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