[948] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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[1270] | 5 | * Copyright (C) 2003-2013 |
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[948] | 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_FRACTIONAL_MATCHING_H |
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| 20 | #define LEMON_FRACTIONAL_MATCHING_H |
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| 21 | |
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| 22 | #include <vector> |
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| 23 | #include <queue> |
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| 24 | #include <set> |
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| 25 | #include <limits> |
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| 26 | |
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| 27 | #include <lemon/core.h> |
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| 28 | #include <lemon/unionfind.h> |
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| 29 | #include <lemon/bin_heap.h> |
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| 30 | #include <lemon/maps.h> |
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| 31 | #include <lemon/assert.h> |
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| 32 | #include <lemon/elevator.h> |
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| 33 | |
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| 34 | ///\ingroup matching |
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| 35 | ///\file |
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| 36 | ///\brief Fractional matching algorithms in general graphs. |
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| 37 | |
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| 38 | namespace lemon { |
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| 39 | |
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| 40 | /// \brief Default traits class of MaxFractionalMatching class. |
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| 41 | /// |
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| 42 | /// Default traits class of MaxFractionalMatching class. |
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| 43 | /// \tparam GR Graph type. |
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| 44 | template <typename GR> |
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| 45 | struct MaxFractionalMatchingDefaultTraits { |
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| 46 | |
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| 47 | /// \brief The type of the graph the algorithm runs on. |
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| 48 | typedef GR Graph; |
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| 49 | |
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| 50 | /// \brief The type of the map that stores the matching. |
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| 51 | /// |
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| 52 | /// The type of the map that stores the matching arcs. |
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| 53 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 54 | typedef typename Graph::template NodeMap<typename GR::Arc> MatchingMap; |
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| 55 | |
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| 56 | /// \brief Instantiates a MatchingMap. |
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| 57 | /// |
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| 58 | /// This function instantiates a \ref MatchingMap. |
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| 59 | /// \param graph The graph for which we would like to define |
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| 60 | /// the matching map. |
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| 61 | static MatchingMap* createMatchingMap(const Graph& graph) { |
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| 62 | return new MatchingMap(graph); |
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| 63 | } |
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| 64 | |
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| 65 | /// \brief The elevator type used by MaxFractionalMatching algorithm. |
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| 66 | /// |
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| 67 | /// The elevator type used by MaxFractionalMatching algorithm. |
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| 68 | /// |
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| 69 | /// \sa Elevator |
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| 70 | /// \sa LinkedElevator |
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| 71 | typedef LinkedElevator<Graph, typename Graph::Node> Elevator; |
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| 72 | |
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| 73 | /// \brief Instantiates an Elevator. |
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| 74 | /// |
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| 75 | /// This function instantiates an \ref Elevator. |
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| 76 | /// \param graph The graph for which we would like to define |
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| 77 | /// the elevator. |
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| 78 | /// \param max_level The maximum level of the elevator. |
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| 79 | static Elevator* createElevator(const Graph& graph, int max_level) { |
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| 80 | return new Elevator(graph, max_level); |
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| 81 | } |
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| 82 | }; |
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| 83 | |
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| 84 | /// \ingroup matching |
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| 85 | /// |
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| 86 | /// \brief Max cardinality fractional matching |
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| 87 | /// |
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| 88 | /// This class provides an implementation of fractional matching |
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| 89 | /// algorithm based on push-relabel principle. |
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| 90 | /// |
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| 91 | /// The maximum cardinality fractional matching is a relaxation of the |
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| 92 | /// maximum cardinality matching problem where the odd set constraints |
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| 93 | /// are omitted. |
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| 94 | /// It can be formulated with the following linear program. |
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| 95 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
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| 96 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
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| 97 | /// \f[\max \sum_{e\in E}x_e\f] |
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| 98 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
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| 99 | /// \f$X\f$. The result can be represented as the union of a |
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| 100 | /// matching with one value edges and a set of odd length cycles |
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| 101 | /// with half value edges. |
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| 102 | /// |
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| 103 | /// The algorithm calculates an optimal fractional matching and a |
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| 104 | /// barrier. The number of adjacents of any node set minus the size |
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| 105 | /// of node set is a lower bound on the uncovered nodes in the |
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| 106 | /// graph. For maximum matching a barrier is computed which |
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| 107 | /// maximizes this difference. |
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| 108 | /// |
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| 109 | /// The algorithm can be executed with the run() function. After it |
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| 110 | /// the matching (the primal solution) and the barrier (the dual |
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| 111 | /// solution) can be obtained using the query functions. |
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| 112 | /// |
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| 113 | /// The primal solution is multiplied by |
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[950] | 114 | /// \ref MaxFractionalMatching::primalScale "2". |
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[948] | 115 | /// |
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| 116 | /// \tparam GR The undirected graph type the algorithm runs on. |
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| 117 | #ifdef DOXYGEN |
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| 118 | template <typename GR, typename TR> |
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| 119 | #else |
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| 120 | template <typename GR, |
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| 121 | typename TR = MaxFractionalMatchingDefaultTraits<GR> > |
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| 122 | #endif |
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| 123 | class MaxFractionalMatching { |
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| 124 | public: |
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| 125 | |
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[1250] | 126 | /// \brief The \ref lemon::MaxFractionalMatchingDefaultTraits |
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| 127 | /// "traits class" of the algorithm. |
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[948] | 128 | typedef TR Traits; |
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| 129 | /// The type of the graph the algorithm runs on. |
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| 130 | typedef typename TR::Graph Graph; |
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| 131 | /// The type of the matching map. |
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| 132 | typedef typename TR::MatchingMap MatchingMap; |
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| 133 | /// The type of the elevator. |
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| 134 | typedef typename TR::Elevator Elevator; |
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| 135 | |
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| 136 | /// \brief Scaling factor for primal solution |
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| 137 | /// |
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| 138 | /// Scaling factor for primal solution. |
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| 139 | static const int primalScale = 2; |
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| 140 | |
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| 141 | private: |
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| 142 | |
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| 143 | const Graph &_graph; |
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| 144 | int _node_num; |
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| 145 | bool _allow_loops; |
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| 146 | int _empty_level; |
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| 147 | |
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| 148 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 149 | |
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| 150 | bool _local_matching; |
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| 151 | MatchingMap *_matching; |
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| 152 | |
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| 153 | bool _local_level; |
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| 154 | Elevator *_level; |
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| 155 | |
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| 156 | typedef typename Graph::template NodeMap<int> InDegMap; |
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| 157 | InDegMap *_indeg; |
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| 158 | |
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| 159 | void createStructures() { |
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| 160 | _node_num = countNodes(_graph); |
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| 161 | |
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| 162 | if (!_matching) { |
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| 163 | _local_matching = true; |
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| 164 | _matching = Traits::createMatchingMap(_graph); |
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| 165 | } |
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| 166 | if (!_level) { |
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| 167 | _local_level = true; |
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| 168 | _level = Traits::createElevator(_graph, _node_num); |
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| 169 | } |
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| 170 | if (!_indeg) { |
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| 171 | _indeg = new InDegMap(_graph); |
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| 172 | } |
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| 173 | } |
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| 174 | |
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| 175 | void destroyStructures() { |
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| 176 | if (_local_matching) { |
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| 177 | delete _matching; |
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| 178 | } |
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| 179 | if (_local_level) { |
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| 180 | delete _level; |
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| 181 | } |
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| 182 | if (_indeg) { |
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| 183 | delete _indeg; |
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| 184 | } |
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| 185 | } |
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| 186 | |
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| 187 | void postprocessing() { |
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| 188 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 189 | if ((*_indeg)[n] != 0) continue; |
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| 190 | _indeg->set(n, -1); |
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| 191 | Node u = n; |
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| 192 | while ((*_matching)[u] != INVALID) { |
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| 193 | Node v = _graph.target((*_matching)[u]); |
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| 194 | _indeg->set(v, -1); |
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| 195 | Arc a = _graph.oppositeArc((*_matching)[u]); |
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| 196 | u = _graph.target((*_matching)[v]); |
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| 197 | _indeg->set(u, -1); |
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| 198 | _matching->set(v, a); |
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| 199 | } |
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| 200 | } |
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| 201 | |
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| 202 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 203 | if ((*_indeg)[n] != 1) continue; |
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| 204 | _indeg->set(n, -1); |
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| 205 | |
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| 206 | int num = 1; |
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| 207 | Node u = _graph.target((*_matching)[n]); |
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| 208 | while (u != n) { |
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| 209 | _indeg->set(u, -1); |
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| 210 | u = _graph.target((*_matching)[u]); |
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| 211 | ++num; |
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| 212 | } |
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| 213 | if (num % 2 == 0 && num > 2) { |
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| 214 | Arc prev = _graph.oppositeArc((*_matching)[n]); |
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| 215 | Node v = _graph.target((*_matching)[n]); |
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| 216 | u = _graph.target((*_matching)[v]); |
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| 217 | _matching->set(v, prev); |
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| 218 | while (u != n) { |
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| 219 | prev = _graph.oppositeArc((*_matching)[u]); |
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| 220 | v = _graph.target((*_matching)[u]); |
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| 221 | u = _graph.target((*_matching)[v]); |
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| 222 | _matching->set(v, prev); |
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| 223 | } |
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| 224 | } |
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| 225 | } |
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| 226 | } |
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| 227 | |
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| 228 | public: |
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| 229 | |
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| 230 | typedef MaxFractionalMatching Create; |
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| 231 | |
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| 232 | ///\name Named Template Parameters |
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| 233 | |
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| 234 | ///@{ |
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| 235 | |
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| 236 | template <typename T> |
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| 237 | struct SetMatchingMapTraits : public Traits { |
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| 238 | typedef T MatchingMap; |
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| 239 | static MatchingMap *createMatchingMap(const Graph&) { |
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| 240 | LEMON_ASSERT(false, "MatchingMap is not initialized"); |
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| 241 | return 0; // ignore warnings |
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| 242 | } |
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| 243 | }; |
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| 244 | |
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| 245 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 246 | /// MatchingMap type |
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| 247 | /// |
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| 248 | /// \ref named-templ-param "Named parameter" for setting MatchingMap |
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| 249 | /// type. |
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| 250 | template <typename T> |
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| 251 | struct SetMatchingMap |
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| 252 | : public MaxFractionalMatching<Graph, SetMatchingMapTraits<T> > { |
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| 253 | typedef MaxFractionalMatching<Graph, SetMatchingMapTraits<T> > Create; |
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| 254 | }; |
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| 255 | |
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| 256 | template <typename T> |
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| 257 | struct SetElevatorTraits : public Traits { |
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| 258 | typedef T Elevator; |
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| 259 | static Elevator *createElevator(const Graph&, int) { |
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| 260 | LEMON_ASSERT(false, "Elevator is not initialized"); |
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| 261 | return 0; // ignore warnings |
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| 262 | } |
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| 263 | }; |
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| 264 | |
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| 265 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 266 | /// Elevator type |
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| 267 | /// |
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| 268 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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| 269 | /// type. If this named parameter is used, then an external |
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| 270 | /// elevator object must be passed to the algorithm using the |
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| 271 | /// \ref elevator(Elevator&) "elevator()" function before calling |
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| 272 | /// \ref run() or \ref init(). |
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| 273 | /// \sa SetStandardElevator |
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| 274 | template <typename T> |
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| 275 | struct SetElevator |
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| 276 | : public MaxFractionalMatching<Graph, SetElevatorTraits<T> > { |
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| 277 | typedef MaxFractionalMatching<Graph, SetElevatorTraits<T> > Create; |
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| 278 | }; |
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| 279 | |
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| 280 | template <typename T> |
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| 281 | struct SetStandardElevatorTraits : public Traits { |
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| 282 | typedef T Elevator; |
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| 283 | static Elevator *createElevator(const Graph& graph, int max_level) { |
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| 284 | return new Elevator(graph, max_level); |
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| 285 | } |
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| 286 | }; |
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| 287 | |
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| 288 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 289 | /// Elevator type with automatic allocation |
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| 290 | /// |
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| 291 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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| 292 | /// type with automatic allocation. |
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| 293 | /// The Elevator should have standard constructor interface to be |
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| 294 | /// able to automatically created by the algorithm (i.e. the |
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| 295 | /// graph and the maximum level should be passed to it). |
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| 296 | /// However an external elevator object could also be passed to the |
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| 297 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
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| 298 | /// before calling \ref run() or \ref init(). |
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| 299 | /// \sa SetElevator |
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| 300 | template <typename T> |
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| 301 | struct SetStandardElevator |
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| 302 | : public MaxFractionalMatching<Graph, SetStandardElevatorTraits<T> > { |
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| 303 | typedef MaxFractionalMatching<Graph, |
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| 304 | SetStandardElevatorTraits<T> > Create; |
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| 305 | }; |
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| 306 | |
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| 307 | /// @} |
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| 308 | |
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| 309 | protected: |
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| 310 | |
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| 311 | MaxFractionalMatching() {} |
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| 312 | |
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| 313 | public: |
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| 314 | |
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| 315 | /// \brief Constructor |
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| 316 | /// |
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| 317 | /// Constructor. |
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| 318 | /// |
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| 319 | MaxFractionalMatching(const Graph &graph, bool allow_loops = true) |
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| 320 | : _graph(graph), _allow_loops(allow_loops), |
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| 321 | _local_matching(false), _matching(0), |
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| 322 | _local_level(false), _level(0), _indeg(0) |
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| 323 | {} |
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| 324 | |
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| 325 | ~MaxFractionalMatching() { |
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| 326 | destroyStructures(); |
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| 327 | } |
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| 328 | |
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| 329 | /// \brief Sets the matching map. |
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| 330 | /// |
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| 331 | /// Sets the matching map. |
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| 332 | /// If you don't use this function before calling \ref run() or |
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| 333 | /// \ref init(), an instance will be allocated automatically. |
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| 334 | /// The destructor deallocates this automatically allocated map, |
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| 335 | /// of course. |
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| 336 | /// \return <tt>(*this)</tt> |
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| 337 | MaxFractionalMatching& matchingMap(MatchingMap& map) { |
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| 338 | if (_local_matching) { |
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| 339 | delete _matching; |
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| 340 | _local_matching = false; |
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| 341 | } |
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| 342 | _matching = ↦ |
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| 343 | return *this; |
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| 344 | } |
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| 345 | |
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| 346 | /// \brief Sets the elevator used by algorithm. |
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| 347 | /// |
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| 348 | /// Sets the elevator used by algorithm. |
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| 349 | /// If you don't use this function before calling \ref run() or |
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| 350 | /// \ref init(), an instance will be allocated automatically. |
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| 351 | /// The destructor deallocates this automatically allocated elevator, |
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| 352 | /// of course. |
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| 353 | /// \return <tt>(*this)</tt> |
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| 354 | MaxFractionalMatching& elevator(Elevator& elevator) { |
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| 355 | if (_local_level) { |
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| 356 | delete _level; |
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| 357 | _local_level = false; |
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| 358 | } |
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| 359 | _level = &elevator; |
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| 360 | return *this; |
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| 361 | } |
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| 362 | |
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| 363 | /// \brief Returns a const reference to the elevator. |
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| 364 | /// |
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| 365 | /// Returns a const reference to the elevator. |
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| 366 | /// |
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| 367 | /// \pre Either \ref run() or \ref init() must be called before |
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| 368 | /// using this function. |
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| 369 | const Elevator& elevator() const { |
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| 370 | return *_level; |
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| 371 | } |
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| 372 | |
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| 373 | /// \name Execution control |
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| 374 | /// The simplest way to execute the algorithm is to use one of the |
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| 375 | /// member functions called \c run(). \n |
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| 376 | /// If you need more control on the execution, first |
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| 377 | /// you must call \ref init() and then one variant of the start() |
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| 378 | /// member. |
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| 379 | |
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| 380 | /// @{ |
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| 381 | |
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| 382 | /// \brief Initializes the internal data structures. |
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| 383 | /// |
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| 384 | /// Initializes the internal data structures and sets the initial |
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| 385 | /// matching. |
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| 386 | void init() { |
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| 387 | createStructures(); |
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| 388 | |
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| 389 | _level->initStart(); |
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| 390 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 391 | _indeg->set(n, 0); |
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| 392 | _matching->set(n, INVALID); |
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| 393 | _level->initAddItem(n); |
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| 394 | } |
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| 395 | _level->initFinish(); |
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| 396 | |
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| 397 | _empty_level = _node_num; |
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| 398 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 399 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
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| 400 | if (_graph.target(a) == n && !_allow_loops) continue; |
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| 401 | _matching->set(n, a); |
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| 402 | Node v = _graph.target((*_matching)[n]); |
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| 403 | _indeg->set(v, (*_indeg)[v] + 1); |
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| 404 | break; |
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| 405 | } |
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| 406 | } |
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| 407 | |
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| 408 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 409 | if ((*_indeg)[n] == 0) { |
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| 410 | _level->activate(n); |
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| 411 | } |
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| 412 | } |
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| 413 | } |
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| 414 | |
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| 415 | /// \brief Starts the algorithm and computes a fractional matching |
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| 416 | /// |
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| 417 | /// The algorithm computes a maximum fractional matching. |
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| 418 | /// |
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| 419 | /// \param postprocess The algorithm computes first a matching |
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| 420 | /// which is a union of a matching with one value edges, cycles |
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| 421 | /// with half value edges and even length paths with half value |
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| 422 | /// edges. If the parameter is true, then after the push-relabel |
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| 423 | /// algorithm it postprocesses the matching to contain only |
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| 424 | /// matching edges and half value odd cycles. |
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| 425 | void start(bool postprocess = true) { |
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| 426 | Node n; |
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| 427 | while ((n = _level->highestActive()) != INVALID) { |
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| 428 | int level = _level->highestActiveLevel(); |
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| 429 | int new_level = _level->maxLevel(); |
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| 430 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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| 431 | Node u = _graph.source(a); |
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| 432 | if (n == u && !_allow_loops) continue; |
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| 433 | Node v = _graph.target((*_matching)[u]); |
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| 434 | if ((*_level)[v] < level) { |
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| 435 | _indeg->set(v, (*_indeg)[v] - 1); |
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| 436 | if ((*_indeg)[v] == 0) { |
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| 437 | _level->activate(v); |
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| 438 | } |
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| 439 | _matching->set(u, a); |
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| 440 | _indeg->set(n, (*_indeg)[n] + 1); |
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| 441 | _level->deactivate(n); |
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| 442 | goto no_more_push; |
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| 443 | } else if (new_level > (*_level)[v]) { |
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| 444 | new_level = (*_level)[v]; |
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| 445 | } |
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| 446 | } |
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| 447 | |
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| 448 | if (new_level + 1 < _level->maxLevel()) { |
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| 449 | _level->liftHighestActive(new_level + 1); |
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| 450 | } else { |
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| 451 | _level->liftHighestActiveToTop(); |
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| 452 | } |
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| 453 | if (_level->emptyLevel(level)) { |
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| 454 | _level->liftToTop(level); |
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| 455 | } |
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| 456 | no_more_push: |
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| 457 | ; |
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| 458 | } |
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| 459 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 460 | if ((*_matching)[n] == INVALID) continue; |
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| 461 | Node u = _graph.target((*_matching)[n]); |
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| 462 | if ((*_indeg)[u] > 1) { |
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| 463 | _indeg->set(u, (*_indeg)[u] - 1); |
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| 464 | _matching->set(n, INVALID); |
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| 465 | } |
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| 466 | } |
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| 467 | if (postprocess) { |
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| 468 | postprocessing(); |
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| 469 | } |
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| 470 | } |
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| 471 | |
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| 472 | /// \brief Starts the algorithm and computes a perfect fractional |
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| 473 | /// matching |
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| 474 | /// |
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| 475 | /// The algorithm computes a perfect fractional matching. If it |
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| 476 | /// does not exists, then the algorithm returns false and the |
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| 477 | /// matching is undefined and the barrier. |
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| 478 | /// |
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| 479 | /// \param postprocess The algorithm computes first a matching |
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| 480 | /// which is a union of a matching with one value edges, cycles |
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| 481 | /// with half value edges and even length paths with half value |
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| 482 | /// edges. If the parameter is true, then after the push-relabel |
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| 483 | /// algorithm it postprocesses the matching to contain only |
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| 484 | /// matching edges and half value odd cycles. |
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| 485 | bool startPerfect(bool postprocess = true) { |
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| 486 | Node n; |
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| 487 | while ((n = _level->highestActive()) != INVALID) { |
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| 488 | int level = _level->highestActiveLevel(); |
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| 489 | int new_level = _level->maxLevel(); |
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| 490 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
---|
| 491 | Node u = _graph.source(a); |
---|
| 492 | if (n == u && !_allow_loops) continue; |
---|
| 493 | Node v = _graph.target((*_matching)[u]); |
---|
| 494 | if ((*_level)[v] < level) { |
---|
| 495 | _indeg->set(v, (*_indeg)[v] - 1); |
---|
| 496 | if ((*_indeg)[v] == 0) { |
---|
| 497 | _level->activate(v); |
---|
| 498 | } |
---|
| 499 | _matching->set(u, a); |
---|
| 500 | _indeg->set(n, (*_indeg)[n] + 1); |
---|
| 501 | _level->deactivate(n); |
---|
| 502 | goto no_more_push; |
---|
| 503 | } else if (new_level > (*_level)[v]) { |
---|
| 504 | new_level = (*_level)[v]; |
---|
| 505 | } |
---|
| 506 | } |
---|
| 507 | |
---|
| 508 | if (new_level + 1 < _level->maxLevel()) { |
---|
| 509 | _level->liftHighestActive(new_level + 1); |
---|
| 510 | } else { |
---|
| 511 | _level->liftHighestActiveToTop(); |
---|
| 512 | _empty_level = _level->maxLevel() - 1; |
---|
| 513 | return false; |
---|
| 514 | } |
---|
| 515 | if (_level->emptyLevel(level)) { |
---|
| 516 | _level->liftToTop(level); |
---|
| 517 | _empty_level = level; |
---|
| 518 | return false; |
---|
| 519 | } |
---|
| 520 | no_more_push: |
---|
| 521 | ; |
---|
| 522 | } |
---|
| 523 | if (postprocess) { |
---|
| 524 | postprocessing(); |
---|
| 525 | } |
---|
| 526 | return true; |
---|
| 527 | } |
---|
| 528 | |
---|
| 529 | /// \brief Runs the algorithm |
---|
| 530 | /// |
---|
| 531 | /// Just a shortcut for the next code: |
---|
| 532 | ///\code |
---|
| 533 | /// init(); |
---|
| 534 | /// start(); |
---|
| 535 | ///\endcode |
---|
| 536 | void run(bool postprocess = true) { |
---|
| 537 | init(); |
---|
| 538 | start(postprocess); |
---|
| 539 | } |
---|
| 540 | |
---|
| 541 | /// \brief Runs the algorithm to find a perfect fractional matching |
---|
| 542 | /// |
---|
| 543 | /// Just a shortcut for the next code: |
---|
| 544 | ///\code |
---|
| 545 | /// init(); |
---|
| 546 | /// startPerfect(); |
---|
| 547 | ///\endcode |
---|
| 548 | bool runPerfect(bool postprocess = true) { |
---|
| 549 | init(); |
---|
| 550 | return startPerfect(postprocess); |
---|
| 551 | } |
---|
| 552 | |
---|
| 553 | ///@} |
---|
| 554 | |
---|
| 555 | /// \name Query Functions |
---|
| 556 | /// The result of the %Matching algorithm can be obtained using these |
---|
| 557 | /// functions.\n |
---|
| 558 | /// Before the use of these functions, |
---|
| 559 | /// either run() or start() must be called. |
---|
| 560 | ///@{ |
---|
| 561 | |
---|
| 562 | |
---|
| 563 | /// \brief Return the number of covered nodes in the matching. |
---|
| 564 | /// |
---|
| 565 | /// This function returns the number of covered nodes in the matching. |
---|
| 566 | /// |
---|
| 567 | /// \pre Either run() or start() must be called before using this function. |
---|
| 568 | int matchingSize() const { |
---|
| 569 | int num = 0; |
---|
| 570 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 571 | if ((*_matching)[n] != INVALID) { |
---|
| 572 | ++num; |
---|
| 573 | } |
---|
| 574 | } |
---|
| 575 | return num; |
---|
| 576 | } |
---|
| 577 | |
---|
| 578 | /// \brief Returns a const reference to the matching map. |
---|
| 579 | /// |
---|
| 580 | /// Returns a const reference to the node map storing the found |
---|
| 581 | /// fractional matching. This method can be called after |
---|
| 582 | /// running the algorithm. |
---|
| 583 | /// |
---|
| 584 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 585 | /// using this function. |
---|
| 586 | const MatchingMap& matchingMap() const { |
---|
| 587 | return *_matching; |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | /// \brief Return \c true if the given edge is in the matching. |
---|
| 591 | /// |
---|
| 592 | /// This function returns \c true if the given edge is in the |
---|
| 593 | /// found matching. The result is scaled by \ref primalScale |
---|
| 594 | /// "primal scale". |
---|
| 595 | /// |
---|
| 596 | /// \pre Either run() or start() must be called before using this function. |
---|
| 597 | int matching(const Edge& edge) const { |
---|
| 598 | return (edge == (*_matching)[_graph.u(edge)] ? 1 : 0) + |
---|
| 599 | (edge == (*_matching)[_graph.v(edge)] ? 1 : 0); |
---|
| 600 | } |
---|
| 601 | |
---|
| 602 | /// \brief Return the fractional matching arc (or edge) incident |
---|
| 603 | /// to the given node. |
---|
| 604 | /// |
---|
| 605 | /// This function returns one of the fractional matching arc (or |
---|
| 606 | /// edge) incident to the given node in the found matching or \c |
---|
| 607 | /// INVALID if the node is not covered by the matching or if the |
---|
| 608 | /// node is on an odd length cycle then it is the successor edge |
---|
| 609 | /// on the cycle. |
---|
| 610 | /// |
---|
| 611 | /// \pre Either run() or start() must be called before using this function. |
---|
| 612 | Arc matching(const Node& node) const { |
---|
| 613 | return (*_matching)[node]; |
---|
| 614 | } |
---|
| 615 | |
---|
| 616 | /// \brief Returns true if the node is in the barrier |
---|
| 617 | /// |
---|
| 618 | /// The barrier is a subset of the nodes. If the nodes in the |
---|
| 619 | /// barrier have less adjacent nodes than the size of the barrier, |
---|
| 620 | /// then at least as much nodes cannot be covered as the |
---|
| 621 | /// difference of the two subsets. |
---|
| 622 | bool barrier(const Node& node) const { |
---|
| 623 | return (*_level)[node] >= _empty_level; |
---|
| 624 | } |
---|
| 625 | |
---|
| 626 | /// @} |
---|
| 627 | |
---|
| 628 | }; |
---|
| 629 | |
---|
| 630 | /// \ingroup matching |
---|
| 631 | /// |
---|
| 632 | /// \brief Weighted fractional matching in general graphs |
---|
| 633 | /// |
---|
| 634 | /// This class provides an efficient implementation of fractional |
---|
[950] | 635 | /// matching algorithm. The implementation uses priority queues and |
---|
| 636 | /// provides \f$O(nm\log n)\f$ time complexity. |
---|
[948] | 637 | /// |
---|
| 638 | /// The maximum weighted fractional matching is a relaxation of the |
---|
| 639 | /// maximum weighted matching problem where the odd set constraints |
---|
| 640 | /// are omitted. |
---|
| 641 | /// It can be formulated with the following linear program. |
---|
| 642 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
| 643 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 644 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
| 645 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 646 | /// \f$X\f$. The result must be the union of a matching with one |
---|
| 647 | /// value edges and a set of odd length cycles with half value edges. |
---|
| 648 | /// |
---|
| 649 | /// The algorithm calculates an optimal fractional matching and a |
---|
| 650 | /// proof of the optimality. The solution of the dual problem can be |
---|
| 651 | /// used to check the result of the algorithm. The dual linear |
---|
| 652 | /// problem is the following. |
---|
| 653 | /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f] |
---|
| 654 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
[950] | 655 | /// \f[\min \sum_{u \in V}y_u \f] |
---|
[948] | 656 | /// |
---|
| 657 | /// The algorithm can be executed with the run() function. |
---|
| 658 | /// After it the matching (the primal solution) and the dual solution |
---|
| 659 | /// can be obtained using the query functions. |
---|
| 660 | /// |
---|
[951] | 661 | /// The primal solution is multiplied by |
---|
| 662 | /// \ref MaxWeightedFractionalMatching::primalScale "2". |
---|
| 663 | /// If the value type is integer, then the dual |
---|
| 664 | /// solution is scaled by |
---|
| 665 | /// \ref MaxWeightedFractionalMatching::dualScale "4". |
---|
[948] | 666 | /// |
---|
| 667 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
| 668 | /// \tparam WM The type edge weight map. The default type is |
---|
| 669 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 670 | #ifdef DOXYGEN |
---|
| 671 | template <typename GR, typename WM> |
---|
| 672 | #else |
---|
| 673 | template <typename GR, |
---|
| 674 | typename WM = typename GR::template EdgeMap<int> > |
---|
| 675 | #endif |
---|
| 676 | class MaxWeightedFractionalMatching { |
---|
| 677 | public: |
---|
| 678 | |
---|
| 679 | /// The graph type of the algorithm |
---|
| 680 | typedef GR Graph; |
---|
| 681 | /// The type of the edge weight map |
---|
| 682 | typedef WM WeightMap; |
---|
| 683 | /// The value type of the edge weights |
---|
| 684 | typedef typename WeightMap::Value Value; |
---|
| 685 | |
---|
| 686 | /// The type of the matching map |
---|
| 687 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 688 | MatchingMap; |
---|
| 689 | |
---|
| 690 | /// \brief Scaling factor for primal solution |
---|
| 691 | /// |
---|
[951] | 692 | /// Scaling factor for primal solution. |
---|
| 693 | static const int primalScale = 2; |
---|
[948] | 694 | |
---|
| 695 | /// \brief Scaling factor for dual solution |
---|
| 696 | /// |
---|
| 697 | /// Scaling factor for dual solution. It is equal to 4 or 1 |
---|
| 698 | /// according to the value type. |
---|
| 699 | static const int dualScale = |
---|
| 700 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 701 | |
---|
| 702 | private: |
---|
| 703 | |
---|
| 704 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 705 | |
---|
| 706 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 707 | |
---|
| 708 | const Graph& _graph; |
---|
| 709 | const WeightMap& _weight; |
---|
| 710 | |
---|
| 711 | MatchingMap* _matching; |
---|
| 712 | NodePotential* _node_potential; |
---|
| 713 | |
---|
| 714 | int _node_num; |
---|
| 715 | bool _allow_loops; |
---|
| 716 | |
---|
| 717 | enum Status { |
---|
| 718 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
| 719 | }; |
---|
| 720 | |
---|
| 721 | typedef typename Graph::template NodeMap<Status> StatusMap; |
---|
| 722 | StatusMap* _status; |
---|
| 723 | |
---|
| 724 | typedef typename Graph::template NodeMap<Arc> PredMap; |
---|
| 725 | PredMap* _pred; |
---|
| 726 | |
---|
| 727 | typedef ExtendFindEnum<IntNodeMap> TreeSet; |
---|
| 728 | |
---|
| 729 | IntNodeMap *_tree_set_index; |
---|
| 730 | TreeSet *_tree_set; |
---|
| 731 | |
---|
| 732 | IntNodeMap *_delta1_index; |
---|
| 733 | BinHeap<Value, IntNodeMap> *_delta1; |
---|
| 734 | |
---|
| 735 | IntNodeMap *_delta2_index; |
---|
| 736 | BinHeap<Value, IntNodeMap> *_delta2; |
---|
| 737 | |
---|
| 738 | IntEdgeMap *_delta3_index; |
---|
| 739 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
| 740 | |
---|
| 741 | Value _delta_sum; |
---|
| 742 | |
---|
| 743 | void createStructures() { |
---|
| 744 | _node_num = countNodes(_graph); |
---|
| 745 | |
---|
| 746 | if (!_matching) { |
---|
| 747 | _matching = new MatchingMap(_graph); |
---|
| 748 | } |
---|
| 749 | if (!_node_potential) { |
---|
| 750 | _node_potential = new NodePotential(_graph); |
---|
| 751 | } |
---|
| 752 | if (!_status) { |
---|
| 753 | _status = new StatusMap(_graph); |
---|
| 754 | } |
---|
| 755 | if (!_pred) { |
---|
| 756 | _pred = new PredMap(_graph); |
---|
| 757 | } |
---|
| 758 | if (!_tree_set) { |
---|
| 759 | _tree_set_index = new IntNodeMap(_graph); |
---|
| 760 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 761 | } |
---|
| 762 | if (!_delta1) { |
---|
| 763 | _delta1_index = new IntNodeMap(_graph); |
---|
| 764 | _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index); |
---|
| 765 | } |
---|
| 766 | if (!_delta2) { |
---|
| 767 | _delta2_index = new IntNodeMap(_graph); |
---|
| 768 | _delta2 = new BinHeap<Value, IntNodeMap>(*_delta2_index); |
---|
| 769 | } |
---|
| 770 | if (!_delta3) { |
---|
| 771 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 772 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
| 773 | } |
---|
| 774 | } |
---|
| 775 | |
---|
| 776 | void destroyStructures() { |
---|
| 777 | if (_matching) { |
---|
| 778 | delete _matching; |
---|
| 779 | } |
---|
| 780 | if (_node_potential) { |
---|
| 781 | delete _node_potential; |
---|
| 782 | } |
---|
| 783 | if (_status) { |
---|
| 784 | delete _status; |
---|
| 785 | } |
---|
| 786 | if (_pred) { |
---|
| 787 | delete _pred; |
---|
| 788 | } |
---|
| 789 | if (_tree_set) { |
---|
| 790 | delete _tree_set_index; |
---|
| 791 | delete _tree_set; |
---|
| 792 | } |
---|
| 793 | if (_delta1) { |
---|
| 794 | delete _delta1_index; |
---|
| 795 | delete _delta1; |
---|
| 796 | } |
---|
| 797 | if (_delta2) { |
---|
| 798 | delete _delta2_index; |
---|
| 799 | delete _delta2; |
---|
| 800 | } |
---|
| 801 | if (_delta3) { |
---|
| 802 | delete _delta3_index; |
---|
| 803 | delete _delta3; |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | |
---|
| 807 | void matchedToEven(Node node, int tree) { |
---|
| 808 | _tree_set->insert(node, tree); |
---|
| 809 | _node_potential->set(node, (*_node_potential)[node] + _delta_sum); |
---|
| 810 | _delta1->push(node, (*_node_potential)[node]); |
---|
| 811 | |
---|
| 812 | if (_delta2->state(node) == _delta2->IN_HEAP) { |
---|
| 813 | _delta2->erase(node); |
---|
| 814 | } |
---|
| 815 | |
---|
| 816 | for (InArcIt a(_graph, node); a != INVALID; ++a) { |
---|
| 817 | Node v = _graph.source(a); |
---|
| 818 | Value rw = (*_node_potential)[node] + (*_node_potential)[v] - |
---|
| 819 | dualScale * _weight[a]; |
---|
| 820 | if (node == v) { |
---|
| 821 | if (_allow_loops && _graph.direction(a)) { |
---|
| 822 | _delta3->push(a, rw / 2); |
---|
| 823 | } |
---|
| 824 | } else if ((*_status)[v] == EVEN) { |
---|
| 825 | _delta3->push(a, rw / 2); |
---|
| 826 | } else if ((*_status)[v] == MATCHED) { |
---|
| 827 | if (_delta2->state(v) != _delta2->IN_HEAP) { |
---|
| 828 | _pred->set(v, a); |
---|
| 829 | _delta2->push(v, rw); |
---|
| 830 | } else if ((*_delta2)[v] > rw) { |
---|
| 831 | _pred->set(v, a); |
---|
| 832 | _delta2->decrease(v, rw); |
---|
| 833 | } |
---|
| 834 | } |
---|
| 835 | } |
---|
| 836 | } |
---|
| 837 | |
---|
| 838 | void matchedToOdd(Node node, int tree) { |
---|
| 839 | _tree_set->insert(node, tree); |
---|
| 840 | _node_potential->set(node, (*_node_potential)[node] - _delta_sum); |
---|
| 841 | |
---|
| 842 | if (_delta2->state(node) == _delta2->IN_HEAP) { |
---|
| 843 | _delta2->erase(node); |
---|
| 844 | } |
---|
| 845 | } |
---|
| 846 | |
---|
| 847 | void evenToMatched(Node node, int tree) { |
---|
| 848 | _delta1->erase(node); |
---|
| 849 | _node_potential->set(node, (*_node_potential)[node] - _delta_sum); |
---|
| 850 | Arc min = INVALID; |
---|
| 851 | Value minrw = std::numeric_limits<Value>::max(); |
---|
| 852 | for (InArcIt a(_graph, node); a != INVALID; ++a) { |
---|
| 853 | Node v = _graph.source(a); |
---|
| 854 | Value rw = (*_node_potential)[node] + (*_node_potential)[v] - |
---|
| 855 | dualScale * _weight[a]; |
---|
| 856 | |
---|
| 857 | if (node == v) { |
---|
| 858 | if (_allow_loops && _graph.direction(a)) { |
---|
| 859 | _delta3->erase(a); |
---|
| 860 | } |
---|
| 861 | } else if ((*_status)[v] == EVEN) { |
---|
| 862 | _delta3->erase(a); |
---|
| 863 | if (minrw > rw) { |
---|
| 864 | min = _graph.oppositeArc(a); |
---|
| 865 | minrw = rw; |
---|
| 866 | } |
---|
| 867 | } else if ((*_status)[v] == MATCHED) { |
---|
| 868 | if ((*_pred)[v] == a) { |
---|
| 869 | Arc mina = INVALID; |
---|
| 870 | Value minrwa = std::numeric_limits<Value>::max(); |
---|
| 871 | for (OutArcIt aa(_graph, v); aa != INVALID; ++aa) { |
---|
| 872 | Node va = _graph.target(aa); |
---|
| 873 | if ((*_status)[va] != EVEN || |
---|
| 874 | _tree_set->find(va) == tree) continue; |
---|
| 875 | Value rwa = (*_node_potential)[v] + (*_node_potential)[va] - |
---|
| 876 | dualScale * _weight[aa]; |
---|
| 877 | if (minrwa > rwa) { |
---|
| 878 | minrwa = rwa; |
---|
| 879 | mina = aa; |
---|
| 880 | } |
---|
| 881 | } |
---|
| 882 | if (mina != INVALID) { |
---|
| 883 | _pred->set(v, mina); |
---|
| 884 | _delta2->increase(v, minrwa); |
---|
| 885 | } else { |
---|
| 886 | _pred->set(v, INVALID); |
---|
| 887 | _delta2->erase(v); |
---|
| 888 | } |
---|
| 889 | } |
---|
| 890 | } |
---|
| 891 | } |
---|
| 892 | if (min != INVALID) { |
---|
| 893 | _pred->set(node, min); |
---|
| 894 | _delta2->push(node, minrw); |
---|
| 895 | } else { |
---|
| 896 | _pred->set(node, INVALID); |
---|
| 897 | } |
---|
| 898 | } |
---|
| 899 | |
---|
| 900 | void oddToMatched(Node node) { |
---|
| 901 | _node_potential->set(node, (*_node_potential)[node] + _delta_sum); |
---|
| 902 | Arc min = INVALID; |
---|
| 903 | Value minrw = std::numeric_limits<Value>::max(); |
---|
| 904 | for (InArcIt a(_graph, node); a != INVALID; ++a) { |
---|
| 905 | Node v = _graph.source(a); |
---|
| 906 | if ((*_status)[v] != EVEN) continue; |
---|
| 907 | Value rw = (*_node_potential)[node] + (*_node_potential)[v] - |
---|
| 908 | dualScale * _weight[a]; |
---|
| 909 | |
---|
| 910 | if (minrw > rw) { |
---|
| 911 | min = _graph.oppositeArc(a); |
---|
| 912 | minrw = rw; |
---|
| 913 | } |
---|
| 914 | } |
---|
| 915 | if (min != INVALID) { |
---|
| 916 | _pred->set(node, min); |
---|
| 917 | _delta2->push(node, minrw); |
---|
| 918 | } else { |
---|
| 919 | _pred->set(node, INVALID); |
---|
| 920 | } |
---|
| 921 | } |
---|
| 922 | |
---|
| 923 | void alternatePath(Node even, int tree) { |
---|
| 924 | Node odd; |
---|
| 925 | |
---|
| 926 | _status->set(even, MATCHED); |
---|
| 927 | evenToMatched(even, tree); |
---|
| 928 | |
---|
| 929 | Arc prev = (*_matching)[even]; |
---|
| 930 | while (prev != INVALID) { |
---|
| 931 | odd = _graph.target(prev); |
---|
| 932 | even = _graph.target((*_pred)[odd]); |
---|
| 933 | _matching->set(odd, (*_pred)[odd]); |
---|
| 934 | _status->set(odd, MATCHED); |
---|
| 935 | oddToMatched(odd); |
---|
| 936 | |
---|
| 937 | prev = (*_matching)[even]; |
---|
| 938 | _status->set(even, MATCHED); |
---|
| 939 | _matching->set(even, _graph.oppositeArc((*_matching)[odd])); |
---|
| 940 | evenToMatched(even, tree); |
---|
| 941 | } |
---|
| 942 | } |
---|
| 943 | |
---|
| 944 | void destroyTree(int tree) { |
---|
| 945 | for (typename TreeSet::ItemIt n(*_tree_set, tree); n != INVALID; ++n) { |
---|
| 946 | if ((*_status)[n] == EVEN) { |
---|
| 947 | _status->set(n, MATCHED); |
---|
| 948 | evenToMatched(n, tree); |
---|
| 949 | } else if ((*_status)[n] == ODD) { |
---|
| 950 | _status->set(n, MATCHED); |
---|
| 951 | oddToMatched(n); |
---|
| 952 | } |
---|
| 953 | } |
---|
| 954 | _tree_set->eraseClass(tree); |
---|
| 955 | } |
---|
| 956 | |
---|
| 957 | |
---|
| 958 | void unmatchNode(const Node& node) { |
---|
| 959 | int tree = _tree_set->find(node); |
---|
| 960 | |
---|
| 961 | alternatePath(node, tree); |
---|
| 962 | destroyTree(tree); |
---|
| 963 | |
---|
| 964 | _matching->set(node, INVALID); |
---|
| 965 | } |
---|
| 966 | |
---|
| 967 | |
---|
| 968 | void augmentOnEdge(const Edge& edge) { |
---|
| 969 | Node left = _graph.u(edge); |
---|
| 970 | int left_tree = _tree_set->find(left); |
---|
| 971 | |
---|
| 972 | alternatePath(left, left_tree); |
---|
| 973 | destroyTree(left_tree); |
---|
| 974 | _matching->set(left, _graph.direct(edge, true)); |
---|
| 975 | |
---|
| 976 | Node right = _graph.v(edge); |
---|
| 977 | int right_tree = _tree_set->find(right); |
---|
| 978 | |
---|
| 979 | alternatePath(right, right_tree); |
---|
| 980 | destroyTree(right_tree); |
---|
| 981 | _matching->set(right, _graph.direct(edge, false)); |
---|
| 982 | } |
---|
| 983 | |
---|
| 984 | void augmentOnArc(const Arc& arc) { |
---|
| 985 | Node left = _graph.source(arc); |
---|
| 986 | _status->set(left, MATCHED); |
---|
| 987 | _matching->set(left, arc); |
---|
| 988 | _pred->set(left, arc); |
---|
| 989 | |
---|
| 990 | Node right = _graph.target(arc); |
---|
| 991 | int right_tree = _tree_set->find(right); |
---|
| 992 | |
---|
| 993 | alternatePath(right, right_tree); |
---|
| 994 | destroyTree(right_tree); |
---|
| 995 | _matching->set(right, _graph.oppositeArc(arc)); |
---|
| 996 | } |
---|
| 997 | |
---|
| 998 | void extendOnArc(const Arc& arc) { |
---|
| 999 | Node base = _graph.target(arc); |
---|
| 1000 | int tree = _tree_set->find(base); |
---|
| 1001 | |
---|
| 1002 | Node odd = _graph.source(arc); |
---|
| 1003 | _tree_set->insert(odd, tree); |
---|
| 1004 | _status->set(odd, ODD); |
---|
| 1005 | matchedToOdd(odd, tree); |
---|
| 1006 | _pred->set(odd, arc); |
---|
| 1007 | |
---|
| 1008 | Node even = _graph.target((*_matching)[odd]); |
---|
| 1009 | _tree_set->insert(even, tree); |
---|
| 1010 | _status->set(even, EVEN); |
---|
| 1011 | matchedToEven(even, tree); |
---|
| 1012 | } |
---|
| 1013 | |
---|
| 1014 | void cycleOnEdge(const Edge& edge, int tree) { |
---|
| 1015 | Node nca = INVALID; |
---|
| 1016 | std::vector<Node> left_path, right_path; |
---|
| 1017 | |
---|
| 1018 | { |
---|
| 1019 | std::set<Node> left_set, right_set; |
---|
| 1020 | Node left = _graph.u(edge); |
---|
| 1021 | left_path.push_back(left); |
---|
| 1022 | left_set.insert(left); |
---|
| 1023 | |
---|
| 1024 | Node right = _graph.v(edge); |
---|
| 1025 | right_path.push_back(right); |
---|
| 1026 | right_set.insert(right); |
---|
| 1027 | |
---|
| 1028 | while (true) { |
---|
| 1029 | |
---|
| 1030 | if (left_set.find(right) != left_set.end()) { |
---|
| 1031 | nca = right; |
---|
| 1032 | break; |
---|
| 1033 | } |
---|
| 1034 | |
---|
| 1035 | if ((*_matching)[left] == INVALID) break; |
---|
| 1036 | |
---|
| 1037 | left = _graph.target((*_matching)[left]); |
---|
| 1038 | left_path.push_back(left); |
---|
| 1039 | left = _graph.target((*_pred)[left]); |
---|
| 1040 | left_path.push_back(left); |
---|
| 1041 | |
---|
| 1042 | left_set.insert(left); |
---|
| 1043 | |
---|
| 1044 | if (right_set.find(left) != right_set.end()) { |
---|
| 1045 | nca = left; |
---|
| 1046 | break; |
---|
| 1047 | } |
---|
| 1048 | |
---|
| 1049 | if ((*_matching)[right] == INVALID) break; |
---|
| 1050 | |
---|
| 1051 | right = _graph.target((*_matching)[right]); |
---|
| 1052 | right_path.push_back(right); |
---|
| 1053 | right = _graph.target((*_pred)[right]); |
---|
| 1054 | right_path.push_back(right); |
---|
| 1055 | |
---|
| 1056 | right_set.insert(right); |
---|
| 1057 | |
---|
| 1058 | } |
---|
| 1059 | |
---|
| 1060 | if (nca == INVALID) { |
---|
| 1061 | if ((*_matching)[left] == INVALID) { |
---|
| 1062 | nca = right; |
---|
| 1063 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1064 | nca = _graph.target((*_matching)[nca]); |
---|
| 1065 | right_path.push_back(nca); |
---|
| 1066 | nca = _graph.target((*_pred)[nca]); |
---|
| 1067 | right_path.push_back(nca); |
---|
| 1068 | } |
---|
| 1069 | } else { |
---|
| 1070 | nca = left; |
---|
| 1071 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1072 | nca = _graph.target((*_matching)[nca]); |
---|
| 1073 | left_path.push_back(nca); |
---|
| 1074 | nca = _graph.target((*_pred)[nca]); |
---|
| 1075 | left_path.push_back(nca); |
---|
| 1076 | } |
---|
| 1077 | } |
---|
| 1078 | } |
---|
| 1079 | } |
---|
| 1080 | |
---|
| 1081 | alternatePath(nca, tree); |
---|
| 1082 | Arc prev; |
---|
| 1083 | |
---|
| 1084 | prev = _graph.direct(edge, true); |
---|
| 1085 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1086 | _matching->set(left_path[i], prev); |
---|
| 1087 | _status->set(left_path[i], MATCHED); |
---|
| 1088 | evenToMatched(left_path[i], tree); |
---|
| 1089 | |
---|
| 1090 | prev = _graph.oppositeArc((*_pred)[left_path[i + 1]]); |
---|
| 1091 | _status->set(left_path[i + 1], MATCHED); |
---|
| 1092 | oddToMatched(left_path[i + 1]); |
---|
| 1093 | } |
---|
| 1094 | _matching->set(nca, prev); |
---|
| 1095 | |
---|
| 1096 | for (int i = 0; right_path[i] != nca; i += 2) { |
---|
| 1097 | _status->set(right_path[i], MATCHED); |
---|
| 1098 | evenToMatched(right_path[i], tree); |
---|
| 1099 | |
---|
| 1100 | _matching->set(right_path[i + 1], (*_pred)[right_path[i + 1]]); |
---|
| 1101 | _status->set(right_path[i + 1], MATCHED); |
---|
| 1102 | oddToMatched(right_path[i + 1]); |
---|
| 1103 | } |
---|
| 1104 | |
---|
| 1105 | destroyTree(tree); |
---|
| 1106 | } |
---|
| 1107 | |
---|
| 1108 | void extractCycle(const Arc &arc) { |
---|
| 1109 | Node left = _graph.source(arc); |
---|
| 1110 | Node odd = _graph.target((*_matching)[left]); |
---|
| 1111 | Arc prev; |
---|
| 1112 | while (odd != left) { |
---|
| 1113 | Node even = _graph.target((*_matching)[odd]); |
---|
| 1114 | prev = (*_matching)[odd]; |
---|
| 1115 | odd = _graph.target((*_matching)[even]); |
---|
| 1116 | _matching->set(even, _graph.oppositeArc(prev)); |
---|
| 1117 | } |
---|
| 1118 | _matching->set(left, arc); |
---|
| 1119 | |
---|
| 1120 | Node right = _graph.target(arc); |
---|
| 1121 | int right_tree = _tree_set->find(right); |
---|
| 1122 | alternatePath(right, right_tree); |
---|
| 1123 | destroyTree(right_tree); |
---|
| 1124 | _matching->set(right, _graph.oppositeArc(arc)); |
---|
| 1125 | } |
---|
| 1126 | |
---|
| 1127 | public: |
---|
| 1128 | |
---|
| 1129 | /// \brief Constructor |
---|
| 1130 | /// |
---|
| 1131 | /// Constructor. |
---|
| 1132 | MaxWeightedFractionalMatching(const Graph& graph, const WeightMap& weight, |
---|
| 1133 | bool allow_loops = true) |
---|
| 1134 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 1135 | _node_potential(0), _node_num(0), _allow_loops(allow_loops), |
---|
| 1136 | _status(0), _pred(0), |
---|
| 1137 | _tree_set_index(0), _tree_set(0), |
---|
| 1138 | |
---|
| 1139 | _delta1_index(0), _delta1(0), |
---|
| 1140 | _delta2_index(0), _delta2(0), |
---|
| 1141 | _delta3_index(0), _delta3(0), |
---|
| 1142 | |
---|
| 1143 | _delta_sum() {} |
---|
| 1144 | |
---|
| 1145 | ~MaxWeightedFractionalMatching() { |
---|
| 1146 | destroyStructures(); |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | /// \name Execution Control |
---|
| 1150 | /// The simplest way to execute the algorithm is to use the |
---|
| 1151 | /// \ref run() member function. |
---|
| 1152 | |
---|
| 1153 | ///@{ |
---|
| 1154 | |
---|
| 1155 | /// \brief Initialize the algorithm |
---|
| 1156 | /// |
---|
| 1157 | /// This function initializes the algorithm. |
---|
| 1158 | void init() { |
---|
| 1159 | createStructures(); |
---|
| 1160 | |
---|
| 1161 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1162 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
| 1163 | (*_delta2_index)[n] = _delta2->PRE_HEAP; |
---|
| 1164 | } |
---|
| 1165 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1166 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
| 1167 | } |
---|
| 1168 | |
---|
[955] | 1169 | _delta1->clear(); |
---|
| 1170 | _delta2->clear(); |
---|
| 1171 | _delta3->clear(); |
---|
| 1172 | _tree_set->clear(); |
---|
| 1173 | |
---|
[948] | 1174 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1175 | Value max = 0; |
---|
| 1176 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1177 | if (_graph.target(e) == n && !_allow_loops) continue; |
---|
| 1178 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 1179 | max = (dualScale * _weight[e]) / 2; |
---|
| 1180 | } |
---|
| 1181 | } |
---|
| 1182 | _node_potential->set(n, max); |
---|
| 1183 | _delta1->push(n, max); |
---|
| 1184 | |
---|
| 1185 | _tree_set->insert(n); |
---|
| 1186 | |
---|
| 1187 | _matching->set(n, INVALID); |
---|
| 1188 | _status->set(n, EVEN); |
---|
| 1189 | } |
---|
| 1190 | |
---|
| 1191 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1192 | Node left = _graph.u(e); |
---|
| 1193 | Node right = _graph.v(e); |
---|
| 1194 | if (left == right && !_allow_loops) continue; |
---|
| 1195 | _delta3->push(e, ((*_node_potential)[left] + |
---|
| 1196 | (*_node_potential)[right] - |
---|
| 1197 | dualScale * _weight[e]) / 2); |
---|
| 1198 | } |
---|
| 1199 | } |
---|
| 1200 | |
---|
| 1201 | /// \brief Start the algorithm |
---|
| 1202 | /// |
---|
| 1203 | /// This function starts the algorithm. |
---|
| 1204 | /// |
---|
| 1205 | /// \pre \ref init() must be called before using this function. |
---|
| 1206 | void start() { |
---|
| 1207 | enum OpType { |
---|
| 1208 | D1, D2, D3 |
---|
| 1209 | }; |
---|
| 1210 | |
---|
| 1211 | int unmatched = _node_num; |
---|
| 1212 | while (unmatched > 0) { |
---|
| 1213 | Value d1 = !_delta1->empty() ? |
---|
| 1214 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
| 1215 | |
---|
| 1216 | Value d2 = !_delta2->empty() ? |
---|
| 1217 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 1218 | |
---|
| 1219 | Value d3 = !_delta3->empty() ? |
---|
| 1220 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 1221 | |
---|
| 1222 | _delta_sum = d3; OpType ot = D3; |
---|
| 1223 | if (d1 < _delta_sum) { _delta_sum = d1; ot = D1; } |
---|
| 1224 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
| 1225 | |
---|
| 1226 | switch (ot) { |
---|
| 1227 | case D1: |
---|
| 1228 | { |
---|
| 1229 | Node n = _delta1->top(); |
---|
| 1230 | unmatchNode(n); |
---|
| 1231 | --unmatched; |
---|
| 1232 | } |
---|
| 1233 | break; |
---|
| 1234 | case D2: |
---|
| 1235 | { |
---|
| 1236 | Node n = _delta2->top(); |
---|
| 1237 | Arc a = (*_pred)[n]; |
---|
| 1238 | if ((*_matching)[n] == INVALID) { |
---|
| 1239 | augmentOnArc(a); |
---|
| 1240 | --unmatched; |
---|
| 1241 | } else { |
---|
| 1242 | Node v = _graph.target((*_matching)[n]); |
---|
| 1243 | if ((*_matching)[n] != |
---|
| 1244 | _graph.oppositeArc((*_matching)[v])) { |
---|
| 1245 | extractCycle(a); |
---|
| 1246 | --unmatched; |
---|
| 1247 | } else { |
---|
| 1248 | extendOnArc(a); |
---|
| 1249 | } |
---|
| 1250 | } |
---|
| 1251 | } break; |
---|
| 1252 | case D3: |
---|
| 1253 | { |
---|
| 1254 | Edge e = _delta3->top(); |
---|
| 1255 | |
---|
| 1256 | Node left = _graph.u(e); |
---|
| 1257 | Node right = _graph.v(e); |
---|
| 1258 | |
---|
| 1259 | int left_tree = _tree_set->find(left); |
---|
| 1260 | int right_tree = _tree_set->find(right); |
---|
| 1261 | |
---|
| 1262 | if (left_tree == right_tree) { |
---|
| 1263 | cycleOnEdge(e, left_tree); |
---|
| 1264 | --unmatched; |
---|
| 1265 | } else { |
---|
| 1266 | augmentOnEdge(e); |
---|
| 1267 | unmatched -= 2; |
---|
| 1268 | } |
---|
| 1269 | } break; |
---|
| 1270 | } |
---|
| 1271 | } |
---|
| 1272 | } |
---|
| 1273 | |
---|
| 1274 | /// \brief Run the algorithm. |
---|
| 1275 | /// |
---|
[950] | 1276 | /// This method runs the \c %MaxWeightedFractionalMatching algorithm. |
---|
[948] | 1277 | /// |
---|
| 1278 | /// \note mwfm.run() is just a shortcut of the following code. |
---|
| 1279 | /// \code |
---|
| 1280 | /// mwfm.init(); |
---|
| 1281 | /// mwfm.start(); |
---|
| 1282 | /// \endcode |
---|
| 1283 | void run() { |
---|
| 1284 | init(); |
---|
| 1285 | start(); |
---|
| 1286 | } |
---|
| 1287 | |
---|
| 1288 | /// @} |
---|
| 1289 | |
---|
| 1290 | /// \name Primal Solution |
---|
| 1291 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
| 1292 | /// matching.\n |
---|
| 1293 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1294 | /// using them. |
---|
| 1295 | |
---|
| 1296 | /// @{ |
---|
| 1297 | |
---|
| 1298 | /// \brief Return the weight of the matching. |
---|
| 1299 | /// |
---|
| 1300 | /// This function returns the weight of the found matching. This |
---|
| 1301 | /// value is scaled by \ref primalScale "primal scale". |
---|
| 1302 | /// |
---|
| 1303 | /// \pre Either run() or start() must be called before using this function. |
---|
| 1304 | Value matchingWeight() const { |
---|
| 1305 | Value sum = 0; |
---|
| 1306 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1307 | if ((*_matching)[n] != INVALID) { |
---|
| 1308 | sum += _weight[(*_matching)[n]]; |
---|
| 1309 | } |
---|
| 1310 | } |
---|
| 1311 | return sum * primalScale / 2; |
---|
| 1312 | } |
---|
| 1313 | |
---|
| 1314 | /// \brief Return the number of covered nodes in the matching. |
---|
| 1315 | /// |
---|
| 1316 | /// This function returns the number of covered nodes in the matching. |
---|
| 1317 | /// |
---|
| 1318 | /// \pre Either run() or start() must be called before using this function. |
---|
| 1319 | int matchingSize() const { |
---|
| 1320 | int num = 0; |
---|
| 1321 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1322 | if ((*_matching)[n] != INVALID) { |
---|
| 1323 | ++num; |
---|
| 1324 | } |
---|
| 1325 | } |
---|
| 1326 | return num; |
---|
| 1327 | } |
---|
| 1328 | |
---|
| 1329 | /// \brief Return \c true if the given edge is in the matching. |
---|
| 1330 | /// |
---|
| 1331 | /// This function returns \c true if the given edge is in the |
---|
| 1332 | /// found matching. The result is scaled by \ref primalScale |
---|
| 1333 | /// "primal scale". |
---|
| 1334 | /// |
---|
| 1335 | /// \pre Either run() or start() must be called before using this function. |
---|
[951] | 1336 | int matching(const Edge& edge) const { |
---|
| 1337 | return (edge == (*_matching)[_graph.u(edge)] ? 1 : 0) |
---|
| 1338 | + (edge == (*_matching)[_graph.v(edge)] ? 1 : 0); |
---|
[948] | 1339 | } |
---|
| 1340 | |
---|
| 1341 | /// \brief Return the fractional matching arc (or edge) incident |
---|
| 1342 | /// to the given node. |
---|
| 1343 | /// |
---|
| 1344 | /// This function returns one of the fractional matching arc (or |
---|
| 1345 | /// edge) incident to the given node in the found matching or \c |
---|
| 1346 | /// INVALID if the node is not covered by the matching or if the |
---|
| 1347 | /// node is on an odd length cycle then it is the successor edge |
---|
| 1348 | /// on the cycle. |
---|
| 1349 | /// |
---|
| 1350 | /// \pre Either run() or start() must be called before using this function. |
---|
| 1351 | Arc matching(const Node& node) const { |
---|
| 1352 | return (*_matching)[node]; |
---|
| 1353 | } |
---|
| 1354 | |
---|
| 1355 | /// \brief Return a const reference to the matching map. |
---|
| 1356 | /// |
---|
| 1357 | /// This function returns a const reference to a node map that stores |
---|
| 1358 | /// the matching arc (or edge) incident to each node. |
---|
| 1359 | const MatchingMap& matchingMap() const { |
---|
| 1360 | return *_matching; |
---|
| 1361 | } |
---|
| 1362 | |
---|
| 1363 | /// @} |
---|
| 1364 | |
---|
| 1365 | /// \name Dual Solution |
---|
| 1366 | /// Functions to get the dual solution.\n |
---|
| 1367 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1368 | /// using them. |
---|
| 1369 | |
---|
| 1370 | /// @{ |
---|
| 1371 | |
---|
| 1372 | /// \brief Return the value of the dual solution. |
---|
| 1373 | /// |
---|
| 1374 | /// This function returns the value of the dual solution. |
---|
| 1375 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
| 1376 | /// "dual scale". |
---|
| 1377 | /// |
---|
| 1378 | /// \pre Either run() or start() must be called before using this function. |
---|
| 1379 | Value dualValue() const { |
---|
| 1380 | Value sum = 0; |
---|
| 1381 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1382 | sum += nodeValue(n); |
---|
| 1383 | } |
---|
| 1384 | return sum; |
---|
| 1385 | } |
---|
| 1386 | |
---|
| 1387 | /// \brief Return the dual value (potential) of the given node. |
---|
| 1388 | /// |
---|
| 1389 | /// This function returns the dual value (potential) of the given node. |
---|
| 1390 | /// |
---|
| 1391 | /// \pre Either run() or start() must be called before using this function. |
---|
| 1392 | Value nodeValue(const Node& n) const { |
---|
| 1393 | return (*_node_potential)[n]; |
---|
| 1394 | } |
---|
| 1395 | |
---|
| 1396 | /// @} |
---|
| 1397 | |
---|
| 1398 | }; |
---|
| 1399 | |
---|
| 1400 | /// \ingroup matching |
---|
| 1401 | /// |
---|
| 1402 | /// \brief Weighted fractional perfect matching in general graphs |
---|
| 1403 | /// |
---|
| 1404 | /// This class provides an efficient implementation of fractional |
---|
[950] | 1405 | /// matching algorithm. The implementation uses priority queues and |
---|
| 1406 | /// provides \f$O(nm\log n)\f$ time complexity. |
---|
[948] | 1407 | /// |
---|
| 1408 | /// The maximum weighted fractional perfect matching is a relaxation |
---|
| 1409 | /// of the maximum weighted perfect matching problem where the odd |
---|
| 1410 | /// set constraints are omitted. |
---|
| 1411 | /// It can be formulated with the following linear program. |
---|
| 1412 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
| 1413 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 1414 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
| 1415 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 1416 | /// \f$X\f$. The result must be the union of a matching with one |
---|
| 1417 | /// value edges and a set of odd length cycles with half value edges. |
---|
| 1418 | /// |
---|
| 1419 | /// The algorithm calculates an optimal fractional matching and a |
---|
| 1420 | /// proof of the optimality. The solution of the dual problem can be |
---|
| 1421 | /// used to check the result of the algorithm. The dual linear |
---|
| 1422 | /// problem is the following. |
---|
| 1423 | /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f] |
---|
[950] | 1424 | /// \f[\min \sum_{u \in V}y_u \f] |
---|
[948] | 1425 | /// |
---|
| 1426 | /// The algorithm can be executed with the run() function. |
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| 1427 | /// After it the matching (the primal solution) and the dual solution |
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| 1428 | /// can be obtained using the query functions. |
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[951] | 1429 | /// |
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| 1430 | /// The primal solution is multiplied by |
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| 1431 | /// \ref MaxWeightedPerfectFractionalMatching::primalScale "2". |
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| 1432 | /// If the value type is integer, then the dual |
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| 1433 | /// solution is scaled by |
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| 1434 | /// \ref MaxWeightedPerfectFractionalMatching::dualScale "4". |
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[948] | 1435 | /// |
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| 1436 | /// \tparam GR The undirected graph type the algorithm runs on. |
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| 1437 | /// \tparam WM The type edge weight map. The default type is |
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| 1438 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
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| 1439 | #ifdef DOXYGEN |
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| 1440 | template <typename GR, typename WM> |
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| 1441 | #else |
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| 1442 | template <typename GR, |
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| 1443 | typename WM = typename GR::template EdgeMap<int> > |
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| 1444 | #endif |
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| 1445 | class MaxWeightedPerfectFractionalMatching { |
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| 1446 | public: |
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| 1447 | |
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| 1448 | /// The graph type of the algorithm |
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| 1449 | typedef GR Graph; |
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| 1450 | /// The type of the edge weight map |
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| 1451 | typedef WM WeightMap; |
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| 1452 | /// The value type of the edge weights |
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| 1453 | typedef typename WeightMap::Value Value; |
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| 1454 | |
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| 1455 | /// The type of the matching map |
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| 1456 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
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| 1457 | MatchingMap; |
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| 1458 | |
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| 1459 | /// \brief Scaling factor for primal solution |
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| 1460 | /// |
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[951] | 1461 | /// Scaling factor for primal solution. |
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| 1462 | static const int primalScale = 2; |
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[948] | 1463 | |
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| 1464 | /// \brief Scaling factor for dual solution |
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| 1465 | /// |
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| 1466 | /// Scaling factor for dual solution. It is equal to 4 or 1 |
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| 1467 | /// according to the value type. |
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| 1468 | static const int dualScale = |
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| 1469 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
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| 1470 | |
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| 1471 | private: |
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| 1472 | |
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| 1473 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 1474 | |
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| 1475 | typedef typename Graph::template NodeMap<Value> NodePotential; |
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| 1476 | |
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| 1477 | const Graph& _graph; |
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| 1478 | const WeightMap& _weight; |
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| 1479 | |
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| 1480 | MatchingMap* _matching; |
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| 1481 | NodePotential* _node_potential; |
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| 1482 | |
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| 1483 | int _node_num; |
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| 1484 | bool _allow_loops; |
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| 1485 | |
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| 1486 | enum Status { |
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| 1487 | EVEN = -1, MATCHED = 0, ODD = 1 |
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| 1488 | }; |
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| 1489 | |
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| 1490 | typedef typename Graph::template NodeMap<Status> StatusMap; |
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| 1491 | StatusMap* _status; |
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| 1492 | |
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| 1493 | typedef typename Graph::template NodeMap<Arc> PredMap; |
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| 1494 | PredMap* _pred; |
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| 1495 | |
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| 1496 | typedef ExtendFindEnum<IntNodeMap> TreeSet; |
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| 1497 | |
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| 1498 | IntNodeMap *_tree_set_index; |
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| 1499 | TreeSet *_tree_set; |
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| 1500 | |
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| 1501 | IntNodeMap *_delta2_index; |
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| 1502 | BinHeap<Value, IntNodeMap> *_delta2; |
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| 1503 | |
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| 1504 | IntEdgeMap *_delta3_index; |
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| 1505 | BinHeap<Value, IntEdgeMap> *_delta3; |
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| 1506 | |
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| 1507 | Value _delta_sum; |
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| 1508 | |
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| 1509 | void createStructures() { |
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| 1510 | _node_num = countNodes(_graph); |
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| 1511 | |
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| 1512 | if (!_matching) { |
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| 1513 | _matching = new MatchingMap(_graph); |
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| 1514 | } |
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| 1515 | if (!_node_potential) { |
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| 1516 | _node_potential = new NodePotential(_graph); |
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| 1517 | } |
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| 1518 | if (!_status) { |
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| 1519 | _status = new StatusMap(_graph); |
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| 1520 | } |
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| 1521 | if (!_pred) { |
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| 1522 | _pred = new PredMap(_graph); |
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| 1523 | } |
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| 1524 | if (!_tree_set) { |
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| 1525 | _tree_set_index = new IntNodeMap(_graph); |
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| 1526 | _tree_set = new TreeSet(*_tree_set_index); |
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| 1527 | } |
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| 1528 | if (!_delta2) { |
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| 1529 | _delta2_index = new IntNodeMap(_graph); |
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| 1530 | _delta2 = new BinHeap<Value, IntNodeMap>(*_delta2_index); |
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| 1531 | } |
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| 1532 | if (!_delta3) { |
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| 1533 | _delta3_index = new IntEdgeMap(_graph); |
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| 1534 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
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| 1535 | } |
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| 1536 | } |
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| 1537 | |
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| 1538 | void destroyStructures() { |
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| 1539 | if (_matching) { |
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| 1540 | delete _matching; |
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| 1541 | } |
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| 1542 | if (_node_potential) { |
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| 1543 | delete _node_potential; |
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| 1544 | } |
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| 1545 | if (_status) { |
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| 1546 | delete _status; |
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| 1547 | } |
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| 1548 | if (_pred) { |
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| 1549 | delete _pred; |
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| 1550 | } |
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| 1551 | if (_tree_set) { |
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| 1552 | delete _tree_set_index; |
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| 1553 | delete _tree_set; |
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| 1554 | } |
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| 1555 | if (_delta2) { |
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| 1556 | delete _delta2_index; |
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| 1557 | delete _delta2; |
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| 1558 | } |
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| 1559 | if (_delta3) { |
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| 1560 | delete _delta3_index; |
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| 1561 | delete _delta3; |
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| 1562 | } |
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| 1563 | } |
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| 1564 | |
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| 1565 | void matchedToEven(Node node, int tree) { |
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| 1566 | _tree_set->insert(node, tree); |
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| 1567 | _node_potential->set(node, (*_node_potential)[node] + _delta_sum); |
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| 1568 | |
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| 1569 | if (_delta2->state(node) == _delta2->IN_HEAP) { |
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| 1570 | _delta2->erase(node); |
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| 1571 | } |
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| 1572 | |
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| 1573 | for (InArcIt a(_graph, node); a != INVALID; ++a) { |
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| 1574 | Node v = _graph.source(a); |
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| 1575 | Value rw = (*_node_potential)[node] + (*_node_potential)[v] - |
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| 1576 | dualScale * _weight[a]; |
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| 1577 | if (node == v) { |
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| 1578 | if (_allow_loops && _graph.direction(a)) { |
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| 1579 | _delta3->push(a, rw / 2); |
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| 1580 | } |
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| 1581 | } else if ((*_status)[v] == EVEN) { |
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| 1582 | _delta3->push(a, rw / 2); |
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| 1583 | } else if ((*_status)[v] == MATCHED) { |
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| 1584 | if (_delta2->state(v) != _delta2->IN_HEAP) { |
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| 1585 | _pred->set(v, a); |
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| 1586 | _delta2->push(v, rw); |
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| 1587 | } else if ((*_delta2)[v] > rw) { |
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| 1588 | _pred->set(v, a); |
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| 1589 | _delta2->decrease(v, rw); |
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| 1590 | } |
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| 1591 | } |
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| 1592 | } |
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| 1593 | } |
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| 1594 | |
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| 1595 | void matchedToOdd(Node node, int tree) { |
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| 1596 | _tree_set->insert(node, tree); |
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| 1597 | _node_potential->set(node, (*_node_potential)[node] - _delta_sum); |
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| 1598 | |
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| 1599 | if (_delta2->state(node) == _delta2->IN_HEAP) { |
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| 1600 | _delta2->erase(node); |
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| 1601 | } |
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| 1602 | } |
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| 1603 | |
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| 1604 | void evenToMatched(Node node, int tree) { |
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| 1605 | _node_potential->set(node, (*_node_potential)[node] - _delta_sum); |
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| 1606 | Arc min = INVALID; |
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| 1607 | Value minrw = std::numeric_limits<Value>::max(); |
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| 1608 | for (InArcIt a(_graph, node); a != INVALID; ++a) { |
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| 1609 | Node v = _graph.source(a); |
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| 1610 | Value rw = (*_node_potential)[node] + (*_node_potential)[v] - |
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| 1611 | dualScale * _weight[a]; |
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| 1612 | |
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| 1613 | if (node == v) { |
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| 1614 | if (_allow_loops && _graph.direction(a)) { |
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| 1615 | _delta3->erase(a); |
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| 1616 | } |
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| 1617 | } else if ((*_status)[v] == EVEN) { |
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| 1618 | _delta3->erase(a); |
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| 1619 | if (minrw > rw) { |
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| 1620 | min = _graph.oppositeArc(a); |
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| 1621 | minrw = rw; |
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| 1622 | } |
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| 1623 | } else if ((*_status)[v] == MATCHED) { |
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| 1624 | if ((*_pred)[v] == a) { |
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| 1625 | Arc mina = INVALID; |
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| 1626 | Value minrwa = std::numeric_limits<Value>::max(); |
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| 1627 | for (OutArcIt aa(_graph, v); aa != INVALID; ++aa) { |
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| 1628 | Node va = _graph.target(aa); |
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| 1629 | if ((*_status)[va] != EVEN || |
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| 1630 | _tree_set->find(va) == tree) continue; |
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| 1631 | Value rwa = (*_node_potential)[v] + (*_node_potential)[va] - |
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| 1632 | dualScale * _weight[aa]; |
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| 1633 | if (minrwa > rwa) { |
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| 1634 | minrwa = rwa; |
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| 1635 | mina = aa; |
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| 1636 | } |
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| 1637 | } |
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| 1638 | if (mina != INVALID) { |
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| 1639 | _pred->set(v, mina); |
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| 1640 | _delta2->increase(v, minrwa); |
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| 1641 | } else { |
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| 1642 | _pred->set(v, INVALID); |
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| 1643 | _delta2->erase(v); |
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| 1644 | } |
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| 1645 | } |
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| 1646 | } |
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| 1647 | } |
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| 1648 | if (min != INVALID) { |
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| 1649 | _pred->set(node, min); |
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| 1650 | _delta2->push(node, minrw); |
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| 1651 | } else { |
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| 1652 | _pred->set(node, INVALID); |
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| 1653 | } |
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| 1654 | } |
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| 1655 | |
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| 1656 | void oddToMatched(Node node) { |
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| 1657 | _node_potential->set(node, (*_node_potential)[node] + _delta_sum); |
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| 1658 | Arc min = INVALID; |
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| 1659 | Value minrw = std::numeric_limits<Value>::max(); |
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| 1660 | for (InArcIt a(_graph, node); a != INVALID; ++a) { |
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| 1661 | Node v = _graph.source(a); |
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| 1662 | if ((*_status)[v] != EVEN) continue; |
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| 1663 | Value rw = (*_node_potential)[node] + (*_node_potential)[v] - |
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| 1664 | dualScale * _weight[a]; |
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| 1665 | |
---|
| 1666 | if (minrw > rw) { |
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| 1667 | min = _graph.oppositeArc(a); |
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| 1668 | minrw = rw; |
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| 1669 | } |
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| 1670 | } |
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| 1671 | if (min != INVALID) { |
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| 1672 | _pred->set(node, min); |
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| 1673 | _delta2->push(node, minrw); |
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| 1674 | } else { |
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| 1675 | _pred->set(node, INVALID); |
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| 1676 | } |
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| 1677 | } |
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| 1678 | |
---|
| 1679 | void alternatePath(Node even, int tree) { |
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| 1680 | Node odd; |
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| 1681 | |
---|
| 1682 | _status->set(even, MATCHED); |
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| 1683 | evenToMatched(even, tree); |
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| 1684 | |
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| 1685 | Arc prev = (*_matching)[even]; |
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| 1686 | while (prev != INVALID) { |
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| 1687 | odd = _graph.target(prev); |
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| 1688 | even = _graph.target((*_pred)[odd]); |
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| 1689 | _matching->set(odd, (*_pred)[odd]); |
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| 1690 | _status->set(odd, MATCHED); |
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| 1691 | oddToMatched(odd); |
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| 1692 | |
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| 1693 | prev = (*_matching)[even]; |
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| 1694 | _status->set(even, MATCHED); |
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| 1695 | _matching->set(even, _graph.oppositeArc((*_matching)[odd])); |
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| 1696 | evenToMatched(even, tree); |
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| 1697 | } |
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| 1698 | } |
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| 1699 | |
---|
| 1700 | void destroyTree(int tree) { |
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| 1701 | for (typename TreeSet::ItemIt n(*_tree_set, tree); n != INVALID; ++n) { |
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| 1702 | if ((*_status)[n] == EVEN) { |
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| 1703 | _status->set(n, MATCHED); |
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| 1704 | evenToMatched(n, tree); |
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| 1705 | } else if ((*_status)[n] == ODD) { |
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| 1706 | _status->set(n, MATCHED); |
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| 1707 | oddToMatched(n); |
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| 1708 | } |
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| 1709 | } |
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| 1710 | _tree_set->eraseClass(tree); |
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| 1711 | } |
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| 1712 | |
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| 1713 | void augmentOnEdge(const Edge& edge) { |
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| 1714 | Node left = _graph.u(edge); |
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| 1715 | int left_tree = _tree_set->find(left); |
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| 1716 | |
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| 1717 | alternatePath(left, left_tree); |
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| 1718 | destroyTree(left_tree); |
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| 1719 | _matching->set(left, _graph.direct(edge, true)); |
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| 1720 | |
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| 1721 | Node right = _graph.v(edge); |
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| 1722 | int right_tree = _tree_set->find(right); |
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| 1723 | |
---|
| 1724 | alternatePath(right, right_tree); |
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| 1725 | destroyTree(right_tree); |
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| 1726 | _matching->set(right, _graph.direct(edge, false)); |
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| 1727 | } |
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| 1728 | |
---|
| 1729 | void augmentOnArc(const Arc& arc) { |
---|
| 1730 | Node left = _graph.source(arc); |
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| 1731 | _status->set(left, MATCHED); |
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| 1732 | _matching->set(left, arc); |
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| 1733 | _pred->set(left, arc); |
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| 1734 | |
---|
| 1735 | Node right = _graph.target(arc); |
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| 1736 | int right_tree = _tree_set->find(right); |
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| 1737 | |
---|
| 1738 | alternatePath(right, right_tree); |
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| 1739 | destroyTree(right_tree); |
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| 1740 | _matching->set(right, _graph.oppositeArc(arc)); |
---|
| 1741 | } |
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| 1742 | |
---|
| 1743 | void extendOnArc(const Arc& arc) { |
---|
| 1744 | Node base = _graph.target(arc); |
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| 1745 | int tree = _tree_set->find(base); |
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| 1746 | |
---|
| 1747 | Node odd = _graph.source(arc); |
---|
| 1748 | _tree_set->insert(odd, tree); |
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| 1749 | _status->set(odd, ODD); |
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| 1750 | matchedToOdd(odd, tree); |
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| 1751 | _pred->set(odd, arc); |
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| 1752 | |
---|
| 1753 | Node even = _graph.target((*_matching)[odd]); |
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| 1754 | _tree_set->insert(even, tree); |
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| 1755 | _status->set(even, EVEN); |
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| 1756 | matchedToEven(even, tree); |
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| 1757 | } |
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| 1758 | |
---|
| 1759 | void cycleOnEdge(const Edge& edge, int tree) { |
---|
| 1760 | Node nca = INVALID; |
---|
| 1761 | std::vector<Node> left_path, right_path; |
---|
| 1762 | |
---|
| 1763 | { |
---|
| 1764 | std::set<Node> left_set, right_set; |
---|
| 1765 | Node left = _graph.u(edge); |
---|
| 1766 | left_path.push_back(left); |
---|
| 1767 | left_set.insert(left); |
---|
| 1768 | |
---|
| 1769 | Node right = _graph.v(edge); |
---|
| 1770 | right_path.push_back(right); |
---|
| 1771 | right_set.insert(right); |
---|
| 1772 | |
---|
| 1773 | while (true) { |
---|
| 1774 | |
---|
| 1775 | if (left_set.find(right) != left_set.end()) { |
---|
| 1776 | nca = right; |
---|
| 1777 | break; |
---|
| 1778 | } |
---|
| 1779 | |
---|
| 1780 | if ((*_matching)[left] == INVALID) break; |
---|
| 1781 | |
---|
| 1782 | left = _graph.target((*_matching)[left]); |
---|
| 1783 | left_path.push_back(left); |
---|
| 1784 | left = _graph.target((*_pred)[left]); |
---|
| 1785 | left_path.push_back(left); |
---|
| 1786 | |
---|
| 1787 | left_set.insert(left); |
---|
| 1788 | |
---|
| 1789 | if (right_set.find(left) != right_set.end()) { |
---|
| 1790 | nca = left; |
---|
| 1791 | break; |
---|
| 1792 | } |
---|
| 1793 | |
---|
| 1794 | if ((*_matching)[right] == INVALID) break; |
---|
| 1795 | |
---|
| 1796 | right = _graph.target((*_matching)[right]); |
---|
| 1797 | right_path.push_back(right); |
---|
| 1798 | right = _graph.target((*_pred)[right]); |
---|
| 1799 | right_path.push_back(right); |
---|
| 1800 | |
---|
| 1801 | right_set.insert(right); |
---|
| 1802 | |
---|
| 1803 | } |
---|
| 1804 | |
---|
| 1805 | if (nca == INVALID) { |
---|
| 1806 | if ((*_matching)[left] == INVALID) { |
---|
| 1807 | nca = right; |
---|
| 1808 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1809 | nca = _graph.target((*_matching)[nca]); |
---|
| 1810 | right_path.push_back(nca); |
---|
| 1811 | nca = _graph.target((*_pred)[nca]); |
---|
| 1812 | right_path.push_back(nca); |
---|
| 1813 | } |
---|
| 1814 | } else { |
---|
| 1815 | nca = left; |
---|
| 1816 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1817 | nca = _graph.target((*_matching)[nca]); |
---|
| 1818 | left_path.push_back(nca); |
---|
| 1819 | nca = _graph.target((*_pred)[nca]); |
---|
| 1820 | left_path.push_back(nca); |
---|
| 1821 | } |
---|
| 1822 | } |
---|
| 1823 | } |
---|
| 1824 | } |
---|
| 1825 | |
---|
| 1826 | alternatePath(nca, tree); |
---|
| 1827 | Arc prev; |
---|
| 1828 | |
---|
| 1829 | prev = _graph.direct(edge, true); |
---|
| 1830 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1831 | _matching->set(left_path[i], prev); |
---|
| 1832 | _status->set(left_path[i], MATCHED); |
---|
| 1833 | evenToMatched(left_path[i], tree); |
---|
| 1834 | |
---|
| 1835 | prev = _graph.oppositeArc((*_pred)[left_path[i + 1]]); |
---|
| 1836 | _status->set(left_path[i + 1], MATCHED); |
---|
| 1837 | oddToMatched(left_path[i + 1]); |
---|
| 1838 | } |
---|
| 1839 | _matching->set(nca, prev); |
---|
| 1840 | |
---|
| 1841 | for (int i = 0; right_path[i] != nca; i += 2) { |
---|
| 1842 | _status->set(right_path[i], MATCHED); |
---|
| 1843 | evenToMatched(right_path[i], tree); |
---|
| 1844 | |
---|
| 1845 | _matching->set(right_path[i + 1], (*_pred)[right_path[i + 1]]); |
---|
| 1846 | _status->set(right_path[i + 1], MATCHED); |
---|
| 1847 | oddToMatched(right_path[i + 1]); |
---|
| 1848 | } |
---|
| 1849 | |
---|
| 1850 | destroyTree(tree); |
---|
| 1851 | } |
---|
| 1852 | |
---|
| 1853 | void extractCycle(const Arc &arc) { |
---|
| 1854 | Node left = _graph.source(arc); |
---|
| 1855 | Node odd = _graph.target((*_matching)[left]); |
---|
| 1856 | Arc prev; |
---|
| 1857 | while (odd != left) { |
---|
| 1858 | Node even = _graph.target((*_matching)[odd]); |
---|
| 1859 | prev = (*_matching)[odd]; |
---|
| 1860 | odd = _graph.target((*_matching)[even]); |
---|
| 1861 | _matching->set(even, _graph.oppositeArc(prev)); |
---|
| 1862 | } |
---|
| 1863 | _matching->set(left, arc); |
---|
| 1864 | |
---|
| 1865 | Node right = _graph.target(arc); |
---|
| 1866 | int right_tree = _tree_set->find(right); |
---|
| 1867 | alternatePath(right, right_tree); |
---|
| 1868 | destroyTree(right_tree); |
---|
| 1869 | _matching->set(right, _graph.oppositeArc(arc)); |
---|
| 1870 | } |
---|
| 1871 | |
---|
| 1872 | public: |
---|
| 1873 | |
---|
| 1874 | /// \brief Constructor |
---|
| 1875 | /// |
---|
| 1876 | /// Constructor. |
---|
| 1877 | MaxWeightedPerfectFractionalMatching(const Graph& graph, |
---|
| 1878 | const WeightMap& weight, |
---|
| 1879 | bool allow_loops = true) |
---|
| 1880 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 1881 | _node_potential(0), _node_num(0), _allow_loops(allow_loops), |
---|
| 1882 | _status(0), _pred(0), |
---|
| 1883 | _tree_set_index(0), _tree_set(0), |
---|
| 1884 | |
---|
| 1885 | _delta2_index(0), _delta2(0), |
---|
| 1886 | _delta3_index(0), _delta3(0), |
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| 1887 | |
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| 1888 | _delta_sum() {} |
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| 1889 | |
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| 1890 | ~MaxWeightedPerfectFractionalMatching() { |
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| 1891 | destroyStructures(); |
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| 1892 | } |
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| 1893 | |
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| 1894 | /// \name Execution Control |
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| 1895 | /// The simplest way to execute the algorithm is to use the |
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| 1896 | /// \ref run() member function. |
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| 1897 | |
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| 1898 | ///@{ |
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| 1899 | |
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| 1900 | /// \brief Initialize the algorithm |
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| 1901 | /// |
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| 1902 | /// This function initializes the algorithm. |
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| 1903 | void init() { |
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| 1904 | createStructures(); |
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| 1905 | |
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| 1906 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 1907 | (*_delta2_index)[n] = _delta2->PRE_HEAP; |
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| 1908 | } |
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| 1909 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 1910 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
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| 1911 | } |
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| 1912 | |
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[955] | 1913 | _delta2->clear(); |
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| 1914 | _delta3->clear(); |
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| 1915 | _tree_set->clear(); |
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| 1916 | |
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[948] | 1917 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 1918 | Value max = - std::numeric_limits<Value>::max(); |
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| 1919 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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| 1920 | if (_graph.target(e) == n && !_allow_loops) continue; |
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| 1921 | if ((dualScale * _weight[e]) / 2 > max) { |
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| 1922 | max = (dualScale * _weight[e]) / 2; |
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| 1923 | } |
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| 1924 | } |
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| 1925 | _node_potential->set(n, max); |
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| 1926 | |
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| 1927 | _tree_set->insert(n); |
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| 1928 | |
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| 1929 | _matching->set(n, INVALID); |
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| 1930 | _status->set(n, EVEN); |
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| 1931 | } |
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| 1932 | |
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| 1933 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 1934 | Node left = _graph.u(e); |
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| 1935 | Node right = _graph.v(e); |
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| 1936 | if (left == right && !_allow_loops) continue; |
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| 1937 | _delta3->push(e, ((*_node_potential)[left] + |
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| 1938 | (*_node_potential)[right] - |
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| 1939 | dualScale * _weight[e]) / 2); |
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| 1940 | } |
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| 1941 | } |
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| 1942 | |
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| 1943 | /// \brief Start the algorithm |
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| 1944 | /// |
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| 1945 | /// This function starts the algorithm. |
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| 1946 | /// |
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| 1947 | /// \pre \ref init() must be called before using this function. |
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| 1948 | bool start() { |
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| 1949 | enum OpType { |
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| 1950 | D2, D3 |
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| 1951 | }; |
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| 1952 | |
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| 1953 | int unmatched = _node_num; |
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| 1954 | while (unmatched > 0) { |
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| 1955 | Value d2 = !_delta2->empty() ? |
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| 1956 | _delta2->prio() : std::numeric_limits<Value>::max(); |
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| 1957 | |
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| 1958 | Value d3 = !_delta3->empty() ? |
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| 1959 | _delta3->prio() : std::numeric_limits<Value>::max(); |
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| 1960 | |
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| 1961 | _delta_sum = d3; OpType ot = D3; |
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| 1962 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
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| 1963 | |
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| 1964 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
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| 1965 | return false; |
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| 1966 | } |
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| 1967 | |
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| 1968 | switch (ot) { |
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| 1969 | case D2: |
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| 1970 | { |
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| 1971 | Node n = _delta2->top(); |
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| 1972 | Arc a = (*_pred)[n]; |
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| 1973 | if ((*_matching)[n] == INVALID) { |
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| 1974 | augmentOnArc(a); |
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| 1975 | --unmatched; |
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| 1976 | } else { |
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| 1977 | Node v = _graph.target((*_matching)[n]); |
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| 1978 | if ((*_matching)[n] != |
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| 1979 | _graph.oppositeArc((*_matching)[v])) { |
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| 1980 | extractCycle(a); |
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| 1981 | --unmatched; |
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| 1982 | } else { |
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| 1983 | extendOnArc(a); |
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| 1984 | } |
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| 1985 | } |
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| 1986 | } break; |
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| 1987 | case D3: |
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| 1988 | { |
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| 1989 | Edge e = _delta3->top(); |
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| 1990 | |
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| 1991 | Node left = _graph.u(e); |
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| 1992 | Node right = _graph.v(e); |
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| 1993 | |
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| 1994 | int left_tree = _tree_set->find(left); |
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| 1995 | int right_tree = _tree_set->find(right); |
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| 1996 | |
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| 1997 | if (left_tree == right_tree) { |
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| 1998 | cycleOnEdge(e, left_tree); |
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| 1999 | --unmatched; |
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| 2000 | } else { |
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| 2001 | augmentOnEdge(e); |
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| 2002 | unmatched -= 2; |
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| 2003 | } |
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| 2004 | } break; |
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| 2005 | } |
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| 2006 | } |
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| 2007 | return true; |
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| 2008 | } |
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| 2009 | |
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| 2010 | /// \brief Run the algorithm. |
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| 2011 | /// |
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[956] | 2012 | /// This method runs the \c %MaxWeightedPerfectFractionalMatching |
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[950] | 2013 | /// algorithm. |
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[948] | 2014 | /// |
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| 2015 | /// \note mwfm.run() is just a shortcut of the following code. |
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| 2016 | /// \code |
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| 2017 | /// mwpfm.init(); |
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| 2018 | /// mwpfm.start(); |
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| 2019 | /// \endcode |
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| 2020 | bool run() { |
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| 2021 | init(); |
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| 2022 | return start(); |
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| 2023 | } |
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| 2024 | |
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| 2025 | /// @} |
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| 2026 | |
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| 2027 | /// \name Primal Solution |
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| 2028 | /// Functions to get the primal solution, i.e. the maximum weighted |
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| 2029 | /// matching.\n |
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| 2030 | /// Either \ref run() or \ref start() function should be called before |
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| 2031 | /// using them. |
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| 2032 | |
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| 2033 | /// @{ |
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| 2034 | |
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| 2035 | /// \brief Return the weight of the matching. |
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| 2036 | /// |
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| 2037 | /// This function returns the weight of the found matching. This |
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| 2038 | /// value is scaled by \ref primalScale "primal scale". |
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| 2039 | /// |
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| 2040 | /// \pre Either run() or start() must be called before using this function. |
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| 2041 | Value matchingWeight() const { |
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| 2042 | Value sum = 0; |
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| 2043 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 2044 | if ((*_matching)[n] != INVALID) { |
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| 2045 | sum += _weight[(*_matching)[n]]; |
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| 2046 | } |
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| 2047 | } |
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| 2048 | return sum * primalScale / 2; |
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| 2049 | } |
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| 2050 | |
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| 2051 | /// \brief Return the number of covered nodes in the matching. |
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| 2052 | /// |
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| 2053 | /// This function returns the number of covered nodes in the matching. |
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| 2054 | /// |
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| 2055 | /// \pre Either run() or start() must be called before using this function. |
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| 2056 | int matchingSize() const { |
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| 2057 | int num = 0; |
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| 2058 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 2059 | if ((*_matching)[n] != INVALID) { |
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| 2060 | ++num; |
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| 2061 | } |
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| 2062 | } |
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| 2063 | return num; |
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| 2064 | } |
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| 2065 | |
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| 2066 | /// \brief Return \c true if the given edge is in the matching. |
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| 2067 | /// |
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| 2068 | /// This function returns \c true if the given edge is in the |
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| 2069 | /// found matching. The result is scaled by \ref primalScale |
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| 2070 | /// "primal scale". |
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| 2071 | /// |
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| 2072 | /// \pre Either run() or start() must be called before using this function. |
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[951] | 2073 | int matching(const Edge& edge) const { |
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| 2074 | return (edge == (*_matching)[_graph.u(edge)] ? 1 : 0) |
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| 2075 | + (edge == (*_matching)[_graph.v(edge)] ? 1 : 0); |
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[948] | 2076 | } |
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| 2077 | |
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| 2078 | /// \brief Return the fractional matching arc (or edge) incident |
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| 2079 | /// to the given node. |
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| 2080 | /// |
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| 2081 | /// This function returns one of the fractional matching arc (or |
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| 2082 | /// edge) incident to the given node in the found matching or \c |
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| 2083 | /// INVALID if the node is not covered by the matching or if the |
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| 2084 | /// node is on an odd length cycle then it is the successor edge |
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| 2085 | /// on the cycle. |
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| 2086 | /// |
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| 2087 | /// \pre Either run() or start() must be called before using this function. |
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| 2088 | Arc matching(const Node& node) const { |
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| 2089 | return (*_matching)[node]; |
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| 2090 | } |
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| 2091 | |
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| 2092 | /// \brief Return a const reference to the matching map. |
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| 2093 | /// |
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| 2094 | /// This function returns a const reference to a node map that stores |
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| 2095 | /// the matching arc (or edge) incident to each node. |
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| 2096 | const MatchingMap& matchingMap() const { |
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| 2097 | return *_matching; |
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| 2098 | } |
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| 2099 | |
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| 2100 | /// @} |
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| 2101 | |
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| 2102 | /// \name Dual Solution |
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| 2103 | /// Functions to get the dual solution.\n |
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| 2104 | /// Either \ref run() or \ref start() function should be called before |
---|
| 2105 | /// using them. |
---|
| 2106 | |
---|
| 2107 | /// @{ |
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| 2108 | |
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| 2109 | /// \brief Return the value of the dual solution. |
---|
| 2110 | /// |
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| 2111 | /// This function returns the value of the dual solution. |
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| 2112 | /// It should be equal to the primal value scaled by \ref dualScale |
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| 2113 | /// "dual scale". |
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| 2114 | /// |
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| 2115 | /// \pre Either run() or start() must be called before using this function. |
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| 2116 | Value dualValue() const { |
---|
| 2117 | Value sum = 0; |
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| 2118 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 2119 | sum += nodeValue(n); |
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| 2120 | } |
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| 2121 | return sum; |
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| 2122 | } |
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| 2123 | |
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| 2124 | /// \brief Return the dual value (potential) of the given node. |
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| 2125 | /// |
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| 2126 | /// This function returns the dual value (potential) of the given node. |
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| 2127 | /// |
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| 2128 | /// \pre Either run() or start() must be called before using this function. |
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| 2129 | Value nodeValue(const Node& n) const { |
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| 2130 | return (*_node_potential)[n]; |
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| 2131 | } |
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| 2132 | |
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| 2133 | /// @} |
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| 2134 | |
---|
| 2135 | }; |
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| 2136 | |
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| 2137 | } //END OF NAMESPACE LEMON |
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| 2138 | |
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| 2139 | #endif //LEMON_FRACTIONAL_MATCHING_H |
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