[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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[956] | 5 | * Copyright (C) 2003-2010 |
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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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| 118 | int _node_num; |
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| 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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| 182 | return; |
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| 183 | } |
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| 184 | } |
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| 185 | } |
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| 186 | |
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| 187 | while (_postpone != _last) { |
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| 188 | Node u = _node_queue[_postpone++]; |
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| 189 | |
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| 190 | for (OutArcIt a(_graph, u); a != INVALID ; ++a) { |
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| 191 | Node v = _graph.target(a); |
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| 192 | |
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| 193 | if ((*_status)[v] == EVEN) { |
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| 194 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 195 | shrinkOnEdge(a); |
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| 196 | } |
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| 197 | } |
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| 198 | |
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| 199 | while (_process != _last) { |
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| 200 | Node w = _node_queue[_process++]; |
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| 201 | for (OutArcIt b(_graph, w); b != INVALID; ++b) { |
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| 202 | Node x = _graph.target(b); |
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| 203 | if ((*_status)[x] == MATCHED) { |
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| 204 | extendOnArc(b); |
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| 205 | } else if ((*_status)[x] == UNMATCHED) { |
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| 206 | augmentOnArc(b); |
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| 207 | return; |
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| 208 | } |
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| 209 | } |
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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 | void processSparse(const Node& n) { |
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| 216 | _process = _last = 0; |
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| 217 | _node_queue[_last++] = n; |
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| 218 | while (_process != _last) { |
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| 219 | Node u = _node_queue[_process++]; |
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| 220 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 221 | Node v = _graph.target(a); |
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| 222 | |
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| 223 | if ((*_status)[v] == EVEN) { |
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| 224 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 225 | shrinkOnEdge(a); |
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| 226 | } |
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| 227 | } else if ((*_status)[v] == MATCHED) { |
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| 228 | extendOnArc(a); |
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| 229 | } else if ((*_status)[v] == UNMATCHED) { |
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| 230 | augmentOnArc(a); |
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| 231 | return; |
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| 232 | } |
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| 233 | } |
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| 234 | } |
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| 235 | } |
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| 236 | |
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| 237 | void shrinkOnEdge(const Edge& e) { |
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| 238 | Node nca = INVALID; |
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| 239 | |
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| 240 | { |
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| 241 | std::set<Node> left_set, right_set; |
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| 242 | |
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| 243 | Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))]; |
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| 244 | left_set.insert(left); |
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| 245 | |
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| 246 | Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))]; |
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| 247 | right_set.insert(right); |
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| 248 | |
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| 249 | while (true) { |
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| 250 | if ((*_matching)[left] == INVALID) break; |
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| 251 | left = _graph.target((*_matching)[left]); |
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| 252 | left = (*_blossom_rep)[_blossom_set-> |
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| 253 | find(_graph.target((*_ear)[left]))]; |
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| 254 | if (right_set.find(left) != right_set.end()) { |
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| 255 | nca = left; |
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| 256 | break; |
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| 257 | } |
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| 258 | left_set.insert(left); |
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| 259 | |
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| 260 | if ((*_matching)[right] == INVALID) break; |
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| 261 | right = _graph.target((*_matching)[right]); |
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| 262 | right = (*_blossom_rep)[_blossom_set-> |
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| 263 | find(_graph.target((*_ear)[right]))]; |
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| 264 | if (left_set.find(right) != left_set.end()) { |
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| 265 | nca = right; |
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| 266 | break; |
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| 267 | } |
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| 268 | right_set.insert(right); |
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| 269 | } |
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| 270 | |
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| 271 | if (nca == INVALID) { |
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| 272 | if ((*_matching)[left] == INVALID) { |
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| 273 | nca = right; |
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| 274 | while (left_set.find(nca) == left_set.end()) { |
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| 275 | nca = _graph.target((*_matching)[nca]); |
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| 276 | nca =(*_blossom_rep)[_blossom_set-> |
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| 277 | find(_graph.target((*_ear)[nca]))]; |
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| 278 | } |
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| 279 | } else { |
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| 280 | nca = left; |
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| 281 | while (right_set.find(nca) == right_set.end()) { |
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| 282 | nca = _graph.target((*_matching)[nca]); |
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| 283 | nca = (*_blossom_rep)[_blossom_set-> |
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| 284 | find(_graph.target((*_ear)[nca]))]; |
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| 285 | } |
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| 286 | } |
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| 287 | } |
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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 | Node node = _graph.u(e); |
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| 293 | Arc arc = _graph.direct(e, true); |
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| 294 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 295 | |
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| 296 | while (base != nca) { |
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[628] | 297 | (*_ear)[node] = arc; |
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[339] | 298 | |
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| 299 | Node n = node; |
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| 300 | while (n != base) { |
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| 301 | n = _graph.target((*_matching)[n]); |
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| 302 | Arc a = (*_ear)[n]; |
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| 303 | n = _graph.target(a); |
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[628] | 304 | (*_ear)[n] = _graph.oppositeArc(a); |
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[339] | 305 | } |
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| 306 | node = _graph.target((*_matching)[base]); |
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| 307 | _tree_set->erase(base); |
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| 308 | _tree_set->erase(node); |
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| 309 | _blossom_set->insert(node, _blossom_set->find(base)); |
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[628] | 310 | (*_status)[node] = EVEN; |
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[339] | 311 | _node_queue[_last++] = node; |
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| 312 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 313 | node = _graph.target((*_ear)[node]); |
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| 314 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 315 | _blossom_set->join(_graph.target(arc), base); |
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| 316 | } |
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| 317 | } |
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| 318 | |
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[628] | 319 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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[339] | 320 | |
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| 321 | { |
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| 322 | |
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| 323 | Node node = _graph.v(e); |
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| 324 | Arc arc = _graph.direct(e, false); |
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| 325 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 326 | |
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| 327 | while (base != nca) { |
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[628] | 328 | (*_ear)[node] = arc; |
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[339] | 329 | |
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| 330 | Node n = node; |
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| 331 | while (n != base) { |
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| 332 | n = _graph.target((*_matching)[n]); |
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| 333 | Arc a = (*_ear)[n]; |
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| 334 | n = _graph.target(a); |
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[628] | 335 | (*_ear)[n] = _graph.oppositeArc(a); |
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[339] | 336 | } |
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| 337 | node = _graph.target((*_matching)[base]); |
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| 338 | _tree_set->erase(base); |
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| 339 | _tree_set->erase(node); |
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| 340 | _blossom_set->insert(node, _blossom_set->find(base)); |
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[628] | 341 | (*_status)[node] = EVEN; |
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[339] | 342 | _node_queue[_last++] = node; |
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| 343 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 344 | node = _graph.target((*_ear)[node]); |
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| 345 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 346 | _blossom_set->join(_graph.target(arc), base); |
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| 347 | } |
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| 348 | } |
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| 349 | |
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[628] | 350 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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[339] | 351 | } |
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| 352 | |
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| 353 | void extendOnArc(const Arc& a) { |
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| 354 | Node base = _graph.source(a); |
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| 355 | Node odd = _graph.target(a); |
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| 356 | |
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[628] | 357 | (*_ear)[odd] = _graph.oppositeArc(a); |
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[339] | 358 | Node even = _graph.target((*_matching)[odd]); |
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[628] | 359 | (*_blossom_rep)[_blossom_set->insert(even)] = even; |
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| 360 | (*_status)[odd] = ODD; |
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| 361 | (*_status)[even] = EVEN; |
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[339] | 362 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]); |
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| 363 | _tree_set->insert(odd, tree); |
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| 364 | _tree_set->insert(even, tree); |
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| 365 | _node_queue[_last++] = even; |
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| 366 | |
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| 367 | } |
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| 368 | |
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| 369 | void augmentOnArc(const Arc& a) { |
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| 370 | Node even = _graph.source(a); |
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| 371 | Node odd = _graph.target(a); |
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| 372 | |
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| 373 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]); |
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| 374 | |
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[628] | 375 | (*_matching)[odd] = _graph.oppositeArc(a); |
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| 376 | (*_status)[odd] = MATCHED; |
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[339] | 377 | |
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| 378 | Arc arc = (*_matching)[even]; |
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[628] | 379 | (*_matching)[even] = a; |
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[339] | 380 | |
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| 381 | while (arc != INVALID) { |
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| 382 | odd = _graph.target(arc); |
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| 383 | arc = (*_ear)[odd]; |
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| 384 | even = _graph.target(arc); |
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[628] | 385 | (*_matching)[odd] = arc; |
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[339] | 386 | arc = (*_matching)[even]; |
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[628] | 387 | (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]); |
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[339] | 388 | } |
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| 389 | |
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| 390 | for (typename TreeSet::ItemIt it(*_tree_set, tree); |
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| 391 | it != INVALID; ++it) { |
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| 392 | if ((*_status)[it] == ODD) { |
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[628] | 393 | (*_status)[it] = MATCHED; |
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[339] | 394 | } else { |
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| 395 | int blossom = _blossom_set->find(it); |
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| 396 | for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom); |
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| 397 | jt != INVALID; ++jt) { |
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[628] | 398 | (*_status)[jt] = MATCHED; |
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[339] | 399 | } |
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| 400 | _blossom_set->eraseClass(blossom); |
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| 401 | } |
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| 402 | } |
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| 403 | _tree_set->eraseClass(tree); |
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| 404 | |
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| 405 | } |
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[338] | 406 | |
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| 407 | public: |
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| 408 | |
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[339] | 409 | /// \brief Constructor |
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[338] | 410 | /// |
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[339] | 411 | /// Constructor. |
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| 412 | MaxMatching(const Graph& graph) |
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| 413 | : _graph(graph), _matching(0), _status(0), _ear(0), |
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| 414 | _blossom_set_index(0), _blossom_set(0), _blossom_rep(0), |
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| 415 | _tree_set_index(0), _tree_set(0) {} |
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| 416 | |
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| 417 | ~MaxMatching() { |
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| 418 | destroyStructures(); |
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| 419 | } |
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| 420 | |
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[637] | 421 | /// \name Execution Control |
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[342] | 422 | /// The simplest way to execute the algorithm is to use the |
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[637] | 423 | /// \c run() member function.\n |
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| 424 | /// If you need better control on the execution, you have to call |
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| 425 | /// one of the functions \ref init(), \ref greedyInit() or |
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| 426 | /// \ref matchingInit() first, then you can start the algorithm with |
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| 427 | /// \ref startSparse() or \ref startDense(). |
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[339] | 428 | |
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| 429 | ///@{ |
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| 430 | |
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[637] | 431 | /// \brief Set the initial matching to the empty matching. |
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[338] | 432 | /// |
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[637] | 433 | /// This function sets the initial matching to the empty matching. |
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[338] | 434 | void init() { |
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[339] | 435 | createStructures(); |
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| 436 | for(NodeIt n(_graph); n != INVALID; ++n) { |
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[628] | 437 | (*_matching)[n] = INVALID; |
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| 438 | (*_status)[n] = UNMATCHED; |
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[338] | 439 | } |
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| 440 | } |
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| 441 | |
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[637] | 442 | /// \brief Find an initial matching in a greedy way. |
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[338] | 443 | /// |
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[637] | 444 | /// This function finds an initial matching in a greedy way. |
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[338] | 445 | void greedyInit() { |
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[339] | 446 | createStructures(); |
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| 447 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[628] | 448 | (*_matching)[n] = INVALID; |
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| 449 | (*_status)[n] = UNMATCHED; |
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[338] | 450 | } |
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[339] | 451 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 452 | if ((*_matching)[n] == INVALID) { |
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| 453 | for (OutArcIt a(_graph, n); a != INVALID ; ++a) { |
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| 454 | Node v = _graph.target(a); |
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| 455 | if ((*_matching)[v] == INVALID && v != n) { |
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[628] | 456 | (*_matching)[n] = a; |
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| 457 | (*_status)[n] = MATCHED; |
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| 458 | (*_matching)[v] = _graph.oppositeArc(a); |
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| 459 | (*_status)[v] = MATCHED; |
---|
[338] | 460 | break; |
---|
| 461 | } |
---|
| 462 | } |
---|
| 463 | } |
---|
| 464 | } |
---|
| 465 | } |
---|
| 466 | |
---|
[339] | 467 | |
---|
[637] | 468 | /// \brief Initialize the matching from a map. |
---|
[338] | 469 | /// |
---|
[637] | 470 | /// This function initializes the matching from a \c bool valued edge |
---|
| 471 | /// map. This map should have the property that there are no two incident |
---|
| 472 | /// edges with \c true value, i.e. it really contains a matching. |
---|
[606] | 473 | /// \return \c true if the map contains a matching. |
---|
[339] | 474 | template <typename MatchingMap> |
---|
| 475 | bool matchingInit(const MatchingMap& matching) { |
---|
| 476 | createStructures(); |
---|
| 477 | |
---|
| 478 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[628] | 479 | (*_matching)[n] = INVALID; |
---|
| 480 | (*_status)[n] = UNMATCHED; |
---|
[338] | 481 | } |
---|
[339] | 482 | for(EdgeIt e(_graph); e!=INVALID; ++e) { |
---|
| 483 | if (matching[e]) { |
---|
| 484 | |
---|
| 485 | Node u = _graph.u(e); |
---|
| 486 | if ((*_matching)[u] != INVALID) return false; |
---|
[628] | 487 | (*_matching)[u] = _graph.direct(e, true); |
---|
| 488 | (*_status)[u] = MATCHED; |
---|
[339] | 489 | |
---|
| 490 | Node v = _graph.v(e); |
---|
| 491 | if ((*_matching)[v] != INVALID) return false; |
---|
[628] | 492 | (*_matching)[v] = _graph.direct(e, false); |
---|
| 493 | (*_status)[v] = MATCHED; |
---|
[339] | 494 | } |
---|
| 495 | } |
---|
| 496 | return true; |
---|
[338] | 497 | } |
---|
| 498 | |
---|
[637] | 499 | /// \brief Start Edmonds' algorithm |
---|
[338] | 500 | /// |
---|
[637] | 501 | /// This function runs the original Edmonds' algorithm. |
---|
| 502 | /// |
---|
[698] | 503 | /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be |
---|
[637] | 504 | /// called before using this function. |
---|
[339] | 505 | void startSparse() { |
---|
| 506 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 507 | if ((*_status)[n] == UNMATCHED) { |
---|
| 508 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 509 | _tree_set->insert(n); |
---|
[628] | 510 | (*_status)[n] = EVEN; |
---|
[339] | 511 | processSparse(n); |
---|
[338] | 512 | } |
---|
| 513 | } |
---|
| 514 | } |
---|
| 515 | |
---|
[947] | 516 | /// \brief Start Edmonds' algorithm with a heuristic improvement |
---|
[637] | 517 | /// for dense graphs |
---|
[338] | 518 | /// |
---|
[637] | 519 | /// This function runs Edmonds' algorithm with a heuristic of postponing |
---|
[342] | 520 | /// shrinks, therefore resulting in a faster algorithm for dense graphs. |
---|
[637] | 521 | /// |
---|
[698] | 522 | /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be |
---|
[637] | 523 | /// called before using this function. |
---|
[339] | 524 | void startDense() { |
---|
| 525 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 526 | if ((*_status)[n] == UNMATCHED) { |
---|
| 527 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 528 | _tree_set->insert(n); |
---|
[628] | 529 | (*_status)[n] = EVEN; |
---|
[339] | 530 | processDense(n); |
---|
| 531 | } |
---|
| 532 | } |
---|
| 533 | } |
---|
| 534 | |
---|
| 535 | |
---|
[637] | 536 | /// \brief Run Edmonds' algorithm |
---|
[339] | 537 | /// |
---|
[947] | 538 | /// This function runs Edmonds' algorithm. An additional heuristic of |
---|
| 539 | /// postponing shrinks is used for relatively dense graphs |
---|
[637] | 540 | /// (for which <tt>m>=2*n</tt> holds). |
---|
[338] | 541 | void run() { |
---|
[339] | 542 | if (countEdges(_graph) < 2 * countNodes(_graph)) { |
---|
[338] | 543 | greedyInit(); |
---|
| 544 | startSparse(); |
---|
| 545 | } else { |
---|
| 546 | init(); |
---|
| 547 | startDense(); |
---|
| 548 | } |
---|
| 549 | } |
---|
| 550 | |
---|
[339] | 551 | /// @} |
---|
| 552 | |
---|
[637] | 553 | /// \name Primal Solution |
---|
| 554 | /// Functions to get the primal solution, i.e. the maximum matching. |
---|
[339] | 555 | |
---|
| 556 | /// @{ |
---|
[338] | 557 | |
---|
[637] | 558 | /// \brief Return the size (cardinality) of the matching. |
---|
[338] | 559 | /// |
---|
[947] | 560 | /// This function returns the size (cardinality) of the current matching. |
---|
[637] | 561 | /// After run() it returns the size of the maximum matching in the graph. |
---|
[339] | 562 | int matchingSize() const { |
---|
| 563 | int size = 0; |
---|
| 564 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 565 | if ((*_matching)[n] != INVALID) { |
---|
| 566 | ++size; |
---|
[338] | 567 | } |
---|
| 568 | } |
---|
[339] | 569 | return size / 2; |
---|
[338] | 570 | } |
---|
| 571 | |
---|
[637] | 572 | /// \brief Return \c true if the given edge is in the matching. |
---|
[339] | 573 | /// |
---|
[947] | 574 | /// This function returns \c true if the given edge is in the current |
---|
[637] | 575 | /// matching. |
---|
[339] | 576 | bool matching(const Edge& edge) const { |
---|
| 577 | return edge == (*_matching)[_graph.u(edge)]; |
---|
| 578 | } |
---|
| 579 | |
---|
[637] | 580 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[339] | 581 | /// |
---|
[637] | 582 | /// This function returns the matching arc (or edge) incident to the |
---|
[947] | 583 | /// given node in the current matching or \c INVALID if the node is |
---|
[637] | 584 | /// not covered by the matching. |
---|
[339] | 585 | Arc matching(const Node& n) const { |
---|
| 586 | return (*_matching)[n]; |
---|
| 587 | } |
---|
[338] | 588 | |
---|
[640] | 589 | /// \brief Return a const reference to the matching map. |
---|
| 590 | /// |
---|
| 591 | /// This function returns a const reference to a node map that stores |
---|
| 592 | /// the matching arc (or edge) incident to each node. |
---|
| 593 | const MatchingMap& matchingMap() const { |
---|
| 594 | return *_matching; |
---|
| 595 | } |
---|
| 596 | |
---|
[637] | 597 | /// \brief Return the mate of the given node. |
---|
[338] | 598 | /// |
---|
[947] | 599 | /// This function returns the mate of the given node in the current |
---|
[637] | 600 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
[339] | 601 | Node mate(const Node& n) const { |
---|
| 602 | return (*_matching)[n] != INVALID ? |
---|
| 603 | _graph.target((*_matching)[n]) : INVALID; |
---|
[338] | 604 | } |
---|
| 605 | |
---|
[339] | 606 | /// @} |
---|
| 607 | |
---|
[637] | 608 | /// \name Dual Solution |
---|
[947] | 609 | /// Functions to get the dual solution, i.e. the Gallai-Edmonds |
---|
[637] | 610 | /// decomposition. |
---|
[339] | 611 | |
---|
| 612 | /// @{ |
---|
[338] | 613 | |
---|
[637] | 614 | /// \brief Return the status of the given node in the Edmonds-Gallai |
---|
[338] | 615 | /// decomposition. |
---|
| 616 | /// |
---|
[637] | 617 | /// This function returns the \ref Status "status" of the given node |
---|
| 618 | /// in the Edmonds-Gallai decomposition. |
---|
[640] | 619 | Status status(const Node& n) const { |
---|
[339] | 620 | return (*_status)[n]; |
---|
[338] | 621 | } |
---|
| 622 | |
---|
[640] | 623 | /// \brief Return a const reference to the status map, which stores |
---|
| 624 | /// the Edmonds-Gallai decomposition. |
---|
| 625 | /// |
---|
| 626 | /// This function returns a const reference to a node map that stores the |
---|
| 627 | /// \ref Status "status" of each node in the Edmonds-Gallai decomposition. |
---|
| 628 | const StatusMap& statusMap() const { |
---|
| 629 | return *_status; |
---|
| 630 | } |
---|
| 631 | |
---|
[637] | 632 | /// \brief Return \c true if the given node is in the barrier. |
---|
[338] | 633 | /// |
---|
[637] | 634 | /// This function returns \c true if the given node is in the barrier. |
---|
[339] | 635 | bool barrier(const Node& n) const { |
---|
| 636 | return (*_status)[n] == ODD; |
---|
[338] | 637 | } |
---|
| 638 | |
---|
[339] | 639 | /// @} |
---|
[338] | 640 | |
---|
| 641 | }; |
---|
| 642 | |
---|
| 643 | /// \ingroup matching |
---|
| 644 | /// |
---|
| 645 | /// \brief Weighted matching in general graphs |
---|
| 646 | /// |
---|
| 647 | /// This class provides an efficient implementation of Edmond's |
---|
| 648 | /// maximum weighted matching algorithm. The implementation is based |
---|
| 649 | /// on extensive use of priority queues and provides |
---|
[606] | 650 | /// \f$O(nm\log n)\f$ time complexity. |
---|
[338] | 651 | /// |
---|
[947] | 652 | /// The maximum weighted matching problem is to find a subset of the |
---|
| 653 | /// edges in an undirected graph with maximum overall weight for which |
---|
[637] | 654 | /// each node has at most one incident edge. |
---|
| 655 | /// It can be formulated with the following linear program. |
---|
[338] | 656 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
[339] | 657 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 658 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[338] | 659 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 660 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[339] | 661 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 662 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 663 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 664 | /// subsets of the nodes. |
---|
[338] | 665 | /// |
---|
| 666 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 667 | /// optimality. The solution of the dual problem can be used to check |
---|
[339] | 668 | /// the result of the algorithm. The dual linear problem is the |
---|
[637] | 669 | /// following. |
---|
[339] | 670 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)} |
---|
| 671 | z_B \ge w_{uv} \quad \forall uv\in E\f] */ |
---|
[338] | 672 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
| 673 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[339] | 674 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 675 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[338] | 676 | /// |
---|
[947] | 677 | /// The algorithm can be executed with the run() function. |
---|
[637] | 678 | /// After it the matching (the primal solution) and the dual solution |
---|
[947] | 679 | /// can be obtained using the query functions and the |
---|
| 680 | /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class, |
---|
| 681 | /// which is able to iterate on the nodes of a blossom. |
---|
[637] | 682 | /// If the value type is integer, then the dual solution is multiplied |
---|
| 683 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
| 684 | /// |
---|
[640] | 685 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
[947] | 686 | /// \tparam WM The type edge weight map. The default type is |
---|
[637] | 687 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 688 | #ifdef DOXYGEN |
---|
| 689 | template <typename GR, typename WM> |
---|
| 690 | #else |
---|
[606] | 691 | template <typename GR, |
---|
| 692 | typename WM = typename GR::template EdgeMap<int> > |
---|
[637] | 693 | #endif |
---|
[338] | 694 | class MaxWeightedMatching { |
---|
| 695 | public: |
---|
| 696 | |
---|
[637] | 697 | /// The graph type of the algorithm |
---|
[606] | 698 | typedef GR Graph; |
---|
[637] | 699 | /// The type of the edge weight map |
---|
[606] | 700 | typedef WM WeightMap; |
---|
[637] | 701 | /// The value type of the edge weights |
---|
[338] | 702 | typedef typename WeightMap::Value Value; |
---|
| 703 | |
---|
[640] | 704 | /// The type of the matching map |
---|
[637] | 705 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 706 | MatchingMap; |
---|
| 707 | |
---|
[338] | 708 | /// \brief Scaling factor for dual solution |
---|
| 709 | /// |
---|
[637] | 710 | /// Scaling factor for dual solution. It is equal to 4 or 1 |
---|
[338] | 711 | /// according to the value type. |
---|
| 712 | static const int dualScale = |
---|
| 713 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 714 | |
---|
| 715 | private: |
---|
| 716 | |
---|
| 717 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 718 | |
---|
| 719 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 720 | typedef std::vector<Node> BlossomNodeList; |
---|
| 721 | |
---|
| 722 | struct BlossomVariable { |
---|
| 723 | int begin, end; |
---|
| 724 | Value value; |
---|
| 725 | |
---|
| 726 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 727 | : begin(_begin), end(_end), value(_value) {} |
---|
| 728 | |
---|
| 729 | }; |
---|
| 730 | |
---|
| 731 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 732 | |
---|
| 733 | const Graph& _graph; |
---|
| 734 | const WeightMap& _weight; |
---|
| 735 | |
---|
| 736 | MatchingMap* _matching; |
---|
| 737 | |
---|
| 738 | NodePotential* _node_potential; |
---|
| 739 | |
---|
| 740 | BlossomPotential _blossom_potential; |
---|
| 741 | BlossomNodeList _blossom_node_list; |
---|
| 742 | |
---|
| 743 | int _node_num; |
---|
| 744 | int _blossom_num; |
---|
| 745 | |
---|
| 746 | typedef RangeMap<int> IntIntMap; |
---|
| 747 | |
---|
| 748 | enum Status { |
---|
[947] | 749 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
[338] | 750 | }; |
---|
| 751 | |
---|
[339] | 752 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[338] | 753 | struct BlossomData { |
---|
| 754 | int tree; |
---|
| 755 | Status status; |
---|
| 756 | Arc pred, next; |
---|
| 757 | Value pot, offset; |
---|
| 758 | Node base; |
---|
| 759 | }; |
---|
| 760 | |
---|
[339] | 761 | IntNodeMap *_blossom_index; |
---|
[338] | 762 | BlossomSet *_blossom_set; |
---|
| 763 | RangeMap<BlossomData>* _blossom_data; |
---|
| 764 | |
---|
[339] | 765 | IntNodeMap *_node_index; |
---|
| 766 | IntArcMap *_node_heap_index; |
---|
[338] | 767 | |
---|
| 768 | struct NodeData { |
---|
| 769 | |
---|
[339] | 770 | NodeData(IntArcMap& node_heap_index) |
---|
[338] | 771 | : heap(node_heap_index) {} |
---|
| 772 | |
---|
| 773 | int blossom; |
---|
| 774 | Value pot; |
---|
[339] | 775 | BinHeap<Value, IntArcMap> heap; |
---|
[338] | 776 | std::map<int, Arc> heap_index; |
---|
| 777 | |
---|
| 778 | int tree; |
---|
| 779 | }; |
---|
| 780 | |
---|
| 781 | RangeMap<NodeData>* _node_data; |
---|
| 782 | |
---|
| 783 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 784 | |
---|
| 785 | IntIntMap *_tree_set_index; |
---|
| 786 | TreeSet *_tree_set; |
---|
| 787 | |
---|
[339] | 788 | IntNodeMap *_delta1_index; |
---|
| 789 | BinHeap<Value, IntNodeMap> *_delta1; |
---|
[338] | 790 | |
---|
| 791 | IntIntMap *_delta2_index; |
---|
| 792 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 793 | |
---|
[339] | 794 | IntEdgeMap *_delta3_index; |
---|
| 795 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[338] | 796 | |
---|
| 797 | IntIntMap *_delta4_index; |
---|
| 798 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 799 | |
---|
| 800 | Value _delta_sum; |
---|
[949] | 801 | int _unmatched; |
---|
| 802 | |
---|
| 803 | typedef MaxWeightedFractionalMatching<Graph, WeightMap> FractionalMatching; |
---|
| 804 | FractionalMatching *_fractional; |
---|
[338] | 805 | |
---|
| 806 | void createStructures() { |
---|
| 807 | _node_num = countNodes(_graph); |
---|
| 808 | _blossom_num = _node_num * 3 / 2; |
---|
| 809 | |
---|
| 810 | if (!_matching) { |
---|
| 811 | _matching = new MatchingMap(_graph); |
---|
| 812 | } |
---|
[945] | 813 | |
---|
[338] | 814 | if (!_node_potential) { |
---|
| 815 | _node_potential = new NodePotential(_graph); |
---|
| 816 | } |
---|
[945] | 817 | |
---|
[338] | 818 | if (!_blossom_set) { |
---|
[339] | 819 | _blossom_index = new IntNodeMap(_graph); |
---|
[338] | 820 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 821 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[945] | 822 | } else if (_blossom_data->size() != _blossom_num) { |
---|
| 823 | delete _blossom_data; |
---|
| 824 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[338] | 825 | } |
---|
| 826 | |
---|
| 827 | if (!_node_index) { |
---|
[339] | 828 | _node_index = new IntNodeMap(_graph); |
---|
| 829 | _node_heap_index = new IntArcMap(_graph); |
---|
[338] | 830 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
[945] | 831 | NodeData(*_node_heap_index)); |
---|
| 832 | } else { |
---|
| 833 | delete _node_data; |
---|
| 834 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
| 835 | NodeData(*_node_heap_index)); |
---|
[338] | 836 | } |
---|
| 837 | |
---|
| 838 | if (!_tree_set) { |
---|
| 839 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 840 | _tree_set = new TreeSet(*_tree_set_index); |
---|
[945] | 841 | } else { |
---|
| 842 | _tree_set_index->resize(_blossom_num); |
---|
[338] | 843 | } |
---|
[945] | 844 | |
---|
[338] | 845 | if (!_delta1) { |
---|
[339] | 846 | _delta1_index = new IntNodeMap(_graph); |
---|
| 847 | _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index); |
---|
[338] | 848 | } |
---|
[945] | 849 | |
---|
[338] | 850 | if (!_delta2) { |
---|
| 851 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 852 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
[945] | 853 | } else { |
---|
| 854 | _delta2_index->resize(_blossom_num); |
---|
[338] | 855 | } |
---|
[945] | 856 | |
---|
[338] | 857 | if (!_delta3) { |
---|
[339] | 858 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 859 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[338] | 860 | } |
---|
[945] | 861 | |
---|
[338] | 862 | if (!_delta4) { |
---|
| 863 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 864 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
[945] | 865 | } else { |
---|
| 866 | _delta4_index->resize(_blossom_num); |
---|
[338] | 867 | } |
---|
| 868 | } |
---|
| 869 | |
---|
| 870 | void destroyStructures() { |
---|
| 871 | if (_matching) { |
---|
| 872 | delete _matching; |
---|
| 873 | } |
---|
| 874 | if (_node_potential) { |
---|
| 875 | delete _node_potential; |
---|
| 876 | } |
---|
| 877 | if (_blossom_set) { |
---|
| 878 | delete _blossom_index; |
---|
| 879 | delete _blossom_set; |
---|
| 880 | delete _blossom_data; |
---|
| 881 | } |
---|
| 882 | |
---|
| 883 | if (_node_index) { |
---|
| 884 | delete _node_index; |
---|
| 885 | delete _node_heap_index; |
---|
| 886 | delete _node_data; |
---|
| 887 | } |
---|
| 888 | |
---|
| 889 | if (_tree_set) { |
---|
| 890 | delete _tree_set_index; |
---|
| 891 | delete _tree_set; |
---|
| 892 | } |
---|
| 893 | if (_delta1) { |
---|
| 894 | delete _delta1_index; |
---|
| 895 | delete _delta1; |
---|
| 896 | } |
---|
| 897 | if (_delta2) { |
---|
| 898 | delete _delta2_index; |
---|
| 899 | delete _delta2; |
---|
| 900 | } |
---|
| 901 | if (_delta3) { |
---|
| 902 | delete _delta3_index; |
---|
| 903 | delete _delta3; |
---|
| 904 | } |
---|
| 905 | if (_delta4) { |
---|
| 906 | delete _delta4_index; |
---|
| 907 | delete _delta4; |
---|
| 908 | } |
---|
| 909 | } |
---|
| 910 | |
---|
| 911 | void matchedToEven(int blossom, int tree) { |
---|
| 912 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 913 | _delta2->erase(blossom); |
---|
| 914 | } |
---|
| 915 | |
---|
| 916 | if (!_blossom_set->trivial(blossom)) { |
---|
| 917 | (*_blossom_data)[blossom].pot -= |
---|
| 918 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 919 | } |
---|
| 920 | |
---|
| 921 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 922 | n != INVALID; ++n) { |
---|
| 923 | |
---|
| 924 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 925 | int ni = (*_node_index)[n]; |
---|
| 926 | |
---|
| 927 | (*_node_data)[ni].heap.clear(); |
---|
| 928 | (*_node_data)[ni].heap_index.clear(); |
---|
| 929 | |
---|
| 930 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 931 | |
---|
| 932 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 933 | |
---|
| 934 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 935 | Node v = _graph.source(e); |
---|
| 936 | int vb = _blossom_set->find(v); |
---|
| 937 | int vi = (*_node_index)[v]; |
---|
| 938 | |
---|
| 939 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 940 | dualScale * _weight[e]; |
---|
| 941 | |
---|
| 942 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 943 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 944 | _delta3->push(e, rw / 2); |
---|
| 945 | } |
---|
| 946 | } else { |
---|
| 947 | typename std::map<int, Arc>::iterator it = |
---|
| 948 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 949 | |
---|
| 950 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 951 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 952 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 953 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 954 | it->second = e; |
---|
| 955 | } |
---|
| 956 | } else { |
---|
| 957 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 958 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 959 | } |
---|
| 960 | |
---|
| 961 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 962 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 963 | |
---|
| 964 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 965 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 966 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 967 | (*_blossom_data)[vb].offset); |
---|
| 968 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 969 | (*_blossom_data)[vb].offset) { |
---|
| 970 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 971 | (*_blossom_data)[vb].offset); |
---|
| 972 | } |
---|
| 973 | } |
---|
| 974 | } |
---|
| 975 | } |
---|
| 976 | } |
---|
| 977 | } |
---|
| 978 | (*_blossom_data)[blossom].offset = 0; |
---|
| 979 | } |
---|
| 980 | |
---|
[947] | 981 | void matchedToOdd(int blossom) { |
---|
[338] | 982 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 983 | _delta2->erase(blossom); |
---|
| 984 | } |
---|
[947] | 985 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 986 | if (!_blossom_set->trivial(blossom)) { |
---|
| 987 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 988 | (*_blossom_data)[blossom].offset); |
---|
| 989 | } |
---|
| 990 | } |
---|
| 991 | |
---|
| 992 | void evenToMatched(int blossom, int tree) { |
---|
| 993 | if (!_blossom_set->trivial(blossom)) { |
---|
| 994 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 995 | } |
---|
[338] | 996 | |
---|
| 997 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 998 | n != INVALID; ++n) { |
---|
| 999 | int ni = (*_node_index)[n]; |
---|
[947] | 1000 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 1001 | |
---|
| 1002 | _delta1->erase(n); |
---|
| 1003 | |
---|
| 1004 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1005 | Node v = _graph.source(e); |
---|
[338] | 1006 | int vb = _blossom_set->find(v); |
---|
| 1007 | int vi = (*_node_index)[v]; |
---|
| 1008 | |
---|
| 1009 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1010 | dualScale * _weight[e]; |
---|
| 1011 | |
---|
[947] | 1012 | if (vb == blossom) { |
---|
| 1013 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1014 | _delta3->erase(e); |
---|
| 1015 | } |
---|
| 1016 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1017 | |
---|
| 1018 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1019 | _delta3->erase(e); |
---|
| 1020 | } |
---|
| 1021 | |
---|
| 1022 | int vt = _tree_set->find(vb); |
---|
| 1023 | |
---|
| 1024 | if (vt != tree) { |
---|
| 1025 | |
---|
| 1026 | Arc r = _graph.oppositeArc(e); |
---|
| 1027 | |
---|
| 1028 | typename std::map<int, Arc>::iterator it = |
---|
| 1029 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1030 | |
---|
| 1031 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1032 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1033 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 1034 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 1035 | it->second = r; |
---|
| 1036 | } |
---|
| 1037 | } else { |
---|
| 1038 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 1039 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 1040 | } |
---|
| 1041 | |
---|
| 1042 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1043 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1044 | |
---|
| 1045 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1046 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1047 | (*_blossom_data)[blossom].offset); |
---|
| 1048 | } else if ((*_delta2)[blossom] > |
---|
| 1049 | _blossom_set->classPrio(blossom) - |
---|
| 1050 | (*_blossom_data)[blossom].offset){ |
---|
| 1051 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1052 | (*_blossom_data)[blossom].offset); |
---|
| 1053 | } |
---|
| 1054 | } |
---|
| 1055 | } |
---|
| 1056 | } else { |
---|
| 1057 | |
---|
| 1058 | typename std::map<int, Arc>::iterator it = |
---|
| 1059 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1060 | |
---|
| 1061 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1062 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 1063 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 1064 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 1065 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 1066 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 1067 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 1068 | } |
---|
| 1069 | |
---|
| 1070 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1071 | if (_blossom_set->classPrio(vb) == |
---|
| 1072 | std::numeric_limits<Value>::max()) { |
---|
| 1073 | _delta2->erase(vb); |
---|
| 1074 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 1075 | (*_blossom_data)[vb].offset) { |
---|
| 1076 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 1077 | (*_blossom_data)[vb].offset); |
---|
| 1078 | } |
---|
| 1079 | } |
---|
[338] | 1080 | } |
---|
| 1081 | } |
---|
| 1082 | } |
---|
| 1083 | } |
---|
| 1084 | } |
---|
| 1085 | |
---|
[947] | 1086 | void oddToMatched(int blossom) { |
---|
| 1087 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 1088 | |
---|
| 1089 | if (_blossom_set->classPrio(blossom) != |
---|
| 1090 | std::numeric_limits<Value>::max()) { |
---|
| 1091 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1092 | (*_blossom_data)[blossom].offset); |
---|
| 1093 | } |
---|
| 1094 | |
---|
| 1095 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1096 | _delta4->erase(blossom); |
---|
| 1097 | } |
---|
| 1098 | } |
---|
| 1099 | |
---|
| 1100 | void oddToEven(int blossom, int tree) { |
---|
| 1101 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1102 | _delta4->erase(blossom); |
---|
| 1103 | (*_blossom_data)[blossom].pot -= |
---|
| 1104 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 1105 | } |
---|
| 1106 | |
---|
[338] | 1107 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1108 | n != INVALID; ++n) { |
---|
| 1109 | int ni = (*_node_index)[n]; |
---|
| 1110 | |
---|
[947] | 1111 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1112 | |
---|
| 1113 | (*_node_data)[ni].heap.clear(); |
---|
| 1114 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1115 | (*_node_data)[ni].pot += |
---|
| 1116 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 1117 | |
---|
| 1118 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 1119 | |
---|
[338] | 1120 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1121 | Node v = _graph.source(e); |
---|
| 1122 | int vb = _blossom_set->find(v); |
---|
| 1123 | int vi = (*_node_index)[v]; |
---|
| 1124 | |
---|
| 1125 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1126 | dualScale * _weight[e]; |
---|
| 1127 | |
---|
[947] | 1128 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1129 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 1130 | _delta3->push(e, rw / 2); |
---|
[338] | 1131 | } |
---|
[947] | 1132 | } else { |
---|
[338] | 1133 | |
---|
| 1134 | typename std::map<int, Arc>::iterator it = |
---|
[947] | 1135 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1136 | |
---|
| 1137 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1138 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 1139 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 1140 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 1141 | it->second = e; |
---|
[338] | 1142 | } |
---|
| 1143 | } else { |
---|
[947] | 1144 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 1145 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
[338] | 1146 | } |
---|
| 1147 | |
---|
[947] | 1148 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 1149 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 1150 | |
---|
| 1151 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1152 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 1153 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 1154 | (*_blossom_data)[vb].offset); |
---|
| 1155 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 1156 | (*_blossom_data)[vb].offset) { |
---|
| 1157 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 1158 | (*_blossom_data)[vb].offset); |
---|
| 1159 | } |
---|
[338] | 1160 | } |
---|
| 1161 | } |
---|
| 1162 | } |
---|
| 1163 | } |
---|
| 1164 | } |
---|
[947] | 1165 | (*_blossom_data)[blossom].offset = 0; |
---|
[338] | 1166 | } |
---|
| 1167 | |
---|
| 1168 | void alternatePath(int even, int tree) { |
---|
| 1169 | int odd; |
---|
| 1170 | |
---|
| 1171 | evenToMatched(even, tree); |
---|
| 1172 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1173 | |
---|
| 1174 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 1175 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 1176 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 1177 | oddToMatched(odd); |
---|
| 1178 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 1179 | |
---|
| 1180 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 1181 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1182 | evenToMatched(even, tree); |
---|
| 1183 | (*_blossom_data)[even].next = |
---|
| 1184 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 1185 | } |
---|
| 1186 | |
---|
| 1187 | } |
---|
| 1188 | |
---|
| 1189 | void destroyTree(int tree) { |
---|
| 1190 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 1191 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 1192 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1193 | evenToMatched(b, tree); |
---|
| 1194 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 1195 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1196 | oddToMatched(b); |
---|
| 1197 | } |
---|
| 1198 | } |
---|
| 1199 | _tree_set->eraseClass(tree); |
---|
| 1200 | } |
---|
| 1201 | |
---|
| 1202 | |
---|
| 1203 | void unmatchNode(const Node& node) { |
---|
| 1204 | int blossom = _blossom_set->find(node); |
---|
| 1205 | int tree = _tree_set->find(blossom); |
---|
| 1206 | |
---|
| 1207 | alternatePath(blossom, tree); |
---|
| 1208 | destroyTree(tree); |
---|
| 1209 | |
---|
| 1210 | (*_blossom_data)[blossom].base = node; |
---|
[947] | 1211 | (*_blossom_data)[blossom].next = INVALID; |
---|
[338] | 1212 | } |
---|
| 1213 | |
---|
[339] | 1214 | void augmentOnEdge(const Edge& edge) { |
---|
| 1215 | |
---|
| 1216 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1217 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[338] | 1218 | |
---|
[947] | 1219 | int left_tree = _tree_set->find(left); |
---|
| 1220 | alternatePath(left, left_tree); |
---|
| 1221 | destroyTree(left_tree); |
---|
| 1222 | |
---|
| 1223 | int right_tree = _tree_set->find(right); |
---|
| 1224 | alternatePath(right, right_tree); |
---|
| 1225 | destroyTree(right_tree); |
---|
[338] | 1226 | |
---|
[339] | 1227 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 1228 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[338] | 1229 | } |
---|
| 1230 | |
---|
[947] | 1231 | void augmentOnArc(const Arc& arc) { |
---|
| 1232 | |
---|
| 1233 | int left = _blossom_set->find(_graph.source(arc)); |
---|
| 1234 | int right = _blossom_set->find(_graph.target(arc)); |
---|
| 1235 | |
---|
| 1236 | (*_blossom_data)[left].status = MATCHED; |
---|
| 1237 | |
---|
| 1238 | int right_tree = _tree_set->find(right); |
---|
| 1239 | alternatePath(right, right_tree); |
---|
| 1240 | destroyTree(right_tree); |
---|
| 1241 | |
---|
| 1242 | (*_blossom_data)[left].next = arc; |
---|
| 1243 | (*_blossom_data)[right].next = _graph.oppositeArc(arc); |
---|
| 1244 | } |
---|
| 1245 | |
---|
[338] | 1246 | void extendOnArc(const Arc& arc) { |
---|
| 1247 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 1248 | int tree = _tree_set->find(base); |
---|
| 1249 | |
---|
| 1250 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 1251 | _tree_set->insert(odd, tree); |
---|
| 1252 | (*_blossom_data)[odd].status = ODD; |
---|
| 1253 | matchedToOdd(odd); |
---|
| 1254 | (*_blossom_data)[odd].pred = arc; |
---|
| 1255 | |
---|
| 1256 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 1257 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 1258 | _tree_set->insert(even, tree); |
---|
| 1259 | (*_blossom_data)[even].status = EVEN; |
---|
| 1260 | matchedToEven(even, tree); |
---|
| 1261 | } |
---|
| 1262 | |
---|
[339] | 1263 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[338] | 1264 | int nca = -1; |
---|
| 1265 | std::vector<int> left_path, right_path; |
---|
| 1266 | |
---|
| 1267 | { |
---|
| 1268 | std::set<int> left_set, right_set; |
---|
| 1269 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1270 | left_path.push_back(left); |
---|
| 1271 | left_set.insert(left); |
---|
| 1272 | |
---|
| 1273 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 1274 | right_path.push_back(right); |
---|
| 1275 | right_set.insert(right); |
---|
| 1276 | |
---|
| 1277 | while (true) { |
---|
| 1278 | |
---|
| 1279 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 1280 | |
---|
| 1281 | left = |
---|
| 1282 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1283 | left_path.push_back(left); |
---|
| 1284 | left = |
---|
| 1285 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1286 | left_path.push_back(left); |
---|
| 1287 | |
---|
| 1288 | left_set.insert(left); |
---|
| 1289 | |
---|
| 1290 | if (right_set.find(left) != right_set.end()) { |
---|
| 1291 | nca = left; |
---|
| 1292 | break; |
---|
| 1293 | } |
---|
| 1294 | |
---|
| 1295 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 1296 | |
---|
| 1297 | right = |
---|
| 1298 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1299 | right_path.push_back(right); |
---|
| 1300 | right = |
---|
| 1301 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1302 | right_path.push_back(right); |
---|
| 1303 | |
---|
| 1304 | right_set.insert(right); |
---|
| 1305 | |
---|
| 1306 | if (left_set.find(right) != left_set.end()) { |
---|
| 1307 | nca = right; |
---|
| 1308 | break; |
---|
| 1309 | } |
---|
| 1310 | |
---|
| 1311 | } |
---|
| 1312 | |
---|
| 1313 | if (nca == -1) { |
---|
| 1314 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 1315 | nca = right; |
---|
| 1316 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1317 | nca = |
---|
| 1318 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1319 | right_path.push_back(nca); |
---|
| 1320 | nca = |
---|
| 1321 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1322 | right_path.push_back(nca); |
---|
| 1323 | } |
---|
| 1324 | } else { |
---|
| 1325 | nca = left; |
---|
| 1326 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1327 | nca = |
---|
| 1328 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1329 | left_path.push_back(nca); |
---|
| 1330 | nca = |
---|
| 1331 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1332 | left_path.push_back(nca); |
---|
| 1333 | } |
---|
| 1334 | } |
---|
| 1335 | } |
---|
| 1336 | } |
---|
| 1337 | |
---|
| 1338 | std::vector<int> subblossoms; |
---|
| 1339 | Arc prev; |
---|
| 1340 | |
---|
| 1341 | prev = _graph.direct(edge, true); |
---|
| 1342 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1343 | subblossoms.push_back(left_path[i]); |
---|
| 1344 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 1345 | _tree_set->erase(left_path[i]); |
---|
| 1346 | |
---|
| 1347 | subblossoms.push_back(left_path[i + 1]); |
---|
| 1348 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 1349 | oddToEven(left_path[i + 1], tree); |
---|
| 1350 | _tree_set->erase(left_path[i + 1]); |
---|
| 1351 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 1352 | } |
---|
| 1353 | |
---|
| 1354 | int k = 0; |
---|
| 1355 | while (right_path[k] != nca) ++k; |
---|
| 1356 | |
---|
| 1357 | subblossoms.push_back(nca); |
---|
| 1358 | (*_blossom_data)[nca].next = prev; |
---|
| 1359 | |
---|
| 1360 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 1361 | subblossoms.push_back(right_path[i + 1]); |
---|
| 1362 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 1363 | oddToEven(right_path[i + 1], tree); |
---|
| 1364 | _tree_set->erase(right_path[i + 1]); |
---|
| 1365 | |
---|
| 1366 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 1367 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 1368 | |
---|
| 1369 | subblossoms.push_back(right_path[i]); |
---|
| 1370 | _tree_set->erase(right_path[i]); |
---|
| 1371 | } |
---|
| 1372 | |
---|
| 1373 | int surface = |
---|
| 1374 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1375 | |
---|
| 1376 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1377 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1378 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 1379 | } |
---|
| 1380 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 1381 | } |
---|
| 1382 | |
---|
| 1383 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 1384 | (*_blossom_data)[surface].offset = 0; |
---|
| 1385 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1386 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 1387 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 1388 | |
---|
| 1389 | _tree_set->insert(surface, tree); |
---|
| 1390 | _tree_set->erase(nca); |
---|
| 1391 | } |
---|
| 1392 | |
---|
| 1393 | void splitBlossom(int blossom) { |
---|
| 1394 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 1395 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 1396 | |
---|
| 1397 | int tree = _tree_set->find(blossom); |
---|
| 1398 | |
---|
| 1399 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1400 | oddToMatched(blossom); |
---|
| 1401 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1402 | _delta2->erase(blossom); |
---|
| 1403 | } |
---|
| 1404 | |
---|
| 1405 | std::vector<int> subblossoms; |
---|
| 1406 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1407 | |
---|
| 1408 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 1409 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 1410 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 1411 | |
---|
| 1412 | int ib = -1, id = -1; |
---|
| 1413 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1414 | if (subblossoms[i] == b) ib = i; |
---|
| 1415 | if (subblossoms[i] == d) id = i; |
---|
| 1416 | |
---|
| 1417 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 1418 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1419 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 1420 | } |
---|
| 1421 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 1422 | std::numeric_limits<Value>::max()) { |
---|
| 1423 | _delta2->push(subblossoms[i], |
---|
| 1424 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 1425 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 1426 | } |
---|
| 1427 | } |
---|
| 1428 | |
---|
| 1429 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 1430 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 1431 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1432 | int sb = subblossoms[i]; |
---|
| 1433 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1434 | (*_blossom_data)[sb].next = |
---|
| 1435 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1436 | } |
---|
| 1437 | |
---|
| 1438 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1439 | int sb = subblossoms[i]; |
---|
| 1440 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1441 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1442 | |
---|
| 1443 | (*_blossom_data)[sb].status = ODD; |
---|
| 1444 | matchedToOdd(sb); |
---|
| 1445 | _tree_set->insert(sb, tree); |
---|
| 1446 | (*_blossom_data)[sb].pred = pred; |
---|
| 1447 | (*_blossom_data)[sb].next = |
---|
[947] | 1448 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
[338] | 1449 | |
---|
| 1450 | pred = (*_blossom_data)[ub].next; |
---|
| 1451 | |
---|
| 1452 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1453 | matchedToEven(tb, tree); |
---|
| 1454 | _tree_set->insert(tb, tree); |
---|
| 1455 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 1456 | } |
---|
| 1457 | |
---|
| 1458 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 1459 | matchedToOdd(subblossoms[id]); |
---|
| 1460 | _tree_set->insert(subblossoms[id], tree); |
---|
| 1461 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 1462 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 1463 | |
---|
| 1464 | } else { |
---|
| 1465 | |
---|
| 1466 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 1467 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1468 | int sb = subblossoms[i]; |
---|
| 1469 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1470 | (*_blossom_data)[sb].next = |
---|
| 1471 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1472 | } |
---|
| 1473 | |
---|
| 1474 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1475 | int sb = subblossoms[i]; |
---|
| 1476 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1477 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1478 | |
---|
| 1479 | (*_blossom_data)[sb].status = ODD; |
---|
| 1480 | matchedToOdd(sb); |
---|
| 1481 | _tree_set->insert(sb, tree); |
---|
| 1482 | (*_blossom_data)[sb].next = next; |
---|
| 1483 | (*_blossom_data)[sb].pred = |
---|
| 1484 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1485 | |
---|
| 1486 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1487 | matchedToEven(tb, tree); |
---|
| 1488 | _tree_set->insert(tb, tree); |
---|
| 1489 | (*_blossom_data)[tb].pred = |
---|
| 1490 | (*_blossom_data)[tb].next = |
---|
| 1491 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 1492 | next = (*_blossom_data)[ub].next; |
---|
| 1493 | } |
---|
| 1494 | |
---|
| 1495 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 1496 | matchedToOdd(subblossoms[ib]); |
---|
| 1497 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 1498 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 1499 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 1500 | } |
---|
| 1501 | _tree_set->erase(blossom); |
---|
| 1502 | } |
---|
| 1503 | |
---|
| 1504 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 1505 | if (_blossom_set->trivial(blossom)) { |
---|
| 1506 | int bi = (*_node_index)[base]; |
---|
| 1507 | Value pot = (*_node_data)[bi].pot; |
---|
| 1508 | |
---|
[628] | 1509 | (*_matching)[base] = matching; |
---|
[338] | 1510 | _blossom_node_list.push_back(base); |
---|
[628] | 1511 | (*_node_potential)[base] = pot; |
---|
[338] | 1512 | } else { |
---|
| 1513 | |
---|
| 1514 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 1515 | int bn = _blossom_node_list.size(); |
---|
| 1516 | |
---|
| 1517 | std::vector<int> subblossoms; |
---|
| 1518 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1519 | int b = _blossom_set->find(base); |
---|
| 1520 | int ib = -1; |
---|
| 1521 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1522 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 1523 | } |
---|
| 1524 | |
---|
| 1525 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 1526 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 1527 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 1528 | |
---|
| 1529 | Arc m = (*_blossom_data)[tb].next; |
---|
| 1530 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 1531 | extractBlossom(tb, _graph.source(m), m); |
---|
| 1532 | } |
---|
| 1533 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 1534 | |
---|
| 1535 | int en = _blossom_node_list.size(); |
---|
| 1536 | |
---|
| 1537 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 1538 | } |
---|
| 1539 | } |
---|
| 1540 | |
---|
| 1541 | void extractMatching() { |
---|
| 1542 | std::vector<int> blossoms; |
---|
| 1543 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 1544 | blossoms.push_back(c); |
---|
| 1545 | } |
---|
| 1546 | |
---|
| 1547 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
[947] | 1548 | if ((*_blossom_data)[blossoms[i]].next != INVALID) { |
---|
[338] | 1549 | |
---|
| 1550 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 1551 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 1552 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 1553 | n != INVALID; ++n) { |
---|
| 1554 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 1555 | } |
---|
| 1556 | |
---|
| 1557 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 1558 | Node base = _graph.source(matching); |
---|
| 1559 | extractBlossom(blossoms[i], base, matching); |
---|
| 1560 | } else { |
---|
| 1561 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
| 1562 | extractBlossom(blossoms[i], base, INVALID); |
---|
| 1563 | } |
---|
| 1564 | } |
---|
| 1565 | } |
---|
| 1566 | |
---|
| 1567 | public: |
---|
| 1568 | |
---|
| 1569 | /// \brief Constructor |
---|
| 1570 | /// |
---|
| 1571 | /// Constructor. |
---|
| 1572 | MaxWeightedMatching(const Graph& graph, const WeightMap& weight) |
---|
| 1573 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 1574 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 1575 | _node_num(0), _blossom_num(0), |
---|
| 1576 | |
---|
| 1577 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 1578 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 1579 | _tree_set_index(0), _tree_set(0), |
---|
| 1580 | |
---|
| 1581 | _delta1_index(0), _delta1(0), |
---|
| 1582 | _delta2_index(0), _delta2(0), |
---|
| 1583 | _delta3_index(0), _delta3(0), |
---|
| 1584 | _delta4_index(0), _delta4(0), |
---|
| 1585 | |
---|
[949] | 1586 | _delta_sum(), _unmatched(0), |
---|
| 1587 | |
---|
| 1588 | _fractional(0) |
---|
| 1589 | {} |
---|
[338] | 1590 | |
---|
| 1591 | ~MaxWeightedMatching() { |
---|
| 1592 | destroyStructures(); |
---|
[949] | 1593 | if (_fractional) { |
---|
| 1594 | delete _fractional; |
---|
| 1595 | } |
---|
[338] | 1596 | } |
---|
| 1597 | |
---|
[637] | 1598 | /// \name Execution Control |
---|
[342] | 1599 | /// The simplest way to execute the algorithm is to use the |
---|
[637] | 1600 | /// \ref run() member function. |
---|
[338] | 1601 | |
---|
| 1602 | ///@{ |
---|
| 1603 | |
---|
| 1604 | /// \brief Initialize the algorithm |
---|
| 1605 | /// |
---|
[637] | 1606 | /// This function initializes the algorithm. |
---|
[338] | 1607 | void init() { |
---|
| 1608 | createStructures(); |
---|
| 1609 | |
---|
[945] | 1610 | _blossom_node_list.clear(); |
---|
| 1611 | _blossom_potential.clear(); |
---|
| 1612 | |
---|
[338] | 1613 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 1614 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
[338] | 1615 | } |
---|
| 1616 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[628] | 1617 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
[338] | 1618 | } |
---|
| 1619 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 1620 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
[338] | 1621 | } |
---|
| 1622 | for (int i = 0; i < _blossom_num; ++i) { |
---|
[628] | 1623 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 1624 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
[338] | 1625 | } |
---|
[956] | 1626 | |
---|
[949] | 1627 | _unmatched = _node_num; |
---|
| 1628 | |
---|
[945] | 1629 | _delta1->clear(); |
---|
| 1630 | _delta2->clear(); |
---|
| 1631 | _delta3->clear(); |
---|
| 1632 | _delta4->clear(); |
---|
| 1633 | _blossom_set->clear(); |
---|
| 1634 | _tree_set->clear(); |
---|
[338] | 1635 | |
---|
| 1636 | int index = 0; |
---|
| 1637 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1638 | Value max = 0; |
---|
| 1639 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1640 | if (_graph.target(e) == n) continue; |
---|
| 1641 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 1642 | max = (dualScale * _weight[e]) / 2; |
---|
| 1643 | } |
---|
| 1644 | } |
---|
[628] | 1645 | (*_node_index)[n] = index; |
---|
[945] | 1646 | (*_node_data)[index].heap_index.clear(); |
---|
| 1647 | (*_node_data)[index].heap.clear(); |
---|
[338] | 1648 | (*_node_data)[index].pot = max; |
---|
| 1649 | _delta1->push(n, max); |
---|
| 1650 | int blossom = |
---|
| 1651 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1652 | |
---|
| 1653 | _tree_set->insert(blossom); |
---|
| 1654 | |
---|
| 1655 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 1656 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1657 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 1658 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1659 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1660 | ++index; |
---|
| 1661 | } |
---|
| 1662 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1663 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 1664 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 1665 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 1666 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1667 | dualScale * _weight[e]) / 2); |
---|
| 1668 | } |
---|
| 1669 | } |
---|
| 1670 | } |
---|
| 1671 | |
---|
[949] | 1672 | /// \brief Initialize the algorithm with fractional matching |
---|
| 1673 | /// |
---|
| 1674 | /// This function initializes the algorithm with a fractional |
---|
| 1675 | /// matching. This initialization is also called jumpstart heuristic. |
---|
| 1676 | void fractionalInit() { |
---|
| 1677 | createStructures(); |
---|
[955] | 1678 | |
---|
| 1679 | _blossom_node_list.clear(); |
---|
| 1680 | _blossom_potential.clear(); |
---|
[956] | 1681 | |
---|
[949] | 1682 | if (_fractional == 0) { |
---|
| 1683 | _fractional = new FractionalMatching(_graph, _weight, false); |
---|
| 1684 | } |
---|
| 1685 | _fractional->run(); |
---|
| 1686 | |
---|
| 1687 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 1688 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
| 1689 | } |
---|
| 1690 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1691 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
| 1692 | } |
---|
| 1693 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1694 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
| 1695 | } |
---|
| 1696 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 1697 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 1698 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
| 1699 | } |
---|
| 1700 | |
---|
| 1701 | _unmatched = 0; |
---|
| 1702 | |
---|
[955] | 1703 | _delta1->clear(); |
---|
| 1704 | _delta2->clear(); |
---|
| 1705 | _delta3->clear(); |
---|
| 1706 | _delta4->clear(); |
---|
| 1707 | _blossom_set->clear(); |
---|
| 1708 | _tree_set->clear(); |
---|
| 1709 | |
---|
[949] | 1710 | int index = 0; |
---|
| 1711 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1712 | Value pot = _fractional->nodeValue(n); |
---|
| 1713 | (*_node_index)[n] = index; |
---|
| 1714 | (*_node_data)[index].pot = pot; |
---|
[955] | 1715 | (*_node_data)[index].heap_index.clear(); |
---|
| 1716 | (*_node_data)[index].heap.clear(); |
---|
[949] | 1717 | int blossom = |
---|
| 1718 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1719 | |
---|
| 1720 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1721 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1722 | (*_blossom_data)[blossom].next = _fractional->matching(n); |
---|
| 1723 | if (_fractional->matching(n) == INVALID) { |
---|
| 1724 | (*_blossom_data)[blossom].base = n; |
---|
| 1725 | } |
---|
| 1726 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1727 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1728 | ++index; |
---|
| 1729 | } |
---|
| 1730 | |
---|
| 1731 | typename Graph::template NodeMap<bool> processed(_graph, false); |
---|
| 1732 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1733 | if (processed[n]) continue; |
---|
| 1734 | processed[n] = true; |
---|
| 1735 | if (_fractional->matching(n) == INVALID) continue; |
---|
| 1736 | int num = 1; |
---|
| 1737 | Node v = _graph.target(_fractional->matching(n)); |
---|
| 1738 | while (n != v) { |
---|
| 1739 | processed[v] = true; |
---|
| 1740 | v = _graph.target(_fractional->matching(v)); |
---|
| 1741 | ++num; |
---|
| 1742 | } |
---|
| 1743 | |
---|
| 1744 | if (num % 2 == 1) { |
---|
| 1745 | std::vector<int> subblossoms(num); |
---|
| 1746 | |
---|
| 1747 | subblossoms[--num] = _blossom_set->find(n); |
---|
| 1748 | _delta1->push(n, _fractional->nodeValue(n)); |
---|
| 1749 | v = _graph.target(_fractional->matching(n)); |
---|
| 1750 | while (n != v) { |
---|
| 1751 | subblossoms[--num] = _blossom_set->find(v); |
---|
| 1752 | _delta1->push(v, _fractional->nodeValue(v)); |
---|
[956] | 1753 | v = _graph.target(_fractional->matching(v)); |
---|
[949] | 1754 | } |
---|
[956] | 1755 | |
---|
| 1756 | int surface = |
---|
[949] | 1757 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1758 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1759 | (*_blossom_data)[surface].pred = INVALID; |
---|
| 1760 | (*_blossom_data)[surface].next = INVALID; |
---|
| 1761 | (*_blossom_data)[surface].pot = 0; |
---|
| 1762 | (*_blossom_data)[surface].offset = 0; |
---|
[956] | 1763 | |
---|
[949] | 1764 | _tree_set->insert(surface); |
---|
| 1765 | ++_unmatched; |
---|
| 1766 | } |
---|
| 1767 | } |
---|
| 1768 | |
---|
| 1769 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1770 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 1771 | int sb = _blossom_set->find(_graph.u(e)); |
---|
| 1772 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 1773 | int tb = _blossom_set->find(_graph.v(e)); |
---|
| 1774 | if ((*_blossom_data)[sb].status == EVEN && |
---|
| 1775 | (*_blossom_data)[tb].status == EVEN && sb != tb) { |
---|
| 1776 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1777 | dualScale * _weight[e]) / 2); |
---|
| 1778 | } |
---|
| 1779 | } |
---|
| 1780 | |
---|
| 1781 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1782 | int nb = _blossom_set->find(n); |
---|
| 1783 | if ((*_blossom_data)[nb].status != MATCHED) continue; |
---|
| 1784 | int ni = (*_node_index)[n]; |
---|
| 1785 | |
---|
| 1786 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1787 | Node v = _graph.target(e); |
---|
| 1788 | int vb = _blossom_set->find(v); |
---|
| 1789 | int vi = (*_node_index)[v]; |
---|
| 1790 | |
---|
| 1791 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1792 | dualScale * _weight[e]; |
---|
| 1793 | |
---|
| 1794 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1795 | |
---|
| 1796 | int vt = _tree_set->find(vb); |
---|
| 1797 | |
---|
| 1798 | typename std::map<int, Arc>::iterator it = |
---|
| 1799 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1800 | |
---|
| 1801 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1802 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1803 | (*_node_data)[ni].heap.replace(it->second, e); |
---|
| 1804 | (*_node_data)[ni].heap.decrease(e, rw); |
---|
| 1805 | it->second = e; |
---|
| 1806 | } |
---|
| 1807 | } else { |
---|
| 1808 | (*_node_data)[ni].heap.push(e, rw); |
---|
| 1809 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, e)); |
---|
| 1810 | } |
---|
| 1811 | } |
---|
| 1812 | } |
---|
[956] | 1813 | |
---|
[949] | 1814 | if (!(*_node_data)[ni].heap.empty()) { |
---|
| 1815 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1816 | _delta2->push(nb, _blossom_set->classPrio(nb)); |
---|
| 1817 | } |
---|
| 1818 | } |
---|
| 1819 | } |
---|
| 1820 | |
---|
[637] | 1821 | /// \brief Start the algorithm |
---|
[338] | 1822 | /// |
---|
[637] | 1823 | /// This function starts the algorithm. |
---|
| 1824 | /// |
---|
[949] | 1825 | /// \pre \ref init() or \ref fractionalInit() must be called |
---|
| 1826 | /// before using this function. |
---|
[338] | 1827 | void start() { |
---|
| 1828 | enum OpType { |
---|
| 1829 | D1, D2, D3, D4 |
---|
| 1830 | }; |
---|
| 1831 | |
---|
[949] | 1832 | while (_unmatched > 0) { |
---|
[338] | 1833 | Value d1 = !_delta1->empty() ? |
---|
| 1834 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
| 1835 | |
---|
| 1836 | Value d2 = !_delta2->empty() ? |
---|
| 1837 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 1838 | |
---|
| 1839 | Value d3 = !_delta3->empty() ? |
---|
| 1840 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 1841 | |
---|
| 1842 | Value d4 = !_delta4->empty() ? |
---|
| 1843 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 1844 | |
---|
[947] | 1845 | _delta_sum = d3; OpType ot = D3; |
---|
| 1846 | if (d1 < _delta_sum) { _delta_sum = d1; ot = D1; } |
---|
[338] | 1847 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
| 1848 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 1849 | |
---|
| 1850 | switch (ot) { |
---|
| 1851 | case D1: |
---|
| 1852 | { |
---|
| 1853 | Node n = _delta1->top(); |
---|
| 1854 | unmatchNode(n); |
---|
[949] | 1855 | --_unmatched; |
---|
[338] | 1856 | } |
---|
| 1857 | break; |
---|
| 1858 | case D2: |
---|
| 1859 | { |
---|
| 1860 | int blossom = _delta2->top(); |
---|
| 1861 | Node n = _blossom_set->classTop(blossom); |
---|
[947] | 1862 | Arc a = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 1863 | if ((*_blossom_data)[blossom].next == INVALID) { |
---|
| 1864 | augmentOnArc(a); |
---|
[949] | 1865 | --_unmatched; |
---|
[947] | 1866 | } else { |
---|
| 1867 | extendOnArc(a); |
---|
| 1868 | } |
---|
[338] | 1869 | } |
---|
| 1870 | break; |
---|
| 1871 | case D3: |
---|
| 1872 | { |
---|
| 1873 | Edge e = _delta3->top(); |
---|
| 1874 | |
---|
| 1875 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 1876 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 1877 | |
---|
| 1878 | if (left_blossom == right_blossom) { |
---|
| 1879 | _delta3->pop(); |
---|
| 1880 | } else { |
---|
[947] | 1881 | int left_tree = _tree_set->find(left_blossom); |
---|
| 1882 | int right_tree = _tree_set->find(right_blossom); |
---|
[338] | 1883 | |
---|
| 1884 | if (left_tree == right_tree) { |
---|
[339] | 1885 | shrinkOnEdge(e, left_tree); |
---|
[338] | 1886 | } else { |
---|
[339] | 1887 | augmentOnEdge(e); |
---|
[949] | 1888 | _unmatched -= 2; |
---|
[338] | 1889 | } |
---|
| 1890 | } |
---|
| 1891 | } break; |
---|
| 1892 | case D4: |
---|
| 1893 | splitBlossom(_delta4->top()); |
---|
| 1894 | break; |
---|
| 1895 | } |
---|
| 1896 | } |
---|
| 1897 | extractMatching(); |
---|
| 1898 | } |
---|
| 1899 | |
---|
[637] | 1900 | /// \brief Run the algorithm. |
---|
[338] | 1901 | /// |
---|
[637] | 1902 | /// This method runs the \c %MaxWeightedMatching algorithm. |
---|
[338] | 1903 | /// |
---|
| 1904 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 1905 | /// \code |
---|
[949] | 1906 | /// mwm.fractionalInit(); |
---|
[338] | 1907 | /// mwm.start(); |
---|
| 1908 | /// \endcode |
---|
| 1909 | void run() { |
---|
[949] | 1910 | fractionalInit(); |
---|
[338] | 1911 | start(); |
---|
| 1912 | } |
---|
| 1913 | |
---|
| 1914 | /// @} |
---|
| 1915 | |
---|
[637] | 1916 | /// \name Primal Solution |
---|
[947] | 1917 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
[637] | 1918 | /// matching.\n |
---|
| 1919 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1920 | /// using them. |
---|
[338] | 1921 | |
---|
| 1922 | /// @{ |
---|
| 1923 | |
---|
[637] | 1924 | /// \brief Return the weight of the matching. |
---|
[338] | 1925 | /// |
---|
[637] | 1926 | /// This function returns the weight of the found matching. |
---|
| 1927 | /// |
---|
| 1928 | /// \pre Either run() or start() must be called before using this function. |
---|
[640] | 1929 | Value matchingWeight() const { |
---|
[338] | 1930 | Value sum = 0; |
---|
| 1931 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1932 | if ((*_matching)[n] != INVALID) { |
---|
| 1933 | sum += _weight[(*_matching)[n]]; |
---|
| 1934 | } |
---|
| 1935 | } |
---|
[947] | 1936 | return sum / 2; |
---|
[338] | 1937 | } |
---|
| 1938 | |
---|
[637] | 1939 | /// \brief Return the size (cardinality) of the matching. |
---|
[338] | 1940 | /// |
---|
[637] | 1941 | /// This function returns the size (cardinality) of the found matching. |
---|
| 1942 | /// |
---|
| 1943 | /// \pre Either run() or start() must be called before using this function. |
---|
[339] | 1944 | int matchingSize() const { |
---|
| 1945 | int num = 0; |
---|
| 1946 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1947 | if ((*_matching)[n] != INVALID) { |
---|
| 1948 | ++num; |
---|
| 1949 | } |
---|
| 1950 | } |
---|
| 1951 | return num /= 2; |
---|
| 1952 | } |
---|
| 1953 | |
---|
[637] | 1954 | /// \brief Return \c true if the given edge is in the matching. |
---|
[339] | 1955 | /// |
---|
[947] | 1956 | /// This function returns \c true if the given edge is in the found |
---|
[637] | 1957 | /// matching. |
---|
| 1958 | /// |
---|
| 1959 | /// \pre Either run() or start() must be called before using this function. |
---|
[339] | 1960 | bool matching(const Edge& edge) const { |
---|
| 1961 | return edge == (*_matching)[_graph.u(edge)]; |
---|
[338] | 1962 | } |
---|
| 1963 | |
---|
[637] | 1964 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[338] | 1965 | /// |
---|
[637] | 1966 | /// This function returns the matching arc (or edge) incident to the |
---|
[947] | 1967 | /// given node in the found matching or \c INVALID if the node is |
---|
[637] | 1968 | /// not covered by the matching. |
---|
| 1969 | /// |
---|
| 1970 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 1971 | Arc matching(const Node& node) const { |
---|
| 1972 | return (*_matching)[node]; |
---|
| 1973 | } |
---|
| 1974 | |
---|
[640] | 1975 | /// \brief Return a const reference to the matching map. |
---|
| 1976 | /// |
---|
| 1977 | /// This function returns a const reference to a node map that stores |
---|
| 1978 | /// the matching arc (or edge) incident to each node. |
---|
| 1979 | const MatchingMap& matchingMap() const { |
---|
| 1980 | return *_matching; |
---|
| 1981 | } |
---|
| 1982 | |
---|
[637] | 1983 | /// \brief Return the mate of the given node. |
---|
[338] | 1984 | /// |
---|
[947] | 1985 | /// This function returns the mate of the given node in the found |
---|
[637] | 1986 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
| 1987 | /// |
---|
| 1988 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 1989 | Node mate(const Node& node) const { |
---|
| 1990 | return (*_matching)[node] != INVALID ? |
---|
| 1991 | _graph.target((*_matching)[node]) : INVALID; |
---|
| 1992 | } |
---|
| 1993 | |
---|
| 1994 | /// @} |
---|
| 1995 | |
---|
[637] | 1996 | /// \name Dual Solution |
---|
| 1997 | /// Functions to get the dual solution.\n |
---|
| 1998 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1999 | /// using them. |
---|
[338] | 2000 | |
---|
| 2001 | /// @{ |
---|
| 2002 | |
---|
[637] | 2003 | /// \brief Return the value of the dual solution. |
---|
[338] | 2004 | /// |
---|
[947] | 2005 | /// This function returns the value of the dual solution. |
---|
| 2006 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
[637] | 2007 | /// "dual scale". |
---|
| 2008 | /// |
---|
| 2009 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2010 | Value dualValue() const { |
---|
| 2011 | Value sum = 0; |
---|
| 2012 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2013 | sum += nodeValue(n); |
---|
| 2014 | } |
---|
| 2015 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 2016 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 2017 | } |
---|
| 2018 | return sum; |
---|
| 2019 | } |
---|
| 2020 | |
---|
[637] | 2021 | /// \brief Return the dual value (potential) of the given node. |
---|
[338] | 2022 | /// |
---|
[637] | 2023 | /// This function returns the dual value (potential) of the given node. |
---|
| 2024 | /// |
---|
| 2025 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2026 | Value nodeValue(const Node& n) const { |
---|
| 2027 | return (*_node_potential)[n]; |
---|
| 2028 | } |
---|
| 2029 | |
---|
[637] | 2030 | /// \brief Return the number of the blossoms in the basis. |
---|
[338] | 2031 | /// |
---|
[637] | 2032 | /// This function returns the number of the blossoms in the basis. |
---|
| 2033 | /// |
---|
| 2034 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2035 | /// \see BlossomIt |
---|
| 2036 | int blossomNum() const { |
---|
| 2037 | return _blossom_potential.size(); |
---|
| 2038 | } |
---|
| 2039 | |
---|
[637] | 2040 | /// \brief Return the number of the nodes in the given blossom. |
---|
[338] | 2041 | /// |
---|
[637] | 2042 | /// This function returns the number of the nodes in the given blossom. |
---|
| 2043 | /// |
---|
| 2044 | /// \pre Either run() or start() must be called before using this function. |
---|
| 2045 | /// \see BlossomIt |
---|
[338] | 2046 | int blossomSize(int k) const { |
---|
| 2047 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 2048 | } |
---|
| 2049 | |
---|
[637] | 2050 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
[338] | 2051 | /// |
---|
[637] | 2052 | /// This function returns the dual value (ptential) of the given blossom. |
---|
| 2053 | /// |
---|
| 2054 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 2055 | Value blossomValue(int k) const { |
---|
| 2056 | return _blossom_potential[k].value; |
---|
| 2057 | } |
---|
| 2058 | |
---|
[637] | 2059 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
[338] | 2060 | /// |
---|
[947] | 2061 | /// This class provides an iterator for obtaining the nodes of the |
---|
[637] | 2062 | /// given blossom. It lists a subset of the nodes. |
---|
[947] | 2063 | /// Before using this iterator, you must allocate a |
---|
[637] | 2064 | /// MaxWeightedMatching class and execute it. |
---|
[338] | 2065 | class BlossomIt { |
---|
| 2066 | public: |
---|
| 2067 | |
---|
| 2068 | /// \brief Constructor. |
---|
| 2069 | /// |
---|
[637] | 2070 | /// Constructor to get the nodes of the given variable. |
---|
| 2071 | /// |
---|
[947] | 2072 | /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or |
---|
| 2073 | /// \ref MaxWeightedMatching::start() "algorithm.start()" must be |
---|
[637] | 2074 | /// called before initializing this iterator. |
---|
[338] | 2075 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
| 2076 | : _algorithm(&algorithm) |
---|
| 2077 | { |
---|
| 2078 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 2079 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 2080 | } |
---|
| 2081 | |
---|
[637] | 2082 | /// \brief Conversion to \c Node. |
---|
[338] | 2083 | /// |
---|
[637] | 2084 | /// Conversion to \c Node. |
---|
[338] | 2085 | operator Node() const { |
---|
[339] | 2086 | return _algorithm->_blossom_node_list[_index]; |
---|
[338] | 2087 | } |
---|
| 2088 | |
---|
| 2089 | /// \brief Increment operator. |
---|
| 2090 | /// |
---|
| 2091 | /// Increment operator. |
---|
| 2092 | BlossomIt& operator++() { |
---|
| 2093 | ++_index; |
---|
| 2094 | return *this; |
---|
| 2095 | } |
---|
| 2096 | |
---|
[339] | 2097 | /// \brief Validity checking |
---|
| 2098 | /// |
---|
| 2099 | /// Checks whether the iterator is invalid. |
---|
| 2100 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 2101 | |
---|
| 2102 | /// \brief Validity checking |
---|
| 2103 | /// |
---|
| 2104 | /// Checks whether the iterator is valid. |
---|
| 2105 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[338] | 2106 | |
---|
| 2107 | private: |
---|
| 2108 | const MaxWeightedMatching* _algorithm; |
---|
| 2109 | int _last; |
---|
| 2110 | int _index; |
---|
| 2111 | }; |
---|
| 2112 | |
---|
| 2113 | /// @} |
---|
| 2114 | |
---|
| 2115 | }; |
---|
| 2116 | |
---|
| 2117 | /// \ingroup matching |
---|
| 2118 | /// |
---|
| 2119 | /// \brief Weighted perfect matching in general graphs |
---|
| 2120 | /// |
---|
| 2121 | /// This class provides an efficient implementation of Edmond's |
---|
[339] | 2122 | /// maximum weighted perfect matching algorithm. The implementation |
---|
[338] | 2123 | /// is based on extensive use of priority queues and provides |
---|
[606] | 2124 | /// \f$O(nm\log n)\f$ time complexity. |
---|
[338] | 2125 | /// |
---|
[947] | 2126 | /// The maximum weighted perfect matching problem is to find a subset of |
---|
| 2127 | /// the edges in an undirected graph with maximum overall weight for which |
---|
[637] | 2128 | /// each node has exactly one incident edge. |
---|
| 2129 | /// It can be formulated with the following linear program. |
---|
[338] | 2130 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
[339] | 2131 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 2132 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[338] | 2133 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 2134 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[339] | 2135 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 2136 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 2137 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 2138 | /// subsets of the nodes. |
---|
[338] | 2139 | /// |
---|
| 2140 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 2141 | /// optimality. The solution of the dual problem can be used to check |
---|
[339] | 2142 | /// the result of the algorithm. The dual linear problem is the |
---|
[637] | 2143 | /// following. |
---|
[339] | 2144 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge |
---|
| 2145 | w_{uv} \quad \forall uv\in E\f] */ |
---|
[338] | 2146 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[339] | 2147 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 2148 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[338] | 2149 | /// |
---|
[947] | 2150 | /// The algorithm can be executed with the run() function. |
---|
[637] | 2151 | /// After it the matching (the primal solution) and the dual solution |
---|
[947] | 2152 | /// can be obtained using the query functions and the |
---|
| 2153 | /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class, |
---|
| 2154 | /// which is able to iterate on the nodes of a blossom. |
---|
[637] | 2155 | /// If the value type is integer, then the dual solution is multiplied |
---|
| 2156 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
| 2157 | /// |
---|
[640] | 2158 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
[947] | 2159 | /// \tparam WM The type edge weight map. The default type is |
---|
[637] | 2160 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 2161 | #ifdef DOXYGEN |
---|
| 2162 | template <typename GR, typename WM> |
---|
| 2163 | #else |
---|
[606] | 2164 | template <typename GR, |
---|
| 2165 | typename WM = typename GR::template EdgeMap<int> > |
---|
[637] | 2166 | #endif |
---|
[338] | 2167 | class MaxWeightedPerfectMatching { |
---|
| 2168 | public: |
---|
| 2169 | |
---|
[637] | 2170 | /// The graph type of the algorithm |
---|
[606] | 2171 | typedef GR Graph; |
---|
[637] | 2172 | /// The type of the edge weight map |
---|
[606] | 2173 | typedef WM WeightMap; |
---|
[637] | 2174 | /// The value type of the edge weights |
---|
[338] | 2175 | typedef typename WeightMap::Value Value; |
---|
| 2176 | |
---|
| 2177 | /// \brief Scaling factor for dual solution |
---|
| 2178 | /// |
---|
| 2179 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 2180 | /// according to the value type. |
---|
| 2181 | static const int dualScale = |
---|
| 2182 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 2183 | |
---|
[640] | 2184 | /// The type of the matching map |
---|
[338] | 2185 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 2186 | MatchingMap; |
---|
| 2187 | |
---|
| 2188 | private: |
---|
| 2189 | |
---|
| 2190 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 2191 | |
---|
| 2192 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 2193 | typedef std::vector<Node> BlossomNodeList; |
---|
| 2194 | |
---|
| 2195 | struct BlossomVariable { |
---|
| 2196 | int begin, end; |
---|
| 2197 | Value value; |
---|
| 2198 | |
---|
| 2199 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 2200 | : begin(_begin), end(_end), value(_value) {} |
---|
| 2201 | |
---|
| 2202 | }; |
---|
| 2203 | |
---|
| 2204 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 2205 | |
---|
| 2206 | const Graph& _graph; |
---|
| 2207 | const WeightMap& _weight; |
---|
| 2208 | |
---|
| 2209 | MatchingMap* _matching; |
---|
| 2210 | |
---|
| 2211 | NodePotential* _node_potential; |
---|
| 2212 | |
---|
| 2213 | BlossomPotential _blossom_potential; |
---|
| 2214 | BlossomNodeList _blossom_node_list; |
---|
| 2215 | |
---|
| 2216 | int _node_num; |
---|
| 2217 | int _blossom_num; |
---|
| 2218 | |
---|
| 2219 | typedef RangeMap<int> IntIntMap; |
---|
| 2220 | |
---|
| 2221 | enum Status { |
---|
| 2222 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
| 2223 | }; |
---|
| 2224 | |
---|
[339] | 2225 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[338] | 2226 | struct BlossomData { |
---|
| 2227 | int tree; |
---|
| 2228 | Status status; |
---|
| 2229 | Arc pred, next; |
---|
| 2230 | Value pot, offset; |
---|
| 2231 | }; |
---|
| 2232 | |
---|
[339] | 2233 | IntNodeMap *_blossom_index; |
---|
[338] | 2234 | BlossomSet *_blossom_set; |
---|
| 2235 | RangeMap<BlossomData>* _blossom_data; |
---|
| 2236 | |
---|
[339] | 2237 | IntNodeMap *_node_index; |
---|
| 2238 | IntArcMap *_node_heap_index; |
---|
[338] | 2239 | |
---|
| 2240 | struct NodeData { |
---|
| 2241 | |
---|
[339] | 2242 | NodeData(IntArcMap& node_heap_index) |
---|
[338] | 2243 | : heap(node_heap_index) {} |
---|
| 2244 | |
---|
| 2245 | int blossom; |
---|
| 2246 | Value pot; |
---|
[339] | 2247 | BinHeap<Value, IntArcMap> heap; |
---|
[338] | 2248 | std::map<int, Arc> heap_index; |
---|
| 2249 | |
---|
| 2250 | int tree; |
---|
| 2251 | }; |
---|
| 2252 | |
---|
| 2253 | RangeMap<NodeData>* _node_data; |
---|
| 2254 | |
---|
| 2255 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 2256 | |
---|
| 2257 | IntIntMap *_tree_set_index; |
---|
| 2258 | TreeSet *_tree_set; |
---|
| 2259 | |
---|
| 2260 | IntIntMap *_delta2_index; |
---|
| 2261 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 2262 | |
---|
[339] | 2263 | IntEdgeMap *_delta3_index; |
---|
| 2264 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[338] | 2265 | |
---|
| 2266 | IntIntMap *_delta4_index; |
---|
| 2267 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 2268 | |
---|
| 2269 | Value _delta_sum; |
---|
[949] | 2270 | int _unmatched; |
---|
| 2271 | |
---|
[956] | 2272 | typedef MaxWeightedPerfectFractionalMatching<Graph, WeightMap> |
---|
[949] | 2273 | FractionalMatching; |
---|
| 2274 | FractionalMatching *_fractional; |
---|
[338] | 2275 | |
---|
| 2276 | void createStructures() { |
---|
| 2277 | _node_num = countNodes(_graph); |
---|
| 2278 | _blossom_num = _node_num * 3 / 2; |
---|
| 2279 | |
---|
| 2280 | if (!_matching) { |
---|
| 2281 | _matching = new MatchingMap(_graph); |
---|
| 2282 | } |
---|
[945] | 2283 | |
---|
[338] | 2284 | if (!_node_potential) { |
---|
| 2285 | _node_potential = new NodePotential(_graph); |
---|
| 2286 | } |
---|
[945] | 2287 | |
---|
[338] | 2288 | if (!_blossom_set) { |
---|
[339] | 2289 | _blossom_index = new IntNodeMap(_graph); |
---|
[338] | 2290 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 2291 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[945] | 2292 | } else if (_blossom_data->size() != _blossom_num) { |
---|
| 2293 | delete _blossom_data; |
---|
| 2294 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
[338] | 2295 | } |
---|
| 2296 | |
---|
| 2297 | if (!_node_index) { |
---|
[339] | 2298 | _node_index = new IntNodeMap(_graph); |
---|
| 2299 | _node_heap_index = new IntArcMap(_graph); |
---|
[338] | 2300 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
[339] | 2301 | NodeData(*_node_heap_index)); |
---|
[945] | 2302 | } else if (_node_data->size() != _node_num) { |
---|
| 2303 | delete _node_data; |
---|
| 2304 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
| 2305 | NodeData(*_node_heap_index)); |
---|
[338] | 2306 | } |
---|
| 2307 | |
---|
| 2308 | if (!_tree_set) { |
---|
| 2309 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 2310 | _tree_set = new TreeSet(*_tree_set_index); |
---|
[945] | 2311 | } else { |
---|
| 2312 | _tree_set_index->resize(_blossom_num); |
---|
[338] | 2313 | } |
---|
[945] | 2314 | |
---|
[338] | 2315 | if (!_delta2) { |
---|
| 2316 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 2317 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
[945] | 2318 | } else { |
---|
| 2319 | _delta2_index->resize(_blossom_num); |
---|
[338] | 2320 | } |
---|
[945] | 2321 | |
---|
[338] | 2322 | if (!_delta3) { |
---|
[339] | 2323 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 2324 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[338] | 2325 | } |
---|
[945] | 2326 | |
---|
[338] | 2327 | if (!_delta4) { |
---|
| 2328 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 2329 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
[945] | 2330 | } else { |
---|
| 2331 | _delta4_index->resize(_blossom_num); |
---|
[338] | 2332 | } |
---|
| 2333 | } |
---|
| 2334 | |
---|
| 2335 | void destroyStructures() { |
---|
| 2336 | if (_matching) { |
---|
| 2337 | delete _matching; |
---|
| 2338 | } |
---|
| 2339 | if (_node_potential) { |
---|
| 2340 | delete _node_potential; |
---|
| 2341 | } |
---|
| 2342 | if (_blossom_set) { |
---|
| 2343 | delete _blossom_index; |
---|
| 2344 | delete _blossom_set; |
---|
| 2345 | delete _blossom_data; |
---|
| 2346 | } |
---|
| 2347 | |
---|
| 2348 | if (_node_index) { |
---|
| 2349 | delete _node_index; |
---|
| 2350 | delete _node_heap_index; |
---|
| 2351 | delete _node_data; |
---|
| 2352 | } |
---|
| 2353 | |
---|
| 2354 | if (_tree_set) { |
---|
| 2355 | delete _tree_set_index; |
---|
| 2356 | delete _tree_set; |
---|
| 2357 | } |
---|
| 2358 | if (_delta2) { |
---|
| 2359 | delete _delta2_index; |
---|
| 2360 | delete _delta2; |
---|
| 2361 | } |
---|
| 2362 | if (_delta3) { |
---|
| 2363 | delete _delta3_index; |
---|
| 2364 | delete _delta3; |
---|
| 2365 | } |
---|
| 2366 | if (_delta4) { |
---|
| 2367 | delete _delta4_index; |
---|
| 2368 | delete _delta4; |
---|
| 2369 | } |
---|
| 2370 | } |
---|
| 2371 | |
---|
| 2372 | void matchedToEven(int blossom, int tree) { |
---|
| 2373 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2374 | _delta2->erase(blossom); |
---|
| 2375 | } |
---|
| 2376 | |
---|
| 2377 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2378 | (*_blossom_data)[blossom].pot -= |
---|
| 2379 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2380 | } |
---|
| 2381 | |
---|
| 2382 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2383 | n != INVALID; ++n) { |
---|
| 2384 | |
---|
| 2385 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2386 | int ni = (*_node_index)[n]; |
---|
| 2387 | |
---|
| 2388 | (*_node_data)[ni].heap.clear(); |
---|
| 2389 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2390 | |
---|
| 2391 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2392 | |
---|
| 2393 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2394 | Node v = _graph.source(e); |
---|
| 2395 | int vb = _blossom_set->find(v); |
---|
| 2396 | int vi = (*_node_index)[v]; |
---|
| 2397 | |
---|
| 2398 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2399 | dualScale * _weight[e]; |
---|
| 2400 | |
---|
| 2401 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2402 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2403 | _delta3->push(e, rw / 2); |
---|
| 2404 | } |
---|
| 2405 | } else { |
---|
| 2406 | typename std::map<int, Arc>::iterator it = |
---|
| 2407 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2408 | |
---|
| 2409 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2410 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2411 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2412 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2413 | it->second = e; |
---|
| 2414 | } |
---|
| 2415 | } else { |
---|
| 2416 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2417 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2418 | } |
---|
| 2419 | |
---|
| 2420 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2421 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2422 | |
---|
| 2423 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2424 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2425 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2426 | (*_blossom_data)[vb].offset); |
---|
| 2427 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2428 | (*_blossom_data)[vb].offset){ |
---|
| 2429 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2430 | (*_blossom_data)[vb].offset); |
---|
| 2431 | } |
---|
| 2432 | } |
---|
| 2433 | } |
---|
| 2434 | } |
---|
| 2435 | } |
---|
| 2436 | } |
---|
| 2437 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2438 | } |
---|
| 2439 | |
---|
| 2440 | void matchedToOdd(int blossom) { |
---|
| 2441 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2442 | _delta2->erase(blossom); |
---|
| 2443 | } |
---|
| 2444 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 2445 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2446 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 2447 | (*_blossom_data)[blossom].offset); |
---|
| 2448 | } |
---|
| 2449 | } |
---|
| 2450 | |
---|
| 2451 | void evenToMatched(int blossom, int tree) { |
---|
| 2452 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2453 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 2454 | } |
---|
| 2455 | |
---|
| 2456 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2457 | n != INVALID; ++n) { |
---|
| 2458 | int ni = (*_node_index)[n]; |
---|
| 2459 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 2460 | |
---|
| 2461 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2462 | Node v = _graph.source(e); |
---|
| 2463 | int vb = _blossom_set->find(v); |
---|
| 2464 | int vi = (*_node_index)[v]; |
---|
| 2465 | |
---|
| 2466 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2467 | dualScale * _weight[e]; |
---|
| 2468 | |
---|
| 2469 | if (vb == blossom) { |
---|
| 2470 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2471 | _delta3->erase(e); |
---|
| 2472 | } |
---|
| 2473 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2474 | |
---|
| 2475 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2476 | _delta3->erase(e); |
---|
| 2477 | } |
---|
| 2478 | |
---|
| 2479 | int vt = _tree_set->find(vb); |
---|
| 2480 | |
---|
| 2481 | if (vt != tree) { |
---|
| 2482 | |
---|
| 2483 | Arc r = _graph.oppositeArc(e); |
---|
| 2484 | |
---|
| 2485 | typename std::map<int, Arc>::iterator it = |
---|
| 2486 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 2487 | |
---|
| 2488 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 2489 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 2490 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 2491 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 2492 | it->second = r; |
---|
| 2493 | } |
---|
| 2494 | } else { |
---|
| 2495 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 2496 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 2497 | } |
---|
| 2498 | |
---|
| 2499 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 2500 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 2501 | |
---|
| 2502 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 2503 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2504 | (*_blossom_data)[blossom].offset); |
---|
| 2505 | } else if ((*_delta2)[blossom] > |
---|
| 2506 | _blossom_set->classPrio(blossom) - |
---|
| 2507 | (*_blossom_data)[blossom].offset){ |
---|
| 2508 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2509 | (*_blossom_data)[blossom].offset); |
---|
| 2510 | } |
---|
| 2511 | } |
---|
| 2512 | } |
---|
| 2513 | } else { |
---|
| 2514 | |
---|
| 2515 | typename std::map<int, Arc>::iterator it = |
---|
| 2516 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2517 | |
---|
| 2518 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2519 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 2520 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 2521 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 2522 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 2523 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 2524 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 2525 | } |
---|
| 2526 | |
---|
| 2527 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2528 | if (_blossom_set->classPrio(vb) == |
---|
| 2529 | std::numeric_limits<Value>::max()) { |
---|
| 2530 | _delta2->erase(vb); |
---|
| 2531 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 2532 | (*_blossom_data)[vb].offset) { |
---|
| 2533 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 2534 | (*_blossom_data)[vb].offset); |
---|
| 2535 | } |
---|
| 2536 | } |
---|
| 2537 | } |
---|
| 2538 | } |
---|
| 2539 | } |
---|
| 2540 | } |
---|
| 2541 | } |
---|
| 2542 | |
---|
| 2543 | void oddToMatched(int blossom) { |
---|
| 2544 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 2545 | |
---|
| 2546 | if (_blossom_set->classPrio(blossom) != |
---|
| 2547 | std::numeric_limits<Value>::max()) { |
---|
| 2548 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2549 | (*_blossom_data)[blossom].offset); |
---|
| 2550 | } |
---|
| 2551 | |
---|
| 2552 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2553 | _delta4->erase(blossom); |
---|
| 2554 | } |
---|
| 2555 | } |
---|
| 2556 | |
---|
| 2557 | void oddToEven(int blossom, int tree) { |
---|
| 2558 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2559 | _delta4->erase(blossom); |
---|
| 2560 | (*_blossom_data)[blossom].pot -= |
---|
| 2561 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2562 | } |
---|
| 2563 | |
---|
| 2564 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2565 | n != INVALID; ++n) { |
---|
| 2566 | int ni = (*_node_index)[n]; |
---|
| 2567 | |
---|
| 2568 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2569 | |
---|
| 2570 | (*_node_data)[ni].heap.clear(); |
---|
| 2571 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2572 | (*_node_data)[ni].pot += |
---|
| 2573 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2574 | |
---|
| 2575 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2576 | Node v = _graph.source(e); |
---|
| 2577 | int vb = _blossom_set->find(v); |
---|
| 2578 | int vi = (*_node_index)[v]; |
---|
| 2579 | |
---|
| 2580 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2581 | dualScale * _weight[e]; |
---|
| 2582 | |
---|
| 2583 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2584 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2585 | _delta3->push(e, rw / 2); |
---|
| 2586 | } |
---|
| 2587 | } else { |
---|
| 2588 | |
---|
| 2589 | typename std::map<int, Arc>::iterator it = |
---|
| 2590 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2591 | |
---|
| 2592 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2593 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2594 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2595 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2596 | it->second = e; |
---|
| 2597 | } |
---|
| 2598 | } else { |
---|
| 2599 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2600 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2601 | } |
---|
| 2602 | |
---|
| 2603 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2604 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2605 | |
---|
| 2606 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2607 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2608 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2609 | (*_blossom_data)[vb].offset); |
---|
| 2610 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2611 | (*_blossom_data)[vb].offset) { |
---|
| 2612 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2613 | (*_blossom_data)[vb].offset); |
---|
| 2614 | } |
---|
| 2615 | } |
---|
| 2616 | } |
---|
| 2617 | } |
---|
| 2618 | } |
---|
| 2619 | } |
---|
| 2620 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2621 | } |
---|
| 2622 | |
---|
| 2623 | void alternatePath(int even, int tree) { |
---|
| 2624 | int odd; |
---|
| 2625 | |
---|
| 2626 | evenToMatched(even, tree); |
---|
| 2627 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2628 | |
---|
| 2629 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 2630 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 2631 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 2632 | oddToMatched(odd); |
---|
| 2633 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 2634 | |
---|
| 2635 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 2636 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2637 | evenToMatched(even, tree); |
---|
| 2638 | (*_blossom_data)[even].next = |
---|
| 2639 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 2640 | } |
---|
| 2641 | |
---|
| 2642 | } |
---|
| 2643 | |
---|
| 2644 | void destroyTree(int tree) { |
---|
| 2645 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 2646 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 2647 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2648 | evenToMatched(b, tree); |
---|
| 2649 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 2650 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2651 | oddToMatched(b); |
---|
| 2652 | } |
---|
| 2653 | } |
---|
| 2654 | _tree_set->eraseClass(tree); |
---|
| 2655 | } |
---|
| 2656 | |
---|
[339] | 2657 | void augmentOnEdge(const Edge& edge) { |
---|
| 2658 | |
---|
| 2659 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2660 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[338] | 2661 | |
---|
| 2662 | int left_tree = _tree_set->find(left); |
---|
| 2663 | alternatePath(left, left_tree); |
---|
| 2664 | destroyTree(left_tree); |
---|
| 2665 | |
---|
| 2666 | int right_tree = _tree_set->find(right); |
---|
| 2667 | alternatePath(right, right_tree); |
---|
| 2668 | destroyTree(right_tree); |
---|
| 2669 | |
---|
[339] | 2670 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 2671 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[338] | 2672 | } |
---|
| 2673 | |
---|
| 2674 | void extendOnArc(const Arc& arc) { |
---|
| 2675 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 2676 | int tree = _tree_set->find(base); |
---|
| 2677 | |
---|
| 2678 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 2679 | _tree_set->insert(odd, tree); |
---|
| 2680 | (*_blossom_data)[odd].status = ODD; |
---|
| 2681 | matchedToOdd(odd); |
---|
| 2682 | (*_blossom_data)[odd].pred = arc; |
---|
| 2683 | |
---|
| 2684 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 2685 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 2686 | _tree_set->insert(even, tree); |
---|
| 2687 | (*_blossom_data)[even].status = EVEN; |
---|
| 2688 | matchedToEven(even, tree); |
---|
| 2689 | } |
---|
| 2690 | |
---|
[339] | 2691 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[338] | 2692 | int nca = -1; |
---|
| 2693 | std::vector<int> left_path, right_path; |
---|
| 2694 | |
---|
| 2695 | { |
---|
| 2696 | std::set<int> left_set, right_set; |
---|
| 2697 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2698 | left_path.push_back(left); |
---|
| 2699 | left_set.insert(left); |
---|
| 2700 | |
---|
| 2701 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 2702 | right_path.push_back(right); |
---|
| 2703 | right_set.insert(right); |
---|
| 2704 | |
---|
| 2705 | while (true) { |
---|
| 2706 | |
---|
| 2707 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 2708 | |
---|
| 2709 | left = |
---|
| 2710 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2711 | left_path.push_back(left); |
---|
| 2712 | left = |
---|
| 2713 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2714 | left_path.push_back(left); |
---|
| 2715 | |
---|
| 2716 | left_set.insert(left); |
---|
| 2717 | |
---|
| 2718 | if (right_set.find(left) != right_set.end()) { |
---|
| 2719 | nca = left; |
---|
| 2720 | break; |
---|
| 2721 | } |
---|
| 2722 | |
---|
| 2723 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 2724 | |
---|
| 2725 | right = |
---|
| 2726 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2727 | right_path.push_back(right); |
---|
| 2728 | right = |
---|
| 2729 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2730 | right_path.push_back(right); |
---|
| 2731 | |
---|
| 2732 | right_set.insert(right); |
---|
| 2733 | |
---|
| 2734 | if (left_set.find(right) != left_set.end()) { |
---|
| 2735 | nca = right; |
---|
| 2736 | break; |
---|
| 2737 | } |
---|
| 2738 | |
---|
| 2739 | } |
---|
| 2740 | |
---|
| 2741 | if (nca == -1) { |
---|
| 2742 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 2743 | nca = right; |
---|
| 2744 | while (left_set.find(nca) == left_set.end()) { |
---|
| 2745 | nca = |
---|
| 2746 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2747 | right_path.push_back(nca); |
---|
| 2748 | nca = |
---|
| 2749 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2750 | right_path.push_back(nca); |
---|
| 2751 | } |
---|
| 2752 | } else { |
---|
| 2753 | nca = left; |
---|
| 2754 | while (right_set.find(nca) == right_set.end()) { |
---|
| 2755 | nca = |
---|
| 2756 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2757 | left_path.push_back(nca); |
---|
| 2758 | nca = |
---|
| 2759 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2760 | left_path.push_back(nca); |
---|
| 2761 | } |
---|
| 2762 | } |
---|
| 2763 | } |
---|
| 2764 | } |
---|
| 2765 | |
---|
| 2766 | std::vector<int> subblossoms; |
---|
| 2767 | Arc prev; |
---|
| 2768 | |
---|
| 2769 | prev = _graph.direct(edge, true); |
---|
| 2770 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 2771 | subblossoms.push_back(left_path[i]); |
---|
| 2772 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 2773 | _tree_set->erase(left_path[i]); |
---|
| 2774 | |
---|
| 2775 | subblossoms.push_back(left_path[i + 1]); |
---|
| 2776 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 2777 | oddToEven(left_path[i + 1], tree); |
---|
| 2778 | _tree_set->erase(left_path[i + 1]); |
---|
| 2779 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 2780 | } |
---|
| 2781 | |
---|
| 2782 | int k = 0; |
---|
| 2783 | while (right_path[k] != nca) ++k; |
---|
| 2784 | |
---|
| 2785 | subblossoms.push_back(nca); |
---|
| 2786 | (*_blossom_data)[nca].next = prev; |
---|
| 2787 | |
---|
| 2788 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 2789 | subblossoms.push_back(right_path[i + 1]); |
---|
| 2790 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 2791 | oddToEven(right_path[i + 1], tree); |
---|
| 2792 | _tree_set->erase(right_path[i + 1]); |
---|
| 2793 | |
---|
| 2794 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 2795 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 2796 | |
---|
| 2797 | subblossoms.push_back(right_path[i]); |
---|
| 2798 | _tree_set->erase(right_path[i]); |
---|
| 2799 | } |
---|
| 2800 | |
---|
| 2801 | int surface = |
---|
| 2802 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 2803 | |
---|
| 2804 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2805 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2806 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 2807 | } |
---|
| 2808 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 2809 | } |
---|
| 2810 | |
---|
| 2811 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 2812 | (*_blossom_data)[surface].offset = 0; |
---|
| 2813 | (*_blossom_data)[surface].status = EVEN; |
---|
| 2814 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 2815 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 2816 | |
---|
| 2817 | _tree_set->insert(surface, tree); |
---|
| 2818 | _tree_set->erase(nca); |
---|
| 2819 | } |
---|
| 2820 | |
---|
| 2821 | void splitBlossom(int blossom) { |
---|
| 2822 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 2823 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 2824 | |
---|
| 2825 | int tree = _tree_set->find(blossom); |
---|
| 2826 | |
---|
| 2827 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 2828 | oddToMatched(blossom); |
---|
| 2829 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2830 | _delta2->erase(blossom); |
---|
| 2831 | } |
---|
| 2832 | |
---|
| 2833 | std::vector<int> subblossoms; |
---|
| 2834 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2835 | |
---|
| 2836 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 2837 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 2838 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 2839 | |
---|
| 2840 | int ib = -1, id = -1; |
---|
| 2841 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2842 | if (subblossoms[i] == b) ib = i; |
---|
| 2843 | if (subblossoms[i] == d) id = i; |
---|
| 2844 | |
---|
| 2845 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 2846 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2847 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 2848 | } |
---|
| 2849 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 2850 | std::numeric_limits<Value>::max()) { |
---|
| 2851 | _delta2->push(subblossoms[i], |
---|
| 2852 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 2853 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 2854 | } |
---|
| 2855 | } |
---|
| 2856 | |
---|
| 2857 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 2858 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 2859 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2860 | int sb = subblossoms[i]; |
---|
| 2861 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2862 | (*_blossom_data)[sb].next = |
---|
| 2863 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2864 | } |
---|
| 2865 | |
---|
| 2866 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2867 | int sb = subblossoms[i]; |
---|
| 2868 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2869 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2870 | |
---|
| 2871 | (*_blossom_data)[sb].status = ODD; |
---|
| 2872 | matchedToOdd(sb); |
---|
| 2873 | _tree_set->insert(sb, tree); |
---|
| 2874 | (*_blossom_data)[sb].pred = pred; |
---|
| 2875 | (*_blossom_data)[sb].next = |
---|
| 2876 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2877 | |
---|
| 2878 | pred = (*_blossom_data)[ub].next; |
---|
| 2879 | |
---|
| 2880 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2881 | matchedToEven(tb, tree); |
---|
| 2882 | _tree_set->insert(tb, tree); |
---|
| 2883 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 2884 | } |
---|
| 2885 | |
---|
| 2886 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 2887 | matchedToOdd(subblossoms[id]); |
---|
| 2888 | _tree_set->insert(subblossoms[id], tree); |
---|
| 2889 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 2890 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 2891 | |
---|
| 2892 | } else { |
---|
| 2893 | |
---|
| 2894 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 2895 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2896 | int sb = subblossoms[i]; |
---|
| 2897 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2898 | (*_blossom_data)[sb].next = |
---|
| 2899 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2900 | } |
---|
| 2901 | |
---|
| 2902 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2903 | int sb = subblossoms[i]; |
---|
| 2904 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2905 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2906 | |
---|
| 2907 | (*_blossom_data)[sb].status = ODD; |
---|
| 2908 | matchedToOdd(sb); |
---|
| 2909 | _tree_set->insert(sb, tree); |
---|
| 2910 | (*_blossom_data)[sb].next = next; |
---|
| 2911 | (*_blossom_data)[sb].pred = |
---|
| 2912 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2913 | |
---|
| 2914 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2915 | matchedToEven(tb, tree); |
---|
| 2916 | _tree_set->insert(tb, tree); |
---|
| 2917 | (*_blossom_data)[tb].pred = |
---|
| 2918 | (*_blossom_data)[tb].next = |
---|
| 2919 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 2920 | next = (*_blossom_data)[ub].next; |
---|
| 2921 | } |
---|
| 2922 | |
---|
| 2923 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 2924 | matchedToOdd(subblossoms[ib]); |
---|
| 2925 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 2926 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 2927 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 2928 | } |
---|
| 2929 | _tree_set->erase(blossom); |
---|
| 2930 | } |
---|
| 2931 | |
---|
| 2932 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 2933 | if (_blossom_set->trivial(blossom)) { |
---|
| 2934 | int bi = (*_node_index)[base]; |
---|
| 2935 | Value pot = (*_node_data)[bi].pot; |
---|
| 2936 | |
---|
[628] | 2937 | (*_matching)[base] = matching; |
---|
[338] | 2938 | _blossom_node_list.push_back(base); |
---|
[628] | 2939 | (*_node_potential)[base] = pot; |
---|
[338] | 2940 | } else { |
---|
| 2941 | |
---|
| 2942 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 2943 | int bn = _blossom_node_list.size(); |
---|
| 2944 | |
---|
| 2945 | std::vector<int> subblossoms; |
---|
| 2946 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2947 | int b = _blossom_set->find(base); |
---|
| 2948 | int ib = -1; |
---|
| 2949 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2950 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 2951 | } |
---|
| 2952 | |
---|
| 2953 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 2954 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 2955 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 2956 | |
---|
| 2957 | Arc m = (*_blossom_data)[tb].next; |
---|
| 2958 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 2959 | extractBlossom(tb, _graph.source(m), m); |
---|
| 2960 | } |
---|
| 2961 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 2962 | |
---|
| 2963 | int en = _blossom_node_list.size(); |
---|
| 2964 | |
---|
| 2965 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 2966 | } |
---|
| 2967 | } |
---|
| 2968 | |
---|
| 2969 | void extractMatching() { |
---|
| 2970 | std::vector<int> blossoms; |
---|
| 2971 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 2972 | blossoms.push_back(c); |
---|
| 2973 | } |
---|
| 2974 | |
---|
| 2975 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 2976 | |
---|
| 2977 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 2978 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 2979 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 2980 | n != INVALID; ++n) { |
---|
| 2981 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 2982 | } |
---|
| 2983 | |
---|
| 2984 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 2985 | Node base = _graph.source(matching); |
---|
| 2986 | extractBlossom(blossoms[i], base, matching); |
---|
| 2987 | } |
---|
| 2988 | } |
---|
| 2989 | |
---|
| 2990 | public: |
---|
| 2991 | |
---|
| 2992 | /// \brief Constructor |
---|
| 2993 | /// |
---|
| 2994 | /// Constructor. |
---|
| 2995 | MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight) |
---|
| 2996 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 2997 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 2998 | _node_num(0), _blossom_num(0), |
---|
| 2999 | |
---|
| 3000 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 3001 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 3002 | _tree_set_index(0), _tree_set(0), |
---|
| 3003 | |
---|
| 3004 | _delta2_index(0), _delta2(0), |
---|
| 3005 | _delta3_index(0), _delta3(0), |
---|
| 3006 | _delta4_index(0), _delta4(0), |
---|
| 3007 | |
---|
[949] | 3008 | _delta_sum(), _unmatched(0), |
---|
| 3009 | |
---|
| 3010 | _fractional(0) |
---|
| 3011 | {} |
---|
[338] | 3012 | |
---|
| 3013 | ~MaxWeightedPerfectMatching() { |
---|
| 3014 | destroyStructures(); |
---|
[949] | 3015 | if (_fractional) { |
---|
| 3016 | delete _fractional; |
---|
| 3017 | } |
---|
[338] | 3018 | } |
---|
| 3019 | |
---|
[637] | 3020 | /// \name Execution Control |
---|
[342] | 3021 | /// The simplest way to execute the algorithm is to use the |
---|
[637] | 3022 | /// \ref run() member function. |
---|
[338] | 3023 | |
---|
| 3024 | ///@{ |
---|
| 3025 | |
---|
| 3026 | /// \brief Initialize the algorithm |
---|
| 3027 | /// |
---|
[637] | 3028 | /// This function initializes the algorithm. |
---|
[338] | 3029 | void init() { |
---|
| 3030 | createStructures(); |
---|
| 3031 | |
---|
[945] | 3032 | _blossom_node_list.clear(); |
---|
| 3033 | _blossom_potential.clear(); |
---|
| 3034 | |
---|
[338] | 3035 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 3036 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
[338] | 3037 | } |
---|
| 3038 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
[628] | 3039 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
[338] | 3040 | } |
---|
| 3041 | for (int i = 0; i < _blossom_num; ++i) { |
---|
[628] | 3042 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 3043 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
[338] | 3044 | } |
---|
| 3045 | |
---|
[949] | 3046 | _unmatched = _node_num; |
---|
| 3047 | |
---|
[945] | 3048 | _delta2->clear(); |
---|
| 3049 | _delta3->clear(); |
---|
| 3050 | _delta4->clear(); |
---|
| 3051 | _blossom_set->clear(); |
---|
| 3052 | _tree_set->clear(); |
---|
| 3053 | |
---|
[338] | 3054 | int index = 0; |
---|
| 3055 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3056 | Value max = - std::numeric_limits<Value>::max(); |
---|
| 3057 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 3058 | if (_graph.target(e) == n) continue; |
---|
| 3059 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 3060 | max = (dualScale * _weight[e]) / 2; |
---|
| 3061 | } |
---|
| 3062 | } |
---|
[628] | 3063 | (*_node_index)[n] = index; |
---|
[945] | 3064 | (*_node_data)[index].heap_index.clear(); |
---|
| 3065 | (*_node_data)[index].heap.clear(); |
---|
[338] | 3066 | (*_node_data)[index].pot = max; |
---|
| 3067 | int blossom = |
---|
| 3068 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 3069 | |
---|
| 3070 | _tree_set->insert(blossom); |
---|
| 3071 | |
---|
| 3072 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 3073 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 3074 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 3075 | (*_blossom_data)[blossom].pot = 0; |
---|
| 3076 | (*_blossom_data)[blossom].offset = 0; |
---|
| 3077 | ++index; |
---|
| 3078 | } |
---|
| 3079 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 3080 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 3081 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 3082 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 3083 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 3084 | dualScale * _weight[e]) / 2); |
---|
| 3085 | } |
---|
| 3086 | } |
---|
| 3087 | } |
---|
| 3088 | |
---|
[949] | 3089 | /// \brief Initialize the algorithm with fractional matching |
---|
| 3090 | /// |
---|
| 3091 | /// This function initializes the algorithm with a fractional |
---|
| 3092 | /// matching. This initialization is also called jumpstart heuristic. |
---|
| 3093 | void fractionalInit() { |
---|
| 3094 | createStructures(); |
---|
[955] | 3095 | |
---|
| 3096 | _blossom_node_list.clear(); |
---|
| 3097 | _blossom_potential.clear(); |
---|
[956] | 3098 | |
---|
[949] | 3099 | if (_fractional == 0) { |
---|
| 3100 | _fractional = new FractionalMatching(_graph, _weight, false); |
---|
| 3101 | } |
---|
| 3102 | if (!_fractional->run()) { |
---|
| 3103 | _unmatched = -1; |
---|
| 3104 | return; |
---|
| 3105 | } |
---|
| 3106 | |
---|
| 3107 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 3108 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
| 3109 | } |
---|
| 3110 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 3111 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
| 3112 | } |
---|
| 3113 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 3114 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 3115 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
| 3116 | } |
---|
| 3117 | |
---|
| 3118 | _unmatched = 0; |
---|
| 3119 | |
---|
[955] | 3120 | _delta2->clear(); |
---|
| 3121 | _delta3->clear(); |
---|
| 3122 | _delta4->clear(); |
---|
| 3123 | _blossom_set->clear(); |
---|
| 3124 | _tree_set->clear(); |
---|
| 3125 | |
---|
[949] | 3126 | int index = 0; |
---|
| 3127 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3128 | Value pot = _fractional->nodeValue(n); |
---|
| 3129 | (*_node_index)[n] = index; |
---|
| 3130 | (*_node_data)[index].pot = pot; |
---|
[955] | 3131 | (*_node_data)[index].heap_index.clear(); |
---|
| 3132 | (*_node_data)[index].heap.clear(); |
---|
[949] | 3133 | int blossom = |
---|
| 3134 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 3135 | |
---|
| 3136 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 3137 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 3138 | (*_blossom_data)[blossom].next = _fractional->matching(n); |
---|
| 3139 | (*_blossom_data)[blossom].pot = 0; |
---|
| 3140 | (*_blossom_data)[blossom].offset = 0; |
---|
| 3141 | ++index; |
---|
| 3142 | } |
---|
| 3143 | |
---|
| 3144 | typename Graph::template NodeMap<bool> processed(_graph, false); |
---|
| 3145 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3146 | if (processed[n]) continue; |
---|
| 3147 | processed[n] = true; |
---|
| 3148 | if (_fractional->matching(n) == INVALID) continue; |
---|
| 3149 | int num = 1; |
---|
| 3150 | Node v = _graph.target(_fractional->matching(n)); |
---|
| 3151 | while (n != v) { |
---|
| 3152 | processed[v] = true; |
---|
| 3153 | v = _graph.target(_fractional->matching(v)); |
---|
| 3154 | ++num; |
---|
| 3155 | } |
---|
| 3156 | |
---|
| 3157 | if (num % 2 == 1) { |
---|
| 3158 | std::vector<int> subblossoms(num); |
---|
| 3159 | |
---|
| 3160 | subblossoms[--num] = _blossom_set->find(n); |
---|
| 3161 | v = _graph.target(_fractional->matching(n)); |
---|
| 3162 | while (n != v) { |
---|
| 3163 | subblossoms[--num] = _blossom_set->find(v); |
---|
[956] | 3164 | v = _graph.target(_fractional->matching(v)); |
---|
[949] | 3165 | } |
---|
[956] | 3166 | |
---|
| 3167 | int surface = |
---|
[949] | 3168 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 3169 | (*_blossom_data)[surface].status = EVEN; |
---|
| 3170 | (*_blossom_data)[surface].pred = INVALID; |
---|
| 3171 | (*_blossom_data)[surface].next = INVALID; |
---|
| 3172 | (*_blossom_data)[surface].pot = 0; |
---|
| 3173 | (*_blossom_data)[surface].offset = 0; |
---|
[956] | 3174 | |
---|
[949] | 3175 | _tree_set->insert(surface); |
---|
| 3176 | ++_unmatched; |
---|
| 3177 | } |
---|
| 3178 | } |
---|
| 3179 | |
---|
| 3180 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 3181 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 3182 | int sb = _blossom_set->find(_graph.u(e)); |
---|
| 3183 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 3184 | int tb = _blossom_set->find(_graph.v(e)); |
---|
| 3185 | if ((*_blossom_data)[sb].status == EVEN && |
---|
| 3186 | (*_blossom_data)[tb].status == EVEN && sb != tb) { |
---|
| 3187 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 3188 | dualScale * _weight[e]) / 2); |
---|
| 3189 | } |
---|
| 3190 | } |
---|
| 3191 | |
---|
| 3192 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3193 | int nb = _blossom_set->find(n); |
---|
| 3194 | if ((*_blossom_data)[nb].status != MATCHED) continue; |
---|
| 3195 | int ni = (*_node_index)[n]; |
---|
| 3196 | |
---|
| 3197 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 3198 | Node v = _graph.target(e); |
---|
| 3199 | int vb = _blossom_set->find(v); |
---|
| 3200 | int vi = (*_node_index)[v]; |
---|
| 3201 | |
---|
| 3202 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 3203 | dualScale * _weight[e]; |
---|
| 3204 | |
---|
| 3205 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 3206 | |
---|
| 3207 | int vt = _tree_set->find(vb); |
---|
| 3208 | |
---|
| 3209 | typename std::map<int, Arc>::iterator it = |
---|
| 3210 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 3211 | |
---|
| 3212 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 3213 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 3214 | (*_node_data)[ni].heap.replace(it->second, e); |
---|
| 3215 | (*_node_data)[ni].heap.decrease(e, rw); |
---|
| 3216 | it->second = e; |
---|
| 3217 | } |
---|
| 3218 | } else { |
---|
| 3219 | (*_node_data)[ni].heap.push(e, rw); |
---|
| 3220 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, e)); |
---|
| 3221 | } |
---|
| 3222 | } |
---|
| 3223 | } |
---|
[956] | 3224 | |
---|
[949] | 3225 | if (!(*_node_data)[ni].heap.empty()) { |
---|
| 3226 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 3227 | _delta2->push(nb, _blossom_set->classPrio(nb)); |
---|
| 3228 | } |
---|
| 3229 | } |
---|
| 3230 | } |
---|
| 3231 | |
---|
[637] | 3232 | /// \brief Start the algorithm |
---|
[338] | 3233 | /// |
---|
[637] | 3234 | /// This function starts the algorithm. |
---|
| 3235 | /// |
---|
[949] | 3236 | /// \pre \ref init() or \ref fractionalInit() must be called before |
---|
| 3237 | /// using this function. |
---|
[338] | 3238 | bool start() { |
---|
| 3239 | enum OpType { |
---|
| 3240 | D2, D3, D4 |
---|
| 3241 | }; |
---|
| 3242 | |
---|
[949] | 3243 | if (_unmatched == -1) return false; |
---|
| 3244 | |
---|
| 3245 | while (_unmatched > 0) { |
---|
[338] | 3246 | Value d2 = !_delta2->empty() ? |
---|
| 3247 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 3248 | |
---|
| 3249 | Value d3 = !_delta3->empty() ? |
---|
| 3250 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 3251 | |
---|
| 3252 | Value d4 = !_delta4->empty() ? |
---|
| 3253 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 3254 | |
---|
[947] | 3255 | _delta_sum = d3; OpType ot = D3; |
---|
| 3256 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
[338] | 3257 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 3258 | |
---|
| 3259 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
| 3260 | return false; |
---|
| 3261 | } |
---|
| 3262 | |
---|
| 3263 | switch (ot) { |
---|
| 3264 | case D2: |
---|
| 3265 | { |
---|
| 3266 | int blossom = _delta2->top(); |
---|
| 3267 | Node n = _blossom_set->classTop(blossom); |
---|
| 3268 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 3269 | extendOnArc(e); |
---|
| 3270 | } |
---|
| 3271 | break; |
---|
| 3272 | case D3: |
---|
| 3273 | { |
---|
| 3274 | Edge e = _delta3->top(); |
---|
| 3275 | |
---|
| 3276 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 3277 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 3278 | |
---|
| 3279 | if (left_blossom == right_blossom) { |
---|
| 3280 | _delta3->pop(); |
---|
| 3281 | } else { |
---|
| 3282 | int left_tree = _tree_set->find(left_blossom); |
---|
| 3283 | int right_tree = _tree_set->find(right_blossom); |
---|
| 3284 | |
---|
| 3285 | if (left_tree == right_tree) { |
---|
[339] | 3286 | shrinkOnEdge(e, left_tree); |
---|
[338] | 3287 | } else { |
---|
[339] | 3288 | augmentOnEdge(e); |
---|
[949] | 3289 | _unmatched -= 2; |
---|
[338] | 3290 | } |
---|
| 3291 | } |
---|
| 3292 | } break; |
---|
| 3293 | case D4: |
---|
| 3294 | splitBlossom(_delta4->top()); |
---|
| 3295 | break; |
---|
| 3296 | } |
---|
| 3297 | } |
---|
| 3298 | extractMatching(); |
---|
| 3299 | return true; |
---|
| 3300 | } |
---|
| 3301 | |
---|
[637] | 3302 | /// \brief Run the algorithm. |
---|
[338] | 3303 | /// |
---|
[637] | 3304 | /// This method runs the \c %MaxWeightedPerfectMatching algorithm. |
---|
[338] | 3305 | /// |
---|
[637] | 3306 | /// \note mwpm.run() is just a shortcut of the following code. |
---|
[338] | 3307 | /// \code |
---|
[949] | 3308 | /// mwpm.fractionalInit(); |
---|
[637] | 3309 | /// mwpm.start(); |
---|
[338] | 3310 | /// \endcode |
---|
| 3311 | bool run() { |
---|
[949] | 3312 | fractionalInit(); |
---|
[338] | 3313 | return start(); |
---|
| 3314 | } |
---|
| 3315 | |
---|
| 3316 | /// @} |
---|
| 3317 | |
---|
[637] | 3318 | /// \name Primal Solution |
---|
[947] | 3319 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
[637] | 3320 | /// perfect matching.\n |
---|
| 3321 | /// Either \ref run() or \ref start() function should be called before |
---|
| 3322 | /// using them. |
---|
[338] | 3323 | |
---|
| 3324 | /// @{ |
---|
| 3325 | |
---|
[637] | 3326 | /// \brief Return the weight of the matching. |
---|
[338] | 3327 | /// |
---|
[637] | 3328 | /// This function returns the weight of the found matching. |
---|
| 3329 | /// |
---|
| 3330 | /// \pre Either run() or start() must be called before using this function. |
---|
[640] | 3331 | Value matchingWeight() const { |
---|
[338] | 3332 | Value sum = 0; |
---|
| 3333 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3334 | if ((*_matching)[n] != INVALID) { |
---|
| 3335 | sum += _weight[(*_matching)[n]]; |
---|
| 3336 | } |
---|
| 3337 | } |
---|
[947] | 3338 | return sum / 2; |
---|
[338] | 3339 | } |
---|
| 3340 | |
---|
[637] | 3341 | /// \brief Return \c true if the given edge is in the matching. |
---|
[338] | 3342 | /// |
---|
[947] | 3343 | /// This function returns \c true if the given edge is in the found |
---|
[637] | 3344 | /// matching. |
---|
| 3345 | /// |
---|
| 3346 | /// \pre Either run() or start() must be called before using this function. |
---|
[339] | 3347 | bool matching(const Edge& edge) const { |
---|
| 3348 | return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge; |
---|
[338] | 3349 | } |
---|
| 3350 | |
---|
[637] | 3351 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[338] | 3352 | /// |
---|
[637] | 3353 | /// This function returns the matching arc (or edge) incident to the |
---|
[947] | 3354 | /// given node in the found matching or \c INVALID if the node is |
---|
[637] | 3355 | /// not covered by the matching. |
---|
| 3356 | /// |
---|
| 3357 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3358 | Arc matching(const Node& node) const { |
---|
| 3359 | return (*_matching)[node]; |
---|
| 3360 | } |
---|
| 3361 | |
---|
[640] | 3362 | /// \brief Return a const reference to the matching map. |
---|
| 3363 | /// |
---|
| 3364 | /// This function returns a const reference to a node map that stores |
---|
| 3365 | /// the matching arc (or edge) incident to each node. |
---|
| 3366 | const MatchingMap& matchingMap() const { |
---|
| 3367 | return *_matching; |
---|
| 3368 | } |
---|
| 3369 | |
---|
[637] | 3370 | /// \brief Return the mate of the given node. |
---|
[338] | 3371 | /// |
---|
[947] | 3372 | /// This function returns the mate of the given node in the found |
---|
[637] | 3373 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
| 3374 | /// |
---|
| 3375 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3376 | Node mate(const Node& node) const { |
---|
| 3377 | return _graph.target((*_matching)[node]); |
---|
| 3378 | } |
---|
| 3379 | |
---|
| 3380 | /// @} |
---|
| 3381 | |
---|
[637] | 3382 | /// \name Dual Solution |
---|
| 3383 | /// Functions to get the dual solution.\n |
---|
| 3384 | /// Either \ref run() or \ref start() function should be called before |
---|
| 3385 | /// using them. |
---|
[338] | 3386 | |
---|
| 3387 | /// @{ |
---|
| 3388 | |
---|
[637] | 3389 | /// \brief Return the value of the dual solution. |
---|
[338] | 3390 | /// |
---|
[947] | 3391 | /// This function returns the value of the dual solution. |
---|
| 3392 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
[637] | 3393 | /// "dual scale". |
---|
| 3394 | /// |
---|
| 3395 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3396 | Value dualValue() const { |
---|
| 3397 | Value sum = 0; |
---|
| 3398 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3399 | sum += nodeValue(n); |
---|
| 3400 | } |
---|
| 3401 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 3402 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 3403 | } |
---|
| 3404 | return sum; |
---|
| 3405 | } |
---|
| 3406 | |
---|
[637] | 3407 | /// \brief Return the dual value (potential) of the given node. |
---|
[338] | 3408 | /// |
---|
[637] | 3409 | /// This function returns the dual value (potential) of the given node. |
---|
| 3410 | /// |
---|
| 3411 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3412 | Value nodeValue(const Node& n) const { |
---|
| 3413 | return (*_node_potential)[n]; |
---|
| 3414 | } |
---|
| 3415 | |
---|
[637] | 3416 | /// \brief Return the number of the blossoms in the basis. |
---|
[338] | 3417 | /// |
---|
[637] | 3418 | /// This function returns the number of the blossoms in the basis. |
---|
| 3419 | /// |
---|
| 3420 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3421 | /// \see BlossomIt |
---|
| 3422 | int blossomNum() const { |
---|
| 3423 | return _blossom_potential.size(); |
---|
| 3424 | } |
---|
| 3425 | |
---|
[637] | 3426 | /// \brief Return the number of the nodes in the given blossom. |
---|
[338] | 3427 | /// |
---|
[637] | 3428 | /// This function returns the number of the nodes in the given blossom. |
---|
| 3429 | /// |
---|
| 3430 | /// \pre Either run() or start() must be called before using this function. |
---|
| 3431 | /// \see BlossomIt |
---|
[338] | 3432 | int blossomSize(int k) const { |
---|
| 3433 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 3434 | } |
---|
| 3435 | |
---|
[637] | 3436 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
[338] | 3437 | /// |
---|
[637] | 3438 | /// This function returns the dual value (ptential) of the given blossom. |
---|
| 3439 | /// |
---|
| 3440 | /// \pre Either run() or start() must be called before using this function. |
---|
[338] | 3441 | Value blossomValue(int k) const { |
---|
| 3442 | return _blossom_potential[k].value; |
---|
| 3443 | } |
---|
| 3444 | |
---|
[637] | 3445 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
[338] | 3446 | /// |
---|
[947] | 3447 | /// This class provides an iterator for obtaining the nodes of the |
---|
[637] | 3448 | /// given blossom. It lists a subset of the nodes. |
---|
[947] | 3449 | /// Before using this iterator, you must allocate a |
---|
[637] | 3450 | /// MaxWeightedPerfectMatching class and execute it. |
---|
[338] | 3451 | class BlossomIt { |
---|
| 3452 | public: |
---|
| 3453 | |
---|
| 3454 | /// \brief Constructor. |
---|
| 3455 | /// |
---|
[637] | 3456 | /// Constructor to get the nodes of the given variable. |
---|
| 3457 | /// |
---|
[947] | 3458 | /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()" |
---|
| 3459 | /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()" |
---|
[637] | 3460 | /// must be called before initializing this iterator. |
---|
[338] | 3461 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
| 3462 | : _algorithm(&algorithm) |
---|
| 3463 | { |
---|
| 3464 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 3465 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 3466 | } |
---|
| 3467 | |
---|
[637] | 3468 | /// \brief Conversion to \c Node. |
---|
[338] | 3469 | /// |
---|
[637] | 3470 | /// Conversion to \c Node. |
---|
[338] | 3471 | operator Node() const { |
---|
[339] | 3472 | return _algorithm->_blossom_node_list[_index]; |
---|
[338] | 3473 | } |
---|
| 3474 | |
---|
| 3475 | /// \brief Increment operator. |
---|
| 3476 | /// |
---|
| 3477 | /// Increment operator. |
---|
| 3478 | BlossomIt& operator++() { |
---|
| 3479 | ++_index; |
---|
| 3480 | return *this; |
---|
| 3481 | } |
---|
| 3482 | |
---|
[339] | 3483 | /// \brief Validity checking |
---|
| 3484 | /// |
---|
[637] | 3485 | /// This function checks whether the iterator is invalid. |
---|
[339] | 3486 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 3487 | |
---|
| 3488 | /// \brief Validity checking |
---|
| 3489 | /// |
---|
[637] | 3490 | /// This function checks whether the iterator is valid. |
---|
[339] | 3491 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[338] | 3492 | |
---|
| 3493 | private: |
---|
| 3494 | const MaxWeightedPerfectMatching* _algorithm; |
---|
| 3495 | int _last; |
---|
| 3496 | int _index; |
---|
| 3497 | }; |
---|
| 3498 | |
---|
| 3499 | /// @} |
---|
| 3500 | |
---|
| 3501 | }; |
---|
| 3502 | |
---|
| 3503 | } //END OF NAMESPACE LEMON |
---|
| 3504 | |
---|
[947] | 3505 | #endif //LEMON_MATCHING_H |
---|