[338] | 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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[338] | 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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[947] | 19 | #ifndef LEMON_MATCHING_H |
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| 20 | #define LEMON_MATCHING_H |
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[338] | 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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[949] | 31 | #include <lemon/fractional_matching.h> |
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[338] | 32 | |
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| 33 | ///\ingroup matching |
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| 34 | ///\file |
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[339] | 35 | ///\brief Maximum matching algorithms in general graphs. |
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[338] | 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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[339] | 39 | /// \ingroup matching |
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[338] | 40 | /// |
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[637] | 41 | /// \brief Maximum cardinality matching in general graphs |
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[338] | 42 | /// |
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[637] | 43 | /// This class implements Edmonds' alternating forest matching algorithm |
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[640] | 44 | /// for finding a maximum cardinality matching in a general undirected graph. |
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[947] | 45 | /// It can be started from an arbitrary initial matching |
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[637] | 46 | /// (the default is the empty one). |
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[338] | 47 | /// |
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[342] | 48 | /// The dual solution of the problem is a map of the nodes to |
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[637] | 49 | /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D), |
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| 50 | /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds |
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| 51 | /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph |
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| 52 | /// with factor-critical components, the nodes in \c ODD/A form the |
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| 53 | /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having |
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| 54 | /// a perfect matching. The number of the factor-critical components |
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[339] | 55 | /// minus the number of barrier nodes is a lower bound on the |
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[342] | 56 | /// unmatched nodes, and the matching is optimal if and only if this bound is |
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[640] | 57 | /// tight. This decomposition can be obtained using \ref status() or |
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| 58 | /// \ref statusMap() after running the algorithm. |
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[338] | 59 | /// |
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[640] | 60 | /// \tparam GR The undirected graph type the algorithm runs on. |
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[606] | 61 | template <typename GR> |
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[338] | 62 | class MaxMatching { |
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[339] | 63 | public: |
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| 64 | |
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[637] | 65 | /// The graph type of the algorithm |
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[606] | 66 | typedef GR Graph; |
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[640] | 67 | /// The type of the matching map |
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[339] | 68 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
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| 69 | MatchingMap; |
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| 70 | |
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[637] | 71 | ///\brief Status constants for Gallai-Edmonds decomposition. |
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[339] | 72 | /// |
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[947] | 73 | ///These constants are used for indicating the Gallai-Edmonds |
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[637] | 74 | ///decomposition of a graph. The nodes with status \c EVEN (or \c D) |
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| 75 | ///induce a subgraph with factor-critical components, the nodes with |
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| 76 | ///status \c ODD (or \c A) form the canonical barrier, and the nodes |
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[947] | 77 | ///with status \c MATCHED (or \c C) induce a subgraph having a |
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[637] | 78 | ///perfect matching. |
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[339] | 79 | enum Status { |
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[637] | 80 | EVEN = 1, ///< = 1. (\c D is an alias for \c EVEN.) |
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| 81 | D = 1, |
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| 82 | MATCHED = 0, ///< = 0. (\c C is an alias for \c MATCHED.) |
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| 83 | C = 0, |
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| 84 | ODD = -1, ///< = -1. (\c A is an alias for \c ODD.) |
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| 85 | A = -1, |
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| 86 | UNMATCHED = -2 ///< = -2. |
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[339] | 87 | }; |
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| 88 | |
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[640] | 89 | /// The type of the status map |
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[339] | 90 | typedef typename Graph::template NodeMap<Status> StatusMap; |
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| 91 | |
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| 92 | private: |
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[338] | 93 | |
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| 94 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 95 | |
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[339] | 96 | typedef UnionFindEnum<IntNodeMap> BlossomSet; |
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| 97 | typedef ExtendFindEnum<IntNodeMap> TreeSet; |
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| 98 | typedef RangeMap<Node> NodeIntMap; |
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| 99 | typedef MatchingMap EarMap; |
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| 100 | typedef std::vector<Node> NodeQueue; |
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| 101 | |
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| 102 | const Graph& _graph; |
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| 103 | MatchingMap* _matching; |
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| 104 | StatusMap* _status; |
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| 105 | |
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| 106 | EarMap* _ear; |
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| 107 | |
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| 108 | IntNodeMap* _blossom_set_index; |
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| 109 | BlossomSet* _blossom_set; |
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| 110 | NodeIntMap* _blossom_rep; |
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| 111 | |
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| 112 | IntNodeMap* _tree_set_index; |
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| 113 | TreeSet* _tree_set; |
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| 114 | |
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| 115 | NodeQueue _node_queue; |
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| 116 | int _process, _postpone, _last; |
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| 117 | |
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[1423] | 118 | int _node_num, _unmatched; |
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[339] | 119 | |
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| 120 | private: |
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| 121 | |
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| 122 | void createStructures() { |
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| 123 | _node_num = countNodes(_graph); |
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| 124 | if (!_matching) { |
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| 125 | _matching = new MatchingMap(_graph); |
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| 126 | } |
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| 127 | if (!_status) { |
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| 128 | _status = new StatusMap(_graph); |
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| 129 | } |
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| 130 | if (!_ear) { |
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| 131 | _ear = new EarMap(_graph); |
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| 132 | } |
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| 133 | if (!_blossom_set) { |
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| 134 | _blossom_set_index = new IntNodeMap(_graph); |
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| 135 | _blossom_set = new BlossomSet(*_blossom_set_index); |
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| 136 | } |
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| 137 | if (!_blossom_rep) { |
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| 138 | _blossom_rep = new NodeIntMap(_node_num); |
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| 139 | } |
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| 140 | if (!_tree_set) { |
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| 141 | _tree_set_index = new IntNodeMap(_graph); |
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| 142 | _tree_set = new TreeSet(*_tree_set_index); |
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| 143 | } |
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| 144 | _node_queue.resize(_node_num); |
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| 145 | } |
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| 146 | |
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| 147 | void destroyStructures() { |
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| 148 | if (_matching) { |
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| 149 | delete _matching; |
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| 150 | } |
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| 151 | if (_status) { |
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| 152 | delete _status; |
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| 153 | } |
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| 154 | if (_ear) { |
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| 155 | delete _ear; |
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| 156 | } |
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| 157 | if (_blossom_set) { |
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| 158 | delete _blossom_set; |
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| 159 | delete _blossom_set_index; |
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| 160 | } |
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| 161 | if (_blossom_rep) { |
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| 162 | delete _blossom_rep; |
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| 163 | } |
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| 164 | if (_tree_set) { |
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| 165 | delete _tree_set_index; |
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| 166 | delete _tree_set; |
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| 167 | } |
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| 168 | } |
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| 169 | |
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| 170 | void processDense(const Node& n) { |
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| 171 | _process = _postpone = _last = 0; |
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| 172 | _node_queue[_last++] = n; |
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| 173 | |
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| 174 | while (_process != _last) { |
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| 175 | Node u = _node_queue[_process++]; |
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| 176 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 177 | Node v = _graph.target(a); |
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| 178 | if ((*_status)[v] == MATCHED) { |
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| 179 | extendOnArc(a); |
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| 180 | } else if ((*_status)[v] == UNMATCHED) { |
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| 181 | augmentOnArc(a); |
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[1423] | 182 | --_unmatched; |
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[339] | 183 | return; |
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| 184 | } |
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| 185 | } |
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| 186 | } |
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| 187 | |
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| 188 | while (_postpone != _last) { |
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| 189 | Node u = _node_queue[_postpone++]; |
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| 190 | |
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| 191 | for (OutArcIt a(_graph, u); a != INVALID ; ++a) { |
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| 192 | Node v = _graph.target(a); |
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| 193 | |
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| 194 | if ((*_status)[v] == EVEN) { |
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| 195 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 196 | shrinkOnEdge(a); |
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| 197 | } |
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| 198 | } |
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| 199 | |
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| 200 | while (_process != _last) { |
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| 201 | Node w = _node_queue[_process++]; |
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| 202 | for (OutArcIt b(_graph, w); b != INVALID; ++b) { |
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| 203 | Node x = _graph.target(b); |
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| 204 | if ((*_status)[x] == MATCHED) { |
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| 205 | extendOnArc(b); |
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| 206 | } else if ((*_status)[x] == UNMATCHED) { |
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| 207 | augmentOnArc(b); |
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[1423] | 208 | --_unmatched; |
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[339] | 209 | return; |
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| 210 | } |
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| 211 | } |
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| 212 | } |
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| 213 | } |
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| 214 | } |
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| 215 | } |
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| 216 | |
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| 217 | void processSparse(const Node& n) { |
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| 218 | _process = _last = 0; |
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| 219 | _node_queue[_last++] = n; |
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| 220 | while (_process != _last) { |
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| 221 | Node u = _node_queue[_process++]; |
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| 222 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 223 | Node v = _graph.target(a); |
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| 224 | |
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| 225 | if ((*_status)[v] == EVEN) { |
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| 226 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 227 | shrinkOnEdge(a); |
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| 228 | } |
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| 229 | } else if ((*_status)[v] == MATCHED) { |
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| 230 | extendOnArc(a); |
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| 231 | } else if ((*_status)[v] == UNMATCHED) { |
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| 232 | augmentOnArc(a); |
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[1423] | 233 | --_unmatched; |
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[339] | 234 | return; |
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| 235 | } |
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| 236 | } |
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| 237 | } |
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| 238 | } |
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| 239 | |
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| 240 | void shrinkOnEdge(const Edge& e) { |
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| 241 | Node nca = INVALID; |
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| 242 | |
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| 243 | { |
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| 244 | std::set<Node> left_set, right_set; |
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| 245 | |
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| 246 | Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))]; |
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| 247 | left_set.insert(left); |
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| 248 | |
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| 249 | Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))]; |
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| 250 | right_set.insert(right); |
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| 251 | |
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| 252 | while (true) { |
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| 253 | if ((*_matching)[left] == INVALID) break; |
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| 254 | left = _graph.target((*_matching)[left]); |
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| 255 | left = (*_blossom_rep)[_blossom_set-> |
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| 256 | find(_graph.target((*_ear)[left]))]; |
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| 257 | if (right_set.find(left) != right_set.end()) { |
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| 258 | nca = left; |
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| 259 | break; |
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| 260 | } |
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| 261 | left_set.insert(left); |
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| 262 | |
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| 263 | if ((*_matching)[right] == INVALID) break; |
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| 264 | right = _graph.target((*_matching)[right]); |
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| 265 | right = (*_blossom_rep)[_blossom_set-> |
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| 266 | find(_graph.target((*_ear)[right]))]; |
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| 267 | if (left_set.find(right) != left_set.end()) { |
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| 268 | nca = right; |
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| 269 | break; |
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| 270 | } |
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| 271 | right_set.insert(right); |
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| 272 | } |
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| 273 | |
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| 274 | if (nca == INVALID) { |
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| 275 | if ((*_matching)[left] == INVALID) { |
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| 276 | nca = right; |
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| 277 | while (left_set.find(nca) == left_set.end()) { |
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| 278 | nca = _graph.target((*_matching)[nca]); |
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| 279 | nca =(*_blossom_rep)[_blossom_set-> |
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| 280 | find(_graph.target((*_ear)[nca]))]; |
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| 281 | } |
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| 282 | } else { |
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| 283 | nca = left; |
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| 284 | while (right_set.find(nca) == right_set.end()) { |
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| 285 | nca = _graph.target((*_matching)[nca]); |
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| 286 | nca = (*_blossom_rep)[_blossom_set-> |
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| 287 | find(_graph.target((*_ear)[nca]))]; |
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| 288 | } |
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| 289 | } |
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| 290 | } |
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| 291 | } |
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| 292 | |
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| 293 | { |
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| 294 | |
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| 295 | Node node = _graph.u(e); |
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| 296 | Arc arc = _graph.direct(e, true); |
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| 297 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 298 | |
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| 299 | while (base != nca) { |
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[628] | 300 | (*_ear)[node] = arc; |
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[339] | 301 | |
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| 302 | Node n = node; |
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| 303 | while (n != base) { |
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| 304 | n = _graph.target((*_matching)[n]); |
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| 305 | Arc a = (*_ear)[n]; |
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| 306 | n = _graph.target(a); |
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[628] | 307 | (*_ear)[n] = _graph.oppositeArc(a); |
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[339] | 308 | } |
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| 309 | node = _graph.target((*_matching)[base]); |
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| 310 | _tree_set->erase(base); |
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| 311 | _tree_set->erase(node); |
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| 312 | _blossom_set->insert(node, _blossom_set->find(base)); |
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[628] | 313 | (*_status)[node] = EVEN; |
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[339] | 314 | _node_queue[_last++] = node; |
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| 315 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 316 | node = _graph.target((*_ear)[node]); |
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| 317 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 318 | _blossom_set->join(_graph.target(arc), base); |
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| 319 | } |
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| 320 | } |
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| 321 | |
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[628] | 322 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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[339] | 323 | |
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| 324 | { |
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| 325 | |
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| 326 | Node node = _graph.v(e); |
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| 327 | Arc arc = _graph.direct(e, false); |
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| 328 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 329 | |
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| 330 | while (base != nca) { |
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[628] | 331 | (*_ear)[node] = arc; |
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[339] | 332 | |
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| 333 | Node n = node; |
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| 334 | while (n != base) { |
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| 335 | n = _graph.target((*_matching)[n]); |
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| 336 | Arc a = (*_ear)[n]; |
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| 337 | n = _graph.target(a); |
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[628] | 338 | (*_ear)[n] = _graph.oppositeArc(a); |
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[339] | 339 | } |
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| 340 | node = _graph.target((*_matching)[base]); |
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| 341 | _tree_set->erase(base); |
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| 342 | _tree_set->erase(node); |
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| 343 | _blossom_set->insert(node, _blossom_set->find(base)); |
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[628] | 344 | (*_status)[node] = EVEN; |
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[339] | 345 | _node_queue[_last++] = node; |
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| 346 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 347 | node = _graph.target((*_ear)[node]); |
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| 348 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 349 | _blossom_set->join(_graph.target(arc), base); |
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| 350 | } |
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| 351 | } |
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| 352 | |
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[628] | 353 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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[339] | 354 | } |
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| 355 | |
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| 356 | void extendOnArc(const Arc& a) { |
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| 357 | Node base = _graph.source(a); |
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| 358 | Node odd = _graph.target(a); |
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| 359 | |
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[628] | 360 | (*_ear)[odd] = _graph.oppositeArc(a); |
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[339] | 361 | Node even = _graph.target((*_matching)[odd]); |
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[628] | 362 | (*_blossom_rep)[_blossom_set->insert(even)] = even; |
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| 363 | (*_status)[odd] = ODD; |
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| 364 | (*_status)[even] = EVEN; |
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[339] | 365 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]); |
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| 366 | _tree_set->insert(odd, tree); |
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| 367 | _tree_set->insert(even, tree); |
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| 368 | _node_queue[_last++] = even; |
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| 369 | |
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| 370 | } |
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| 371 | |
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| 372 | void augmentOnArc(const Arc& a) { |
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| 373 | Node even = _graph.source(a); |
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| 374 | Node odd = _graph.target(a); |
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| 375 | |
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| 376 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]); |
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| 377 | |
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[628] | 378 | (*_matching)[odd] = _graph.oppositeArc(a); |
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| 379 | (*_status)[odd] = MATCHED; |
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[339] | 380 | |
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| 381 | Arc arc = (*_matching)[even]; |
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[628] | 382 | (*_matching)[even] = a; |
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[339] | 383 | |
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| 384 | while (arc != INVALID) { |
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| 385 | odd = _graph.target(arc); |
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| 386 | arc = (*_ear)[odd]; |
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| 387 | even = _graph.target(arc); |
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[628] | 388 | (*_matching)[odd] = arc; |
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[339] | 389 | arc = (*_matching)[even]; |
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[628] | 390 | (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]); |
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[339] | 391 | } |
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| 392 | |
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| 393 | for (typename TreeSet::ItemIt it(*_tree_set, tree); |
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| 394 | it != INVALID; ++it) { |
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| 395 | if ((*_status)[it] == ODD) { |
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[628] | 396 | (*_status)[it] = MATCHED; |
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[339] | 397 | } else { |
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| 398 | int blossom = _blossom_set->find(it); |
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| 399 | for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom); |
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| 400 | jt != INVALID; ++jt) { |
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[628] | 401 | (*_status)[jt] = MATCHED; |
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[339] | 402 | } |
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| 403 | _blossom_set->eraseClass(blossom); |
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| 404 | } |
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| 405 | } |
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| 406 | _tree_set->eraseClass(tree); |
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| 407 | |
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| 408 | } |
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[338] | 409 | |
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| 410 | public: |
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| 411 | |
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[339] | 412 | /// \brief Constructor |
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[338] | 413 | /// |
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[339] | 414 | /// Constructor. |
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| 415 | MaxMatching(const Graph& graph) |
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| 416 | : _graph(graph), _matching(0), _status(0), _ear(0), |
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| 417 | _blossom_set_index(0), _blossom_set(0), _blossom_rep(0), |
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| 418 | _tree_set_index(0), _tree_set(0) {} |
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| 419 | |
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| 420 | ~MaxMatching() { |
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| 421 | destroyStructures(); |
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| 422 | } |
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| 423 | |
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[637] | 424 | /// \name Execution Control |
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[342] | 425 | /// The simplest way to execute the algorithm is to use the |
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[637] | 426 | /// \c run() member function.\n |
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| 427 | /// If you need better control on the execution, you have to call |
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| 428 | /// one of the functions \ref init(), \ref greedyInit() or |
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| 429 | /// \ref matchingInit() first, then you can start the algorithm with |
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| 430 | /// \ref startSparse() or \ref startDense(). |
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[339] | 431 | |
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| 432 | ///@{ |
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| 433 | |
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[637] | 434 | /// \brief Set the initial matching to the empty matching. |
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[338] | 435 | /// |
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[637] | 436 | /// This function sets the initial matching to the empty matching. |
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[338] | 437 | void init() { |
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[339] | 438 | createStructures(); |
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| 439 | for(NodeIt n(_graph); n != INVALID; ++n) { |
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[628] | 440 | (*_matching)[n] = INVALID; |
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| 441 | (*_status)[n] = UNMATCHED; |
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[338] | 442 | } |
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[1423] | 443 | _unmatched = _node_num; |
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[338] | 444 | } |
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| 445 | |
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[637] | 446 | /// \brief Find an initial matching in a greedy way. |
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[338] | 447 | /// |
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[637] | 448 | /// This function finds an initial matching in a greedy way. |
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[338] | 449 | void greedyInit() { |
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[339] | 450 | createStructures(); |
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| 451 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[628] | 452 | (*_matching)[n] = INVALID; |
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| 453 | (*_status)[n] = UNMATCHED; |
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[338] | 454 | } |
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[1423] | 455 | _unmatched = _node_num; |
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[339] | 456 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 457 | if ((*_matching)[n] == INVALID) { |
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| 458 | for (OutArcIt a(_graph, n); a != INVALID ; ++a) { |
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| 459 | Node v = _graph.target(a); |
---|
| 460 | if ((*_matching)[v] == INVALID && v != n) { |
---|
[628] | 461 | (*_matching)[n] = a; |
---|
| 462 | (*_status)[n] = MATCHED; |
---|
| 463 | (*_matching)[v] = _graph.oppositeArc(a); |
---|
| 464 | (*_status)[v] = MATCHED; |
---|
[1423] | 465 | _unmatched -= 2; |
---|
[338] | 466 | break; |
---|
| 467 | } |
---|
| 468 | } |
---|
| 469 | } |
---|
| 470 | } |
---|
| 471 | } |
---|
| 472 | |
---|
[339] | 473 | |
---|
[637] | 474 | /// \brief Initialize the matching from a map. |
---|
[338] | 475 | /// |
---|
[637] | 476 | /// This function initializes the matching from a \c bool valued edge |
---|
| 477 | /// map. This map should have the property that there are no two incident |
---|
| 478 | /// edges with \c true value, i.e. it really contains a matching. |
---|
[606] | 479 | /// \return \c true if the map contains a matching. |
---|
[339] | 480 | template <typename MatchingMap> |
---|
| 481 | bool matchingInit(const MatchingMap& matching) { |
---|
| 482 | createStructures(); |
---|
| 483 | |
---|
| 484 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[628] | 485 | (*_matching)[n] = INVALID; |
---|
| 486 | (*_status)[n] = UNMATCHED; |
---|
[338] | 487 | } |
---|
[1423] | 488 | _unmatched = _node_num; |
---|
[339] | 489 | for(EdgeIt e(_graph); e!=INVALID; ++e) { |
---|
| 490 | if (matching[e]) { |
---|
| 491 | |
---|
| 492 | Node u = _graph.u(e); |
---|
| 493 | if ((*_matching)[u] != INVALID) return false; |
---|
[628] | 494 | (*_matching)[u] = _graph.direct(e, true); |
---|
| 495 | (*_status)[u] = MATCHED; |
---|
[339] | 496 | |
---|
| 497 | Node v = _graph.v(e); |
---|
| 498 | if ((*_matching)[v] != INVALID) return false; |
---|
[628] | 499 | (*_matching)[v] = _graph.direct(e, false); |
---|
| 500 | (*_status)[v] = MATCHED; |
---|
[1423] | 501 | |
---|
| 502 | _unmatched -= 2; |
---|
[339] | 503 | } |
---|
| 504 | } |
---|
| 505 | return true; |
---|
[338] | 506 | } |
---|
| 507 | |
---|
[637] | 508 | /// \brief Start Edmonds' algorithm |
---|
[338] | 509 | /// |
---|
[1423] | 510 | /// This function runs the original Edmonds' algorithm. If the |
---|
| 511 | /// \c decomposition parameter is set to false, then the Gallai-Edmonds |
---|
| 512 | /// decomposition is not computed. |
---|
[637] | 513 | /// |
---|
[698] | 514 | /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be |
---|
[637] | 515 | /// called before using this function. |
---|
[1423] | 516 | void startSparse(bool decomposition = true) { |
---|
| 517 | int _unmatched_limit = decomposition ? 0 : 1; |
---|
| 518 | for(NodeIt n(_graph); _unmatched > _unmatched_limit; ++n) { |
---|
[339] | 519 | if ((*_status)[n] == UNMATCHED) { |
---|
| 520 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 521 | _tree_set->insert(n); |
---|
[628] | 522 | (*_status)[n] = EVEN; |
---|
[1423] | 523 | --_unmatched; |
---|
[339] | 524 | processSparse(n); |
---|
[338] | 525 | } |
---|
| 526 | } |
---|
| 527 | } |
---|
| 528 | |
---|
[947] | 529 | /// \brief Start Edmonds' algorithm with a heuristic improvement |
---|
[637] | 530 | /// for dense graphs |
---|
[338] | 531 | /// |
---|
[637] | 532 | /// This function runs Edmonds' algorithm with a heuristic of postponing |
---|
[1423] | 533 | /// shrinks, therefore resulting in a faster algorithm for dense graphs. If |
---|
| 534 | /// the \c decomposition parameter is set to false, then the Gallai-Edmonds |
---|
| 535 | /// decomposition is not computed. |
---|
[637] | 536 | /// |
---|
[698] | 537 | /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be |
---|
[637] | 538 | /// called before using this function. |
---|
[1423] | 539 | void startDense(bool decomposition = true) { |
---|
| 540 | int _unmatched_limit = decomposition ? 0 : 1; |
---|
| 541 | for(NodeIt n(_graph); _unmatched > _unmatched_limit; ++n) { |
---|
[339] | 542 | if ((*_status)[n] == UNMATCHED) { |
---|
| 543 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 544 | _tree_set->insert(n); |
---|
[628] | 545 | (*_status)[n] = EVEN; |
---|
[1423] | 546 | --_unmatched; |
---|
[339] | 547 | processDense(n); |
---|
| 548 | } |
---|
| 549 | } |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | |
---|
[637] | 553 | /// \brief Run Edmonds' algorithm |
---|
[339] | 554 | /// |
---|
[947] | 555 | /// This function runs Edmonds' algorithm. An additional heuristic of |
---|
[1423] | 556 | /// postponing shrinks is used for relatively dense graphs (for which |
---|
| 557 | /// <tt>m>=2*n</tt> holds). If the \c decomposition parameter is set to |
---|
| 558 | /// false, then the Gallai-Edmonds decomposition is not computed. In some |
---|
| 559 | /// cases, this can speed up the algorithm significantly, especially when a |
---|
| 560 | /// maximum matching is computed in a dense graph with odd number of nodes. |
---|
| 561 | void run(bool decomposition = true) { |
---|
[339] | 562 | if (countEdges(_graph) < 2 * countNodes(_graph)) { |
---|
[338] | 563 | greedyInit(); |
---|
[1423] | 564 | startSparse(decomposition); |
---|
[338] | 565 | } else { |
---|
| 566 | init(); |
---|
[1423] | 567 | startDense(decomposition); |
---|
[338] | 568 | } |
---|
| 569 | } |
---|
| 570 | |
---|
[339] | 571 | /// @} |
---|
| 572 | |
---|
[637] | 573 | /// \name Primal Solution |
---|
| 574 | /// Functions to get the primal solution, i.e. the maximum matching. |
---|
[339] | 575 | |
---|
| 576 | /// @{ |
---|
[338] | 577 | |
---|
[637] | 578 | /// \brief Return the size (cardinality) of the matching. |
---|
[338] | 579 | /// |
---|
[947] | 580 | /// This function returns the size (cardinality) of the current matching. |
---|
[637] | 581 | /// After run() it returns the size of the maximum matching in the graph. |
---|
[339] | 582 | int matchingSize() const { |
---|
| 583 | int size = 0; |
---|
| 584 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 585 | if ((*_matching)[n] != INVALID) { |
---|
| 586 | ++size; |
---|
[338] | 587 | } |
---|
| 588 | } |
---|
[339] | 589 | return size / 2; |
---|
[338] | 590 | } |
---|
| 591 | |
---|
[637] | 592 | /// \brief Return \c true if the given edge is in the matching. |
---|
[339] | 593 | /// |
---|
[947] | 594 | /// This function returns \c true if the given edge is in the current |
---|
[637] | 595 | /// matching. |
---|
[339] | 596 | bool matching(const Edge& edge) const { |
---|
| 597 | return edge == (*_matching)[_graph.u(edge)]; |
---|
| 598 | } |
---|
| 599 | |
---|
[637] | 600 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[339] | 601 | /// |
---|
[637] | 602 | /// This function returns the matching arc (or edge) incident to the |
---|
[947] | 603 | /// given node in the current matching or \c INVALID if the node is |
---|
[637] | 604 | /// not covered by the matching. |
---|
[339] | 605 | Arc matching(const Node& n) const { |
---|
| 606 | return (*_matching)[n]; |
---|
| 607 | } |
---|
[338] | 608 | |
---|
[640] | 609 | /// \brief Return a const reference to the matching map. |
---|
| 610 | /// |
---|
| 611 | /// This function returns a const reference to a node map that stores |
---|
| 612 | /// the matching arc (or edge) incident to each node. |
---|
| 613 | const MatchingMap& matchingMap() const { |
---|
| 614 | return *_matching; |
---|
| 615 | } |
---|
| 616 | |
---|
[637] | 617 | /// \brief Return the mate of the given node. |
---|
[338] | 618 | /// |
---|
[947] | 619 | /// This function returns the mate of the given node in the current |
---|
[637] | 620 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
[339] | 621 | Node mate(const Node& n) const { |
---|
| 622 | return (*_matching)[n] != INVALID ? |
---|
| 623 | _graph.target((*_matching)[n]) : INVALID; |
---|
[338] | 624 | } |
---|
| 625 | |
---|
[339] | 626 | /// @} |
---|
| 627 | |
---|
[637] | 628 | /// \name Dual Solution |
---|
[947] | 629 | /// Functions to get the dual solution, i.e. the Gallai-Edmonds |
---|
[637] | 630 | /// decomposition. |
---|
[339] | 631 | |
---|
| 632 | /// @{ |
---|
[338] | 633 | |
---|
[637] | 634 | /// \brief Return the status of the given node in the Edmonds-Gallai |
---|
[338] | 635 | /// decomposition. |
---|
| 636 | /// |
---|
[637] | 637 | /// This function returns the \ref Status "status" of the given node |
---|
| 638 | /// in the Edmonds-Gallai decomposition. |
---|
[640] | 639 | Status status(const Node& n) const { |
---|
[339] | 640 | return (*_status)[n]; |
---|
[338] | 641 | } |
---|
| 642 | |
---|
[640] | 643 | /// \brief Return a const reference to the status map, which stores |
---|
| 644 | /// the Edmonds-Gallai decomposition. |
---|
| 645 | /// |
---|
| 646 | /// This function returns a const reference to a node map that stores the |
---|
| 647 | /// \ref Status "status" of each node in the Edmonds-Gallai decomposition. |
---|
| 648 | const StatusMap& statusMap() const { |
---|
| 649 | return *_status; |
---|
| 650 | } |
---|
| 651 | |
---|
[637] | 652 | /// \brief Return \c true if the given node is in the barrier. |
---|
[338] | 653 | /// |
---|
[637] | 654 | /// This function returns \c true if the given node is in the barrier. |
---|
[339] | 655 | bool barrier(const Node& n) const { |
---|
| 656 | return (*_status)[n] == ODD; |
---|
[338] | 657 | } |
---|
| 658 | |
---|
[339] | 659 | /// @} |
---|
[338] | 660 | |
---|
| 661 | }; |
---|
| 662 | |
---|
| 663 | /// \ingroup matching |
---|
| 664 | /// |
---|
| 665 | /// \brief Weighted matching in general graphs |
---|
| 666 | /// |
---|
| 667 | /// This class provides an efficient implementation of Edmond's |
---|
| 668 | /// maximum weighted matching algorithm. The implementation is based |
---|
| 669 | /// on extensive use of priority queues and provides |
---|
[606] | 670 | /// \f$O(nm\log n)\f$ time complexity. |
---|
[338] | 671 | /// |
---|
[947] | 672 | /// The maximum weighted matching problem is to find a subset of the |
---|
| 673 | /// edges in an undirected graph with maximum overall weight for which |
---|
[637] | 674 | /// each node has at most one incident edge. |
---|
| 675 | /// It can be formulated with the following linear program. |
---|
[338] | 676 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
[339] | 677 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 678 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[338] | 679 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 680 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[339] | 681 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 682 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 683 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 684 | /// subsets of the nodes. |
---|
[338] | 685 | /// |
---|
| 686 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 687 | /// optimality. The solution of the dual problem can be used to check |
---|
[339] | 688 | /// the result of the algorithm. The dual linear problem is the |
---|
[637] | 689 | /// following. |
---|
[339] | 690 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)} |
---|
| 691 | z_B \ge w_{uv} \quad \forall uv\in E\f] */ |
---|
[338] | 692 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
| 693 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[339] | 694 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 695 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[338] | 696 | /// |
---|
[947] | 697 | /// The algorithm can be executed with the run() function. |
---|
[637] | 698 | /// After it the matching (the primal solution) and the dual solution |
---|
[947] | 699 | /// can be obtained using the query functions and the |
---|
| 700 | /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class, |
---|
| 701 | /// which is able to iterate on the nodes of a blossom. |
---|
[637] | 702 | /// If the value type is integer, then the dual solution is multiplied |
---|
| 703 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
| 704 | /// |
---|
[640] | 705 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
[947] | 706 | /// \tparam WM The type edge weight map. The default type is |
---|
[637] | 707 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 708 | #ifdef DOXYGEN |
---|
| 709 | template <typename GR, typename WM> |
---|
| 710 | #else |
---|
[606] | 711 | template <typename GR, |
---|
| 712 | typename WM = typename GR::template EdgeMap<int> > |
---|
[637] | 713 | #endif |
---|
[338] | 714 | class MaxWeightedMatching { |
---|
| 715 | public: |
---|
| 716 | |
---|
[637] | 717 | /// The graph type of the algorithm |
---|
[606] | 718 | typedef GR Graph; |
---|
[637] | 719 | /// The type of the edge weight map |
---|
[606] | 720 | typedef WM WeightMap; |
---|
[637] | 721 | /// The value type of the edge weights |
---|
[338] | 722 | typedef typename WeightMap::Value Value; |
---|
| 723 | |
---|
[640] | 724 | /// The type of the matching map |
---|
[637] | 725 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 726 | MatchingMap; |
---|
| 727 | |
---|
[338] | 728 | /// \brief Scaling factor for dual solution |
---|
| 729 | /// |
---|
[637] | 730 | /// Scaling factor for dual solution. It is equal to 4 or 1 |
---|
[338] | 731 | /// according to the value type. |
---|
| 732 | static const int dualScale = |
---|
| 733 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 734 | |
---|
| 735 | private: |
---|
| 736 | |
---|
| 737 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 738 | |
---|
| 739 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 740 | typedef std::vector<Node> BlossomNodeList; |
---|
| 741 | |
---|
| 742 | struct BlossomVariable { |
---|
| 743 | int begin, end; |
---|
| 744 | Value value; |
---|
| 745 | |
---|
| 746 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 747 | : begin(_begin), end(_end), value(_value) {} |
---|
| 748 | |
---|
| 749 | }; |
---|
| 750 | |
---|
| 751 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 752 | |
---|
| 753 | const Graph& _graph; |
---|
| 754 | const WeightMap& _weight; |
---|
| 755 | |
---|
| 756 | MatchingMap* _matching; |
---|
| 757 | |
---|
| 758 | NodePotential* _node_potential; |
---|
| 759 | |
---|
| 760 | BlossomPotential _blossom_potential; |
---|
| 761 | BlossomNodeList _blossom_node_list; |
---|
| 762 | |
---|
| 763 | int _node_num; |
---|
| 764 | int _blossom_num; |
---|
| 765 | |
---|
| 766 | typedef RangeMap<int> IntIntMap; |
---|
| 767 | |
---|
| 768 | enum Status { |
---|
[947] | 769 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
[338] | 770 | }; |
---|
| 771 | |
---|
[339] | 772 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[338] | 773 | struct BlossomData { |
---|
| 774 | int tree; |
---|
| 775 | Status status; |
---|
| 776 | Arc pred, next; |
---|
| 777 | Value pot, offset; |
---|
| 778 | Node base; |
---|
| 779 | }; |
---|
| 780 | |
---|
[339] | 781 | IntNodeMap *_blossom_index; |
---|
[338] | 782 | BlossomSet *_blossom_set; |
---|
| 783 | RangeMap<BlossomData>* _blossom_data; |
---|
| 784 | |
---|
[339] | 785 | IntNodeMap *_node_index; |
---|
| 786 | IntArcMap *_node_heap_index; |
---|
[338] | 787 | |
---|
| 788 | struct NodeData { |
---|
| 789 | |
---|
[339] | 790 | NodeData(IntArcMap& node_heap_index) |
---|
[338] | 791 | : heap(node_heap_index) {} |
---|
| 792 | |
---|
| 793 | int blossom; |
---|
| 794 | Value pot; |
---|
[339] | 795 | BinHeap<Value, IntArcMap> heap; |
---|
[338] | 796 | std::map<int, Arc> heap_index; |
---|
| 797 | |
---|
| 798 | int tree; |
---|
| 799 | }; |
---|
| 800 | |
---|
| 801 | RangeMap<NodeData>* _node_data; |
---|
| 802 | |
---|
| 803 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 804 | |
---|
| 805 | IntIntMap *_tree_set_index; |
---|
| 806 | TreeSet *_tree_set; |
---|
| 807 | |
---|
[339] | 808 | IntNodeMap *_delta1_index; |
---|
| 809 | BinHeap<Value, IntNodeMap> *_delta1; |
---|
[338] | 810 | |
---|
| 811 | IntIntMap *_delta2_index; |
---|
| 812 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 813 | |
---|
[339] | 814 | IntEdgeMap *_delta3_index; |
---|
| 815 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[338] | 816 | |
---|
| 817 | IntIntMap *_delta4_index; |
---|
| 818 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 819 | |
---|
| 820 | Value _delta_sum; |
---|
[949] | 821 | int _unmatched; |
---|
| 822 | |
---|
| 823 | typedef MaxWeightedFractionalMatching<Graph, WeightMap> FractionalMatching; |
---|
| 824 | FractionalMatching *_fractional; |
---|
[338] | 825 | |
---|
| 826 | void createStructures() { |
---|
| 827 | _node_num = countNodes(_graph); |
---|
| 828 | _blossom_num = _node_num * 3 / 2; |
---|
| 829 | |
---|
| 830 | if (!_matching) { |
---|
| 831 | _matching = new MatchingMap(_graph); |
---|
| 832 | } |
---|
[945] | 833 | |
---|
[338] | 834 | if (!_node_potential) { |
---|
| 835 | _node_potential = new NodePotential(_graph); |
---|
| 836 | } |
---|
[945] | 837 | |
---|
[338] | 838 | if (!_blossom_set) { |
---|
[339] | 839 | _blossom_index = new IntNodeMap(_graph); |
---|
[338] | 840 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 841 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[945] | 842 | } else if (_blossom_data->size() != _blossom_num) { |
---|
| 843 | delete _blossom_data; |
---|
| 844 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[338] | 845 | } |
---|
| 846 | |
---|
| 847 | if (!_node_index) { |
---|
[339] | 848 | _node_index = new IntNodeMap(_graph); |
---|
| 849 | _node_heap_index = new IntArcMap(_graph); |
---|
[338] | 850 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
[945] | 851 | NodeData(*_node_heap_index)); |
---|
| 852 | } else { |
---|
| 853 | delete _node_data; |
---|
| 854 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
| 855 | NodeData(*_node_heap_index)); |
---|
[338] | 856 | } |
---|
| 857 | |
---|
| 858 | if (!_tree_set) { |
---|
| 859 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 860 | _tree_set = new TreeSet(*_tree_set_index); |
---|
[945] | 861 | } else { |
---|
| 862 | _tree_set_index->resize(_blossom_num); |
---|
[338] | 863 | } |
---|
[945] | 864 | |
---|
[338] | 865 | if (!_delta1) { |
---|
[339] | 866 | _delta1_index = new IntNodeMap(_graph); |
---|
| 867 | _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index); |
---|
[338] | 868 | } |
---|
[945] | 869 | |
---|
[338] | 870 | if (!_delta2) { |
---|
| 871 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 872 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
[945] | 873 | } else { |
---|
| 874 | _delta2_index->resize(_blossom_num); |
---|
[338] | 875 | } |
---|
[945] | 876 | |
---|
[338] | 877 | if (!_delta3) { |
---|
[339] | 878 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 879 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[338] | 880 | } |
---|
[945] | 881 | |
---|
[338] | 882 | if (!_delta4) { |
---|
| 883 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 884 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
[945] | 885 | } else { |
---|
| 886 | _delta4_index->resize(_blossom_num); |
---|
[338] | 887 | } |
---|
| 888 | } |
---|
| 889 | |
---|
| 890 | void destroyStructures() { |
---|
| 891 | if (_matching) { |
---|
| 892 | delete _matching; |
---|
| 893 | } |
---|
| 894 | if (_node_potential) { |
---|
| 895 | delete _node_potential; |
---|
| 896 | } |
---|
| 897 | if (_blossom_set) { |
---|
| 898 | delete _blossom_index; |
---|
| 899 | delete _blossom_set; |
---|
| 900 | delete _blossom_data; |
---|
| 901 | } |
---|
| 902 | |
---|
| 903 | if (_node_index) { |
---|
| 904 | delete _node_index; |
---|
| 905 | delete _node_heap_index; |
---|
| 906 | delete _node_data; |
---|
| 907 | } |
---|
| 908 | |
---|
| 909 | if (_tree_set) { |
---|
| 910 | delete _tree_set_index; |
---|
| 911 | delete _tree_set; |
---|
| 912 | } |
---|
| 913 | if (_delta1) { |
---|
| 914 | delete _delta1_index; |
---|
| 915 | delete _delta1; |
---|
| 916 | } |
---|
| 917 | if (_delta2) { |
---|
| 918 | delete _delta2_index; |
---|
| 919 | delete _delta2; |
---|
| 920 | } |
---|
| 921 | if (_delta3) { |
---|
| 922 | delete _delta3_index; |
---|
| 923 | delete _delta3; |
---|
| 924 | } |
---|
| 925 | if (_delta4) { |
---|
| 926 | delete _delta4_index; |
---|
| 927 | delete _delta4; |
---|
| 928 | } |
---|
| 929 | } |
---|
| 930 | |
---|
| 931 | void matchedToEven(int blossom, int tree) { |
---|
| 932 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 933 | _delta2->erase(blossom); |
---|
| 934 | } |
---|
| 935 | |
---|
| 936 | if (!_blossom_set->trivial(blossom)) { |
---|
| 937 | (*_blossom_data)[blossom].pot -= |
---|
| 938 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 939 | } |
---|
| 940 | |
---|
| 941 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 942 | n != INVALID; ++n) { |
---|
| 943 | |
---|
| 944 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 945 | int ni = (*_node_index)[n]; |
---|
| 946 | |
---|
| 947 | (*_node_data)[ni].heap.clear(); |
---|
| 948 | (*_node_data)[ni].heap_index.clear(); |
---|
| 949 | |
---|
| 950 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 951 | |
---|
| 952 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 953 | |
---|
| 954 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 955 | Node v = _graph.source(e); |
---|
| 956 | int vb = _blossom_set->find(v); |
---|
| 957 | int vi = (*_node_index)[v]; |
---|
| 958 | |
---|
| 959 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 960 | dualScale * _weight[e]; |
---|
| 961 | |
---|
| 962 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 963 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 964 | _delta3->push(e, rw / 2); |
---|
| 965 | } |
---|
| 966 | } else { |
---|
| 967 | typename std::map<int, Arc>::iterator it = |
---|
| 968 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 969 | |
---|
| 970 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 971 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 972 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 973 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 974 | it->second = e; |
---|
| 975 | } |
---|
| 976 | } else { |
---|
| 977 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 978 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 979 | } |
---|
| 980 | |
---|
| 981 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 982 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 983 | |
---|
| 984 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 985 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 986 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 987 | (*_blossom_data)[vb].offset); |
---|
| 988 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 989 | (*_blossom_data)[vb].offset) { |
---|
| 990 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 991 | (*_blossom_data)[vb].offset); |
---|
| 992 | } |
---|
| 993 | } |
---|
| 994 | } |
---|
| 995 | } |
---|
| 996 | } |
---|
| 997 | } |
---|
| 998 | (*_blossom_data)[blossom].offset = 0; |
---|
| 999 | } |
---|
| 1000 | |
---|
[947] | 1001 | void matchedToOdd(int blossom) { |
---|
[338] | 1002 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1003 | _delta2->erase(blossom); |
---|
| 1004 | } |
---|
[947] | 1005 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 1006 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1007 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 1008 | (*_blossom_data)[blossom].offset); |
---|
| 1009 | } |
---|
| 1010 | } |
---|
| 1011 | |
---|
| 1012 | void evenToMatched(int blossom, int tree) { |
---|
| 1013 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1014 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 1015 | } |
---|
[338] | 1016 | |
---|
| 1017 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1018 | n != INVALID; ++n) { |
---|
| 1019 | int ni = (*_node_index)[n]; |
---|
[947] | 1020 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 1021 | |
---|
| 1022 | _delta1->erase(n); |
---|
| 1023 | |
---|
| 1024 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1025 | Node v = _graph.source(e); |
---|
[338] | 1026 | int vb = _blossom_set->find(v); |
---|
| 1027 | int vi = (*_node_index)[v]; |
---|
| 1028 | |
---|
| 1029 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1030 | dualScale * _weight[e]; |
---|
| 1031 | |
---|
[947] | 1032 | if (vb == blossom) { |
---|
| 1033 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1034 | _delta3->erase(e); |
---|
| 1035 | } |
---|
| 1036 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1037 | |
---|
| 1038 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1039 | _delta3->erase(e); |
---|
| 1040 | } |
---|
| 1041 | |
---|
| 1042 | int vt = _tree_set->find(vb); |
---|
| 1043 | |
---|
| 1044 | if (vt != tree) { |
---|
| 1045 | |
---|
| 1046 | Arc r = _graph.oppositeArc(e); |
---|
| 1047 | |
---|
| 1048 | typename std::map<int, Arc>::iterator it = |
---|
| 1049 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1050 | |
---|
| 1051 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1052 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1053 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 1054 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 1055 | it->second = r; |
---|
| 1056 | } |
---|
| 1057 | } else { |
---|
| 1058 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 1059 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 1060 | } |
---|
| 1061 | |
---|
| 1062 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1063 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1064 | |
---|
| 1065 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1066 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1067 | (*_blossom_data)[blossom].offset); |
---|
| 1068 | } else if ((*_delta2)[blossom] > |
---|
| 1069 | _blossom_set->classPrio(blossom) - |
---|
| 1070 | (*_blossom_data)[blossom].offset){ |
---|
| 1071 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1072 | (*_blossom_data)[blossom].offset); |
---|
| 1073 | } |
---|
| 1074 | } |
---|
| 1075 | } |
---|
| 1076 | } else { |
---|
| 1077 | |
---|
| 1078 | typename std::map<int, Arc>::iterator it = |
---|
| 1079 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1080 | |
---|
| 1081 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1082 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 1083 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 1084 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 1085 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 1086 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 1087 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 1088 | } |
---|
| 1089 | |
---|
| 1090 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1091 | if (_blossom_set->classPrio(vb) == |
---|
| 1092 | std::numeric_limits<Value>::max()) { |
---|
| 1093 | _delta2->erase(vb); |
---|
| 1094 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 1095 | (*_blossom_data)[vb].offset) { |
---|
| 1096 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 1097 | (*_blossom_data)[vb].offset); |
---|
| 1098 | } |
---|
| 1099 | } |
---|
[338] | 1100 | } |
---|
| 1101 | } |
---|
| 1102 | } |
---|
| 1103 | } |
---|
| 1104 | } |
---|
| 1105 | |
---|
[947] | 1106 | void oddToMatched(int blossom) { |
---|
| 1107 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 1108 | |
---|
| 1109 | if (_blossom_set->classPrio(blossom) != |
---|
| 1110 | std::numeric_limits<Value>::max()) { |
---|
| 1111 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1112 | (*_blossom_data)[blossom].offset); |
---|
| 1113 | } |
---|
| 1114 | |
---|
| 1115 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1116 | _delta4->erase(blossom); |
---|
| 1117 | } |
---|
| 1118 | } |
---|
| 1119 | |
---|
| 1120 | void oddToEven(int blossom, int tree) { |
---|
| 1121 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1122 | _delta4->erase(blossom); |
---|
| 1123 | (*_blossom_data)[blossom].pot -= |
---|
| 1124 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 1125 | } |
---|
| 1126 | |
---|
[338] | 1127 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1128 | n != INVALID; ++n) { |
---|
| 1129 | int ni = (*_node_index)[n]; |
---|
| 1130 | |
---|
[947] | 1131 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1132 | |
---|
| 1133 | (*_node_data)[ni].heap.clear(); |
---|
| 1134 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1135 | (*_node_data)[ni].pot += |
---|
| 1136 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 1137 | |
---|
| 1138 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 1139 | |
---|
[338] | 1140 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1141 | Node v = _graph.source(e); |
---|
| 1142 | int vb = _blossom_set->find(v); |
---|
| 1143 | int vi = (*_node_index)[v]; |
---|
| 1144 | |
---|
| 1145 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1146 | dualScale * _weight[e]; |
---|
| 1147 | |
---|
[947] | 1148 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1149 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 1150 | _delta3->push(e, rw / 2); |
---|
[338] | 1151 | } |
---|
[947] | 1152 | } else { |
---|
[338] | 1153 | |
---|
| 1154 | typename std::map<int, Arc>::iterator it = |
---|
[947] | 1155 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1156 | |
---|
| 1157 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1158 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 1159 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 1160 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 1161 | it->second = e; |
---|
[338] | 1162 | } |
---|
| 1163 | } else { |
---|
[947] | 1164 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 1165 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
[338] | 1166 | } |
---|
| 1167 | |
---|
[947] | 1168 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 1169 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 1170 | |
---|
| 1171 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1172 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 1173 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 1174 | (*_blossom_data)[vb].offset); |
---|
| 1175 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 1176 | (*_blossom_data)[vb].offset) { |
---|
| 1177 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 1178 | (*_blossom_data)[vb].offset); |
---|
| 1179 | } |
---|
[338] | 1180 | } |
---|
| 1181 | } |
---|
| 1182 | } |
---|
| 1183 | } |
---|
| 1184 | } |
---|
[947] | 1185 | (*_blossom_data)[blossom].offset = 0; |
---|
[338] | 1186 | } |
---|
| 1187 | |
---|
| 1188 | void alternatePath(int even, int tree) { |
---|
| 1189 | int odd; |
---|
| 1190 | |
---|
| 1191 | evenToMatched(even, tree); |
---|
| 1192 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1193 | |
---|
| 1194 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 1195 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 1196 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 1197 | oddToMatched(odd); |
---|
| 1198 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 1199 | |
---|
| 1200 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 1201 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1202 | evenToMatched(even, tree); |
---|
| 1203 | (*_blossom_data)[even].next = |
---|
| 1204 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 1205 | } |
---|
| 1206 | |
---|
| 1207 | } |
---|
| 1208 | |
---|
| 1209 | void destroyTree(int tree) { |
---|
| 1210 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 1211 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 1212 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1213 | evenToMatched(b, tree); |
---|
| 1214 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 1215 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1216 | oddToMatched(b); |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | _tree_set->eraseClass(tree); |
---|
| 1220 | } |
---|
| 1221 | |
---|
| 1222 | |
---|
| 1223 | void unmatchNode(const Node& node) { |
---|
| 1224 | int blossom = _blossom_set->find(node); |
---|
| 1225 | int tree = _tree_set->find(blossom); |
---|
| 1226 | |
---|
| 1227 | alternatePath(blossom, tree); |
---|
| 1228 | destroyTree(tree); |
---|
| 1229 | |
---|
| 1230 | (*_blossom_data)[blossom].base = node; |
---|
[947] | 1231 | (*_blossom_data)[blossom].next = INVALID; |
---|
[338] | 1232 | } |
---|
| 1233 | |
---|
[339] | 1234 | void augmentOnEdge(const Edge& edge) { |
---|
| 1235 | |
---|
| 1236 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1237 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[338] | 1238 | |
---|
[947] | 1239 | int left_tree = _tree_set->find(left); |
---|
| 1240 | alternatePath(left, left_tree); |
---|
| 1241 | destroyTree(left_tree); |
---|
| 1242 | |
---|
| 1243 | int right_tree = _tree_set->find(right); |
---|
| 1244 | alternatePath(right, right_tree); |
---|
| 1245 | destroyTree(right_tree); |
---|
[338] | 1246 | |
---|
[339] | 1247 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 1248 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[338] | 1249 | } |
---|
| 1250 | |
---|
[947] | 1251 | void augmentOnArc(const Arc& arc) { |
---|
| 1252 | |
---|
| 1253 | int left = _blossom_set->find(_graph.source(arc)); |
---|
| 1254 | int right = _blossom_set->find(_graph.target(arc)); |
---|
| 1255 | |
---|
| 1256 | (*_blossom_data)[left].status = MATCHED; |
---|
| 1257 | |
---|
| 1258 | int right_tree = _tree_set->find(right); |
---|
| 1259 | alternatePath(right, right_tree); |
---|
| 1260 | destroyTree(right_tree); |
---|
| 1261 | |
---|
| 1262 | (*_blossom_data)[left].next = arc; |
---|
| 1263 | (*_blossom_data)[right].next = _graph.oppositeArc(arc); |
---|
| 1264 | } |
---|
| 1265 | |
---|
[338] | 1266 | void extendOnArc(const Arc& arc) { |
---|
| 1267 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 1268 | int tree = _tree_set->find(base); |
---|
| 1269 | |
---|
| 1270 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 1271 | _tree_set->insert(odd, tree); |
---|
| 1272 | (*_blossom_data)[odd].status = ODD; |
---|
| 1273 | matchedToOdd(odd); |
---|
| 1274 | (*_blossom_data)[odd].pred = arc; |
---|
| 1275 | |
---|
| 1276 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 1277 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 1278 | _tree_set->insert(even, tree); |
---|
| 1279 | (*_blossom_data)[even].status = EVEN; |
---|
| 1280 | matchedToEven(even, tree); |
---|
| 1281 | } |
---|
| 1282 | |
---|
[339] | 1283 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[338] | 1284 | int nca = -1; |
---|
| 1285 | std::vector<int> left_path, right_path; |
---|
| 1286 | |
---|
| 1287 | { |
---|
| 1288 | std::set<int> left_set, right_set; |
---|
| 1289 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1290 | left_path.push_back(left); |
---|
| 1291 | left_set.insert(left); |
---|
| 1292 | |
---|
| 1293 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 1294 | right_path.push_back(right); |
---|
| 1295 | right_set.insert(right); |
---|
| 1296 | |
---|
| 1297 | while (true) { |
---|
| 1298 | |
---|
| 1299 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 1300 | |
---|
| 1301 | left = |
---|
| 1302 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1303 | left_path.push_back(left); |
---|
| 1304 | left = |
---|
| 1305 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1306 | left_path.push_back(left); |
---|
| 1307 | |
---|
| 1308 | left_set.insert(left); |
---|
| 1309 | |
---|
| 1310 | if (right_set.find(left) != right_set.end()) { |
---|
| 1311 | nca = left; |
---|
| 1312 | break; |
---|
| 1313 | } |
---|
| 1314 | |
---|
| 1315 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 1316 | |
---|
| 1317 | right = |
---|
| 1318 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1319 | right_path.push_back(right); |
---|
| 1320 | right = |
---|
| 1321 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1322 | right_path.push_back(right); |
---|
| 1323 | |
---|
| 1324 | right_set.insert(right); |
---|
| 1325 | |
---|
| 1326 | if (left_set.find(right) != left_set.end()) { |
---|
| 1327 | nca = right; |
---|
| 1328 | break; |
---|
| 1329 | } |
---|
| 1330 | |
---|
| 1331 | } |
---|
| 1332 | |
---|
| 1333 | if (nca == -1) { |
---|
| 1334 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 1335 | nca = right; |
---|
| 1336 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1337 | nca = |
---|
| 1338 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1339 | right_path.push_back(nca); |
---|
| 1340 | nca = |
---|
| 1341 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1342 | right_path.push_back(nca); |
---|
| 1343 | } |
---|
| 1344 | } else { |
---|
| 1345 | nca = left; |
---|
| 1346 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1347 | nca = |
---|
| 1348 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1349 | left_path.push_back(nca); |
---|
| 1350 | nca = |
---|
| 1351 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1352 | left_path.push_back(nca); |
---|
| 1353 | } |
---|
| 1354 | } |
---|
| 1355 | } |
---|
| 1356 | } |
---|
| 1357 | |
---|
| 1358 | std::vector<int> subblossoms; |
---|
| 1359 | Arc prev; |
---|
| 1360 | |
---|
| 1361 | prev = _graph.direct(edge, true); |
---|
| 1362 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1363 | subblossoms.push_back(left_path[i]); |
---|
| 1364 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 1365 | _tree_set->erase(left_path[i]); |
---|
| 1366 | |
---|
| 1367 | subblossoms.push_back(left_path[i + 1]); |
---|
| 1368 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 1369 | oddToEven(left_path[i + 1], tree); |
---|
| 1370 | _tree_set->erase(left_path[i + 1]); |
---|
| 1371 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 1372 | } |
---|
| 1373 | |
---|
| 1374 | int k = 0; |
---|
| 1375 | while (right_path[k] != nca) ++k; |
---|
| 1376 | |
---|
| 1377 | subblossoms.push_back(nca); |
---|
| 1378 | (*_blossom_data)[nca].next = prev; |
---|
| 1379 | |
---|
| 1380 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 1381 | subblossoms.push_back(right_path[i + 1]); |
---|
| 1382 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 1383 | oddToEven(right_path[i + 1], tree); |
---|
| 1384 | _tree_set->erase(right_path[i + 1]); |
---|
| 1385 | |
---|
| 1386 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 1387 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 1388 | |
---|
| 1389 | subblossoms.push_back(right_path[i]); |
---|
| 1390 | _tree_set->erase(right_path[i]); |
---|
| 1391 | } |
---|
| 1392 | |
---|
| 1393 | int surface = |
---|
| 1394 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1395 | |
---|
| 1396 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1397 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1398 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 1399 | } |
---|
| 1400 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 1401 | } |
---|
| 1402 | |
---|
| 1403 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 1404 | (*_blossom_data)[surface].offset = 0; |
---|
| 1405 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1406 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 1407 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 1408 | |
---|
| 1409 | _tree_set->insert(surface, tree); |
---|
| 1410 | _tree_set->erase(nca); |
---|
| 1411 | } |
---|
| 1412 | |
---|
| 1413 | void splitBlossom(int blossom) { |
---|
| 1414 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 1415 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 1416 | |
---|
| 1417 | int tree = _tree_set->find(blossom); |
---|
| 1418 | |
---|
| 1419 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1420 | oddToMatched(blossom); |
---|
| 1421 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1422 | _delta2->erase(blossom); |
---|
| 1423 | } |
---|
| 1424 | |
---|
| 1425 | std::vector<int> subblossoms; |
---|
| 1426 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1427 | |
---|
| 1428 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 1429 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 1430 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 1431 | |
---|
| 1432 | int ib = -1, id = -1; |
---|
| 1433 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1434 | if (subblossoms[i] == b) ib = i; |
---|
| 1435 | if (subblossoms[i] == d) id = i; |
---|
| 1436 | |
---|
| 1437 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 1438 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1439 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 1440 | } |
---|
| 1441 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 1442 | std::numeric_limits<Value>::max()) { |
---|
| 1443 | _delta2->push(subblossoms[i], |
---|
| 1444 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 1445 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 1446 | } |
---|
| 1447 | } |
---|
| 1448 | |
---|
| 1449 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 1450 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 1451 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1452 | int sb = subblossoms[i]; |
---|
| 1453 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1454 | (*_blossom_data)[sb].next = |
---|
| 1455 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1456 | } |
---|
| 1457 | |
---|
| 1458 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1459 | int sb = subblossoms[i]; |
---|
| 1460 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1461 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1462 | |
---|
| 1463 | (*_blossom_data)[sb].status = ODD; |
---|
| 1464 | matchedToOdd(sb); |
---|
| 1465 | _tree_set->insert(sb, tree); |
---|
| 1466 | (*_blossom_data)[sb].pred = pred; |
---|
| 1467 | (*_blossom_data)[sb].next = |
---|
[947] | 1468 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
[338] | 1469 | |
---|
| 1470 | pred = (*_blossom_data)[ub].next; |
---|
| 1471 | |
---|
| 1472 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1473 | matchedToEven(tb, tree); |
---|
| 1474 | _tree_set->insert(tb, tree); |
---|
| 1475 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 1476 | } |
---|
| 1477 | |
---|
| 1478 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 1479 | matchedToOdd(subblossoms[id]); |
---|
| 1480 | _tree_set->insert(subblossoms[id], tree); |
---|
| 1481 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 1482 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 1483 | |
---|
| 1484 | } else { |
---|
| 1485 | |
---|
| 1486 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 1487 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1488 | int sb = subblossoms[i]; |
---|
| 1489 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1490 | (*_blossom_data)[sb].next = |
---|
| 1491 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1492 | } |
---|
| 1493 | |
---|
| 1494 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1495 | int sb = subblossoms[i]; |
---|
| 1496 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1497 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1498 | |
---|
| 1499 | (*_blossom_data)[sb].status = ODD; |
---|
| 1500 | matchedToOdd(sb); |
---|
| 1501 | _tree_set->insert(sb, tree); |
---|
| 1502 | (*_blossom_data)[sb].next = next; |
---|
| 1503 | (*_blossom_data)[sb].pred = |
---|
| 1504 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1505 | |
---|
| 1506 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1507 | matchedToEven(tb, tree); |
---|
| 1508 | _tree_set->insert(tb, tree); |
---|
| 1509 | (*_blossom_data)[tb].pred = |
---|
| 1510 | (*_blossom_data)[tb].next = |
---|
| 1511 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 1512 | next = (*_blossom_data)[ub].next; |
---|
| 1513 | } |
---|
| 1514 | |
---|
| 1515 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 1516 | matchedToOdd(subblossoms[ib]); |
---|
| 1517 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 1518 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 1519 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 1520 | } |
---|
| 1521 | _tree_set->erase(blossom); |
---|
| 1522 | } |
---|
| 1523 | |
---|
| 1524 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 1525 | if (_blossom_set->trivial(blossom)) { |
---|
| 1526 | int bi = (*_node_index)[base]; |
---|
| 1527 | Value pot = (*_node_data)[bi].pot; |
---|
| 1528 | |
---|
[628] | 1529 | (*_matching)[base] = matching; |
---|
[338] | 1530 | _blossom_node_list.push_back(base); |
---|
[628] | 1531 | (*_node_potential)[base] = pot; |
---|
[338] | 1532 | } else { |
---|
| 1533 | |
---|
| 1534 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 1535 | int bn = _blossom_node_list.size(); |
---|
| 1536 | |
---|
| 1537 | std::vector<int> subblossoms; |
---|
| 1538 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1539 | int b = _blossom_set->find(base); |
---|
| 1540 | int ib = -1; |
---|
| 1541 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1542 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 1543 | } |
---|
| 1544 | |
---|
| 1545 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 1546 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 1547 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 1548 | |
---|
| 1549 | Arc m = (*_blossom_data)[tb].next; |
---|
| 1550 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 1551 | extractBlossom(tb, _graph.source(m), m); |
---|
| 1552 | } |
---|
| 1553 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 1554 | |
---|
| 1555 | int en = _blossom_node_list.size(); |
---|
| 1556 | |
---|
| 1557 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 1558 | } |
---|
| 1559 | } |
---|
| 1560 | |
---|
| 1561 | void extractMatching() { |
---|
| 1562 | std::vector<int> blossoms; |
---|
| 1563 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 1564 | blossoms.push_back(c); |
---|
| 1565 | } |
---|
| 1566 | |
---|
| 1567 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
[947] | 1568 | if ((*_blossom_data)[blossoms[i]].next != INVALID) { |
---|
[338] | 1569 | |
---|
| 1570 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 1571 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 1572 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 1573 | n != INVALID; ++n) { |
---|
| 1574 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 1575 | } |
---|
| 1576 | |
---|
| 1577 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 1578 | Node base = _graph.source(matching); |
---|
| 1579 | extractBlossom(blossoms[i], base, matching); |
---|
| 1580 | } else { |
---|
| 1581 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
| 1582 | extractBlossom(blossoms[i], base, INVALID); |
---|
| 1583 | } |
---|
| 1584 | } |
---|
| 1585 | } |
---|
| 1586 | |
---|
| 1587 | public: |
---|
| 1588 | |
---|
| 1589 | /// \brief Constructor |
---|
| 1590 | /// |
---|
| 1591 | /// Constructor. |
---|
| 1592 | MaxWeightedMatching(const Graph& graph, const WeightMap& weight) |
---|
| 1593 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 1594 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 1595 | _node_num(0), _blossom_num(0), |
---|
| 1596 | |
---|
| 1597 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 1598 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 1599 | _tree_set_index(0), _tree_set(0), |
---|
| 1600 | |
---|
| 1601 | _delta1_index(0), _delta1(0), |
---|
| 1602 | _delta2_index(0), _delta2(0), |
---|
| 1603 | _delta3_index(0), _delta3(0), |
---|
| 1604 | _delta4_index(0), _delta4(0), |
---|
| 1605 | |
---|
[949] | 1606 | _delta_sum(), _unmatched(0), |
---|
| 1607 | |
---|
| 1608 | _fractional(0) |
---|
| 1609 | {} |
---|
[338] | 1610 | |
---|
| 1611 | ~MaxWeightedMatching() { |
---|
| 1612 | destroyStructures(); |
---|
[949] | 1613 | if (_fractional) { |
---|
| 1614 | delete _fractional; |
---|
| 1615 | } |
---|
[338] | 1616 | } |
---|
| 1617 | |
---|
[637] | 1618 | /// \name Execution Control |
---|
[342] | 1619 | /// The simplest way to execute the algorithm is to use the |
---|
[637] | 1620 | /// \ref run() member function. |
---|
[338] | 1621 | |
---|
| 1622 | ///@{ |
---|
| 1623 | |
---|
| 1624 | /// \brief Initialize the algorithm |
---|
| 1625 | /// |
---|
[637] | 1626 | /// This function initializes the algorithm. |
---|
[338] | 1627 | void init() { |
---|
| 1628 | createStructures(); |
---|
| 1629 | |
---|
[945] | 1630 | _blossom_node_list.clear(); |
---|
| 1631 | _blossom_potential.clear(); |
---|
| 1632 | |
---|
[338] | 1633 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 1634 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
[338] | 1635 | } |
---|
| 1636 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[628] | 1637 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
[338] | 1638 | } |
---|
| 1639 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 1640 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
[338] | 1641 | } |
---|
| 1642 | for (int i = 0; i < _blossom_num; ++i) { |
---|
[628] | 1643 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 1644 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
[338] | 1645 | } |
---|
[956] | 1646 | |
---|
[949] | 1647 | _unmatched = _node_num; |
---|
| 1648 | |
---|
[945] | 1649 | _delta1->clear(); |
---|
| 1650 | _delta2->clear(); |
---|
| 1651 | _delta3->clear(); |
---|
| 1652 | _delta4->clear(); |
---|
| 1653 | _blossom_set->clear(); |
---|
| 1654 | _tree_set->clear(); |
---|
[338] | 1655 | |
---|
| 1656 | int index = 0; |
---|
| 1657 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1658 | Value max = 0; |
---|
| 1659 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1660 | if (_graph.target(e) == n) continue; |
---|
| 1661 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 1662 | max = (dualScale * _weight[e]) / 2; |
---|
| 1663 | } |
---|
| 1664 | } |
---|
[628] | 1665 | (*_node_index)[n] = index; |
---|
[945] | 1666 | (*_node_data)[index].heap_index.clear(); |
---|
| 1667 | (*_node_data)[index].heap.clear(); |
---|
[338] | 1668 | (*_node_data)[index].pot = max; |
---|
| 1669 | _delta1->push(n, max); |
---|
| 1670 | int blossom = |
---|
| 1671 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1672 | |
---|
| 1673 | _tree_set->insert(blossom); |
---|
| 1674 | |
---|
| 1675 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 1676 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1677 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 1678 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1679 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1680 | ++index; |
---|
| 1681 | } |
---|
| 1682 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1683 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 1684 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 1685 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 1686 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1687 | dualScale * _weight[e]) / 2); |
---|
| 1688 | } |
---|
| 1689 | } |
---|
| 1690 | } |
---|
| 1691 | |
---|
[949] | 1692 | /// \brief Initialize the algorithm with fractional matching |
---|
| 1693 | /// |
---|
| 1694 | /// This function initializes the algorithm with a fractional |
---|
| 1695 | /// matching. This initialization is also called jumpstart heuristic. |
---|
| 1696 | void fractionalInit() { |
---|
| 1697 | createStructures(); |
---|
[955] | 1698 | |
---|
| 1699 | _blossom_node_list.clear(); |
---|
| 1700 | _blossom_potential.clear(); |
---|
[956] | 1701 | |
---|
[949] | 1702 | if (_fractional == 0) { |
---|
| 1703 | _fractional = new FractionalMatching(_graph, _weight, false); |
---|
| 1704 | } |
---|
| 1705 | _fractional->run(); |
---|
| 1706 | |
---|
| 1707 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 1708 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
| 1709 | } |
---|
| 1710 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1711 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
| 1712 | } |
---|
| 1713 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1714 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
| 1715 | } |
---|
| 1716 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 1717 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 1718 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
| 1719 | } |
---|
| 1720 | |
---|
| 1721 | _unmatched = 0; |
---|
| 1722 | |
---|
[955] | 1723 | _delta1->clear(); |
---|
| 1724 | _delta2->clear(); |
---|
| 1725 | _delta3->clear(); |
---|
| 1726 | _delta4->clear(); |
---|
| 1727 | _blossom_set->clear(); |
---|
| 1728 | _tree_set->clear(); |
---|
| 1729 | |
---|
[949] | 1730 | int index = 0; |
---|
| 1731 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1732 | Value pot = _fractional->nodeValue(n); |
---|
| 1733 | (*_node_index)[n] = index; |
---|
| 1734 | (*_node_data)[index].pot = pot; |
---|
[955] | 1735 | (*_node_data)[index].heap_index.clear(); |
---|
| 1736 | (*_node_data)[index].heap.clear(); |
---|
[949] | 1737 | int blossom = |
---|
| 1738 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1739 | |
---|
| 1740 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1741 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1742 | (*_blossom_data)[blossom].next = _fractional->matching(n); |
---|
| 1743 | if (_fractional->matching(n) == INVALID) { |
---|
| 1744 | (*_blossom_data)[blossom].base = n; |
---|
| 1745 | } |
---|
| 1746 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1747 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1748 | ++index; |
---|
| 1749 | } |
---|
| 1750 | |
---|
| 1751 | typename Graph::template NodeMap<bool> processed(_graph, false); |
---|
| 1752 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1753 | if (processed[n]) continue; |
---|
| 1754 | processed[n] = true; |
---|
| 1755 | if (_fractional->matching(n) == INVALID) continue; |
---|
| 1756 | int num = 1; |
---|
| 1757 | Node v = _graph.target(_fractional->matching(n)); |
---|
| 1758 | while (n != v) { |
---|
| 1759 | processed[v] = true; |
---|
| 1760 | v = _graph.target(_fractional->matching(v)); |
---|
| 1761 | ++num; |
---|
| 1762 | } |
---|
| 1763 | |
---|
| 1764 | if (num % 2 == 1) { |
---|
| 1765 | std::vector<int> subblossoms(num); |
---|
| 1766 | |
---|
| 1767 | subblossoms[--num] = _blossom_set->find(n); |
---|
| 1768 | _delta1->push(n, _fractional->nodeValue(n)); |
---|
| 1769 | v = _graph.target(_fractional->matching(n)); |
---|
| 1770 | while (n != v) { |
---|
| 1771 | subblossoms[--num] = _blossom_set->find(v); |
---|
| 1772 | _delta1->push(v, _fractional->nodeValue(v)); |
---|
[956] | 1773 | v = _graph.target(_fractional->matching(v)); |
---|
[949] | 1774 | } |
---|
[956] | 1775 | |
---|
| 1776 | int surface = |
---|
[949] | 1777 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1778 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1779 | (*_blossom_data)[surface].pred = INVALID; |
---|
| 1780 | (*_blossom_data)[surface].next = INVALID; |
---|
| 1781 | (*_blossom_data)[surface].pot = 0; |
---|
| 1782 | (*_blossom_data)[surface].offset = 0; |
---|
[956] | 1783 | |
---|
[949] | 1784 | _tree_set->insert(surface); |
---|
| 1785 | ++_unmatched; |
---|
| 1786 | } |
---|
| 1787 | } |
---|
| 1788 | |
---|
| 1789 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1790 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 1791 | int sb = _blossom_set->find(_graph.u(e)); |
---|
| 1792 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 1793 | int tb = _blossom_set->find(_graph.v(e)); |
---|
| 1794 | if ((*_blossom_data)[sb].status == EVEN && |
---|
| 1795 | (*_blossom_data)[tb].status == EVEN && sb != tb) { |
---|
| 1796 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1797 | dualScale * _weight[e]) / 2); |
---|
| 1798 | } |
---|
| 1799 | } |
---|
| 1800 | |
---|
| 1801 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1802 | int nb = _blossom_set->find(n); |
---|
| 1803 | if ((*_blossom_data)[nb].status != MATCHED) continue; |
---|
| 1804 | int ni = (*_node_index)[n]; |
---|
| 1805 | |
---|
| 1806 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1807 | Node v = _graph.target(e); |
---|
| 1808 | int vb = _blossom_set->find(v); |
---|
| 1809 | int vi = (*_node_index)[v]; |
---|
| 1810 | |
---|
| 1811 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1812 | dualScale * _weight[e]; |
---|
| 1813 | |
---|
| 1814 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1815 | |
---|
| 1816 | int vt = _tree_set->find(vb); |
---|
| 1817 | |
---|
| 1818 | typename std::map<int, Arc>::iterator it = |
---|
| 1819 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1820 | |
---|
| 1821 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1822 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1823 | (*_node_data)[ni].heap.replace(it->second, e); |
---|
| 1824 | (*_node_data)[ni].heap.decrease(e, rw); |
---|
| 1825 | it->second = e; |
---|
| 1826 | } |
---|
| 1827 | } else { |
---|
| 1828 | (*_node_data)[ni].heap.push(e, rw); |
---|
| 1829 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, e)); |
---|
| 1830 | } |
---|
| 1831 | } |
---|
| 1832 | } |
---|
[956] | 1833 | |
---|
[949] | 1834 | if (!(*_node_data)[ni].heap.empty()) { |
---|
| 1835 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1836 | _delta2->push(nb, _blossom_set->classPrio(nb)); |
---|
| 1837 | } |
---|
| 1838 | } |
---|
| 1839 | } |
---|
| 1840 | |
---|
[637] | 1841 | /// \brief Start the algorithm |
---|
[338] | 1842 | /// |
---|
[637] | 1843 | /// This function starts the algorithm. |
---|
| 1844 | /// |
---|
[949] | 1845 | /// \pre \ref init() or \ref fractionalInit() must be called |
---|
| 1846 | /// before using this function. |
---|
[338] | 1847 | void start() { |
---|
| 1848 | enum OpType { |
---|
| 1849 | D1, D2, D3, D4 |
---|
| 1850 | }; |
---|
| 1851 | |
---|
[949] | 1852 | while (_unmatched > 0) { |
---|
[338] | 1853 | Value d1 = !_delta1->empty() ? |
---|
| 1854 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
| 1855 | |
---|
| 1856 | Value d2 = !_delta2->empty() ? |
---|
| 1857 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 1858 | |
---|
| 1859 | Value d3 = !_delta3->empty() ? |
---|
| 1860 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 1861 | |
---|
| 1862 | Value d4 = !_delta4->empty() ? |
---|
| 1863 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 1864 | |
---|
[947] | 1865 | _delta_sum = d3; OpType ot = D3; |
---|
| 1866 | if (d1 < _delta_sum) { _delta_sum = d1; ot = D1; } |
---|
[338] | 1867 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
| 1868 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 1869 | |
---|
| 1870 | switch (ot) { |
---|
| 1871 | case D1: |
---|
| 1872 | { |
---|
| 1873 | Node n = _delta1->top(); |
---|
| 1874 | unmatchNode(n); |
---|
[949] | 1875 | --_unmatched; |
---|
[338] | 1876 | } |
---|
| 1877 | break; |
---|
| 1878 | case D2: |
---|
| 1879 | { |
---|
| 1880 | int blossom = _delta2->top(); |
---|
| 1881 | Node n = _blossom_set->classTop(blossom); |
---|
[947] | 1882 | Arc a = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 1883 | if ((*_blossom_data)[blossom].next == INVALID) { |
---|
| 1884 | augmentOnArc(a); |
---|
[949] | 1885 | --_unmatched; |
---|
[947] | 1886 | } else { |
---|
| 1887 | extendOnArc(a); |
---|
| 1888 | } |
---|
[338] | 1889 | } |
---|
| 1890 | break; |
---|
| 1891 | case D3: |
---|
| 1892 | { |
---|
| 1893 | Edge e = _delta3->top(); |
---|
| 1894 | |
---|
| 1895 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 1896 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 1897 | |
---|
| 1898 | if (left_blossom == right_blossom) { |
---|
| 1899 | _delta3->pop(); |
---|
| 1900 | } else { |
---|
[947] | 1901 | int left_tree = _tree_set->find(left_blossom); |
---|
| 1902 | int right_tree = _tree_set->find(right_blossom); |
---|
[338] | 1903 | |
---|
| 1904 | if (left_tree == right_tree) { |
---|
[339] | 1905 | shrinkOnEdge(e, left_tree); |
---|
[338] | 1906 | } else { |
---|
[339] | 1907 | augmentOnEdge(e); |
---|
[949] | 1908 | _unmatched -= 2; |
---|
[338] | 1909 | } |
---|
| 1910 | } |
---|
| 1911 | } break; |
---|
| 1912 | case D4: |
---|
| 1913 | splitBlossom(_delta4->top()); |
---|
| 1914 | break; |
---|
| 1915 | } |
---|
| 1916 | } |
---|
| 1917 | extractMatching(); |
---|
| 1918 | } |
---|
| 1919 | |
---|
[637] | 1920 | /// \brief Run the algorithm. |
---|
[338] | 1921 | /// |
---|
[637] | 1922 | /// This method runs the \c %MaxWeightedMatching algorithm. |
---|
[338] | 1923 | /// |
---|
| 1924 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 1925 | /// \code |
---|
[949] | 1926 | /// mwm.fractionalInit(); |
---|
[338] | 1927 | /// mwm.start(); |
---|
| 1928 | /// \endcode |
---|
| 1929 | void run() { |
---|
[949] | 1930 | fractionalInit(); |
---|
[338] | 1931 | start(); |
---|
| 1932 | } |
---|
| 1933 | |
---|
| 1934 | /// @} |
---|
| 1935 | |
---|
[637] | 1936 | /// \name Primal Solution |
---|
[947] | 1937 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
[637] | 1938 | /// matching.\n |
---|
| 1939 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1940 | /// using them. |
---|
[338] | 1941 | |
---|
| 1942 | /// @{ |
---|
| 1943 | |
---|
[637] | 1944 | /// \brief Return the weight of the matching. |
---|
[338] | 1945 | /// |
---|
[637] | 1946 | /// This function returns the weight of the found matching. |
---|
| 1947 | /// |
---|
| 1948 | /// \pre Either run() or start() must be called before using this function. |
---|
[640] | 1949 | Value matchingWeight() const { |
---|
[338] | 1950 | Value sum = 0; |
---|
| 1951 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1952 | if ((*_matching)[n] != INVALID) { |
---|
| 1953 | sum += _weight[(*_matching)[n]]; |
---|
| 1954 | } |
---|
| 1955 | } |
---|
[947] | 1956 | return sum / 2; |
---|
[338] | 1957 | } |
---|
| 1958 | |
---|
[637] | 1959 | /// \brief Return the size (cardinality) of the matching. |
---|
[338] | 1960 | /// |
---|
[637] | 1961 | /// This function returns the size (cardinality) of the found matching. |
---|
| 1962 | /// |
---|
| 1963 | /// \pre Either run() or start() must be called before using this function. |
---|
[339] | 1964 | int matchingSize() const { |
---|
| 1965 | int num = 0; |
---|
| 1966 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1967 | if ((*_matching)[n] != INVALID) { |
---|
| 1968 | ++num; |
---|
| 1969 | } |
---|
| 1970 | } |
---|
| 1971 | return num /= 2; |
---|
| 1972 | } |
---|
| 1973 | |
---|
[637] | 1974 | /// \brief Return \c true if the given edge is in the matching. |
---|
[339] | 1975 | /// |
---|
[947] | 1976 | /// This function returns \c true if the given edge is in the found |
---|
[637] | 1977 | /// matching. |
---|
| 1978 | /// |
---|
| 1979 | /// \pre Either run() or start() must be called before using this function. |
---|
[339] | 1980 | bool matching(const Edge& edge) const { |
---|
| 1981 | return edge == (*_matching)[_graph.u(edge)]; |
---|
[338] | 1982 | } |
---|
| 1983 | |
---|
[637] | 1984 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[338] | 1985 | /// |
---|
[637] | 1986 | /// This function returns the matching arc (or edge) incident to the |
---|
[947] | 1987 | /// given node in the found matching or \c INVALID if the node is |
---|
[637] | 1988 | /// not covered by the matching. |
---|
| 1989 | /// |
---|
| 1990 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 1991 | Arc matching(const Node& node) const { |
---|
| 1992 | return (*_matching)[node]; |
---|
| 1993 | } |
---|
| 1994 | |
---|
[640] | 1995 | /// \brief Return a const reference to the matching map. |
---|
| 1996 | /// |
---|
| 1997 | /// This function returns a const reference to a node map that stores |
---|
| 1998 | /// the matching arc (or edge) incident to each node. |
---|
| 1999 | const MatchingMap& matchingMap() const { |
---|
| 2000 | return *_matching; |
---|
| 2001 | } |
---|
| 2002 | |
---|
[637] | 2003 | /// \brief Return the mate of the given node. |
---|
[338] | 2004 | /// |
---|
[947] | 2005 | /// This function returns the mate of the given node in the found |
---|
[637] | 2006 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
| 2007 | /// |
---|
| 2008 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2009 | Node mate(const Node& node) const { |
---|
| 2010 | return (*_matching)[node] != INVALID ? |
---|
| 2011 | _graph.target((*_matching)[node]) : INVALID; |
---|
| 2012 | } |
---|
| 2013 | |
---|
| 2014 | /// @} |
---|
| 2015 | |
---|
[637] | 2016 | /// \name Dual Solution |
---|
| 2017 | /// Functions to get the dual solution.\n |
---|
| 2018 | /// Either \ref run() or \ref start() function should be called before |
---|
| 2019 | /// using them. |
---|
[338] | 2020 | |
---|
| 2021 | /// @{ |
---|
| 2022 | |
---|
[637] | 2023 | /// \brief Return the value of the dual solution. |
---|
[338] | 2024 | /// |
---|
[947] | 2025 | /// This function returns the value of the dual solution. |
---|
| 2026 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
[637] | 2027 | /// "dual scale". |
---|
| 2028 | /// |
---|
| 2029 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2030 | Value dualValue() const { |
---|
| 2031 | Value sum = 0; |
---|
| 2032 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2033 | sum += nodeValue(n); |
---|
| 2034 | } |
---|
| 2035 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 2036 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 2037 | } |
---|
| 2038 | return sum; |
---|
| 2039 | } |
---|
| 2040 | |
---|
[637] | 2041 | /// \brief Return the dual value (potential) of the given node. |
---|
[338] | 2042 | /// |
---|
[637] | 2043 | /// This function returns the dual value (potential) of the given node. |
---|
| 2044 | /// |
---|
| 2045 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2046 | Value nodeValue(const Node& n) const { |
---|
| 2047 | return (*_node_potential)[n]; |
---|
| 2048 | } |
---|
| 2049 | |
---|
[637] | 2050 | /// \brief Return the number of the blossoms in the basis. |
---|
[338] | 2051 | /// |
---|
[637] | 2052 | /// This function returns the number of the blossoms in the basis. |
---|
| 2053 | /// |
---|
| 2054 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2055 | /// \see BlossomIt |
---|
| 2056 | int blossomNum() const { |
---|
| 2057 | return _blossom_potential.size(); |
---|
| 2058 | } |
---|
| 2059 | |
---|
[637] | 2060 | /// \brief Return the number of the nodes in the given blossom. |
---|
[338] | 2061 | /// |
---|
[637] | 2062 | /// This function returns the number of the nodes in the given blossom. |
---|
| 2063 | /// |
---|
| 2064 | /// \pre Either run() or start() must be called before using this function. |
---|
| 2065 | /// \see BlossomIt |
---|
[338] | 2066 | int blossomSize(int k) const { |
---|
| 2067 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 2068 | } |
---|
| 2069 | |
---|
[637] | 2070 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
[338] | 2071 | /// |
---|
[637] | 2072 | /// This function returns the dual value (ptential) of the given blossom. |
---|
| 2073 | /// |
---|
| 2074 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2075 | Value blossomValue(int k) const { |
---|
| 2076 | return _blossom_potential[k].value; |
---|
| 2077 | } |
---|
| 2078 | |
---|
[637] | 2079 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
[338] | 2080 | /// |
---|
[947] | 2081 | /// This class provides an iterator for obtaining the nodes of the |
---|
[637] | 2082 | /// given blossom. It lists a subset of the nodes. |
---|
[947] | 2083 | /// Before using this iterator, you must allocate a |
---|
[637] | 2084 | /// MaxWeightedMatching class and execute it. |
---|
[338] | 2085 | class BlossomIt { |
---|
| 2086 | public: |
---|
| 2087 | |
---|
| 2088 | /// \brief Constructor. |
---|
| 2089 | /// |
---|
[637] | 2090 | /// Constructor to get the nodes of the given variable. |
---|
| 2091 | /// |
---|
[947] | 2092 | /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or |
---|
| 2093 | /// \ref MaxWeightedMatching::start() "algorithm.start()" must be |
---|
[637] | 2094 | /// called before initializing this iterator. |
---|
[338] | 2095 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
| 2096 | : _algorithm(&algorithm) |
---|
| 2097 | { |
---|
| 2098 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 2099 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 2100 | } |
---|
| 2101 | |
---|
[637] | 2102 | /// \brief Conversion to \c Node. |
---|
[338] | 2103 | /// |
---|
[637] | 2104 | /// Conversion to \c Node. |
---|
[338] | 2105 | operator Node() const { |
---|
[339] | 2106 | return _algorithm->_blossom_node_list[_index]; |
---|
[338] | 2107 | } |
---|
| 2108 | |
---|
| 2109 | /// \brief Increment operator. |
---|
| 2110 | /// |
---|
| 2111 | /// Increment operator. |
---|
| 2112 | BlossomIt& operator++() { |
---|
| 2113 | ++_index; |
---|
| 2114 | return *this; |
---|
| 2115 | } |
---|
| 2116 | |
---|
[339] | 2117 | /// \brief Validity checking |
---|
| 2118 | /// |
---|
| 2119 | /// Checks whether the iterator is invalid. |
---|
| 2120 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 2121 | |
---|
| 2122 | /// \brief Validity checking |
---|
| 2123 | /// |
---|
| 2124 | /// Checks whether the iterator is valid. |
---|
| 2125 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[338] | 2126 | |
---|
| 2127 | private: |
---|
| 2128 | const MaxWeightedMatching* _algorithm; |
---|
| 2129 | int _last; |
---|
| 2130 | int _index; |
---|
| 2131 | }; |
---|
| 2132 | |
---|
| 2133 | /// @} |
---|
| 2134 | |
---|
| 2135 | }; |
---|
| 2136 | |
---|
| 2137 | /// \ingroup matching |
---|
| 2138 | /// |
---|
| 2139 | /// \brief Weighted perfect matching in general graphs |
---|
| 2140 | /// |
---|
| 2141 | /// This class provides an efficient implementation of Edmond's |
---|
[339] | 2142 | /// maximum weighted perfect matching algorithm. The implementation |
---|
[338] | 2143 | /// is based on extensive use of priority queues and provides |
---|
[606] | 2144 | /// \f$O(nm\log n)\f$ time complexity. |
---|
[338] | 2145 | /// |
---|
[947] | 2146 | /// The maximum weighted perfect matching problem is to find a subset of |
---|
| 2147 | /// the edges in an undirected graph with maximum overall weight for which |
---|
[637] | 2148 | /// each node has exactly one incident edge. |
---|
| 2149 | /// It can be formulated with the following linear program. |
---|
[338] | 2150 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
[339] | 2151 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 2152 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[338] | 2153 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 2154 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[339] | 2155 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 2156 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 2157 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 2158 | /// subsets of the nodes. |
---|
[338] | 2159 | /// |
---|
| 2160 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 2161 | /// optimality. The solution of the dual problem can be used to check |
---|
[339] | 2162 | /// the result of the algorithm. The dual linear problem is the |
---|
[637] | 2163 | /// following. |
---|
[339] | 2164 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge |
---|
| 2165 | w_{uv} \quad \forall uv\in E\f] */ |
---|
[338] | 2166 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[339] | 2167 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 2168 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[338] | 2169 | /// |
---|
[947] | 2170 | /// The algorithm can be executed with the run() function. |
---|
[637] | 2171 | /// After it the matching (the primal solution) and the dual solution |
---|
[947] | 2172 | /// can be obtained using the query functions and the |
---|
| 2173 | /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class, |
---|
| 2174 | /// which is able to iterate on the nodes of a blossom. |
---|
[637] | 2175 | /// If the value type is integer, then the dual solution is multiplied |
---|
| 2176 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
| 2177 | /// |
---|
[640] | 2178 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
[947] | 2179 | /// \tparam WM The type edge weight map. The default type is |
---|
[637] | 2180 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 2181 | #ifdef DOXYGEN |
---|
| 2182 | template <typename GR, typename WM> |
---|
| 2183 | #else |
---|
[606] | 2184 | template <typename GR, |
---|
| 2185 | typename WM = typename GR::template EdgeMap<int> > |
---|
[637] | 2186 | #endif |
---|
[338] | 2187 | class MaxWeightedPerfectMatching { |
---|
| 2188 | public: |
---|
| 2189 | |
---|
[637] | 2190 | /// The graph type of the algorithm |
---|
[606] | 2191 | typedef GR Graph; |
---|
[637] | 2192 | /// The type of the edge weight map |
---|
[606] | 2193 | typedef WM WeightMap; |
---|
[637] | 2194 | /// The value type of the edge weights |
---|
[338] | 2195 | typedef typename WeightMap::Value Value; |
---|
| 2196 | |
---|
| 2197 | /// \brief Scaling factor for dual solution |
---|
| 2198 | /// |
---|
| 2199 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 2200 | /// according to the value type. |
---|
| 2201 | static const int dualScale = |
---|
| 2202 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 2203 | |
---|
[640] | 2204 | /// The type of the matching map |
---|
[338] | 2205 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 2206 | MatchingMap; |
---|
| 2207 | |
---|
| 2208 | private: |
---|
| 2209 | |
---|
| 2210 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 2211 | |
---|
| 2212 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 2213 | typedef std::vector<Node> BlossomNodeList; |
---|
| 2214 | |
---|
| 2215 | struct BlossomVariable { |
---|
| 2216 | int begin, end; |
---|
| 2217 | Value value; |
---|
| 2218 | |
---|
| 2219 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 2220 | : begin(_begin), end(_end), value(_value) {} |
---|
| 2221 | |
---|
| 2222 | }; |
---|
| 2223 | |
---|
| 2224 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 2225 | |
---|
| 2226 | const Graph& _graph; |
---|
| 2227 | const WeightMap& _weight; |
---|
| 2228 | |
---|
| 2229 | MatchingMap* _matching; |
---|
| 2230 | |
---|
| 2231 | NodePotential* _node_potential; |
---|
| 2232 | |
---|
| 2233 | BlossomPotential _blossom_potential; |
---|
| 2234 | BlossomNodeList _blossom_node_list; |
---|
| 2235 | |
---|
| 2236 | int _node_num; |
---|
| 2237 | int _blossom_num; |
---|
| 2238 | |
---|
| 2239 | typedef RangeMap<int> IntIntMap; |
---|
| 2240 | |
---|
| 2241 | enum Status { |
---|
| 2242 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
| 2243 | }; |
---|
| 2244 | |
---|
[339] | 2245 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[338] | 2246 | struct BlossomData { |
---|
| 2247 | int tree; |
---|
| 2248 | Status status; |
---|
| 2249 | Arc pred, next; |
---|
| 2250 | Value pot, offset; |
---|
| 2251 | }; |
---|
| 2252 | |
---|
[339] | 2253 | IntNodeMap *_blossom_index; |
---|
[338] | 2254 | BlossomSet *_blossom_set; |
---|
| 2255 | RangeMap<BlossomData>* _blossom_data; |
---|
| 2256 | |
---|
[339] | 2257 | IntNodeMap *_node_index; |
---|
| 2258 | IntArcMap *_node_heap_index; |
---|
[338] | 2259 | |
---|
| 2260 | struct NodeData { |
---|
| 2261 | |
---|
[339] | 2262 | NodeData(IntArcMap& node_heap_index) |
---|
[338] | 2263 | : heap(node_heap_index) {} |
---|
| 2264 | |
---|
| 2265 | int blossom; |
---|
| 2266 | Value pot; |
---|
[339] | 2267 | BinHeap<Value, IntArcMap> heap; |
---|
[338] | 2268 | std::map<int, Arc> heap_index; |
---|
| 2269 | |
---|
| 2270 | int tree; |
---|
| 2271 | }; |
---|
| 2272 | |
---|
| 2273 | RangeMap<NodeData>* _node_data; |
---|
| 2274 | |
---|
| 2275 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 2276 | |
---|
| 2277 | IntIntMap *_tree_set_index; |
---|
| 2278 | TreeSet *_tree_set; |
---|
| 2279 | |
---|
| 2280 | IntIntMap *_delta2_index; |
---|
| 2281 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 2282 | |
---|
[339] | 2283 | IntEdgeMap *_delta3_index; |
---|
| 2284 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[338] | 2285 | |
---|
| 2286 | IntIntMap *_delta4_index; |
---|
| 2287 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 2288 | |
---|
| 2289 | Value _delta_sum; |
---|
[949] | 2290 | int _unmatched; |
---|
| 2291 | |
---|
[956] | 2292 | typedef MaxWeightedPerfectFractionalMatching<Graph, WeightMap> |
---|
[949] | 2293 | FractionalMatching; |
---|
| 2294 | FractionalMatching *_fractional; |
---|
[338] | 2295 | |
---|
| 2296 | void createStructures() { |
---|
| 2297 | _node_num = countNodes(_graph); |
---|
| 2298 | _blossom_num = _node_num * 3 / 2; |
---|
| 2299 | |
---|
| 2300 | if (!_matching) { |
---|
| 2301 | _matching = new MatchingMap(_graph); |
---|
| 2302 | } |
---|
[945] | 2303 | |
---|
[338] | 2304 | if (!_node_potential) { |
---|
| 2305 | _node_potential = new NodePotential(_graph); |
---|
| 2306 | } |
---|
[945] | 2307 | |
---|
[338] | 2308 | if (!_blossom_set) { |
---|
[339] | 2309 | _blossom_index = new IntNodeMap(_graph); |
---|
[338] | 2310 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 2311 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[945] | 2312 | } else if (_blossom_data->size() != _blossom_num) { |
---|
| 2313 | delete _blossom_data; |
---|
| 2314 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[338] | 2315 | } |
---|
| 2316 | |
---|
| 2317 | if (!_node_index) { |
---|
[339] | 2318 | _node_index = new IntNodeMap(_graph); |
---|
| 2319 | _node_heap_index = new IntArcMap(_graph); |
---|
[338] | 2320 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
[339] | 2321 | NodeData(*_node_heap_index)); |
---|
[945] | 2322 | } else if (_node_data->size() != _node_num) { |
---|
| 2323 | delete _node_data; |
---|
| 2324 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
| 2325 | NodeData(*_node_heap_index)); |
---|
[338] | 2326 | } |
---|
| 2327 | |
---|
| 2328 | if (!_tree_set) { |
---|
| 2329 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 2330 | _tree_set = new TreeSet(*_tree_set_index); |
---|
[945] | 2331 | } else { |
---|
| 2332 | _tree_set_index->resize(_blossom_num); |
---|
[338] | 2333 | } |
---|
[945] | 2334 | |
---|
[338] | 2335 | if (!_delta2) { |
---|
| 2336 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 2337 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
[945] | 2338 | } else { |
---|
| 2339 | _delta2_index->resize(_blossom_num); |
---|
[338] | 2340 | } |
---|
[945] | 2341 | |
---|
[338] | 2342 | if (!_delta3) { |
---|
[339] | 2343 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 2344 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[338] | 2345 | } |
---|
[945] | 2346 | |
---|
[338] | 2347 | if (!_delta4) { |
---|
| 2348 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 2349 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
[945] | 2350 | } else { |
---|
| 2351 | _delta4_index->resize(_blossom_num); |
---|
[338] | 2352 | } |
---|
| 2353 | } |
---|
| 2354 | |
---|
| 2355 | void destroyStructures() { |
---|
| 2356 | if (_matching) { |
---|
| 2357 | delete _matching; |
---|
| 2358 | } |
---|
| 2359 | if (_node_potential) { |
---|
| 2360 | delete _node_potential; |
---|
| 2361 | } |
---|
| 2362 | if (_blossom_set) { |
---|
| 2363 | delete _blossom_index; |
---|
| 2364 | delete _blossom_set; |
---|
| 2365 | delete _blossom_data; |
---|
| 2366 | } |
---|
| 2367 | |
---|
| 2368 | if (_node_index) { |
---|
| 2369 | delete _node_index; |
---|
| 2370 | delete _node_heap_index; |
---|
| 2371 | delete _node_data; |
---|
| 2372 | } |
---|
| 2373 | |
---|
| 2374 | if (_tree_set) { |
---|
| 2375 | delete _tree_set_index; |
---|
| 2376 | delete _tree_set; |
---|
| 2377 | } |
---|
| 2378 | if (_delta2) { |
---|
| 2379 | delete _delta2_index; |
---|
| 2380 | delete _delta2; |
---|
| 2381 | } |
---|
| 2382 | if (_delta3) { |
---|
| 2383 | delete _delta3_index; |
---|
| 2384 | delete _delta3; |
---|
| 2385 | } |
---|
| 2386 | if (_delta4) { |
---|
| 2387 | delete _delta4_index; |
---|
| 2388 | delete _delta4; |
---|
| 2389 | } |
---|
| 2390 | } |
---|
| 2391 | |
---|
| 2392 | void matchedToEven(int blossom, int tree) { |
---|
| 2393 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2394 | _delta2->erase(blossom); |
---|
| 2395 | } |
---|
| 2396 | |
---|
| 2397 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2398 | (*_blossom_data)[blossom].pot -= |
---|
| 2399 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2400 | } |
---|
| 2401 | |
---|
| 2402 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2403 | n != INVALID; ++n) { |
---|
| 2404 | |
---|
| 2405 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2406 | int ni = (*_node_index)[n]; |
---|
| 2407 | |
---|
| 2408 | (*_node_data)[ni].heap.clear(); |
---|
| 2409 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2410 | |
---|
| 2411 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2412 | |
---|
| 2413 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2414 | Node v = _graph.source(e); |
---|
| 2415 | int vb = _blossom_set->find(v); |
---|
| 2416 | int vi = (*_node_index)[v]; |
---|
| 2417 | |
---|
| 2418 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2419 | dualScale * _weight[e]; |
---|
| 2420 | |
---|
| 2421 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2422 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2423 | _delta3->push(e, rw / 2); |
---|
| 2424 | } |
---|
| 2425 | } else { |
---|
| 2426 | typename std::map<int, Arc>::iterator it = |
---|
| 2427 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2428 | |
---|
| 2429 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2430 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2431 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2432 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2433 | it->second = e; |
---|
| 2434 | } |
---|
| 2435 | } else { |
---|
| 2436 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2437 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2438 | } |
---|
| 2439 | |
---|
| 2440 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2441 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2442 | |
---|
| 2443 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2444 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2445 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2446 | (*_blossom_data)[vb].offset); |
---|
| 2447 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2448 | (*_blossom_data)[vb].offset){ |
---|
| 2449 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2450 | (*_blossom_data)[vb].offset); |
---|
| 2451 | } |
---|
| 2452 | } |
---|
| 2453 | } |
---|
| 2454 | } |
---|
| 2455 | } |
---|
| 2456 | } |
---|
| 2457 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2458 | } |
---|
| 2459 | |
---|
| 2460 | void matchedToOdd(int blossom) { |
---|
| 2461 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2462 | _delta2->erase(blossom); |
---|
| 2463 | } |
---|
| 2464 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 2465 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2466 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 2467 | (*_blossom_data)[blossom].offset); |
---|
| 2468 | } |
---|
| 2469 | } |
---|
| 2470 | |
---|
| 2471 | void evenToMatched(int blossom, int tree) { |
---|
| 2472 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2473 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 2474 | } |
---|
| 2475 | |
---|
| 2476 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2477 | n != INVALID; ++n) { |
---|
| 2478 | int ni = (*_node_index)[n]; |
---|
| 2479 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 2480 | |
---|
| 2481 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2482 | Node v = _graph.source(e); |
---|
| 2483 | int vb = _blossom_set->find(v); |
---|
| 2484 | int vi = (*_node_index)[v]; |
---|
| 2485 | |
---|
| 2486 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2487 | dualScale * _weight[e]; |
---|
| 2488 | |
---|
| 2489 | if (vb == blossom) { |
---|
| 2490 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2491 | _delta3->erase(e); |
---|
| 2492 | } |
---|
| 2493 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2494 | |
---|
| 2495 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2496 | _delta3->erase(e); |
---|
| 2497 | } |
---|
| 2498 | |
---|
| 2499 | int vt = _tree_set->find(vb); |
---|
| 2500 | |
---|
| 2501 | if (vt != tree) { |
---|
| 2502 | |
---|
| 2503 | Arc r = _graph.oppositeArc(e); |
---|
| 2504 | |
---|
| 2505 | typename std::map<int, Arc>::iterator it = |
---|
| 2506 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 2507 | |
---|
| 2508 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 2509 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 2510 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 2511 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 2512 | it->second = r; |
---|
| 2513 | } |
---|
| 2514 | } else { |
---|
| 2515 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 2516 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 2517 | } |
---|
| 2518 | |
---|
| 2519 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 2520 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 2521 | |
---|
| 2522 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 2523 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2524 | (*_blossom_data)[blossom].offset); |
---|
| 2525 | } else if ((*_delta2)[blossom] > |
---|
| 2526 | _blossom_set->classPrio(blossom) - |
---|
| 2527 | (*_blossom_data)[blossom].offset){ |
---|
| 2528 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2529 | (*_blossom_data)[blossom].offset); |
---|
| 2530 | } |
---|
| 2531 | } |
---|
| 2532 | } |
---|
| 2533 | } else { |
---|
| 2534 | |
---|
| 2535 | typename std::map<int, Arc>::iterator it = |
---|
| 2536 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2537 | |
---|
| 2538 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2539 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 2540 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 2541 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 2542 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 2543 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 2544 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 2545 | } |
---|
| 2546 | |
---|
| 2547 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2548 | if (_blossom_set->classPrio(vb) == |
---|
| 2549 | std::numeric_limits<Value>::max()) { |
---|
| 2550 | _delta2->erase(vb); |
---|
| 2551 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 2552 | (*_blossom_data)[vb].offset) { |
---|
| 2553 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 2554 | (*_blossom_data)[vb].offset); |
---|
| 2555 | } |
---|
| 2556 | } |
---|
| 2557 | } |
---|
| 2558 | } |
---|
| 2559 | } |
---|
| 2560 | } |
---|
| 2561 | } |
---|
| 2562 | |
---|
| 2563 | void oddToMatched(int blossom) { |
---|
| 2564 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 2565 | |
---|
| 2566 | if (_blossom_set->classPrio(blossom) != |
---|
| 2567 | std::numeric_limits<Value>::max()) { |
---|
| 2568 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2569 | (*_blossom_data)[blossom].offset); |
---|
| 2570 | } |
---|
| 2571 | |
---|
| 2572 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2573 | _delta4->erase(blossom); |
---|
| 2574 | } |
---|
| 2575 | } |
---|
| 2576 | |
---|
| 2577 | void oddToEven(int blossom, int tree) { |
---|
| 2578 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2579 | _delta4->erase(blossom); |
---|
| 2580 | (*_blossom_data)[blossom].pot -= |
---|
| 2581 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2582 | } |
---|
| 2583 | |
---|
| 2584 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2585 | n != INVALID; ++n) { |
---|
| 2586 | int ni = (*_node_index)[n]; |
---|
| 2587 | |
---|
| 2588 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2589 | |
---|
| 2590 | (*_node_data)[ni].heap.clear(); |
---|
| 2591 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2592 | (*_node_data)[ni].pot += |
---|
| 2593 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2594 | |
---|
| 2595 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2596 | Node v = _graph.source(e); |
---|
| 2597 | int vb = _blossom_set->find(v); |
---|
| 2598 | int vi = (*_node_index)[v]; |
---|
| 2599 | |
---|
| 2600 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2601 | dualScale * _weight[e]; |
---|
| 2602 | |
---|
| 2603 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2604 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2605 | _delta3->push(e, rw / 2); |
---|
| 2606 | } |
---|
| 2607 | } else { |
---|
| 2608 | |
---|
| 2609 | typename std::map<int, Arc>::iterator it = |
---|
| 2610 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2611 | |
---|
| 2612 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2613 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2614 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2615 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2616 | it->second = e; |
---|
| 2617 | } |
---|
| 2618 | } else { |
---|
| 2619 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2620 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2621 | } |
---|
| 2622 | |
---|
| 2623 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2624 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2625 | |
---|
| 2626 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2627 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2628 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2629 | (*_blossom_data)[vb].offset); |
---|
| 2630 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2631 | (*_blossom_data)[vb].offset) { |
---|
| 2632 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2633 | (*_blossom_data)[vb].offset); |
---|
| 2634 | } |
---|
| 2635 | } |
---|
| 2636 | } |
---|
| 2637 | } |
---|
| 2638 | } |
---|
| 2639 | } |
---|
| 2640 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2641 | } |
---|
| 2642 | |
---|
| 2643 | void alternatePath(int even, int tree) { |
---|
| 2644 | int odd; |
---|
| 2645 | |
---|
| 2646 | evenToMatched(even, tree); |
---|
| 2647 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2648 | |
---|
| 2649 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 2650 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 2651 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 2652 | oddToMatched(odd); |
---|
| 2653 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 2654 | |
---|
| 2655 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 2656 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2657 | evenToMatched(even, tree); |
---|
| 2658 | (*_blossom_data)[even].next = |
---|
| 2659 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 2660 | } |
---|
| 2661 | |
---|
| 2662 | } |
---|
| 2663 | |
---|
| 2664 | void destroyTree(int tree) { |
---|
| 2665 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 2666 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 2667 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2668 | evenToMatched(b, tree); |
---|
| 2669 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 2670 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2671 | oddToMatched(b); |
---|
| 2672 | } |
---|
| 2673 | } |
---|
| 2674 | _tree_set->eraseClass(tree); |
---|
| 2675 | } |
---|
| 2676 | |
---|
[339] | 2677 | void augmentOnEdge(const Edge& edge) { |
---|
| 2678 | |
---|
| 2679 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2680 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[338] | 2681 | |
---|
| 2682 | int left_tree = _tree_set->find(left); |
---|
| 2683 | alternatePath(left, left_tree); |
---|
| 2684 | destroyTree(left_tree); |
---|
| 2685 | |
---|
| 2686 | int right_tree = _tree_set->find(right); |
---|
| 2687 | alternatePath(right, right_tree); |
---|
| 2688 | destroyTree(right_tree); |
---|
| 2689 | |
---|
[339] | 2690 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 2691 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[338] | 2692 | } |
---|
| 2693 | |
---|
| 2694 | void extendOnArc(const Arc& arc) { |
---|
| 2695 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 2696 | int tree = _tree_set->find(base); |
---|
| 2697 | |
---|
| 2698 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 2699 | _tree_set->insert(odd, tree); |
---|
| 2700 | (*_blossom_data)[odd].status = ODD; |
---|
| 2701 | matchedToOdd(odd); |
---|
| 2702 | (*_blossom_data)[odd].pred = arc; |
---|
| 2703 | |
---|
| 2704 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 2705 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 2706 | _tree_set->insert(even, tree); |
---|
| 2707 | (*_blossom_data)[even].status = EVEN; |
---|
| 2708 | matchedToEven(even, tree); |
---|
| 2709 | } |
---|
| 2710 | |
---|
[339] | 2711 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[338] | 2712 | int nca = -1; |
---|
| 2713 | std::vector<int> left_path, right_path; |
---|
| 2714 | |
---|
| 2715 | { |
---|
| 2716 | std::set<int> left_set, right_set; |
---|
| 2717 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2718 | left_path.push_back(left); |
---|
| 2719 | left_set.insert(left); |
---|
| 2720 | |
---|
| 2721 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 2722 | right_path.push_back(right); |
---|
| 2723 | right_set.insert(right); |
---|
| 2724 | |
---|
| 2725 | while (true) { |
---|
| 2726 | |
---|
| 2727 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 2728 | |
---|
| 2729 | left = |
---|
| 2730 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2731 | left_path.push_back(left); |
---|
| 2732 | left = |
---|
| 2733 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2734 | left_path.push_back(left); |
---|
| 2735 | |
---|
| 2736 | left_set.insert(left); |
---|
| 2737 | |
---|
| 2738 | if (right_set.find(left) != right_set.end()) { |
---|
| 2739 | nca = left; |
---|
| 2740 | break; |
---|
| 2741 | } |
---|
| 2742 | |
---|
| 2743 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 2744 | |
---|
| 2745 | right = |
---|
| 2746 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2747 | right_path.push_back(right); |
---|
| 2748 | right = |
---|
| 2749 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2750 | right_path.push_back(right); |
---|
| 2751 | |
---|
| 2752 | right_set.insert(right); |
---|
| 2753 | |
---|
| 2754 | if (left_set.find(right) != left_set.end()) { |
---|
| 2755 | nca = right; |
---|
| 2756 | break; |
---|
| 2757 | } |
---|
| 2758 | |
---|
| 2759 | } |
---|
| 2760 | |
---|
| 2761 | if (nca == -1) { |
---|
| 2762 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 2763 | nca = right; |
---|
| 2764 | while (left_set.find(nca) == left_set.end()) { |
---|
| 2765 | nca = |
---|
| 2766 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2767 | right_path.push_back(nca); |
---|
| 2768 | nca = |
---|
| 2769 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2770 | right_path.push_back(nca); |
---|
| 2771 | } |
---|
| 2772 | } else { |
---|
| 2773 | nca = left; |
---|
| 2774 | while (right_set.find(nca) == right_set.end()) { |
---|
| 2775 | nca = |
---|
| 2776 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2777 | left_path.push_back(nca); |
---|
| 2778 | nca = |
---|
| 2779 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2780 | left_path.push_back(nca); |
---|
| 2781 | } |
---|
| 2782 | } |
---|
| 2783 | } |
---|
| 2784 | } |
---|
| 2785 | |
---|
| 2786 | std::vector<int> subblossoms; |
---|
| 2787 | Arc prev; |
---|
| 2788 | |
---|
| 2789 | prev = _graph.direct(edge, true); |
---|
| 2790 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 2791 | subblossoms.push_back(left_path[i]); |
---|
| 2792 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 2793 | _tree_set->erase(left_path[i]); |
---|
| 2794 | |
---|
| 2795 | subblossoms.push_back(left_path[i + 1]); |
---|
| 2796 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 2797 | oddToEven(left_path[i + 1], tree); |
---|
| 2798 | _tree_set->erase(left_path[i + 1]); |
---|
| 2799 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 2800 | } |
---|
| 2801 | |
---|
| 2802 | int k = 0; |
---|
| 2803 | while (right_path[k] != nca) ++k; |
---|
| 2804 | |
---|
| 2805 | subblossoms.push_back(nca); |
---|
| 2806 | (*_blossom_data)[nca].next = prev; |
---|
| 2807 | |
---|
| 2808 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 2809 | subblossoms.push_back(right_path[i + 1]); |
---|
| 2810 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 2811 | oddToEven(right_path[i + 1], tree); |
---|
| 2812 | _tree_set->erase(right_path[i + 1]); |
---|
| 2813 | |
---|
| 2814 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 2815 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 2816 | |
---|
| 2817 | subblossoms.push_back(right_path[i]); |
---|
| 2818 | _tree_set->erase(right_path[i]); |
---|
| 2819 | } |
---|
| 2820 | |
---|
| 2821 | int surface = |
---|
| 2822 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 2823 | |
---|
| 2824 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2825 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2826 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 2827 | } |
---|
| 2828 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 2829 | } |
---|
| 2830 | |
---|
| 2831 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 2832 | (*_blossom_data)[surface].offset = 0; |
---|
| 2833 | (*_blossom_data)[surface].status = EVEN; |
---|
| 2834 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 2835 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 2836 | |
---|
| 2837 | _tree_set->insert(surface, tree); |
---|
| 2838 | _tree_set->erase(nca); |
---|
| 2839 | } |
---|
| 2840 | |
---|
| 2841 | void splitBlossom(int blossom) { |
---|
| 2842 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 2843 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 2844 | |
---|
| 2845 | int tree = _tree_set->find(blossom); |
---|
| 2846 | |
---|
| 2847 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 2848 | oddToMatched(blossom); |
---|
| 2849 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2850 | _delta2->erase(blossom); |
---|
| 2851 | } |
---|
| 2852 | |
---|
| 2853 | std::vector<int> subblossoms; |
---|
| 2854 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2855 | |
---|
| 2856 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 2857 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 2858 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 2859 | |
---|
| 2860 | int ib = -1, id = -1; |
---|
| 2861 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2862 | if (subblossoms[i] == b) ib = i; |
---|
| 2863 | if (subblossoms[i] == d) id = i; |
---|
| 2864 | |
---|
| 2865 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 2866 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2867 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 2868 | } |
---|
| 2869 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 2870 | std::numeric_limits<Value>::max()) { |
---|
| 2871 | _delta2->push(subblossoms[i], |
---|
| 2872 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 2873 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 2874 | } |
---|
| 2875 | } |
---|
| 2876 | |
---|
| 2877 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 2878 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 2879 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2880 | int sb = subblossoms[i]; |
---|
| 2881 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2882 | (*_blossom_data)[sb].next = |
---|
| 2883 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2884 | } |
---|
| 2885 | |
---|
| 2886 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2887 | int sb = subblossoms[i]; |
---|
| 2888 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2889 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2890 | |
---|
| 2891 | (*_blossom_data)[sb].status = ODD; |
---|
| 2892 | matchedToOdd(sb); |
---|
| 2893 | _tree_set->insert(sb, tree); |
---|
| 2894 | (*_blossom_data)[sb].pred = pred; |
---|
| 2895 | (*_blossom_data)[sb].next = |
---|
| 2896 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2897 | |
---|
| 2898 | pred = (*_blossom_data)[ub].next; |
---|
| 2899 | |
---|
| 2900 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2901 | matchedToEven(tb, tree); |
---|
| 2902 | _tree_set->insert(tb, tree); |
---|
| 2903 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 2904 | } |
---|
| 2905 | |
---|
| 2906 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 2907 | matchedToOdd(subblossoms[id]); |
---|
| 2908 | _tree_set->insert(subblossoms[id], tree); |
---|
| 2909 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 2910 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 2911 | |
---|
| 2912 | } else { |
---|
| 2913 | |
---|
| 2914 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 2915 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2916 | int sb = subblossoms[i]; |
---|
| 2917 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2918 | (*_blossom_data)[sb].next = |
---|
| 2919 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2920 | } |
---|
| 2921 | |
---|
| 2922 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2923 | int sb = subblossoms[i]; |
---|
| 2924 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2925 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2926 | |
---|
| 2927 | (*_blossom_data)[sb].status = ODD; |
---|
| 2928 | matchedToOdd(sb); |
---|
| 2929 | _tree_set->insert(sb, tree); |
---|
| 2930 | (*_blossom_data)[sb].next = next; |
---|
| 2931 | (*_blossom_data)[sb].pred = |
---|
| 2932 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2933 | |
---|
| 2934 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2935 | matchedToEven(tb, tree); |
---|
| 2936 | _tree_set->insert(tb, tree); |
---|
| 2937 | (*_blossom_data)[tb].pred = |
---|
| 2938 | (*_blossom_data)[tb].next = |
---|
| 2939 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 2940 | next = (*_blossom_data)[ub].next; |
---|
| 2941 | } |
---|
| 2942 | |
---|
| 2943 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 2944 | matchedToOdd(subblossoms[ib]); |
---|
| 2945 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 2946 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 2947 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 2948 | } |
---|
| 2949 | _tree_set->erase(blossom); |
---|
| 2950 | } |
---|
| 2951 | |
---|
| 2952 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 2953 | if (_blossom_set->trivial(blossom)) { |
---|
| 2954 | int bi = (*_node_index)[base]; |
---|
| 2955 | Value pot = (*_node_data)[bi].pot; |
---|
| 2956 | |
---|
[628] | 2957 | (*_matching)[base] = matching; |
---|
[338] | 2958 | _blossom_node_list.push_back(base); |
---|
[628] | 2959 | (*_node_potential)[base] = pot; |
---|
[338] | 2960 | } else { |
---|
| 2961 | |
---|
| 2962 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 2963 | int bn = _blossom_node_list.size(); |
---|
| 2964 | |
---|
| 2965 | std::vector<int> subblossoms; |
---|
| 2966 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2967 | int b = _blossom_set->find(base); |
---|
| 2968 | int ib = -1; |
---|
| 2969 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2970 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 2971 | } |
---|
| 2972 | |
---|
| 2973 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 2974 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 2975 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 2976 | |
---|
| 2977 | Arc m = (*_blossom_data)[tb].next; |
---|
| 2978 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 2979 | extractBlossom(tb, _graph.source(m), m); |
---|
| 2980 | } |
---|
| 2981 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 2982 | |
---|
| 2983 | int en = _blossom_node_list.size(); |
---|
| 2984 | |
---|
| 2985 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 2986 | } |
---|
| 2987 | } |
---|
| 2988 | |
---|
| 2989 | void extractMatching() { |
---|
| 2990 | std::vector<int> blossoms; |
---|
| 2991 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 2992 | blossoms.push_back(c); |
---|
| 2993 | } |
---|
| 2994 | |
---|
| 2995 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 2996 | |
---|
| 2997 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 2998 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 2999 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 3000 | n != INVALID; ++n) { |
---|
| 3001 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 3002 | } |
---|
| 3003 | |
---|
| 3004 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 3005 | Node base = _graph.source(matching); |
---|
| 3006 | extractBlossom(blossoms[i], base, matching); |
---|
| 3007 | } |
---|
| 3008 | } |
---|
| 3009 | |
---|
| 3010 | public: |
---|
| 3011 | |
---|
| 3012 | /// \brief Constructor |
---|
| 3013 | /// |
---|
| 3014 | /// Constructor. |
---|
| 3015 | MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight) |
---|
| 3016 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 3017 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 3018 | _node_num(0), _blossom_num(0), |
---|
| 3019 | |
---|
| 3020 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 3021 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 3022 | _tree_set_index(0), _tree_set(0), |
---|
| 3023 | |
---|
| 3024 | _delta2_index(0), _delta2(0), |
---|
| 3025 | _delta3_index(0), _delta3(0), |
---|
| 3026 | _delta4_index(0), _delta4(0), |
---|
| 3027 | |
---|
[949] | 3028 | _delta_sum(), _unmatched(0), |
---|
| 3029 | |
---|
| 3030 | _fractional(0) |
---|
| 3031 | {} |
---|
[338] | 3032 | |
---|
| 3033 | ~MaxWeightedPerfectMatching() { |
---|
| 3034 | destroyStructures(); |
---|
[949] | 3035 | if (_fractional) { |
---|
| 3036 | delete _fractional; |
---|
| 3037 | } |
---|
[338] | 3038 | } |
---|
| 3039 | |
---|
[637] | 3040 | /// \name Execution Control |
---|
[342] | 3041 | /// The simplest way to execute the algorithm is to use the |
---|
[637] | 3042 | /// \ref run() member function. |
---|
[338] | 3043 | |
---|
| 3044 | ///@{ |
---|
| 3045 | |
---|
| 3046 | /// \brief Initialize the algorithm |
---|
| 3047 | /// |
---|
[637] | 3048 | /// This function initializes the algorithm. |
---|
[338] | 3049 | void init() { |
---|
| 3050 | createStructures(); |
---|
| 3051 | |
---|
[945] | 3052 | _blossom_node_list.clear(); |
---|
| 3053 | _blossom_potential.clear(); |
---|
| 3054 | |
---|
[338] | 3055 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 3056 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
[338] | 3057 | } |
---|
| 3058 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 3059 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
[338] | 3060 | } |
---|
| 3061 | for (int i = 0; i < _blossom_num; ++i) { |
---|
[628] | 3062 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 3063 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
[338] | 3064 | } |
---|
| 3065 | |
---|
[949] | 3066 | _unmatched = _node_num; |
---|
| 3067 | |
---|
[945] | 3068 | _delta2->clear(); |
---|
| 3069 | _delta3->clear(); |
---|
| 3070 | _delta4->clear(); |
---|
| 3071 | _blossom_set->clear(); |
---|
| 3072 | _tree_set->clear(); |
---|
| 3073 | |
---|
[338] | 3074 | int index = 0; |
---|
| 3075 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3076 | Value max = - std::numeric_limits<Value>::max(); |
---|
| 3077 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 3078 | if (_graph.target(e) == n) continue; |
---|
| 3079 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 3080 | max = (dualScale * _weight[e]) / 2; |
---|
| 3081 | } |
---|
| 3082 | } |
---|
[628] | 3083 | (*_node_index)[n] = index; |
---|
[945] | 3084 | (*_node_data)[index].heap_index.clear(); |
---|
| 3085 | (*_node_data)[index].heap.clear(); |
---|
[338] | 3086 | (*_node_data)[index].pot = max; |
---|
| 3087 | int blossom = |
---|
| 3088 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 3089 | |
---|
| 3090 | _tree_set->insert(blossom); |
---|
| 3091 | |
---|
| 3092 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 3093 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 3094 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 3095 | (*_blossom_data)[blossom].pot = 0; |
---|
| 3096 | (*_blossom_data)[blossom].offset = 0; |
---|
| 3097 | ++index; |
---|
| 3098 | } |
---|
| 3099 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 3100 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 3101 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 3102 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 3103 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 3104 | dualScale * _weight[e]) / 2); |
---|
| 3105 | } |
---|
| 3106 | } |
---|
| 3107 | } |
---|
| 3108 | |
---|
[949] | 3109 | /// \brief Initialize the algorithm with fractional matching |
---|
| 3110 | /// |
---|
| 3111 | /// This function initializes the algorithm with a fractional |
---|
| 3112 | /// matching. This initialization is also called jumpstart heuristic. |
---|
| 3113 | void fractionalInit() { |
---|
| 3114 | createStructures(); |
---|
[955] | 3115 | |
---|
| 3116 | _blossom_node_list.clear(); |
---|
| 3117 | _blossom_potential.clear(); |
---|
[956] | 3118 | |
---|
[949] | 3119 | if (_fractional == 0) { |
---|
| 3120 | _fractional = new FractionalMatching(_graph, _weight, false); |
---|
| 3121 | } |
---|
| 3122 | if (!_fractional->run()) { |
---|
| 3123 | _unmatched = -1; |
---|
| 3124 | return; |
---|
| 3125 | } |
---|
| 3126 | |
---|
| 3127 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 3128 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
| 3129 | } |
---|
| 3130 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 3131 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
| 3132 | } |
---|
| 3133 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 3134 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 3135 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
| 3136 | } |
---|
| 3137 | |
---|
| 3138 | _unmatched = 0; |
---|
| 3139 | |
---|
[955] | 3140 | _delta2->clear(); |
---|
| 3141 | _delta3->clear(); |
---|
| 3142 | _delta4->clear(); |
---|
| 3143 | _blossom_set->clear(); |
---|
| 3144 | _tree_set->clear(); |
---|
| 3145 | |
---|
[949] | 3146 | int index = 0; |
---|
| 3147 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3148 | Value pot = _fractional->nodeValue(n); |
---|
| 3149 | (*_node_index)[n] = index; |
---|
| 3150 | (*_node_data)[index].pot = pot; |
---|
[955] | 3151 | (*_node_data)[index].heap_index.clear(); |
---|
| 3152 | (*_node_data)[index].heap.clear(); |
---|
[949] | 3153 | int blossom = |
---|
| 3154 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 3155 | |
---|
| 3156 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 3157 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 3158 | (*_blossom_data)[blossom].next = _fractional->matching(n); |
---|
| 3159 | (*_blossom_data)[blossom].pot = 0; |
---|
| 3160 | (*_blossom_data)[blossom].offset = 0; |
---|
| 3161 | ++index; |
---|
| 3162 | } |
---|
| 3163 | |
---|
| 3164 | typename Graph::template NodeMap<bool> processed(_graph, false); |
---|
| 3165 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3166 | if (processed[n]) continue; |
---|
| 3167 | processed[n] = true; |
---|
| 3168 | if (_fractional->matching(n) == INVALID) continue; |
---|
| 3169 | int num = 1; |
---|
| 3170 | Node v = _graph.target(_fractional->matching(n)); |
---|
| 3171 | while (n != v) { |
---|
| 3172 | processed[v] = true; |
---|
| 3173 | v = _graph.target(_fractional->matching(v)); |
---|
| 3174 | ++num; |
---|
| 3175 | } |
---|
| 3176 | |
---|
| 3177 | if (num % 2 == 1) { |
---|
| 3178 | std::vector<int> subblossoms(num); |
---|
| 3179 | |
---|
| 3180 | subblossoms[--num] = _blossom_set->find(n); |
---|
| 3181 | v = _graph.target(_fractional->matching(n)); |
---|
| 3182 | while (n != v) { |
---|
| 3183 | subblossoms[--num] = _blossom_set->find(v); |
---|
[956] | 3184 | v = _graph.target(_fractional->matching(v)); |
---|
[949] | 3185 | } |
---|
[956] | 3186 | |
---|
| 3187 | int surface = |
---|
[949] | 3188 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 3189 | (*_blossom_data)[surface].status = EVEN; |
---|
| 3190 | (*_blossom_data)[surface].pred = INVALID; |
---|
| 3191 | (*_blossom_data)[surface].next = INVALID; |
---|
| 3192 | (*_blossom_data)[surface].pot = 0; |
---|
| 3193 | (*_blossom_data)[surface].offset = 0; |
---|
[956] | 3194 | |
---|
[949] | 3195 | _tree_set->insert(surface); |
---|
| 3196 | ++_unmatched; |
---|
| 3197 | } |
---|
| 3198 | } |
---|
| 3199 | |
---|
| 3200 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 3201 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 3202 | int sb = _blossom_set->find(_graph.u(e)); |
---|
| 3203 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 3204 | int tb = _blossom_set->find(_graph.v(e)); |
---|
| 3205 | if ((*_blossom_data)[sb].status == EVEN && |
---|
| 3206 | (*_blossom_data)[tb].status == EVEN && sb != tb) { |
---|
| 3207 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 3208 | dualScale * _weight[e]) / 2); |
---|
| 3209 | } |
---|
| 3210 | } |
---|
| 3211 | |
---|
| 3212 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3213 | int nb = _blossom_set->find(n); |
---|
| 3214 | if ((*_blossom_data)[nb].status != MATCHED) continue; |
---|
| 3215 | int ni = (*_node_index)[n]; |
---|
| 3216 | |
---|
| 3217 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 3218 | Node v = _graph.target(e); |
---|
| 3219 | int vb = _blossom_set->find(v); |
---|
| 3220 | int vi = (*_node_index)[v]; |
---|
| 3221 | |
---|
| 3222 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 3223 | dualScale * _weight[e]; |
---|
| 3224 | |
---|
| 3225 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 3226 | |
---|
| 3227 | int vt = _tree_set->find(vb); |
---|
| 3228 | |
---|
| 3229 | typename std::map<int, Arc>::iterator it = |
---|
| 3230 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 3231 | |
---|
| 3232 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 3233 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 3234 | (*_node_data)[ni].heap.replace(it->second, e); |
---|
| 3235 | (*_node_data)[ni].heap.decrease(e, rw); |
---|
| 3236 | it->second = e; |
---|
| 3237 | } |
---|
| 3238 | } else { |
---|
| 3239 | (*_node_data)[ni].heap.push(e, rw); |
---|
| 3240 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, e)); |
---|
| 3241 | } |
---|
| 3242 | } |
---|
| 3243 | } |
---|
[956] | 3244 | |
---|
[949] | 3245 | if (!(*_node_data)[ni].heap.empty()) { |
---|
| 3246 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 3247 | _delta2->push(nb, _blossom_set->classPrio(nb)); |
---|
| 3248 | } |
---|
| 3249 | } |
---|
| 3250 | } |
---|
| 3251 | |
---|
[637] | 3252 | /// \brief Start the algorithm |
---|
[338] | 3253 | /// |
---|
[637] | 3254 | /// This function starts the algorithm. |
---|
| 3255 | /// |
---|
[949] | 3256 | /// \pre \ref init() or \ref fractionalInit() must be called before |
---|
| 3257 | /// using this function. |
---|
[338] | 3258 | bool start() { |
---|
| 3259 | enum OpType { |
---|
| 3260 | D2, D3, D4 |
---|
| 3261 | }; |
---|
| 3262 | |
---|
[949] | 3263 | if (_unmatched == -1) return false; |
---|
| 3264 | |
---|
| 3265 | while (_unmatched > 0) { |
---|
[338] | 3266 | Value d2 = !_delta2->empty() ? |
---|
| 3267 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 3268 | |
---|
| 3269 | Value d3 = !_delta3->empty() ? |
---|
| 3270 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 3271 | |
---|
| 3272 | Value d4 = !_delta4->empty() ? |
---|
| 3273 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 3274 | |
---|
[947] | 3275 | _delta_sum = d3; OpType ot = D3; |
---|
| 3276 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
[338] | 3277 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 3278 | |
---|
| 3279 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
| 3280 | return false; |
---|
| 3281 | } |
---|
| 3282 | |
---|
| 3283 | switch (ot) { |
---|
| 3284 | case D2: |
---|
| 3285 | { |
---|
| 3286 | int blossom = _delta2->top(); |
---|
| 3287 | Node n = _blossom_set->classTop(blossom); |
---|
| 3288 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 3289 | extendOnArc(e); |
---|
| 3290 | } |
---|
| 3291 | break; |
---|
| 3292 | case D3: |
---|
| 3293 | { |
---|
| 3294 | Edge e = _delta3->top(); |
---|
| 3295 | |
---|
| 3296 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 3297 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 3298 | |
---|
| 3299 | if (left_blossom == right_blossom) { |
---|
| 3300 | _delta3->pop(); |
---|
| 3301 | } else { |
---|
| 3302 | int left_tree = _tree_set->find(left_blossom); |
---|
| 3303 | int right_tree = _tree_set->find(right_blossom); |
---|
| 3304 | |
---|
| 3305 | if (left_tree == right_tree) { |
---|
[339] | 3306 | shrinkOnEdge(e, left_tree); |
---|
[338] | 3307 | } else { |
---|
[339] | 3308 | augmentOnEdge(e); |
---|
[949] | 3309 | _unmatched -= 2; |
---|
[338] | 3310 | } |
---|
| 3311 | } |
---|
| 3312 | } break; |
---|
| 3313 | case D4: |
---|
| 3314 | splitBlossom(_delta4->top()); |
---|
| 3315 | break; |
---|
| 3316 | } |
---|
| 3317 | } |
---|
| 3318 | extractMatching(); |
---|
| 3319 | return true; |
---|
| 3320 | } |
---|
| 3321 | |
---|
[637] | 3322 | /// \brief Run the algorithm. |
---|
[338] | 3323 | /// |
---|
[637] | 3324 | /// This method runs the \c %MaxWeightedPerfectMatching algorithm. |
---|
[338] | 3325 | /// |
---|
[637] | 3326 | /// \note mwpm.run() is just a shortcut of the following code. |
---|
[338] | 3327 | /// \code |
---|
[949] | 3328 | /// mwpm.fractionalInit(); |
---|
[637] | 3329 | /// mwpm.start(); |
---|
[338] | 3330 | /// \endcode |
---|
| 3331 | bool run() { |
---|
[949] | 3332 | fractionalInit(); |
---|
[338] | 3333 | return start(); |
---|
| 3334 | } |
---|
| 3335 | |
---|
| 3336 | /// @} |
---|
| 3337 | |
---|
[637] | 3338 | /// \name Primal Solution |
---|
[947] | 3339 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
[637] | 3340 | /// perfect matching.\n |
---|
| 3341 | /// Either \ref run() or \ref start() function should be called before |
---|
| 3342 | /// using them. |
---|
[338] | 3343 | |
---|
| 3344 | /// @{ |
---|
| 3345 | |
---|
[637] | 3346 | /// \brief Return the weight of the matching. |
---|
[338] | 3347 | /// |
---|
[637] | 3348 | /// This function returns the weight of the found matching. |
---|
| 3349 | /// |
---|
| 3350 | /// \pre Either run() or start() must be called before using this function. |
---|
[640] | 3351 | Value matchingWeight() const { |
---|
[338] | 3352 | Value sum = 0; |
---|
| 3353 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3354 | if ((*_matching)[n] != INVALID) { |
---|
| 3355 | sum += _weight[(*_matching)[n]]; |
---|
| 3356 | } |
---|
| 3357 | } |
---|
[947] | 3358 | return sum / 2; |
---|
[338] | 3359 | } |
---|
| 3360 | |
---|
[637] | 3361 | /// \brief Return \c true if the given edge is in the matching. |
---|
[338] | 3362 | /// |
---|
[947] | 3363 | /// This function returns \c true if the given edge is in the found |
---|
[637] | 3364 | /// matching. |
---|
| 3365 | /// |
---|
| 3366 | /// \pre Either run() or start() must be called before using this function. |
---|
[339] | 3367 | bool matching(const Edge& edge) const { |
---|
| 3368 | return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge; |
---|
[338] | 3369 | } |
---|
| 3370 | |
---|
[637] | 3371 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[338] | 3372 | /// |
---|
[637] | 3373 | /// This function returns the matching arc (or edge) incident to the |
---|
[947] | 3374 | /// given node in the found matching or \c INVALID if the node is |
---|
[637] | 3375 | /// not covered by the matching. |
---|
| 3376 | /// |
---|
| 3377 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3378 | Arc matching(const Node& node) const { |
---|
| 3379 | return (*_matching)[node]; |
---|
| 3380 | } |
---|
| 3381 | |
---|
[640] | 3382 | /// \brief Return a const reference to the matching map. |
---|
| 3383 | /// |
---|
| 3384 | /// This function returns a const reference to a node map that stores |
---|
| 3385 | /// the matching arc (or edge) incident to each node. |
---|
| 3386 | const MatchingMap& matchingMap() const { |
---|
| 3387 | return *_matching; |
---|
| 3388 | } |
---|
| 3389 | |
---|
[637] | 3390 | /// \brief Return the mate of the given node. |
---|
[338] | 3391 | /// |
---|
[947] | 3392 | /// This function returns the mate of the given node in the found |
---|
[637] | 3393 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
| 3394 | /// |
---|
| 3395 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3396 | Node mate(const Node& node) const { |
---|
| 3397 | return _graph.target((*_matching)[node]); |
---|
| 3398 | } |
---|
| 3399 | |
---|
| 3400 | /// @} |
---|
| 3401 | |
---|
[637] | 3402 | /// \name Dual Solution |
---|
| 3403 | /// Functions to get the dual solution.\n |
---|
| 3404 | /// Either \ref run() or \ref start() function should be called before |
---|
| 3405 | /// using them. |
---|
[338] | 3406 | |
---|
| 3407 | /// @{ |
---|
| 3408 | |
---|
[637] | 3409 | /// \brief Return the value of the dual solution. |
---|
[338] | 3410 | /// |
---|
[947] | 3411 | /// This function returns the value of the dual solution. |
---|
| 3412 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
[637] | 3413 | /// "dual scale". |
---|
| 3414 | /// |
---|
| 3415 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3416 | Value dualValue() const { |
---|
| 3417 | Value sum = 0; |
---|
| 3418 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3419 | sum += nodeValue(n); |
---|
| 3420 | } |
---|
| 3421 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 3422 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 3423 | } |
---|
| 3424 | return sum; |
---|
| 3425 | } |
---|
| 3426 | |
---|
[637] | 3427 | /// \brief Return the dual value (potential) of the given node. |
---|
[338] | 3428 | /// |
---|
[637] | 3429 | /// This function returns the dual value (potential) of the given node. |
---|
| 3430 | /// |
---|
| 3431 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3432 | Value nodeValue(const Node& n) const { |
---|
| 3433 | return (*_node_potential)[n]; |
---|
| 3434 | } |
---|
| 3435 | |
---|
[637] | 3436 | /// \brief Return the number of the blossoms in the basis. |
---|
[338] | 3437 | /// |
---|
[637] | 3438 | /// This function returns the number of the blossoms in the basis. |
---|
| 3439 | /// |
---|
| 3440 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3441 | /// \see BlossomIt |
---|
| 3442 | int blossomNum() const { |
---|
| 3443 | return _blossom_potential.size(); |
---|
| 3444 | } |
---|
| 3445 | |
---|
[637] | 3446 | /// \brief Return the number of the nodes in the given blossom. |
---|
[338] | 3447 | /// |
---|
[637] | 3448 | /// This function returns the number of the nodes in the given blossom. |
---|
| 3449 | /// |
---|
| 3450 | /// \pre Either run() or start() must be called before using this function. |
---|
| 3451 | /// \see BlossomIt |
---|
[338] | 3452 | int blossomSize(int k) const { |
---|
| 3453 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 3454 | } |
---|
| 3455 | |
---|
[637] | 3456 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
[338] | 3457 | /// |
---|
[637] | 3458 | /// This function returns the dual value (ptential) of the given blossom. |
---|
| 3459 | /// |
---|
| 3460 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3461 | Value blossomValue(int k) const { |
---|
| 3462 | return _blossom_potential[k].value; |
---|
| 3463 | } |
---|
| 3464 | |
---|
[637] | 3465 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
[338] | 3466 | /// |
---|
[947] | 3467 | /// This class provides an iterator for obtaining the nodes of the |
---|
[637] | 3468 | /// given blossom. It lists a subset of the nodes. |
---|
[947] | 3469 | /// Before using this iterator, you must allocate a |
---|
[637] | 3470 | /// MaxWeightedPerfectMatching class and execute it. |
---|
[338] | 3471 | class BlossomIt { |
---|
| 3472 | public: |
---|
| 3473 | |
---|
| 3474 | /// \brief Constructor. |
---|
| 3475 | /// |
---|
[637] | 3476 | /// Constructor to get the nodes of the given variable. |
---|
| 3477 | /// |
---|
[947] | 3478 | /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()" |
---|
| 3479 | /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()" |
---|
[637] | 3480 | /// must be called before initializing this iterator. |
---|
[338] | 3481 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
| 3482 | : _algorithm(&algorithm) |
---|
| 3483 | { |
---|
| 3484 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 3485 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 3486 | } |
---|
| 3487 | |
---|
[637] | 3488 | /// \brief Conversion to \c Node. |
---|
[338] | 3489 | /// |
---|
[637] | 3490 | /// Conversion to \c Node. |
---|
[338] | 3491 | operator Node() const { |
---|
[339] | 3492 | return _algorithm->_blossom_node_list[_index]; |
---|
[338] | 3493 | } |
---|
| 3494 | |
---|
| 3495 | /// \brief Increment operator. |
---|
| 3496 | /// |
---|
| 3497 | /// Increment operator. |
---|
| 3498 | BlossomIt& operator++() { |
---|
| 3499 | ++_index; |
---|
| 3500 | return *this; |
---|
| 3501 | } |
---|
| 3502 | |
---|
[339] | 3503 | /// \brief Validity checking |
---|
| 3504 | /// |
---|
[637] | 3505 | /// This function checks whether the iterator is invalid. |
---|
[339] | 3506 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 3507 | |
---|
| 3508 | /// \brief Validity checking |
---|
| 3509 | /// |
---|
[637] | 3510 | /// This function checks whether the iterator is valid. |
---|
[339] | 3511 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[338] | 3512 | |
---|
| 3513 | private: |
---|
| 3514 | const MaxWeightedPerfectMatching* _algorithm; |
---|
| 3515 | int _last; |
---|
| 3516 | int _index; |
---|
| 3517 | }; |
---|
| 3518 | |
---|
| 3519 | /// @} |
---|
| 3520 | |
---|
| 3521 | }; |
---|
| 3522 | |
---|
| 3523 | } //END OF NAMESPACE LEMON |
---|
| 3524 | |
---|
[947] | 3525 | #endif //LEMON_MATCHING_H |
---|