector _reverse; |
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| 255 | |
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| 256 | // Node and arc data |
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| 257 | ValueVector _lower; |
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| 258 | ValueVector _upper; |
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| 259 | CostVector _scost; |
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| 260 | ValueVector _supply; |
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| 261 | |
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| 262 | ValueVector _res_cap; |
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| 263 | LargeCostVector _cost; |
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| 264 | LargeCostVector _pi; |
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| 265 | ValueVector _excess; |
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| 266 | IntVector _next_out; |
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| 267 | std::deque<int> _active_nodes; |
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| 268 | |
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| 269 | // Data for scaling |
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| 270 | LargeCost _epsilon; |
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[808] | 271 | int _alpha; |
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| 272 | |
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[809] | 273 | // Data for a StaticDigraph structure |
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| 274 | typedef std::pair<int, int> IntPair; |
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| 275 | StaticDigraph _sgr; |
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| 276 | std::vector<IntPair> _arc_vec; |
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| 277 | std::vector<LargeCost> _cost_vec; |
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| 278 | LargeCostArcMap _cost_map; |
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| 279 | LargeCostNodeMap _pi_map; |
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| 280 | |
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| 281 | public: |
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| 282 | |
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| 283 | /// \brief Constant for infinite upper bounds (capacities). |
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| 284 | /// |
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| 285 | /// Constant for infinite upper bounds (capacities). |
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| 286 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 287 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 288 | const Value INF; |
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| 289 | |
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[808] | 290 | public: |
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| 291 | |
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[809] | 292 | /// \name Named Template Parameters |
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| 293 | /// @{ |
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| 294 | |
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| 295 | template <typename T> |
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| 296 | struct SetLargeCostTraits : public Traits { |
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| 297 | typedef T LargeCost; |
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| 298 | }; |
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| 299 | |
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| 300 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 301 | /// \c LargeCost type. |
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[808] | 302 | /// |
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[809] | 303 | /// \ref named-templ-param "Named parameter" for setting \c LargeCost |
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| 304 | /// type, which is used for internal computations in the algorithm. |
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| 305 | /// \c Cost must be convertible to \c LargeCost. |
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| 306 | template <typename T> |
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| 307 | struct SetLargeCost |
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| 308 | : public CostScaling<GR, V, C, SetLargeCostTraits<T> > { |
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| 309 | typedef CostScaling<GR, V, C, SetLargeCostTraits<T> > Create; |
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| 310 | }; |
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| 311 | |
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| 312 | /// @} |
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| 313 | |
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| 314 | public: |
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| 315 | |
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| 316 | /// \brief Constructor. |
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[808] | 317 | /// |
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[809] | 318 | /// The constructor of the class. |
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| 319 | /// |
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| 320 | /// \param graph The digraph the algorithm runs on. |
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| 321 | CostScaling(const GR& graph) : |
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| 322 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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| 323 | _cost_map(_cost_vec), _pi_map(_pi), |
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| 324 | INF(std::numeric_limits<Value>::has_infinity ? |
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| 325 | std::numeric_limits<Value>::infinity() : |
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| 326 | std::numeric_limits<Value>::max()) |
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[808] | 327 | { |
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[809] | 328 | // Check the value types |
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| 329 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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| 330 | "The flow type of CostScaling must be signed"); |
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| 331 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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| 332 | "The cost type of CostScaling must be signed"); |
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| 333 | |
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| 334 | // Resize vectors |
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| 335 | _node_num = countNodes(_graph); |
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| 336 | _arc_num = countArcs(_graph); |
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| 337 | _res_node_num = _node_num + 1; |
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| 338 | _res_arc_num = 2 * (_arc_num + _node_num); |
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| 339 | _root = _node_num; |
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| 340 | |
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| 341 | _first_out.resize(_res_node_num + 1); |
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| 342 | _forward.resize(_res_arc_num); |
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| 343 | _source.resize(_res_arc_num); |
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| 344 | _target.resize(_res_arc_num); |
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| 345 | _reverse.resize(_res_arc_num); |
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| 346 | |
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| 347 | _lower.resize(_res_arc_num); |
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| 348 | _upper.resize(_res_arc_num); |
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| 349 | _scost.resize(_res_arc_num); |
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| 350 | _supply.resize(_res_node_num); |
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[808] | 351 | |
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[809] | 352 | _res_cap.resize(_res_arc_num); |
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| 353 | _cost.resize(_res_arc_num); |
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| 354 | _pi.resize(_res_node_num); |
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| 355 | _excess.resize(_res_node_num); |
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| 356 | _next_out.resize(_res_node_num); |
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[808] | 357 | |
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[809] | 358 | _arc_vec.reserve(_res_arc_num); |
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| 359 | _cost_vec.reserve(_res_arc_num); |
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| 360 | |
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| 361 | // Copy the graph |
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| 362 | int i = 0, j = 0, k = 2 * _arc_num + _node_num; |
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| 363 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
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| 364 | _node_id[n] = i; |
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| 365 | } |
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| 366 | i = 0; |
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| 367 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
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| 368 | _first_out[i] = j; |
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| 369 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
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| 370 | _arc_idf[a] = j; |
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| 371 | _forward[j] = true; |
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| 372 | _source[j] = i; |
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| 373 | _target[j] = _node_id[_graph.runningNode(a)]; |
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[808] | 374 | } |
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[809] | 375 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
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| 376 | _arc_idb[a] = j; |
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| 377 | _forward[j] = false; |
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| 378 | _source[j] = i; |
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| 379 | _target[j] = _node_id[_graph.runningNode(a)]; |
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| 380 | } |
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| 381 | _forward[j] = false; |
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| 382 | _source[j] = i; |
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| 383 | _target[j] = _root; |
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| 384 | _reverse[j] = k; |
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| 385 | _forward[k] = true; |
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| 386 | _source[k] = _root; |
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| 387 | _target[k] = i; |
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| 388 | _reverse[k] = j; |
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| 389 | ++j; ++k; |
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[808] | 390 | } |
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[809] | 391 | _first_out[i] = j; |
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| 392 | _first_out[_res_node_num] = k; |
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| 393 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 394 | int fi = _arc_idf[a]; |
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| 395 | int bi = _arc_idb[a]; |
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| 396 | _reverse[fi] = bi; |
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| 397 | _reverse[bi] = fi; |
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| 398 | } |
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| 399 | |
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| 400 | // Reset parameters |
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| 401 | reset(); |
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[808] | 402 | } |
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| 403 | |
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[809] | 404 | /// \name Parameters |
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| 405 | /// The parameters of the algorithm can be specified using these |
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| 406 | /// functions. |
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| 407 | |
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| 408 | /// @{ |
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| 409 | |
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| 410 | /// \brief Set the lower bounds on the arcs. |
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[808] | 411 | /// |
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[809] | 412 | /// This function sets the lower bounds on the arcs. |
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| 413 | /// If it is not used before calling \ref run(), the lower bounds |
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| 414 | /// will be set to zero on all arcs. |
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[808] | 415 | /// |
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[809] | 416 | /// \param map An arc map storing the lower bounds. |
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| 417 | /// Its \c Value type must be convertible to the \c Value type |
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| 418 | /// of the algorithm. |
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| 419 | /// |
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| 420 | /// \return <tt>(*this)</tt> |
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| 421 | template <typename LowerMap> |
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| 422 | CostScaling& lowerMap(const LowerMap& map) { |
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| 423 | _have_lower = true; |
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| 424 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 425 | _lower[_arc_idf[a]] = map[a]; |
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| 426 | _lower[_arc_idb[a]] = map[a]; |
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[808] | 427 | } |
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| 428 | return *this; |
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| 429 | } |
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| 430 | |
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[809] | 431 | /// \brief Set the upper bounds (capacities) on the arcs. |
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[808] | 432 | /// |
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[809] | 433 | /// This function sets the upper bounds (capacities) on the arcs. |
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| 434 | /// If it is not used before calling \ref run(), the upper bounds |
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| 435 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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| 436 | /// unbounded from above on each arc). |
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[808] | 437 | /// |
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[809] | 438 | /// \param map An arc map storing the upper bounds. |
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| 439 | /// Its \c Value type must be convertible to the \c Value type |
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| 440 | /// of the algorithm. |
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| 441 | /// |
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| 442 | /// \return <tt>(*this)</tt> |
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| 443 | template<typename UpperMap> |
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| 444 | CostScaling& upperMap(const UpperMap& map) { |
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| 445 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 446 | _upper[_arc_idf[a]] = map[a]; |
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[808] | 447 | } |
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| 448 | return *this; |
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| 449 | } |
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| 450 | |
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[809] | 451 | /// \brief Set the costs of the arcs. |
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| 452 | /// |
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| 453 | /// This function sets the costs of the arcs. |
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| 454 | /// If it is not used before calling \ref run(), the costs |
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| 455 | /// will be set to \c 1 on all arcs. |
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| 456 | /// |
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| 457 | /// \param map An arc map storing the costs. |
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| 458 | /// Its \c Value type must be convertible to the \c Cost type |
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| 459 | /// of the algorithm. |
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| 460 | /// |
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| 461 | /// \return <tt>(*this)</tt> |
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| 462 | template<typename CostMap> |
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| 463 | CostScaling& costMap(const CostMap& map) { |
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| 464 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 465 | _scost[_arc_idf[a]] = map[a]; |
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| 466 | _scost[_arc_idb[a]] = -map[a]; |
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| 467 | } |
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| 468 | return *this; |
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| 469 | } |
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| 470 | |
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| 471 | /// \brief Set the supply values of the nodes. |
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| 472 | /// |
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| 473 | /// This function sets the supply values of the nodes. |
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| 474 | /// If neither this function nor \ref stSupply() is used before |
---|
| 475 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 476 | /// |
---|
| 477 | /// \param map A node map storing the supply values. |
---|
| 478 | /// Its \c Value type must be convertible to the \c Value type |
---|
| 479 | /// of the algorithm. |
---|
| 480 | /// |
---|
| 481 | /// \return <tt>(*this)</tt> |
---|
| 482 | template<typename SupplyMap> |
---|
| 483 | CostScaling& supplyMap(const SupplyMap& map) { |
---|
| 484 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 485 | _supply[_node_id[n]] = map[n]; |
---|
| 486 | } |
---|
| 487 | return *this; |
---|
| 488 | } |
---|
| 489 | |
---|
| 490 | /// \brief Set single source and target nodes and a supply value. |
---|
| 491 | /// |
---|
| 492 | /// This function sets a single source node and a single target node |
---|
| 493 | /// and the required flow value. |
---|
| 494 | /// If neither this function nor \ref supplyMap() is used before |
---|
| 495 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
| 496 | /// |
---|
| 497 | /// Using this function has the same effect as using \ref supplyMap() |
---|
| 498 | /// with such a map in which \c k is assigned to \c s, \c -k is |
---|
| 499 | /// assigned to \c t and all other nodes have zero supply value. |
---|
| 500 | /// |
---|
| 501 | /// \param s The source node. |
---|
| 502 | /// \param t The target node. |
---|
| 503 | /// \param k The required amount of flow from node \c s to node \c t |
---|
| 504 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
| 505 | /// |
---|
| 506 | /// \return <tt>(*this)</tt> |
---|
| 507 | CostScaling& stSupply(const Node& s, const Node& t, Value k) { |
---|
| 508 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 509 | _supply[i] = 0; |
---|
| 510 | } |
---|
| 511 | _supply[_node_id[s]] = k; |
---|
| 512 | _supply[_node_id[t]] = -k; |
---|
| 513 | return *this; |
---|
| 514 | } |
---|
| 515 | |
---|
| 516 | /// @} |
---|
| 517 | |
---|
[808] | 518 | /// \name Execution control |
---|
[809] | 519 | /// The algorithm can be executed using \ref run(). |
---|
[808] | 520 | |
---|
| 521 | /// @{ |
---|
| 522 | |
---|
| 523 | /// \brief Run the algorithm. |
---|
| 524 | /// |
---|
[809] | 525 | /// This function runs the algorithm. |
---|
| 526 | /// The paramters can be specified using functions \ref lowerMap(), |
---|
| 527 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
| 528 | /// For example, |
---|
| 529 | /// \code |
---|
| 530 | /// CostScaling<ListDigraph> cs(graph); |
---|
| 531 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
| 532 | /// .supplyMap(sup).run(); |
---|
| 533 | /// \endcode |
---|
| 534 | /// |
---|
| 535 | /// This function can be called more than once. All the parameters |
---|
| 536 | /// that have been given are kept for the next call, unless |
---|
| 537 | /// \ref reset() is called, thus only the modified parameters |
---|
| 538 | /// have to be set again. See \ref reset() for examples. |
---|
[810] | 539 | /// However, the underlying digraph must not be modified after this |
---|
| 540 | /// class have been constructed, since it copies and extends the graph. |
---|
[808] | 541 | /// |
---|
[810] | 542 | /// \param method The internal method that will be used in the |
---|
| 543 | /// algorithm. For more information, see \ref Method. |
---|
| 544 | /// \param factor The cost scaling factor. It must be larger than one. |
---|
[808] | 545 | /// |
---|
[809] | 546 | /// \return \c INFEASIBLE if no feasible flow exists, |
---|
| 547 | /// \n \c OPTIMAL if the problem has optimal solution |
---|
| 548 | /// (i.e. it is feasible and bounded), and the algorithm has found |
---|
| 549 | /// optimal flow and node potentials (primal and dual solutions), |
---|
| 550 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
---|
| 551 | /// and infinite upper bound. It means that the objective function |
---|
| 552 | /// is unbounded on that arc, however note that it could actually be |
---|
| 553 | /// bounded over the feasible flows, but this algroithm cannot handle |
---|
| 554 | /// these cases. |
---|
| 555 | /// |
---|
[810] | 556 | /// \see ProblemType, Method |
---|
| 557 | ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) { |
---|
| 558 | _alpha = factor; |
---|
[809] | 559 | ProblemType pt = init(); |
---|
| 560 | if (pt != OPTIMAL) return pt; |
---|
[810] | 561 | start(method); |
---|
[809] | 562 | return OPTIMAL; |
---|
| 563 | } |
---|
| 564 | |
---|
| 565 | /// \brief Reset all the parameters that have been given before. |
---|
| 566 | /// |
---|
| 567 | /// This function resets all the paramaters that have been given |
---|
| 568 | /// before using functions \ref lowerMap(), \ref upperMap(), |
---|
| 569 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
| 570 | /// |
---|
| 571 | /// It is useful for multiple run() calls. If this function is not |
---|
| 572 | /// used, all the parameters given before are kept for the next |
---|
| 573 | /// \ref run() call. |
---|
| 574 | /// However the underlying digraph must not be modified after this |
---|
| 575 | /// class have been constructed, since it copies and extends the graph. |
---|
| 576 | /// |
---|
| 577 | /// For example, |
---|
| 578 | /// \code |
---|
| 579 | /// CostScaling<ListDigraph> cs(graph); |
---|
| 580 | /// |
---|
| 581 | /// // First run |
---|
| 582 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
| 583 | /// .supplyMap(sup).run(); |
---|
| 584 | /// |
---|
| 585 | /// // Run again with modified cost map (reset() is not called, |
---|
| 586 | /// // so only the cost map have to be set again) |
---|
| 587 | /// cost[e] += 100; |
---|
| 588 | /// cs.costMap(cost).run(); |
---|
| 589 | /// |
---|
| 590 | /// // Run again from scratch using reset() |
---|
| 591 | /// // (the lower bounds will be set to zero on all arcs) |
---|
| 592 | /// cs.reset(); |
---|
| 593 | /// cs.upperMap(capacity).costMap(cost) |
---|
| 594 | /// .supplyMap(sup).run(); |
---|
| 595 | /// \endcode |
---|
| 596 | /// |
---|
| 597 | /// \return <tt>(*this)</tt> |
---|
| 598 | CostScaling& reset() { |
---|
| 599 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 600 | _supply[i] = 0; |
---|
[808] | 601 | } |
---|
[809] | 602 | int limit = _first_out[_root]; |
---|
| 603 | for (int j = 0; j != limit; ++j) { |
---|
| 604 | _lower[j] = 0; |
---|
| 605 | _upper[j] = INF; |
---|
| 606 | _scost[j] = _forward[j] ? 1 : -1; |
---|
| 607 | } |
---|
| 608 | for (int j = limit; j != _res_arc_num; ++j) { |
---|
| 609 | _lower[j] = 0; |
---|
| 610 | _upper[j] = INF; |
---|
| 611 | _scost[j] = 0; |
---|
| 612 | _scost[_reverse[j]] = 0; |
---|
| 613 | } |
---|
| 614 | _have_lower = false; |
---|
| 615 | return *this; |
---|
[808] | 616 | } |
---|
| 617 | |
---|
| 618 | /// @} |
---|
| 619 | |
---|
| 620 | /// \name Query Functions |
---|
[809] | 621 | /// The results of the algorithm can be obtained using these |
---|
[808] | 622 | /// functions.\n |
---|
[809] | 623 | /// The \ref run() function must be called before using them. |
---|
[808] | 624 | |
---|
| 625 | /// @{ |
---|
| 626 | |
---|
[809] | 627 | /// \brief Return the total cost of the found flow. |
---|
[808] | 628 | /// |
---|
[809] | 629 | /// This function returns the total cost of the found flow. |
---|
| 630 | /// Its complexity is O(e). |
---|
| 631 | /// |
---|
| 632 | /// \note The return type of the function can be specified as a |
---|
| 633 | /// template parameter. For example, |
---|
| 634 | /// \code |
---|
| 635 | /// cs.totalCost<double>(); |
---|
| 636 | /// \endcode |
---|
| 637 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
| 638 | /// type of the algorithm, which is the default return type of the |
---|
| 639 | /// function. |
---|
[808] | 640 | /// |
---|
| 641 | /// \pre \ref run() must be called before using this function. |
---|
[809] | 642 | template <typename Number> |
---|
| 643 | Number totalCost() const { |
---|
| 644 | Number c = 0; |
---|
| 645 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 646 | int i = _arc_idb[a]; |
---|
| 647 | c += static_cast<Number>(_res_cap[i]) * |
---|
| 648 | (-static_cast<Number>(_scost[i])); |
---|
| 649 | } |
---|
| 650 | return c; |
---|
[808] | 651 | } |
---|
| 652 | |
---|
[809] | 653 | #ifndef DOXYGEN |
---|
| 654 | Cost totalCost() const { |
---|
| 655 | return totalCost<Cost>(); |
---|
[808] | 656 | } |
---|
[809] | 657 | #endif |
---|
[808] | 658 | |
---|
| 659 | /// \brief Return the flow on the given arc. |
---|
| 660 | /// |
---|
[809] | 661 | /// This function returns the flow on the given arc. |
---|
[808] | 662 | /// |
---|
| 663 | /// \pre \ref run() must be called before using this function. |
---|
[809] | 664 | Value flow(const Arc& a) const { |
---|
| 665 | return _res_cap[_arc_idb[a]]; |
---|
[808] | 666 | } |
---|
| 667 | |
---|
[809] | 668 | /// \brief Return the flow map (the primal solution). |
---|
[808] | 669 | /// |
---|
[809] | 670 | /// This function copies the flow value on each arc into the given |
---|
| 671 | /// map. The \c Value type of the algorithm must be convertible to |
---|
| 672 | /// the \c Value type of the map. |
---|
[808] | 673 | /// |
---|
| 674 | /// \pre \ref run() must be called before using this function. |
---|
[809] | 675 | template <typename FlowMap> |
---|
| 676 | void flowMap(FlowMap &map) const { |
---|
| 677 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 678 | map.set(a, _res_cap[_arc_idb[a]]); |
---|
| 679 | } |
---|
[808] | 680 | } |
---|
| 681 | |
---|
[809] | 682 | /// \brief Return the potential (dual value) of the given node. |
---|
[808] | 683 | /// |
---|
[809] | 684 | /// This function returns the potential (dual value) of the |
---|
| 685 | /// given node. |
---|
[808] | 686 | /// |
---|
| 687 | /// \pre \ref run() must be called before using this function. |
---|
[809] | 688 | Cost potential(const Node& n) const { |
---|
| 689 | return static_cast<Cost>(_pi[_node_id[n]]); |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | /// \brief Return the potential map (the dual solution). |
---|
| 693 | /// |
---|
| 694 | /// This function copies the potential (dual value) of each node |
---|
| 695 | /// into the given map. |
---|
| 696 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 697 | /// \c Value type of the map. |
---|
| 698 | /// |
---|
| 699 | /// \pre \ref run() must be called before using this function. |
---|
| 700 | template <typename PotentialMap> |
---|
| 701 | void potentialMap(PotentialMap &map) const { |
---|
| 702 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 703 | map.set(n, static_cast<Cost>(_pi[_node_id[n]])); |
---|
| 704 | } |
---|
[808] | 705 | } |
---|
| 706 | |
---|
| 707 | /// @} |
---|
| 708 | |
---|
| 709 | private: |
---|
| 710 | |
---|
[809] | 711 | // Initialize the algorithm |
---|
| 712 | ProblemType init() { |
---|
| 713 | if (_res_node_num == 0) return INFEASIBLE; |
---|
| 714 | |
---|
| 715 | // Check the sum of supply values |
---|
| 716 | _sum_supply = 0; |
---|
| 717 | for (int i = 0; i != _root; ++i) { |
---|
| 718 | _sum_supply += _supply[i]; |
---|
[808] | 719 | } |
---|
[809] | 720 | if (_sum_supply > 0) return INFEASIBLE; |
---|
| 721 | |
---|
| 722 | |
---|
| 723 | // Initialize vectors |
---|
| 724 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 725 | _pi[i] = 0; |
---|
| 726 | _excess[i] = _supply[i]; |
---|
| 727 | } |
---|
| 728 | |
---|
| 729 | // Remove infinite upper bounds and check negative arcs |
---|
| 730 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
| 731 | int last_out; |
---|
| 732 | if (_have_lower) { |
---|
| 733 | for (int i = 0; i != _root; ++i) { |
---|
| 734 | last_out = _first_out[i+1]; |
---|
| 735 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 736 | if (_forward[j]) { |
---|
| 737 | Value c = _scost[j] < 0 ? _upper[j] : _lower[j]; |
---|
| 738 | if (c >= MAX) return UNBOUNDED; |
---|
| 739 | _excess[i] -= c; |
---|
| 740 | _excess[_target[j]] += c; |
---|
| 741 | } |
---|
| 742 | } |
---|
| 743 | } |
---|
| 744 | } else { |
---|
| 745 | for (int i = 0; i != _root; ++i) { |
---|
| 746 | last_out = _first_out[i+1]; |
---|
| 747 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 748 | if (_forward[j] && _scost[j] < 0) { |
---|
| 749 | Value c = _upper[j]; |
---|
| 750 | if (c >= MAX) return UNBOUNDED; |
---|
| 751 | _excess[i] -= c; |
---|
| 752 | _excess[_target[j]] += c; |
---|
| 753 | } |
---|
| 754 | } |
---|
| 755 | } |
---|
| 756 | } |
---|
| 757 | Value ex, max_cap = 0; |
---|
| 758 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 759 | ex = _excess[i]; |
---|
| 760 | _excess[i] = 0; |
---|
| 761 | if (ex < 0) max_cap -= ex; |
---|
| 762 | } |
---|
| 763 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 764 | if (_upper[j] >= MAX) _upper[j] = max_cap; |
---|
[808] | 765 | } |
---|
| 766 | |
---|
[809] | 767 | // Initialize the large cost vector and the epsilon parameter |
---|
| 768 | _epsilon = 0; |
---|
| 769 | LargeCost lc; |
---|
| 770 | for (int i = 0; i != _root; ++i) { |
---|
| 771 | last_out = _first_out[i+1]; |
---|
| 772 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 773 | lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha; |
---|
| 774 | _cost[j] = lc; |
---|
| 775 | if (lc > _epsilon) _epsilon = lc; |
---|
| 776 | } |
---|
| 777 | } |
---|
| 778 | _epsilon /= _alpha; |
---|
[808] | 779 | |
---|
[809] | 780 | // Initialize maps for Circulation and remove non-zero lower bounds |
---|
| 781 | ConstMap<Arc, Value> low(0); |
---|
| 782 | typedef typename Digraph::template ArcMap<Value> ValueArcMap; |
---|
| 783 | typedef typename Digraph::template NodeMap<Value> ValueNodeMap; |
---|
| 784 | ValueArcMap cap(_graph), flow(_graph); |
---|
| 785 | ValueNodeMap sup(_graph); |
---|
| 786 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 787 | sup[n] = _supply[_node_id[n]]; |
---|
[808] | 788 | } |
---|
[809] | 789 | if (_have_lower) { |
---|
| 790 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 791 | int j = _arc_idf[a]; |
---|
| 792 | Value c = _lower[j]; |
---|
| 793 | cap[a] = _upper[j] - c; |
---|
| 794 | sup[_graph.source(a)] -= c; |
---|
| 795 | sup[_graph.target(a)] += c; |
---|
| 796 | } |
---|
| 797 | } else { |
---|
| 798 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 799 | cap[a] = _upper[_arc_idf[a]]; |
---|
| 800 | } |
---|
| 801 | } |
---|
[808] | 802 | |
---|
| 803 | // Find a feasible flow using Circulation |
---|
[809] | 804 | Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> |
---|
| 805 | circ(_graph, low, cap, sup); |
---|
| 806 | if (!circ.flowMap(flow).run()) return INFEASIBLE; |
---|
| 807 | |
---|
| 808 | // Set residual capacities and handle GEQ supply type |
---|
| 809 | if (_sum_supply < 0) { |
---|
| 810 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 811 | Value fa = flow[a]; |
---|
| 812 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
| 813 | _res_cap[_arc_idb[a]] = fa; |
---|
| 814 | sup[_graph.source(a)] -= fa; |
---|
| 815 | sup[_graph.target(a)] += fa; |
---|
| 816 | } |
---|
| 817 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 818 | _excess[_node_id[n]] = sup[n]; |
---|
| 819 | } |
---|
| 820 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
| 821 | int u = _target[a]; |
---|
| 822 | int ra = _reverse[a]; |
---|
| 823 | _res_cap[a] = -_sum_supply + 1; |
---|
| 824 | _res_cap[ra] = -_excess[u]; |
---|
| 825 | _cost[a] = 0; |
---|
| 826 | _cost[ra] = 0; |
---|
| 827 | _excess[u] = 0; |
---|
| 828 | } |
---|
| 829 | } else { |
---|
| 830 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 831 | Value fa = flow[a]; |
---|
| 832 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
| 833 | _res_cap[_arc_idb[a]] = fa; |
---|
| 834 | } |
---|
| 835 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
| 836 | int ra = _reverse[a]; |
---|
| 837 | _res_cap[a] = 1; |
---|
| 838 | _res_cap[ra] = 0; |
---|
| 839 | _cost[a] = 0; |
---|
| 840 | _cost[ra] = 0; |
---|
| 841 | } |
---|
| 842 | } |
---|
| 843 | |
---|
| 844 | return OPTIMAL; |
---|
| 845 | } |
---|
| 846 | |
---|
| 847 | // Execute the algorithm and transform the results |
---|
[810] | 848 | void start(Method method) { |
---|
| 849 | // Maximum path length for partial augment |
---|
| 850 | const int MAX_PATH_LENGTH = 4; |
---|
| 851 | |
---|
[809] | 852 | // Execute the algorithm |
---|
[810] | 853 | switch (method) { |
---|
| 854 | case PUSH: |
---|
| 855 | startPush(); |
---|
| 856 | break; |
---|
| 857 | case AUGMENT: |
---|
| 858 | startAugment(); |
---|
| 859 | break; |
---|
| 860 | case PARTIAL_AUGMENT: |
---|
| 861 | startAugment(MAX_PATH_LENGTH); |
---|
| 862 | break; |
---|
[809] | 863 | } |
---|
| 864 | |
---|
| 865 | // Compute node potentials for the original costs |
---|
| 866 | _arc_vec.clear(); |
---|
| 867 | _cost_vec.clear(); |
---|
| 868 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 869 | if (_res_cap[j] > 0) { |
---|
| 870 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
| 871 | _cost_vec.push_back(_scost[j]); |
---|
| 872 | } |
---|
| 873 | } |
---|
| 874 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
| 875 | |
---|
| 876 | typename BellmanFord<StaticDigraph, LargeCostArcMap> |
---|
| 877 | ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map); |
---|
| 878 | bf.distMap(_pi_map); |
---|
| 879 | bf.init(0); |
---|
| 880 | bf.start(); |
---|
| 881 | |
---|
| 882 | // Handle non-zero lower bounds |
---|
| 883 | if (_have_lower) { |
---|
| 884 | int limit = _first_out[_root]; |
---|
| 885 | for (int j = 0; j != limit; ++j) { |
---|
| 886 | if (!_forward[j]) _res_cap[j] += _lower[j]; |
---|
| 887 | } |
---|
| 888 | } |
---|
[808] | 889 | } |
---|
| 890 | |
---|
[810] | 891 | /// Execute the algorithm performing augment and relabel operations |
---|
| 892 | void startAugment(int max_length = std::numeric_limits<int>::max()) { |
---|
[808] | 893 | // Paramters for heuristics |
---|
[809] | 894 | const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
---|
| 895 | const int BF_HEURISTIC_BOUND_FACTOR = 3; |
---|
[808] | 896 | |
---|
[809] | 897 | // Perform cost scaling phases |
---|
| 898 | IntVector pred_arc(_res_node_num); |
---|
| 899 | std::vector<int> path_nodes; |
---|
[808] | 900 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
| 901 | 1 : _epsilon / _alpha ) |
---|
| 902 | { |
---|
| 903 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
---|
| 904 | // to check if the current flow is optimal |
---|
| 905 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
---|
[809] | 906 | _arc_vec.clear(); |
---|
| 907 | _cost_vec.clear(); |
---|
| 908 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 909 | if (_res_cap[j] > 0) { |
---|
| 910 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
| 911 | _cost_vec.push_back(_cost[j] + 1); |
---|
| 912 | } |
---|
| 913 | } |
---|
| 914 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
| 915 | |
---|
| 916 | BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map); |
---|
[808] | 917 | bf.init(0); |
---|
| 918 | bool done = false; |
---|
[809] | 919 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num)); |
---|
[808] | 920 | for (int i = 0; i < K && !done; ++i) |
---|
| 921 | done = bf.processNextWeakRound(); |
---|
| 922 | if (done) break; |
---|
| 923 | } |
---|
[809] | 924 | |
---|
[808] | 925 | // Saturate arcs not satisfying the optimality condition |
---|
[809] | 926 | for (int a = 0; a != _res_arc_num; ++a) { |
---|
| 927 | if (_res_cap[a] > 0 && |
---|
| 928 | _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) { |
---|
| 929 | Value delta = _res_cap[a]; |
---|
| 930 | _excess[_source[a]] -= delta; |
---|
| 931 | _excess[_target[a]] += delta; |
---|
| 932 | _res_cap[a] = 0; |
---|
| 933 | _res_cap[_reverse[a]] += delta; |
---|
[808] | 934 | } |
---|
| 935 | } |
---|
[809] | 936 | |
---|
[808] | 937 | // Find active nodes (i.e. nodes with positive excess) |
---|
[809] | 938 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 939 | if (_excess[u] > 0) _active_nodes.push_back(u); |
---|
[808] | 940 | } |
---|
| 941 | |
---|
[809] | 942 | // Initialize the next arcs |
---|
| 943 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 944 | _next_out[u] = _first_out[u]; |
---|
[808] | 945 | } |
---|
| 946 | |
---|
| 947 | // Perform partial augment and relabel operations |
---|
[809] | 948 | while (true) { |
---|
[808] | 949 | // Select an active node (FIFO selection) |
---|
[809] | 950 | while (_active_nodes.size() > 0 && |
---|
| 951 | _excess[_active_nodes.front()] <= 0) { |
---|
| 952 | _active_nodes.pop_front(); |
---|
[808] | 953 | } |
---|
[809] | 954 | if (_active_nodes.size() == 0) break; |
---|
| 955 | int start = _active_nodes.front(); |
---|
[808] | 956 | path_nodes.clear(); |
---|
| 957 | path_nodes.push_back(start); |
---|
| 958 | |
---|
| 959 | // Find an augmenting path from the start node |
---|
[809] | 960 | int tip = start; |
---|
| 961 | while (_excess[tip] >= 0 && |
---|
[810] | 962 | int(path_nodes.size()) <= max_length) { |
---|
[809] | 963 | int u; |
---|
| 964 | LargeCost min_red_cost, rc; |
---|
| 965 | int last_out = _sum_supply < 0 ? |
---|
| 966 | _first_out[tip+1] : _first_out[tip+1] - 1; |
---|
| 967 | for (int a = _next_out[tip]; a != last_out; ++a) { |
---|
| 968 | if (_res_cap[a] > 0 && |
---|
| 969 | _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) { |
---|
| 970 | u = _target[a]; |
---|
| 971 | pred_arc[u] = a; |
---|
| 972 | _next_out[tip] = a; |
---|
[808] | 973 | tip = u; |
---|
| 974 | path_nodes.push_back(tip); |
---|
| 975 | goto next_step; |
---|
| 976 | } |
---|
| 977 | } |
---|
| 978 | |
---|
| 979 | // Relabel tip node |
---|
[809] | 980 | min_red_cost = std::numeric_limits<LargeCost>::max() / 2; |
---|
| 981 | for (int a = _first_out[tip]; a != last_out; ++a) { |
---|
| 982 | rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]]; |
---|
| 983 | if (_res_cap[a] > 0 && rc < min_red_cost) { |
---|
| 984 | min_red_cost = rc; |
---|
| 985 | } |
---|
[808] | 986 | } |
---|
[809] | 987 | _pi[tip] -= min_red_cost + _epsilon; |
---|
[808] | 988 | |
---|
[809] | 989 | // Reset the next arc of tip |
---|
| 990 | _next_out[tip] = _first_out[tip]; |
---|
[808] | 991 | |
---|
| 992 | // Step back |
---|
| 993 | if (tip != start) { |
---|
| 994 | path_nodes.pop_back(); |
---|
[809] | 995 | tip = path_nodes.back(); |
---|
[808] | 996 | } |
---|
| 997 | |
---|
[809] | 998 | next_step: ; |
---|
[808] | 999 | } |
---|
| 1000 | |
---|
| 1001 | // Augment along the found path (as much flow as possible) |
---|
[809] | 1002 | Value delta; |
---|
| 1003 | int u, v = path_nodes.front(), pa; |
---|
[808] | 1004 | for (int i = 1; i < int(path_nodes.size()); ++i) { |
---|
[809] | 1005 | u = v; |
---|
| 1006 | v = path_nodes[i]; |
---|
| 1007 | pa = pred_arc[v]; |
---|
| 1008 | delta = std::min(_res_cap[pa], _excess[u]); |
---|
| 1009 | _res_cap[pa] -= delta; |
---|
| 1010 | _res_cap[_reverse[pa]] += delta; |
---|
| 1011 | _excess[u] -= delta; |
---|
| 1012 | _excess[v] += delta; |
---|
| 1013 | if (_excess[v] > 0 && _excess[v] <= delta) |
---|
| 1014 | _active_nodes.push_back(v); |
---|
[808] | 1015 | } |
---|
| 1016 | } |
---|
| 1017 | } |
---|
| 1018 | } |
---|
| 1019 | |
---|
[809] | 1020 | /// Execute the algorithm performing push and relabel operations |
---|
[810] | 1021 | void startPush() { |
---|
[808] | 1022 | // Paramters for heuristics |
---|
[809] | 1023 | const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
---|
| 1024 | const int BF_HEURISTIC_BOUND_FACTOR = 3; |
---|
[808] | 1025 | |
---|
[809] | 1026 | // Perform cost scaling phases |
---|
| 1027 | BoolVector hyper(_res_node_num, false); |
---|
[808] | 1028 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
| 1029 | 1 : _epsilon / _alpha ) |
---|
| 1030 | { |
---|
| 1031 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
---|
| 1032 | // to check if the current flow is optimal |
---|
| 1033 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
---|
[809] | 1034 | _arc_vec.clear(); |
---|
| 1035 | _cost_vec.clear(); |
---|
| 1036 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 1037 | if (_res_cap[j] > 0) { |
---|
| 1038 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
| 1039 | _cost_vec.push_back(_cost[j] + 1); |
---|
| 1040 | } |
---|
| 1041 | } |
---|
| 1042 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
| 1043 | |
---|
| 1044 | BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map); |
---|
[808] | 1045 | bf.init(0); |
---|
| 1046 | bool done = false; |
---|
[809] | 1047 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num)); |
---|
[808] | 1048 | for (int i = 0; i < K && !done; ++i) |
---|
| 1049 | done = bf.processNextWeakRound(); |
---|
| 1050 | if (done) break; |
---|
| 1051 | } |
---|
| 1052 | |
---|
| 1053 | // Saturate arcs not satisfying the optimality condition |
---|
[809] | 1054 | for (int a = 0; a != _res_arc_num; ++a) { |
---|
| 1055 | if (_res_cap[a] > 0 && |
---|
| 1056 | _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) { |
---|
| 1057 | Value delta = _res_cap[a]; |
---|
| 1058 | _excess[_source[a]] -= delta; |
---|
| 1059 | _excess[_target[a]] += delta; |
---|
| 1060 | _res_cap[a] = 0; |
---|
| 1061 | _res_cap[_reverse[a]] += delta; |
---|
[808] | 1062 | } |
---|
| 1063 | } |
---|
| 1064 | |
---|
| 1065 | // Find active nodes (i.e. nodes with positive excess) |
---|
[809] | 1066 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1067 | if (_excess[u] > 0) _active_nodes.push_back(u); |
---|
[808] | 1068 | } |
---|
| 1069 | |
---|
[809] | 1070 | // Initialize the next arcs |
---|
| 1071 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1072 | _next_out[u] = _first_out[u]; |
---|
[808] | 1073 | } |
---|
| 1074 | |
---|
| 1075 | // Perform push and relabel operations |
---|
[809] | 1076 | while (_active_nodes.size() > 0) { |
---|
| 1077 | LargeCost min_red_cost, rc; |
---|
| 1078 | Value delta; |
---|
| 1079 | int n, t, a, last_out = _res_arc_num; |
---|
| 1080 | |
---|
[808] | 1081 | // Select an active node (FIFO selection) |
---|
[809] | 1082 | next_node: |
---|
| 1083 | n = _active_nodes.front(); |
---|
| 1084 | last_out = _sum_supply < 0 ? |
---|
| 1085 | _first_out[n+1] : _first_out[n+1] - 1; |
---|
[808] | 1086 | |
---|
| 1087 | // Perform push operations if there are admissible arcs |
---|
[809] | 1088 | if (_excess[n] > 0) { |
---|
| 1089 | for (a = _next_out[n]; a != last_out; ++a) { |
---|
| 1090 | if (_res_cap[a] > 0 && |
---|
| 1091 | _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) { |
---|
| 1092 | delta = std::min(_res_cap[a], _excess[n]); |
---|
| 1093 | t = _target[a]; |
---|
[808] | 1094 | |
---|
| 1095 | // Push-look-ahead heuristic |
---|
[809] | 1096 | Value ahead = -_excess[t]; |
---|
| 1097 | int last_out_t = _sum_supply < 0 ? |
---|
| 1098 | _first_out[t+1] : _first_out[t+1] - 1; |
---|
| 1099 | for (int ta = _next_out[t]; ta != last_out_t; ++ta) { |
---|
| 1100 | if (_res_cap[ta] > 0 && |
---|
| 1101 | _cost[ta] + _pi[_source[ta]] - _pi[_target[ta]] < 0) |
---|
| 1102 | ahead += _res_cap[ta]; |
---|
| 1103 | if (ahead >= delta) break; |
---|
[808] | 1104 | } |
---|
| 1105 | if (ahead < 0) ahead = 0; |
---|
| 1106 | |
---|
| 1107 | // Push flow along the arc |
---|
| 1108 | if (ahead < delta) { |
---|
[809] | 1109 | _res_cap[a] -= ahead; |
---|
| 1110 | _res_cap[_reverse[a]] += ahead; |
---|
[808] | 1111 | _excess[n] -= ahead; |
---|
| 1112 | _excess[t] += ahead; |
---|
[809] | 1113 | _active_nodes.push_front(t); |
---|
[808] | 1114 | hyper[t] = true; |
---|
[809] | 1115 | _next_out[n] = a; |
---|
| 1116 | goto next_node; |
---|
[808] | 1117 | } else { |
---|
[809] | 1118 | _res_cap[a] -= delta; |
---|
| 1119 | _res_cap[_reverse[a]] += delta; |
---|
[808] | 1120 | _excess[n] -= delta; |
---|
| 1121 | _excess[t] += delta; |
---|
| 1122 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
[809] | 1123 | _active_nodes.push_back(t); |
---|
[808] | 1124 | } |
---|
| 1125 | |
---|
[809] | 1126 | if (_excess[n] == 0) { |
---|
| 1127 | _next_out[n] = a; |
---|
| 1128 | goto remove_nodes; |
---|
| 1129 | } |
---|
[808] | 1130 | } |
---|
| 1131 | } |
---|
[809] | 1132 | _next_out[n] = a; |
---|
[808] | 1133 | } |
---|
| 1134 | |
---|
| 1135 | // Relabel the node if it is still active (or hyper) |
---|
[809] | 1136 | if (_excess[n] > 0 || hyper[n]) { |
---|
| 1137 | min_red_cost = std::numeric_limits<LargeCost>::max() / 2; |
---|
| 1138 | for (int a = _first_out[n]; a != last_out; ++a) { |
---|
| 1139 | rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]]; |
---|
| 1140 | if (_res_cap[a] > 0 && rc < min_red_cost) { |
---|
| 1141 | min_red_cost = rc; |
---|
| 1142 | } |
---|
[808] | 1143 | } |
---|
[809] | 1144 | _pi[n] -= min_red_cost + _epsilon; |
---|
[808] | 1145 | hyper[n] = false; |
---|
| 1146 | |
---|
[809] | 1147 | // Reset the next arc |
---|
| 1148 | _next_out[n] = _first_out[n]; |
---|
[808] | 1149 | } |
---|
[809] | 1150 | |
---|
[808] | 1151 | // Remove nodes that are not active nor hyper |
---|
[809] | 1152 | remove_nodes: |
---|
| 1153 | while ( _active_nodes.size() > 0 && |
---|
| 1154 | _excess[_active_nodes.front()] <= 0 && |
---|
| 1155 | !hyper[_active_nodes.front()] ) { |
---|
| 1156 | _active_nodes.pop_front(); |
---|
[808] | 1157 | } |
---|
| 1158 | } |
---|
| 1159 | } |
---|
| 1160 | } |
---|
| 1161 | |
---|
| 1162 | }; //class CostScaling |
---|
| 1163 | |
---|
| 1164 | ///@} |
---|
| 1165 | |
---|
| 1166 | } //namespace lemon |
---|
| 1167 | |
---|
| 1168 | #endif //LEMON_COST_SCALING_H |
---|