[956] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[880] | 2 | * |
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[956] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[880] | 4 | * |
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[956] | 5 | * Copyright (C) 2003-2010 |
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[880] | 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_CYCLE_CANCELING_H |
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| 20 | #define LEMON_CYCLE_CANCELING_H |
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| 21 | |
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[881] | 22 | /// \ingroup min_cost_flow_algs |
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[880] | 23 | /// \file |
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[881] | 24 | /// \brief Cycle-canceling algorithms for finding a minimum cost flow. |
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[880] | 25 | |
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| 26 | #include <vector> |
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[881] | 27 | #include <limits> |
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| 28 | |
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| 29 | #include <lemon/core.h> |
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| 30 | #include <lemon/maps.h> |
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| 31 | #include <lemon/path.h> |
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| 32 | #include <lemon/math.h> |
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| 33 | #include <lemon/static_graph.h> |
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[880] | 34 | #include <lemon/adaptors.h> |
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| 35 | #include <lemon/circulation.h> |
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| 36 | #include <lemon/bellman_ford.h> |
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[942] | 37 | #include <lemon/howard_mmc.h> |
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[1179] | 38 | #include <lemon/hartmann_orlin_mmc.h> |
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[880] | 39 | |
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| 40 | namespace lemon { |
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| 41 | |
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[881] | 42 | /// \addtogroup min_cost_flow_algs |
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[880] | 43 | /// @{ |
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| 44 | |
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[881] | 45 | /// \brief Implementation of cycle-canceling algorithms for |
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| 46 | /// finding a \ref min_cost_flow "minimum cost flow". |
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[880] | 47 | /// |
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[881] | 48 | /// \ref CycleCanceling implements three different cycle-canceling |
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[882] | 49 | /// algorithms for finding a \ref min_cost_flow "minimum cost flow" |
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| 50 | /// \ref amo93networkflows, \ref klein67primal, |
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| 51 | /// \ref goldberg89cyclecanceling. |
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[1165] | 52 | /// The most efficent one is the \ref CANCEL_AND_TIGHTEN |
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| 53 | /// "Cancel-and-Tighten" algorithm, thus it is the default method. |
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| 54 | /// It runs in strongly polynomial time, but in practice, it is typically |
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| 55 | /// orders of magnitude slower than the scaling algorithms and |
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| 56 | /// \ref NetworkSimplex. |
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| 57 | /// (For more information, see \ref min_cost_flow_algs "the module page".) |
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[880] | 58 | /// |
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[881] | 59 | /// Most of the parameters of the problem (except for the digraph) |
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| 60 | /// can be given using separate functions, and the algorithm can be |
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| 61 | /// executed using the \ref run() function. If some parameters are not |
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| 62 | /// specified, then default values will be used. |
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[880] | 63 | /// |
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[881] | 64 | /// \tparam GR The digraph type the algorithm runs on. |
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| 65 | /// \tparam V The number type used for flow amounts, capacity bounds |
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| 66 | /// and supply values in the algorithm. By default, it is \c int. |
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| 67 | /// \tparam C The number type used for costs and potentials in the |
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| 68 | /// algorithm. By default, it is the same as \c V. |
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[880] | 69 | /// |
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[1025] | 70 | /// \warning Both \c V and \c C must be signed number types. |
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| 71 | /// \warning All input data (capacities, supply values, and costs) must |
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[881] | 72 | /// be integer. |
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[1023] | 73 | /// \warning This algorithm does not support negative costs for |
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| 74 | /// arcs having infinite upper bound. |
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[880] | 75 | /// |
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[881] | 76 | /// \note For more information about the three available methods, |
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| 77 | /// see \ref Method. |
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| 78 | #ifdef DOXYGEN |
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| 79 | template <typename GR, typename V, typename C> |
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| 80 | #else |
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| 81 | template <typename GR, typename V = int, typename C = V> |
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| 82 | #endif |
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[880] | 83 | class CycleCanceling |
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| 84 | { |
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[881] | 85 | public: |
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[880] | 86 | |
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[881] | 87 | /// The type of the digraph |
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| 88 | typedef GR Digraph; |
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| 89 | /// The type of the flow amounts, capacity bounds and supply values |
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| 90 | typedef V Value; |
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| 91 | /// The type of the arc costs |
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| 92 | typedef C Cost; |
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[880] | 93 | |
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| 94 | public: |
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| 95 | |
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[881] | 96 | /// \brief Problem type constants for the \c run() function. |
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| 97 | /// |
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| 98 | /// Enum type containing the problem type constants that can be |
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| 99 | /// returned by the \ref run() function of the algorithm. |
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| 100 | enum ProblemType { |
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| 101 | /// The problem has no feasible solution (flow). |
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| 102 | INFEASIBLE, |
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| 103 | /// The problem has optimal solution (i.e. it is feasible and |
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| 104 | /// bounded), and the algorithm has found optimal flow and node |
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| 105 | /// potentials (primal and dual solutions). |
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| 106 | OPTIMAL, |
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| 107 | /// The digraph contains an arc of negative cost and infinite |
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| 108 | /// upper bound. It means that the objective function is unbounded |
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| 109 | /// on that arc, however, note that it could actually be bounded |
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| 110 | /// over the feasible flows, but this algroithm cannot handle |
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| 111 | /// these cases. |
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| 112 | UNBOUNDED |
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| 113 | }; |
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| 114 | |
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| 115 | /// \brief Constants for selecting the used method. |
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| 116 | /// |
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| 117 | /// Enum type containing constants for selecting the used method |
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| 118 | /// for the \ref run() function. |
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| 119 | /// |
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| 120 | /// \ref CycleCanceling provides three different cycle-canceling |
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[1165] | 121 | /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel-and-Tighten" |
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[1023] | 122 | /// is used, which is by far the most efficient and the most robust. |
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[881] | 123 | /// However, the other methods can be selected using the \ref run() |
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| 124 | /// function with the proper parameter. |
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| 125 | enum Method { |
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| 126 | /// A simple cycle-canceling method, which uses the |
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[1165] | 127 | /// \ref BellmanFord "Bellman-Ford" algorithm for detecting negative |
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| 128 | /// cycles in the residual network. |
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| 129 | /// The number of Bellman-Ford iterations is bounded by a successively |
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| 130 | /// increased limit. |
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[881] | 131 | SIMPLE_CYCLE_CANCELING, |
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| 132 | /// The "Minimum Mean Cycle-Canceling" algorithm, which is a |
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[882] | 133 | /// well-known strongly polynomial method |
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| 134 | /// \ref goldberg89cyclecanceling. It improves along a |
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[881] | 135 | /// \ref min_mean_cycle "minimum mean cycle" in each iteration. |
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[1165] | 136 | /// Its running time complexity is O(n<sup>2</sup>e<sup>3</sup>log(n)). |
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[881] | 137 | MINIMUM_MEAN_CYCLE_CANCELING, |
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[1165] | 138 | /// The "Cancel-and-Tighten" algorithm, which can be viewed as an |
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[882] | 139 | /// improved version of the previous method |
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| 140 | /// \ref goldberg89cyclecanceling. |
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[881] | 141 | /// It is faster both in theory and in practice, its running time |
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[1165] | 142 | /// complexity is O(n<sup>2</sup>e<sup>2</sup>log(n)). |
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[881] | 143 | CANCEL_AND_TIGHTEN |
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| 144 | }; |
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[880] | 145 | |
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| 146 | private: |
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| 147 | |
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[881] | 148 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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[956] | 149 | |
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[881] | 150 | typedef std::vector<int> IntVector; |
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| 151 | typedef std::vector<double> DoubleVector; |
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| 152 | typedef std::vector<Value> ValueVector; |
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| 153 | typedef std::vector<Cost> CostVector; |
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[910] | 154 | typedef std::vector<char> BoolVector; |
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| 155 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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[880] | 156 | |
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[881] | 157 | private: |
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[956] | 158 | |
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[881] | 159 | template <typename KT, typename VT> |
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[886] | 160 | class StaticVectorMap { |
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[880] | 161 | public: |
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[881] | 162 | typedef KT Key; |
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| 163 | typedef VT Value; |
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[956] | 164 | |
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[886] | 165 | StaticVectorMap(std::vector<Value>& v) : _v(v) {} |
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[956] | 166 | |
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[881] | 167 | const Value& operator[](const Key& key) const { |
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| 168 | return _v[StaticDigraph::id(key)]; |
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[880] | 169 | } |
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| 170 | |
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[881] | 171 | Value& operator[](const Key& key) { |
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| 172 | return _v[StaticDigraph::id(key)]; |
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| 173 | } |
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[956] | 174 | |
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[881] | 175 | void set(const Key& key, const Value& val) { |
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| 176 | _v[StaticDigraph::id(key)] = val; |
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| 177 | } |
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| 178 | |
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| 179 | private: |
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| 180 | std::vector<Value>& _v; |
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| 181 | }; |
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| 182 | |
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[886] | 183 | typedef StaticVectorMap<StaticDigraph::Node, Cost> CostNodeMap; |
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| 184 | typedef StaticVectorMap<StaticDigraph::Arc, Cost> CostArcMap; |
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[880] | 185 | |
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| 186 | private: |
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| 187 | |
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| 188 | |
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[881] | 189 | // Data related to the underlying digraph |
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| 190 | const GR &_graph; |
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| 191 | int _node_num; |
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| 192 | int _arc_num; |
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| 193 | int _res_node_num; |
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| 194 | int _res_arc_num; |
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| 195 | int _root; |
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[880] | 196 | |
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[881] | 197 | // Parameters of the problem |
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| 198 | bool _have_lower; |
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| 199 | Value _sum_supply; |
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[880] | 200 | |
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[881] | 201 | // Data structures for storing the digraph |
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| 202 | IntNodeMap _node_id; |
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| 203 | IntArcMap _arc_idf; |
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| 204 | IntArcMap _arc_idb; |
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| 205 | IntVector _first_out; |
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[910] | 206 | BoolVector _forward; |
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[881] | 207 | IntVector _source; |
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| 208 | IntVector _target; |
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| 209 | IntVector _reverse; |
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[880] | 210 | |
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[881] | 211 | // Node and arc data |
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| 212 | ValueVector _lower; |
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| 213 | ValueVector _upper; |
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| 214 | CostVector _cost; |
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| 215 | ValueVector _supply; |
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| 216 | |
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| 217 | ValueVector _res_cap; |
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| 218 | CostVector _pi; |
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| 219 | |
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| 220 | // Data for a StaticDigraph structure |
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| 221 | typedef std::pair<int, int> IntPair; |
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| 222 | StaticDigraph _sgr; |
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| 223 | std::vector<IntPair> _arc_vec; |
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| 224 | std::vector<Cost> _cost_vec; |
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| 225 | IntVector _id_vec; |
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| 226 | CostArcMap _cost_map; |
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| 227 | CostNodeMap _pi_map; |
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[956] | 228 | |
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[881] | 229 | public: |
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[956] | 230 | |
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[881] | 231 | /// \brief Constant for infinite upper bounds (capacities). |
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| 232 | /// |
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| 233 | /// Constant for infinite upper bounds (capacities). |
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| 234 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 235 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 236 | const Value INF; |
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[880] | 237 | |
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| 238 | public: |
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| 239 | |
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[881] | 240 | /// \brief Constructor. |
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[880] | 241 | /// |
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[881] | 242 | /// The constructor of the class. |
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[880] | 243 | /// |
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[881] | 244 | /// \param graph The digraph the algorithm runs on. |
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| 245 | CycleCanceling(const GR& graph) : |
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| 246 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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| 247 | _cost_map(_cost_vec), _pi_map(_pi), |
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| 248 | INF(std::numeric_limits<Value>::has_infinity ? |
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| 249 | std::numeric_limits<Value>::infinity() : |
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| 250 | std::numeric_limits<Value>::max()) |
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[880] | 251 | { |
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[881] | 252 | // Check the number types |
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| 253 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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| 254 | "The flow type of CycleCanceling must be signed"); |
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| 255 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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| 256 | "The cost type of CycleCanceling must be signed"); |
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| 257 | |
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[898] | 258 | // Reset data structures |
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[881] | 259 | reset(); |
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[880] | 260 | } |
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| 261 | |
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[881] | 262 | /// \name Parameters |
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| 263 | /// The parameters of the algorithm can be specified using these |
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| 264 | /// functions. |
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| 265 | |
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| 266 | /// @{ |
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| 267 | |
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| 268 | /// \brief Set the lower bounds on the arcs. |
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[880] | 269 | /// |
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[881] | 270 | /// This function sets the lower bounds on the arcs. |
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| 271 | /// If it is not used before calling \ref run(), the lower bounds |
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| 272 | /// will be set to zero on all arcs. |
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[880] | 273 | /// |
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[881] | 274 | /// \param map An arc map storing the lower bounds. |
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| 275 | /// Its \c Value type must be convertible to the \c Value type |
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| 276 | /// of the algorithm. |
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| 277 | /// |
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| 278 | /// \return <tt>(*this)</tt> |
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| 279 | template <typename LowerMap> |
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| 280 | CycleCanceling& lowerMap(const LowerMap& map) { |
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| 281 | _have_lower = true; |
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| 282 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 283 | _lower[_arc_idf[a]] = map[a]; |
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| 284 | _lower[_arc_idb[a]] = map[a]; |
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[880] | 285 | } |
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| 286 | return *this; |
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| 287 | } |
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| 288 | |
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[881] | 289 | /// \brief Set the upper bounds (capacities) on the arcs. |
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[880] | 290 | /// |
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[881] | 291 | /// This function sets the upper bounds (capacities) on the arcs. |
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| 292 | /// If it is not used before calling \ref run(), the upper bounds |
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| 293 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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| 294 | /// unbounded from above). |
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[880] | 295 | /// |
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[881] | 296 | /// \param map An arc map storing the upper bounds. |
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| 297 | /// Its \c Value type must be convertible to the \c Value type |
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| 298 | /// of the algorithm. |
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| 299 | /// |
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| 300 | /// \return <tt>(*this)</tt> |
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| 301 | template<typename UpperMap> |
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| 302 | CycleCanceling& upperMap(const UpperMap& map) { |
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| 303 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 304 | _upper[_arc_idf[a]] = map[a]; |
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[880] | 305 | } |
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| 306 | return *this; |
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| 307 | } |
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| 308 | |
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[881] | 309 | /// \brief Set the costs of the arcs. |
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| 310 | /// |
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| 311 | /// This function sets the costs of the arcs. |
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| 312 | /// If it is not used before calling \ref run(), the costs |
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| 313 | /// will be set to \c 1 on all arcs. |
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| 314 | /// |
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| 315 | /// \param map An arc map storing the costs. |
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| 316 | /// Its \c Value type must be convertible to the \c Cost type |
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| 317 | /// of the algorithm. |
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| 318 | /// |
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| 319 | /// \return <tt>(*this)</tt> |
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| 320 | template<typename CostMap> |
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| 321 | CycleCanceling& costMap(const CostMap& map) { |
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| 322 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 323 | _cost[_arc_idf[a]] = map[a]; |
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| 324 | _cost[_arc_idb[a]] = -map[a]; |
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| 325 | } |
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| 326 | return *this; |
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| 327 | } |
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| 328 | |
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| 329 | /// \brief Set the supply values of the nodes. |
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| 330 | /// |
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| 331 | /// This function sets the supply values of the nodes. |
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| 332 | /// If neither this function nor \ref stSupply() is used before |
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| 333 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 334 | /// |
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| 335 | /// \param map A node map storing the supply values. |
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| 336 | /// Its \c Value type must be convertible to the \c Value type |
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| 337 | /// of the algorithm. |
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| 338 | /// |
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| 339 | /// \return <tt>(*this)</tt> |
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| 340 | template<typename SupplyMap> |
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| 341 | CycleCanceling& supplyMap(const SupplyMap& map) { |
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| 342 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 343 | _supply[_node_id[n]] = map[n]; |
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| 344 | } |
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| 345 | return *this; |
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| 346 | } |
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| 347 | |
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| 348 | /// \brief Set single source and target nodes and a supply value. |
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| 349 | /// |
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| 350 | /// This function sets a single source node and a single target node |
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| 351 | /// and the required flow value. |
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| 352 | /// If neither this function nor \ref supplyMap() is used before |
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| 353 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 354 | /// |
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| 355 | /// Using this function has the same effect as using \ref supplyMap() |
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[1023] | 356 | /// with a map in which \c k is assigned to \c s, \c -k is |
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[881] | 357 | /// assigned to \c t and all other nodes have zero supply value. |
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| 358 | /// |
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| 359 | /// \param s The source node. |
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| 360 | /// \param t The target node. |
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| 361 | /// \param k The required amount of flow from node \c s to node \c t |
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| 362 | /// (i.e. the supply of \c s and the demand of \c t). |
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| 363 | /// |
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| 364 | /// \return <tt>(*this)</tt> |
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| 365 | CycleCanceling& stSupply(const Node& s, const Node& t, Value k) { |
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| 366 | for (int i = 0; i != _res_node_num; ++i) { |
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| 367 | _supply[i] = 0; |
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| 368 | } |
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| 369 | _supply[_node_id[s]] = k; |
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| 370 | _supply[_node_id[t]] = -k; |
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| 371 | return *this; |
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| 372 | } |
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[956] | 373 | |
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[881] | 374 | /// @} |
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| 375 | |
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[880] | 376 | /// \name Execution control |
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[881] | 377 | /// The algorithm can be executed using \ref run(). |
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[880] | 378 | |
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| 379 | /// @{ |
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| 380 | |
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| 381 | /// \brief Run the algorithm. |
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| 382 | /// |
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[881] | 383 | /// This function runs the algorithm. |
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| 384 | /// The paramters can be specified using functions \ref lowerMap(), |
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| 385 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 386 | /// For example, |
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| 387 | /// \code |
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| 388 | /// CycleCanceling<ListDigraph> cc(graph); |
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| 389 | /// cc.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 390 | /// .supplyMap(sup).run(); |
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| 391 | /// \endcode |
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[880] | 392 | /// |
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[898] | 393 | /// This function can be called more than once. All the given parameters |
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| 394 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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| 395 | /// is used, thus only the modified parameters have to be set again. |
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| 396 | /// If the underlying digraph was also modified after the construction |
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| 397 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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| 398 | /// function must be called. |
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[880] | 399 | /// |
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[881] | 400 | /// \param method The cycle-canceling method that will be used. |
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| 401 | /// For more information, see \ref Method. |
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| 402 | /// |
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| 403 | /// \return \c INFEASIBLE if no feasible flow exists, |
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| 404 | /// \n \c OPTIMAL if the problem has optimal solution |
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| 405 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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| 406 | /// optimal flow and node potentials (primal and dual solutions), |
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| 407 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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| 408 | /// and infinite upper bound. It means that the objective function |
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| 409 | /// is unbounded on that arc, however, note that it could actually be |
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| 410 | /// bounded over the feasible flows, but this algroithm cannot handle |
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| 411 | /// these cases. |
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| 412 | /// |
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| 413 | /// \see ProblemType, Method |
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[898] | 414 | /// \see resetParams(), reset() |
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[881] | 415 | ProblemType run(Method method = CANCEL_AND_TIGHTEN) { |
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| 416 | ProblemType pt = init(); |
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| 417 | if (pt != OPTIMAL) return pt; |
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| 418 | start(method); |
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| 419 | return OPTIMAL; |
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| 420 | } |
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| 421 | |
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| 422 | /// \brief Reset all the parameters that have been given before. |
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| 423 | /// |
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| 424 | /// This function resets all the paramaters that have been given |
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| 425 | /// before using functions \ref lowerMap(), \ref upperMap(), |
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| 426 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 427 | /// |
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[898] | 428 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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| 429 | /// parameters are kept for the next \ref run() call, unless |
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| 430 | /// \ref resetParams() or \ref reset() is used. |
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| 431 | /// If the underlying digraph was also modified after the construction |
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| 432 | /// of the class or the last \ref reset() call, then the \ref reset() |
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| 433 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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[881] | 434 | /// |
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| 435 | /// For example, |
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| 436 | /// \code |
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| 437 | /// CycleCanceling<ListDigraph> cs(graph); |
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| 438 | /// |
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| 439 | /// // First run |
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| 440 | /// cc.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 441 | /// .supplyMap(sup).run(); |
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| 442 | /// |
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[898] | 443 | /// // Run again with modified cost map (resetParams() is not called, |
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[881] | 444 | /// // so only the cost map have to be set again) |
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| 445 | /// cost[e] += 100; |
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| 446 | /// cc.costMap(cost).run(); |
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| 447 | /// |
---|
[898] | 448 | /// // Run again from scratch using resetParams() |
---|
[881] | 449 | /// // (the lower bounds will be set to zero on all arcs) |
---|
[898] | 450 | /// cc.resetParams(); |
---|
[881] | 451 | /// cc.upperMap(capacity).costMap(cost) |
---|
| 452 | /// .supplyMap(sup).run(); |
---|
| 453 | /// \endcode |
---|
| 454 | /// |
---|
| 455 | /// \return <tt>(*this)</tt> |
---|
[898] | 456 | /// |
---|
| 457 | /// \see reset(), run() |
---|
| 458 | CycleCanceling& resetParams() { |
---|
[881] | 459 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 460 | _supply[i] = 0; |
---|
| 461 | } |
---|
| 462 | int limit = _first_out[_root]; |
---|
| 463 | for (int j = 0; j != limit; ++j) { |
---|
| 464 | _lower[j] = 0; |
---|
| 465 | _upper[j] = INF; |
---|
| 466 | _cost[j] = _forward[j] ? 1 : -1; |
---|
| 467 | } |
---|
| 468 | for (int j = limit; j != _res_arc_num; ++j) { |
---|
| 469 | _lower[j] = 0; |
---|
| 470 | _upper[j] = INF; |
---|
| 471 | _cost[j] = 0; |
---|
| 472 | _cost[_reverse[j]] = 0; |
---|
[956] | 473 | } |
---|
[881] | 474 | _have_lower = false; |
---|
| 475 | return *this; |
---|
[880] | 476 | } |
---|
| 477 | |
---|
[898] | 478 | /// \brief Reset the internal data structures and all the parameters |
---|
| 479 | /// that have been given before. |
---|
| 480 | /// |
---|
| 481 | /// This function resets the internal data structures and all the |
---|
| 482 | /// paramaters that have been given before using functions \ref lowerMap(), |
---|
| 483 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
| 484 | /// |
---|
| 485 | /// It is useful for multiple \ref run() calls. Basically, all the given |
---|
| 486 | /// parameters are kept for the next \ref run() call, unless |
---|
| 487 | /// \ref resetParams() or \ref reset() is used. |
---|
| 488 | /// If the underlying digraph was also modified after the construction |
---|
| 489 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
| 490 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
| 491 | /// |
---|
| 492 | /// See \ref resetParams() for examples. |
---|
| 493 | /// |
---|
| 494 | /// \return <tt>(*this)</tt> |
---|
| 495 | /// |
---|
| 496 | /// \see resetParams(), run() |
---|
| 497 | CycleCanceling& reset() { |
---|
| 498 | // Resize vectors |
---|
| 499 | _node_num = countNodes(_graph); |
---|
| 500 | _arc_num = countArcs(_graph); |
---|
| 501 | _res_node_num = _node_num + 1; |
---|
| 502 | _res_arc_num = 2 * (_arc_num + _node_num); |
---|
| 503 | _root = _node_num; |
---|
| 504 | |
---|
| 505 | _first_out.resize(_res_node_num + 1); |
---|
| 506 | _forward.resize(_res_arc_num); |
---|
| 507 | _source.resize(_res_arc_num); |
---|
| 508 | _target.resize(_res_arc_num); |
---|
| 509 | _reverse.resize(_res_arc_num); |
---|
| 510 | |
---|
| 511 | _lower.resize(_res_arc_num); |
---|
| 512 | _upper.resize(_res_arc_num); |
---|
| 513 | _cost.resize(_res_arc_num); |
---|
| 514 | _supply.resize(_res_node_num); |
---|
[956] | 515 | |
---|
[898] | 516 | _res_cap.resize(_res_arc_num); |
---|
| 517 | _pi.resize(_res_node_num); |
---|
| 518 | |
---|
| 519 | _arc_vec.reserve(_res_arc_num); |
---|
| 520 | _cost_vec.reserve(_res_arc_num); |
---|
| 521 | _id_vec.reserve(_res_arc_num); |
---|
| 522 | |
---|
| 523 | // Copy the graph |
---|
| 524 | int i = 0, j = 0, k = 2 * _arc_num + _node_num; |
---|
| 525 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 526 | _node_id[n] = i; |
---|
| 527 | } |
---|
| 528 | i = 0; |
---|
| 529 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 530 | _first_out[i] = j; |
---|
| 531 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
| 532 | _arc_idf[a] = j; |
---|
| 533 | _forward[j] = true; |
---|
| 534 | _source[j] = i; |
---|
| 535 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
| 536 | } |
---|
| 537 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
| 538 | _arc_idb[a] = j; |
---|
| 539 | _forward[j] = false; |
---|
| 540 | _source[j] = i; |
---|
| 541 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
| 542 | } |
---|
| 543 | _forward[j] = false; |
---|
| 544 | _source[j] = i; |
---|
| 545 | _target[j] = _root; |
---|
| 546 | _reverse[j] = k; |
---|
| 547 | _forward[k] = true; |
---|
| 548 | _source[k] = _root; |
---|
| 549 | _target[k] = i; |
---|
| 550 | _reverse[k] = j; |
---|
| 551 | ++j; ++k; |
---|
| 552 | } |
---|
| 553 | _first_out[i] = j; |
---|
| 554 | _first_out[_res_node_num] = k; |
---|
| 555 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 556 | int fi = _arc_idf[a]; |
---|
| 557 | int bi = _arc_idb[a]; |
---|
| 558 | _reverse[fi] = bi; |
---|
| 559 | _reverse[bi] = fi; |
---|
| 560 | } |
---|
[956] | 561 | |
---|
[898] | 562 | // Reset parameters |
---|
| 563 | resetParams(); |
---|
| 564 | return *this; |
---|
| 565 | } |
---|
| 566 | |
---|
[880] | 567 | /// @} |
---|
| 568 | |
---|
| 569 | /// \name Query Functions |
---|
[881] | 570 | /// The results of the algorithm can be obtained using these |
---|
[880] | 571 | /// functions.\n |
---|
[881] | 572 | /// The \ref run() function must be called before using them. |
---|
[880] | 573 | |
---|
| 574 | /// @{ |
---|
| 575 | |
---|
[881] | 576 | /// \brief Return the total cost of the found flow. |
---|
[880] | 577 | /// |
---|
[881] | 578 | /// This function returns the total cost of the found flow. |
---|
| 579 | /// Its complexity is O(e). |
---|
| 580 | /// |
---|
| 581 | /// \note The return type of the function can be specified as a |
---|
| 582 | /// template parameter. For example, |
---|
| 583 | /// \code |
---|
| 584 | /// cc.totalCost<double>(); |
---|
| 585 | /// \endcode |
---|
| 586 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
| 587 | /// type of the algorithm, which is the default return type of the |
---|
| 588 | /// function. |
---|
[880] | 589 | /// |
---|
| 590 | /// \pre \ref run() must be called before using this function. |
---|
[881] | 591 | template <typename Number> |
---|
| 592 | Number totalCost() const { |
---|
| 593 | Number c = 0; |
---|
| 594 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 595 | int i = _arc_idb[a]; |
---|
| 596 | c += static_cast<Number>(_res_cap[i]) * |
---|
| 597 | (-static_cast<Number>(_cost[i])); |
---|
| 598 | } |
---|
| 599 | return c; |
---|
[880] | 600 | } |
---|
| 601 | |
---|
[881] | 602 | #ifndef DOXYGEN |
---|
| 603 | Cost totalCost() const { |
---|
| 604 | return totalCost<Cost>(); |
---|
[880] | 605 | } |
---|
[881] | 606 | #endif |
---|
[880] | 607 | |
---|
| 608 | /// \brief Return the flow on the given arc. |
---|
| 609 | /// |
---|
[881] | 610 | /// This function returns the flow on the given arc. |
---|
[880] | 611 | /// |
---|
| 612 | /// \pre \ref run() must be called before using this function. |
---|
[881] | 613 | Value flow(const Arc& a) const { |
---|
| 614 | return _res_cap[_arc_idb[a]]; |
---|
[880] | 615 | } |
---|
| 616 | |
---|
[1165] | 617 | /// \brief Copy the flow values (the primal solution) into the |
---|
| 618 | /// given map. |
---|
[880] | 619 | /// |
---|
[881] | 620 | /// This function copies the flow value on each arc into the given |
---|
| 621 | /// map. The \c Value type of the algorithm must be convertible to |
---|
| 622 | /// the \c Value type of the map. |
---|
[880] | 623 | /// |
---|
| 624 | /// \pre \ref run() must be called before using this function. |
---|
[881] | 625 | template <typename FlowMap> |
---|
| 626 | void flowMap(FlowMap &map) const { |
---|
| 627 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 628 | map.set(a, _res_cap[_arc_idb[a]]); |
---|
| 629 | } |
---|
[880] | 630 | } |
---|
| 631 | |
---|
[881] | 632 | /// \brief Return the potential (dual value) of the given node. |
---|
[880] | 633 | /// |
---|
[881] | 634 | /// This function returns the potential (dual value) of the |
---|
| 635 | /// given node. |
---|
[880] | 636 | /// |
---|
| 637 | /// \pre \ref run() must be called before using this function. |
---|
[881] | 638 | Cost potential(const Node& n) const { |
---|
| 639 | return static_cast<Cost>(_pi[_node_id[n]]); |
---|
| 640 | } |
---|
| 641 | |
---|
[1165] | 642 | /// \brief Copy the potential values (the dual solution) into the |
---|
| 643 | /// given map. |
---|
[881] | 644 | /// |
---|
| 645 | /// This function copies the potential (dual value) of each node |
---|
| 646 | /// into the given map. |
---|
| 647 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 648 | /// \c Value type of the map. |
---|
| 649 | /// |
---|
| 650 | /// \pre \ref run() must be called before using this function. |
---|
| 651 | template <typename PotentialMap> |
---|
| 652 | void potentialMap(PotentialMap &map) const { |
---|
| 653 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 654 | map.set(n, static_cast<Cost>(_pi[_node_id[n]])); |
---|
| 655 | } |
---|
[880] | 656 | } |
---|
| 657 | |
---|
| 658 | /// @} |
---|
| 659 | |
---|
| 660 | private: |
---|
| 661 | |
---|
[881] | 662 | // Initialize the algorithm |
---|
| 663 | ProblemType init() { |
---|
| 664 | if (_res_node_num <= 1) return INFEASIBLE; |
---|
[880] | 665 | |
---|
[881] | 666 | // Check the sum of supply values |
---|
| 667 | _sum_supply = 0; |
---|
| 668 | for (int i = 0; i != _root; ++i) { |
---|
| 669 | _sum_supply += _supply[i]; |
---|
[880] | 670 | } |
---|
[881] | 671 | if (_sum_supply > 0) return INFEASIBLE; |
---|
[956] | 672 | |
---|
[881] | 673 | |
---|
| 674 | // Initialize vectors |
---|
| 675 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 676 | _pi[i] = 0; |
---|
| 677 | } |
---|
| 678 | ValueVector excess(_supply); |
---|
[956] | 679 | |
---|
[881] | 680 | // Remove infinite upper bounds and check negative arcs |
---|
| 681 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
| 682 | int last_out; |
---|
| 683 | if (_have_lower) { |
---|
| 684 | for (int i = 0; i != _root; ++i) { |
---|
| 685 | last_out = _first_out[i+1]; |
---|
| 686 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 687 | if (_forward[j]) { |
---|
| 688 | Value c = _cost[j] < 0 ? _upper[j] : _lower[j]; |
---|
| 689 | if (c >= MAX) return UNBOUNDED; |
---|
| 690 | excess[i] -= c; |
---|
| 691 | excess[_target[j]] += c; |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | } |
---|
| 695 | } else { |
---|
| 696 | for (int i = 0; i != _root; ++i) { |
---|
| 697 | last_out = _first_out[i+1]; |
---|
| 698 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 699 | if (_forward[j] && _cost[j] < 0) { |
---|
| 700 | Value c = _upper[j]; |
---|
| 701 | if (c >= MAX) return UNBOUNDED; |
---|
| 702 | excess[i] -= c; |
---|
| 703 | excess[_target[j]] += c; |
---|
| 704 | } |
---|
| 705 | } |
---|
| 706 | } |
---|
| 707 | } |
---|
| 708 | Value ex, max_cap = 0; |
---|
| 709 | for (int i = 0; i != _res_node_num; ++i) { |
---|
| 710 | ex = excess[i]; |
---|
| 711 | if (ex < 0) max_cap -= ex; |
---|
| 712 | } |
---|
| 713 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 714 | if (_upper[j] >= MAX) _upper[j] = max_cap; |
---|
[880] | 715 | } |
---|
| 716 | |
---|
[881] | 717 | // Initialize maps for Circulation and remove non-zero lower bounds |
---|
| 718 | ConstMap<Arc, Value> low(0); |
---|
| 719 | typedef typename Digraph::template ArcMap<Value> ValueArcMap; |
---|
| 720 | typedef typename Digraph::template NodeMap<Value> ValueNodeMap; |
---|
| 721 | ValueArcMap cap(_graph), flow(_graph); |
---|
| 722 | ValueNodeMap sup(_graph); |
---|
| 723 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 724 | sup[n] = _supply[_node_id[n]]; |
---|
| 725 | } |
---|
| 726 | if (_have_lower) { |
---|
| 727 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 728 | int j = _arc_idf[a]; |
---|
| 729 | Value c = _lower[j]; |
---|
| 730 | cap[a] = _upper[j] - c; |
---|
| 731 | sup[_graph.source(a)] -= c; |
---|
| 732 | sup[_graph.target(a)] += c; |
---|
| 733 | } |
---|
| 734 | } else { |
---|
| 735 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 736 | cap[a] = _upper[_arc_idf[a]]; |
---|
| 737 | } |
---|
| 738 | } |
---|
[880] | 739 | |
---|
[881] | 740 | // Find a feasible flow using Circulation |
---|
| 741 | Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> |
---|
| 742 | circ(_graph, low, cap, sup); |
---|
| 743 | if (!circ.flowMap(flow).run()) return INFEASIBLE; |
---|
| 744 | |
---|
| 745 | // Set residual capacities and handle GEQ supply type |
---|
| 746 | if (_sum_supply < 0) { |
---|
| 747 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 748 | Value fa = flow[a]; |
---|
| 749 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
| 750 | _res_cap[_arc_idb[a]] = fa; |
---|
| 751 | sup[_graph.source(a)] -= fa; |
---|
| 752 | sup[_graph.target(a)] += fa; |
---|
| 753 | } |
---|
| 754 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 755 | excess[_node_id[n]] = sup[n]; |
---|
| 756 | } |
---|
| 757 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
| 758 | int u = _target[a]; |
---|
| 759 | int ra = _reverse[a]; |
---|
| 760 | _res_cap[a] = -_sum_supply + 1; |
---|
| 761 | _res_cap[ra] = -excess[u]; |
---|
| 762 | _cost[a] = 0; |
---|
| 763 | _cost[ra] = 0; |
---|
| 764 | } |
---|
| 765 | } else { |
---|
| 766 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 767 | Value fa = flow[a]; |
---|
| 768 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
| 769 | _res_cap[_arc_idb[a]] = fa; |
---|
| 770 | } |
---|
| 771 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
| 772 | int ra = _reverse[a]; |
---|
| 773 | _res_cap[a] = 1; |
---|
| 774 | _res_cap[ra] = 0; |
---|
| 775 | _cost[a] = 0; |
---|
| 776 | _cost[ra] = 0; |
---|
| 777 | } |
---|
| 778 | } |
---|
[956] | 779 | |
---|
[881] | 780 | return OPTIMAL; |
---|
| 781 | } |
---|
[956] | 782 | |
---|
[881] | 783 | // Build a StaticDigraph structure containing the current |
---|
| 784 | // residual network |
---|
| 785 | void buildResidualNetwork() { |
---|
| 786 | _arc_vec.clear(); |
---|
| 787 | _cost_vec.clear(); |
---|
| 788 | _id_vec.clear(); |
---|
| 789 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 790 | if (_res_cap[j] > 0) { |
---|
| 791 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
| 792 | _cost_vec.push_back(_cost[j]); |
---|
| 793 | _id_vec.push_back(j); |
---|
| 794 | } |
---|
| 795 | } |
---|
| 796 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
[880] | 797 | } |
---|
| 798 | |
---|
[881] | 799 | // Execute the algorithm and transform the results |
---|
| 800 | void start(Method method) { |
---|
| 801 | // Execute the algorithm |
---|
| 802 | switch (method) { |
---|
| 803 | case SIMPLE_CYCLE_CANCELING: |
---|
| 804 | startSimpleCycleCanceling(); |
---|
| 805 | break; |
---|
| 806 | case MINIMUM_MEAN_CYCLE_CANCELING: |
---|
| 807 | startMinMeanCycleCanceling(); |
---|
| 808 | break; |
---|
| 809 | case CANCEL_AND_TIGHTEN: |
---|
| 810 | startCancelAndTighten(); |
---|
| 811 | break; |
---|
| 812 | } |
---|
[880] | 813 | |
---|
[881] | 814 | // Compute node potentials |
---|
| 815 | if (method != SIMPLE_CYCLE_CANCELING) { |
---|
| 816 | buildResidualNetwork(); |
---|
| 817 | typename BellmanFord<StaticDigraph, CostArcMap> |
---|
| 818 | ::template SetDistMap<CostNodeMap>::Create bf(_sgr, _cost_map); |
---|
| 819 | bf.distMap(_pi_map); |
---|
| 820 | bf.init(0); |
---|
| 821 | bf.start(); |
---|
[880] | 822 | } |
---|
[881] | 823 | |
---|
| 824 | // Handle non-zero lower bounds |
---|
| 825 | if (_have_lower) { |
---|
| 826 | int limit = _first_out[_root]; |
---|
| 827 | for (int j = 0; j != limit; ++j) { |
---|
| 828 | if (!_forward[j]) _res_cap[j] += _lower[j]; |
---|
| 829 | } |
---|
| 830 | } |
---|
[880] | 831 | } |
---|
| 832 | |
---|
[881] | 833 | // Execute the "Simple Cycle Canceling" method |
---|
| 834 | void startSimpleCycleCanceling() { |
---|
| 835 | // Constants for computing the iteration limits |
---|
| 836 | const int BF_FIRST_LIMIT = 2; |
---|
| 837 | const double BF_LIMIT_FACTOR = 1.5; |
---|
[956] | 838 | |
---|
[886] | 839 | typedef StaticVectorMap<StaticDigraph::Arc, Value> FilterMap; |
---|
[881] | 840 | typedef FilterArcs<StaticDigraph, FilterMap> ResDigraph; |
---|
[886] | 841 | typedef StaticVectorMap<StaticDigraph::Node, StaticDigraph::Arc> PredMap; |
---|
[881] | 842 | typedef typename BellmanFord<ResDigraph, CostArcMap> |
---|
| 843 | ::template SetDistMap<CostNodeMap> |
---|
| 844 | ::template SetPredMap<PredMap>::Create BF; |
---|
[956] | 845 | |
---|
[881] | 846 | // Build the residual network |
---|
| 847 | _arc_vec.clear(); |
---|
| 848 | _cost_vec.clear(); |
---|
| 849 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 850 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
| 851 | _cost_vec.push_back(_cost[j]); |
---|
| 852 | } |
---|
| 853 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
| 854 | |
---|
| 855 | FilterMap filter_map(_res_cap); |
---|
| 856 | ResDigraph rgr(_sgr, filter_map); |
---|
| 857 | std::vector<int> cycle; |
---|
| 858 | std::vector<StaticDigraph::Arc> pred(_res_arc_num); |
---|
| 859 | PredMap pred_map(pred); |
---|
| 860 | BF bf(rgr, _cost_map); |
---|
| 861 | bf.distMap(_pi_map).predMap(pred_map); |
---|
[880] | 862 | |
---|
| 863 | int length_bound = BF_FIRST_LIMIT; |
---|
| 864 | bool optimal = false; |
---|
| 865 | while (!optimal) { |
---|
| 866 | bf.init(0); |
---|
| 867 | int iter_num = 0; |
---|
| 868 | bool cycle_found = false; |
---|
| 869 | while (!cycle_found) { |
---|
[881] | 870 | // Perform some iterations of the Bellman-Ford algorithm |
---|
| 871 | int curr_iter_num = iter_num + length_bound <= _node_num ? |
---|
| 872 | length_bound : _node_num - iter_num; |
---|
[880] | 873 | iter_num += curr_iter_num; |
---|
| 874 | int real_iter_num = curr_iter_num; |
---|
| 875 | for (int i = 0; i < curr_iter_num; ++i) { |
---|
| 876 | if (bf.processNextWeakRound()) { |
---|
| 877 | real_iter_num = i; |
---|
| 878 | break; |
---|
| 879 | } |
---|
| 880 | } |
---|
| 881 | if (real_iter_num < curr_iter_num) { |
---|
| 882 | // Optimal flow is found |
---|
| 883 | optimal = true; |
---|
| 884 | break; |
---|
| 885 | } else { |
---|
[881] | 886 | // Search for node disjoint negative cycles |
---|
| 887 | std::vector<int> state(_res_node_num, 0); |
---|
[880] | 888 | int id = 0; |
---|
[881] | 889 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 890 | if (state[u] != 0) continue; |
---|
| 891 | ++id; |
---|
| 892 | int v = u; |
---|
| 893 | for (; v != -1 && state[v] == 0; v = pred[v] == INVALID ? |
---|
| 894 | -1 : rgr.id(rgr.source(pred[v]))) { |
---|
| 895 | state[v] = id; |
---|
[880] | 896 | } |
---|
[881] | 897 | if (v != -1 && state[v] == id) { |
---|
| 898 | // A negative cycle is found |
---|
[880] | 899 | cycle_found = true; |
---|
| 900 | cycle.clear(); |
---|
[881] | 901 | StaticDigraph::Arc a = pred[v]; |
---|
| 902 | Value d, delta = _res_cap[rgr.id(a)]; |
---|
| 903 | cycle.push_back(rgr.id(a)); |
---|
| 904 | while (rgr.id(rgr.source(a)) != v) { |
---|
| 905 | a = pred_map[rgr.source(a)]; |
---|
| 906 | d = _res_cap[rgr.id(a)]; |
---|
| 907 | if (d < delta) delta = d; |
---|
| 908 | cycle.push_back(rgr.id(a)); |
---|
[880] | 909 | } |
---|
| 910 | |
---|
[881] | 911 | // Augment along the cycle |
---|
| 912 | for (int i = 0; i < int(cycle.size()); ++i) { |
---|
| 913 | int j = cycle[i]; |
---|
| 914 | _res_cap[j] -= delta; |
---|
| 915 | _res_cap[_reverse[j]] += delta; |
---|
| 916 | } |
---|
[880] | 917 | } |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | |
---|
[881] | 921 | // Increase iteration limit if no cycle is found |
---|
| 922 | if (!cycle_found) { |
---|
| 923 | length_bound = static_cast<int>(length_bound * BF_LIMIT_FACTOR); |
---|
| 924 | } |
---|
[880] | 925 | } |
---|
| 926 | } |
---|
| 927 | } |
---|
| 928 | |
---|
[881] | 929 | // Execute the "Minimum Mean Cycle Canceling" method |
---|
| 930 | void startMinMeanCycleCanceling() { |
---|
[1179] | 931 | typedef Path<StaticDigraph> SPath; |
---|
[881] | 932 | typedef typename SPath::ArcIt SPathArcIt; |
---|
[942] | 933 | typedef typename HowardMmc<StaticDigraph, CostArcMap> |
---|
[1179] | 934 | ::template SetPath<SPath>::Create HwMmc; |
---|
| 935 | typedef typename HartmannOrlinMmc<StaticDigraph, CostArcMap> |
---|
| 936 | ::template SetPath<SPath>::Create HoMmc; |
---|
| 937 | |
---|
| 938 | const double HW_ITER_LIMIT_FACTOR = 1.0; |
---|
| 939 | const int HW_ITER_LIMIT_MIN_VALUE = 5; |
---|
| 940 | |
---|
| 941 | const int hw_iter_limit = |
---|
| 942 | std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num), |
---|
| 943 | HW_ITER_LIMIT_MIN_VALUE); |
---|
[956] | 944 | |
---|
[881] | 945 | SPath cycle; |
---|
[1179] | 946 | HwMmc hw_mmc(_sgr, _cost_map); |
---|
| 947 | hw_mmc.cycle(cycle); |
---|
[881] | 948 | buildResidualNetwork(); |
---|
[1179] | 949 | while (true) { |
---|
| 950 | |
---|
| 951 | typename HwMmc::TerminationCause hw_tc = |
---|
| 952 | hw_mmc.findCycleMean(hw_iter_limit); |
---|
| 953 | if (hw_tc == HwMmc::ITERATION_LIMIT) { |
---|
| 954 | // Howard's algorithm reached the iteration limit, start a |
---|
| 955 | // strongly polynomial algorithm instead |
---|
| 956 | HoMmc ho_mmc(_sgr, _cost_map); |
---|
| 957 | ho_mmc.cycle(cycle); |
---|
| 958 | // Find a minimum mean cycle (Hartmann-Orlin algorithm) |
---|
| 959 | if (!(ho_mmc.findCycleMean() && ho_mmc.cycleCost() < 0)) break; |
---|
| 960 | ho_mmc.findCycle(); |
---|
| 961 | } else { |
---|
| 962 | // Find a minimum mean cycle (Howard algorithm) |
---|
| 963 | if (!(hw_tc == HwMmc::OPTIMAL && hw_mmc.cycleCost() < 0)) break; |
---|
| 964 | hw_mmc.findCycle(); |
---|
| 965 | } |
---|
| 966 | |
---|
[881] | 967 | // Compute delta value |
---|
| 968 | Value delta = INF; |
---|
| 969 | for (SPathArcIt a(cycle); a != INVALID; ++a) { |
---|
| 970 | Value d = _res_cap[_id_vec[_sgr.id(a)]]; |
---|
| 971 | if (d < delta) delta = d; |
---|
| 972 | } |
---|
[880] | 973 | |
---|
[881] | 974 | // Augment along the cycle |
---|
| 975 | for (SPathArcIt a(cycle); a != INVALID; ++a) { |
---|
| 976 | int j = _id_vec[_sgr.id(a)]; |
---|
| 977 | _res_cap[j] -= delta; |
---|
| 978 | _res_cap[_reverse[j]] += delta; |
---|
| 979 | } |
---|
| 980 | |
---|
[956] | 981 | // Rebuild the residual network |
---|
[881] | 982 | buildResidualNetwork(); |
---|
| 983 | } |
---|
| 984 | } |
---|
| 985 | |
---|
[1165] | 986 | // Execute the "Cancel-and-Tighten" method |
---|
[881] | 987 | void startCancelAndTighten() { |
---|
| 988 | // Constants for the min mean cycle computations |
---|
| 989 | const double LIMIT_FACTOR = 1.0; |
---|
| 990 | const int MIN_LIMIT = 5; |
---|
[1179] | 991 | const double HW_ITER_LIMIT_FACTOR = 1.0; |
---|
| 992 | const int HW_ITER_LIMIT_MIN_VALUE = 5; |
---|
| 993 | |
---|
| 994 | const int hw_iter_limit = |
---|
| 995 | std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num), |
---|
| 996 | HW_ITER_LIMIT_MIN_VALUE); |
---|
[881] | 997 | |
---|
| 998 | // Contruct auxiliary data vectors |
---|
| 999 | DoubleVector pi(_res_node_num, 0.0); |
---|
| 1000 | IntVector level(_res_node_num); |
---|
[910] | 1001 | BoolVector reached(_res_node_num); |
---|
| 1002 | BoolVector processed(_res_node_num); |
---|
[881] | 1003 | IntVector pred_node(_res_node_num); |
---|
| 1004 | IntVector pred_arc(_res_node_num); |
---|
| 1005 | std::vector<int> stack(_res_node_num); |
---|
| 1006 | std::vector<int> proc_vector(_res_node_num); |
---|
| 1007 | |
---|
| 1008 | // Initialize epsilon |
---|
| 1009 | double epsilon = 0; |
---|
| 1010 | for (int a = 0; a != _res_arc_num; ++a) { |
---|
| 1011 | if (_res_cap[a] > 0 && -_cost[a] > epsilon) |
---|
| 1012 | epsilon = -_cost[a]; |
---|
| 1013 | } |
---|
| 1014 | |
---|
| 1015 | // Start phases |
---|
| 1016 | Tolerance<double> tol; |
---|
| 1017 | tol.epsilon(1e-6); |
---|
| 1018 | int limit = int(LIMIT_FACTOR * std::sqrt(double(_res_node_num))); |
---|
| 1019 | if (limit < MIN_LIMIT) limit = MIN_LIMIT; |
---|
| 1020 | int iter = limit; |
---|
| 1021 | while (epsilon * _res_node_num >= 1) { |
---|
| 1022 | // Find and cancel cycles in the admissible network using DFS |
---|
| 1023 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1024 | reached[u] = false; |
---|
| 1025 | processed[u] = false; |
---|
| 1026 | } |
---|
| 1027 | int stack_head = -1; |
---|
| 1028 | int proc_head = -1; |
---|
| 1029 | for (int start = 0; start != _res_node_num; ++start) { |
---|
| 1030 | if (reached[start]) continue; |
---|
| 1031 | |
---|
| 1032 | // New start node |
---|
| 1033 | reached[start] = true; |
---|
| 1034 | pred_arc[start] = -1; |
---|
| 1035 | pred_node[start] = -1; |
---|
| 1036 | |
---|
| 1037 | // Find the first admissible outgoing arc |
---|
| 1038 | double p = pi[start]; |
---|
| 1039 | int a = _first_out[start]; |
---|
| 1040 | int last_out = _first_out[start+1]; |
---|
| 1041 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
| 1042 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
| 1043 | if (a == last_out) { |
---|
| 1044 | processed[start] = true; |
---|
| 1045 | proc_vector[++proc_head] = start; |
---|
| 1046 | continue; |
---|
| 1047 | } |
---|
| 1048 | stack[++stack_head] = a; |
---|
| 1049 | |
---|
| 1050 | while (stack_head >= 0) { |
---|
| 1051 | int sa = stack[stack_head]; |
---|
| 1052 | int u = _source[sa]; |
---|
| 1053 | int v = _target[sa]; |
---|
| 1054 | |
---|
| 1055 | if (!reached[v]) { |
---|
| 1056 | // A new node is reached |
---|
| 1057 | reached[v] = true; |
---|
| 1058 | pred_node[v] = u; |
---|
| 1059 | pred_arc[v] = sa; |
---|
| 1060 | p = pi[v]; |
---|
| 1061 | a = _first_out[v]; |
---|
| 1062 | last_out = _first_out[v+1]; |
---|
| 1063 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
| 1064 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
| 1065 | stack[++stack_head] = a == last_out ? -1 : a; |
---|
| 1066 | } else { |
---|
| 1067 | if (!processed[v]) { |
---|
| 1068 | // A cycle is found |
---|
| 1069 | int n, w = u; |
---|
| 1070 | Value d, delta = _res_cap[sa]; |
---|
| 1071 | for (n = u; n != v; n = pred_node[n]) { |
---|
| 1072 | d = _res_cap[pred_arc[n]]; |
---|
| 1073 | if (d <= delta) { |
---|
| 1074 | delta = d; |
---|
| 1075 | w = pred_node[n]; |
---|
| 1076 | } |
---|
| 1077 | } |
---|
| 1078 | |
---|
| 1079 | // Augment along the cycle |
---|
| 1080 | _res_cap[sa] -= delta; |
---|
| 1081 | _res_cap[_reverse[sa]] += delta; |
---|
| 1082 | for (n = u; n != v; n = pred_node[n]) { |
---|
| 1083 | int pa = pred_arc[n]; |
---|
| 1084 | _res_cap[pa] -= delta; |
---|
| 1085 | _res_cap[_reverse[pa]] += delta; |
---|
| 1086 | } |
---|
| 1087 | for (n = u; stack_head > 0 && n != w; n = pred_node[n]) { |
---|
| 1088 | --stack_head; |
---|
| 1089 | reached[n] = false; |
---|
| 1090 | } |
---|
| 1091 | u = w; |
---|
| 1092 | } |
---|
| 1093 | v = u; |
---|
| 1094 | |
---|
| 1095 | // Find the next admissible outgoing arc |
---|
| 1096 | p = pi[v]; |
---|
| 1097 | a = stack[stack_head] + 1; |
---|
| 1098 | last_out = _first_out[v+1]; |
---|
| 1099 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
| 1100 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
| 1101 | stack[stack_head] = a == last_out ? -1 : a; |
---|
| 1102 | } |
---|
| 1103 | |
---|
| 1104 | while (stack_head >= 0 && stack[stack_head] == -1) { |
---|
| 1105 | processed[v] = true; |
---|
| 1106 | proc_vector[++proc_head] = v; |
---|
| 1107 | if (--stack_head >= 0) { |
---|
| 1108 | // Find the next admissible outgoing arc |
---|
| 1109 | v = _source[stack[stack_head]]; |
---|
| 1110 | p = pi[v]; |
---|
| 1111 | a = stack[stack_head] + 1; |
---|
| 1112 | last_out = _first_out[v+1]; |
---|
| 1113 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
| 1114 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
| 1115 | stack[stack_head] = a == last_out ? -1 : a; |
---|
| 1116 | } |
---|
| 1117 | } |
---|
| 1118 | } |
---|
| 1119 | } |
---|
| 1120 | |
---|
| 1121 | // Tighten potentials and epsilon |
---|
| 1122 | if (--iter > 0) { |
---|
| 1123 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1124 | level[u] = 0; |
---|
| 1125 | } |
---|
| 1126 | for (int i = proc_head; i > 0; --i) { |
---|
| 1127 | int u = proc_vector[i]; |
---|
| 1128 | double p = pi[u]; |
---|
| 1129 | int l = level[u] + 1; |
---|
| 1130 | int last_out = _first_out[u+1]; |
---|
| 1131 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
| 1132 | int v = _target[a]; |
---|
| 1133 | if (_res_cap[a] > 0 && tol.negative(_cost[a] + p - pi[v]) && |
---|
| 1134 | l > level[v]) level[v] = l; |
---|
| 1135 | } |
---|
[880] | 1136 | } |
---|
| 1137 | |
---|
[881] | 1138 | // Modify potentials |
---|
| 1139 | double q = std::numeric_limits<double>::max(); |
---|
| 1140 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1141 | int lu = level[u]; |
---|
| 1142 | double p, pu = pi[u]; |
---|
| 1143 | int last_out = _first_out[u+1]; |
---|
| 1144 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
| 1145 | if (_res_cap[a] == 0) continue; |
---|
| 1146 | int v = _target[a]; |
---|
| 1147 | int ld = lu - level[v]; |
---|
| 1148 | if (ld > 0) { |
---|
| 1149 | p = (_cost[a] + pu - pi[v] + epsilon) / (ld + 1); |
---|
| 1150 | if (p < q) q = p; |
---|
| 1151 | } |
---|
| 1152 | } |
---|
| 1153 | } |
---|
| 1154 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1155 | pi[u] -= q * level[u]; |
---|
| 1156 | } |
---|
[880] | 1157 | |
---|
[881] | 1158 | // Modify epsilon |
---|
| 1159 | epsilon = 0; |
---|
| 1160 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1161 | double curr, pu = pi[u]; |
---|
| 1162 | int last_out = _first_out[u+1]; |
---|
| 1163 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
| 1164 | if (_res_cap[a] == 0) continue; |
---|
| 1165 | curr = _cost[a] + pu - pi[_target[a]]; |
---|
| 1166 | if (-curr > epsilon) epsilon = -curr; |
---|
| 1167 | } |
---|
| 1168 | } |
---|
| 1169 | } else { |
---|
[1179] | 1170 | typedef HowardMmc<StaticDigraph, CostArcMap> HwMmc; |
---|
| 1171 | typedef HartmannOrlinMmc<StaticDigraph, CostArcMap> HoMmc; |
---|
[881] | 1172 | typedef typename BellmanFord<StaticDigraph, CostArcMap> |
---|
| 1173 | ::template SetDistMap<CostNodeMap>::Create BF; |
---|
| 1174 | |
---|
| 1175 | // Set epsilon to the minimum cycle mean |
---|
[1179] | 1176 | Cost cycle_cost = 0; |
---|
| 1177 | int cycle_size = 1; |
---|
[881] | 1178 | buildResidualNetwork(); |
---|
[1179] | 1179 | HwMmc hw_mmc(_sgr, _cost_map); |
---|
| 1180 | if (hw_mmc.findCycleMean(hw_iter_limit) == HwMmc::ITERATION_LIMIT) { |
---|
| 1181 | // Howard's algorithm reached the iteration limit, start a |
---|
| 1182 | // strongly polynomial algorithm instead |
---|
| 1183 | HoMmc ho_mmc(_sgr, _cost_map); |
---|
| 1184 | ho_mmc.findCycleMean(); |
---|
| 1185 | epsilon = -ho_mmc.cycleMean(); |
---|
| 1186 | cycle_cost = ho_mmc.cycleCost(); |
---|
| 1187 | cycle_size = ho_mmc.cycleSize(); |
---|
| 1188 | } else { |
---|
| 1189 | // Set epsilon |
---|
| 1190 | epsilon = -hw_mmc.cycleMean(); |
---|
| 1191 | cycle_cost = hw_mmc.cycleCost(); |
---|
| 1192 | cycle_size = hw_mmc.cycleSize(); |
---|
| 1193 | } |
---|
[956] | 1194 | |
---|
[881] | 1195 | // Compute feasible potentials for the current epsilon |
---|
| 1196 | for (int i = 0; i != int(_cost_vec.size()); ++i) { |
---|
| 1197 | _cost_vec[i] = cycle_size * _cost_vec[i] - cycle_cost; |
---|
| 1198 | } |
---|
| 1199 | BF bf(_sgr, _cost_map); |
---|
| 1200 | bf.distMap(_pi_map); |
---|
| 1201 | bf.init(0); |
---|
| 1202 | bf.start(); |
---|
| 1203 | for (int u = 0; u != _res_node_num; ++u) { |
---|
| 1204 | pi[u] = static_cast<double>(_pi[u]) / cycle_size; |
---|
| 1205 | } |
---|
[956] | 1206 | |
---|
[881] | 1207 | iter = limit; |
---|
[880] | 1208 | } |
---|
| 1209 | } |
---|
| 1210 | } |
---|
| 1211 | |
---|
| 1212 | }; //class CycleCanceling |
---|
| 1213 | |
---|
| 1214 | ///@} |
---|
| 1215 | |
---|
| 1216 | } //namespace lemon |
---|
| 1217 | |
---|
| 1218 | #endif //LEMON_CYCLE_CANCELING_H |
---|