[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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[463] | 5 | * Copyright (C) 2003-2009 |
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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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| 19 | #ifndef LEMON_MAX_MATCHING_H |
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| 20 | #define LEMON_MAX_MATCHING_H |
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| 21 | |
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| 22 | #include <vector> |
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| 23 | #include <queue> |
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| 24 | #include <set> |
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| 25 | #include <limits> |
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| 26 | |
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| 27 | #include <lemon/core.h> |
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| 28 | #include <lemon/unionfind.h> |
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| 29 | #include <lemon/bin_heap.h> |
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| 30 | #include <lemon/maps.h> |
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| 31 | |
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| 32 | ///\ingroup matching |
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| 33 | ///\file |
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[339] | 34 | ///\brief Maximum matching algorithms in general graphs. |
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[338] | 35 | |
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| 36 | namespace lemon { |
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| 37 | |
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[339] | 38 | /// \ingroup matching |
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[338] | 39 | /// |
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[339] | 40 | /// \brief Edmonds' alternating forest maximum matching algorithm. |
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[338] | 41 | /// |
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[342] | 42 | /// This class implements Edmonds' alternating forest matching |
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| 43 | /// algorithm. The algorithm can be started from an arbitrary initial |
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| 44 | /// matching (the default is the empty one) |
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[338] | 45 | /// |
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[342] | 46 | /// The dual solution of the problem is a map of the nodes to |
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[339] | 47 | /// MaxMatching::Status, having values \c EVEN/D, \c ODD/A and \c |
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| 48 | /// MATCHED/C showing the Gallai-Edmonds decomposition of the |
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| 49 | /// graph. The nodes in \c EVEN/D induce a graph with |
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| 50 | /// factor-critical components, the nodes in \c ODD/A form the |
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| 51 | /// barrier, and the nodes in \c MATCHED/C induce a graph having a |
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[342] | 52 | /// perfect matching. The number of the factor-critical components |
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[339] | 53 | /// minus the number of barrier nodes is a lower bound on the |
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[342] | 54 | /// unmatched nodes, and the matching is optimal if and only if this bound is |
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[339] | 55 | /// tight. This decomposition can be attained by calling \c |
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| 56 | /// decomposition() after running the algorithm. |
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[338] | 57 | /// |
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[339] | 58 | /// \param _Graph The graph type the algorithm runs on. |
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| 59 | template <typename _Graph> |
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[338] | 60 | class MaxMatching { |
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[339] | 61 | public: |
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| 62 | |
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| 63 | typedef _Graph Graph; |
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| 64 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
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| 65 | MatchingMap; |
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| 66 | |
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| 67 | ///\brief Indicates the Gallai-Edmonds decomposition of the graph. |
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| 68 | /// |
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[342] | 69 | ///Indicates the Gallai-Edmonds decomposition of the graph. The |
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[339] | 70 | ///nodes with Status \c EVEN/D induce a graph with factor-critical |
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| 71 | ///components, the nodes in \c ODD/A form the canonical barrier, |
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| 72 | ///and the nodes in \c MATCHED/C induce a graph having a perfect |
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| 73 | ///matching. |
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| 74 | enum Status { |
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| 75 | EVEN = 1, D = 1, MATCHED = 0, C = 0, ODD = -1, A = -1, UNMATCHED = -2 |
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| 76 | }; |
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| 77 | |
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| 78 | typedef typename Graph::template NodeMap<Status> StatusMap; |
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| 79 | |
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| 80 | private: |
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[338] | 81 | |
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| 82 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 83 | |
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[339] | 84 | typedef UnionFindEnum<IntNodeMap> BlossomSet; |
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| 85 | typedef ExtendFindEnum<IntNodeMap> TreeSet; |
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| 86 | typedef RangeMap<Node> NodeIntMap; |
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| 87 | typedef MatchingMap EarMap; |
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| 88 | typedef std::vector<Node> NodeQueue; |
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| 89 | |
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| 90 | const Graph& _graph; |
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| 91 | MatchingMap* _matching; |
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| 92 | StatusMap* _status; |
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| 93 | |
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| 94 | EarMap* _ear; |
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| 95 | |
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| 96 | IntNodeMap* _blossom_set_index; |
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| 97 | BlossomSet* _blossom_set; |
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| 98 | NodeIntMap* _blossom_rep; |
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| 99 | |
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| 100 | IntNodeMap* _tree_set_index; |
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| 101 | TreeSet* _tree_set; |
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| 102 | |
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| 103 | NodeQueue _node_queue; |
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| 104 | int _process, _postpone, _last; |
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| 105 | |
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| 106 | int _node_num; |
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| 107 | |
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| 108 | private: |
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| 109 | |
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| 110 | void createStructures() { |
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| 111 | _node_num = countNodes(_graph); |
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| 112 | if (!_matching) { |
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| 113 | _matching = new MatchingMap(_graph); |
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| 114 | } |
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| 115 | if (!_status) { |
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| 116 | _status = new StatusMap(_graph); |
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| 117 | } |
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| 118 | if (!_ear) { |
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| 119 | _ear = new EarMap(_graph); |
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| 120 | } |
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| 121 | if (!_blossom_set) { |
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| 122 | _blossom_set_index = new IntNodeMap(_graph); |
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| 123 | _blossom_set = new BlossomSet(*_blossom_set_index); |
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| 124 | } |
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| 125 | if (!_blossom_rep) { |
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| 126 | _blossom_rep = new NodeIntMap(_node_num); |
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| 127 | } |
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| 128 | if (!_tree_set) { |
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| 129 | _tree_set_index = new IntNodeMap(_graph); |
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| 130 | _tree_set = new TreeSet(*_tree_set_index); |
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| 131 | } |
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| 132 | _node_queue.resize(_node_num); |
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| 133 | } |
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| 134 | |
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| 135 | void destroyStructures() { |
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| 136 | if (_matching) { |
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| 137 | delete _matching; |
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| 138 | } |
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| 139 | if (_status) { |
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| 140 | delete _status; |
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| 141 | } |
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| 142 | if (_ear) { |
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| 143 | delete _ear; |
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| 144 | } |
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| 145 | if (_blossom_set) { |
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| 146 | delete _blossom_set; |
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| 147 | delete _blossom_set_index; |
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| 148 | } |
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| 149 | if (_blossom_rep) { |
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| 150 | delete _blossom_rep; |
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| 151 | } |
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| 152 | if (_tree_set) { |
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| 153 | delete _tree_set_index; |
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| 154 | delete _tree_set; |
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| 155 | } |
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| 156 | } |
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| 157 | |
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| 158 | void processDense(const Node& n) { |
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| 159 | _process = _postpone = _last = 0; |
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| 160 | _node_queue[_last++] = n; |
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| 161 | |
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| 162 | while (_process != _last) { |
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| 163 | Node u = _node_queue[_process++]; |
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| 164 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 165 | Node v = _graph.target(a); |
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| 166 | if ((*_status)[v] == MATCHED) { |
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| 167 | extendOnArc(a); |
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| 168 | } else if ((*_status)[v] == UNMATCHED) { |
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| 169 | augmentOnArc(a); |
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| 170 | return; |
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| 171 | } |
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| 172 | } |
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| 173 | } |
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| 174 | |
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| 175 | while (_postpone != _last) { |
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| 176 | Node u = _node_queue[_postpone++]; |
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| 177 | |
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| 178 | for (OutArcIt a(_graph, u); a != INVALID ; ++a) { |
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| 179 | Node v = _graph.target(a); |
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| 180 | |
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| 181 | if ((*_status)[v] == EVEN) { |
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| 182 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 183 | shrinkOnEdge(a); |
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| 184 | } |
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| 185 | } |
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| 186 | |
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| 187 | while (_process != _last) { |
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| 188 | Node w = _node_queue[_process++]; |
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| 189 | for (OutArcIt b(_graph, w); b != INVALID; ++b) { |
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| 190 | Node x = _graph.target(b); |
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| 191 | if ((*_status)[x] == MATCHED) { |
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| 192 | extendOnArc(b); |
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| 193 | } else if ((*_status)[x] == UNMATCHED) { |
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| 194 | augmentOnArc(b); |
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| 195 | return; |
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| 196 | } |
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| 197 | } |
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| 198 | } |
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| 199 | } |
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| 200 | } |
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| 201 | } |
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| 202 | |
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| 203 | void processSparse(const Node& n) { |
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| 204 | _process = _last = 0; |
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| 205 | _node_queue[_last++] = n; |
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| 206 | while (_process != _last) { |
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| 207 | Node u = _node_queue[_process++]; |
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| 208 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 209 | Node v = _graph.target(a); |
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| 210 | |
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| 211 | if ((*_status)[v] == EVEN) { |
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| 212 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 213 | shrinkOnEdge(a); |
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| 214 | } |
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| 215 | } else if ((*_status)[v] == MATCHED) { |
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| 216 | extendOnArc(a); |
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| 217 | } else if ((*_status)[v] == UNMATCHED) { |
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| 218 | augmentOnArc(a); |
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| 219 | return; |
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| 220 | } |
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| 221 | } |
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| 222 | } |
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| 223 | } |
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| 224 | |
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| 225 | void shrinkOnEdge(const Edge& e) { |
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| 226 | Node nca = INVALID; |
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| 227 | |
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| 228 | { |
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| 229 | std::set<Node> left_set, right_set; |
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| 230 | |
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| 231 | Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))]; |
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| 232 | left_set.insert(left); |
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| 233 | |
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| 234 | Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))]; |
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| 235 | right_set.insert(right); |
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| 236 | |
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| 237 | while (true) { |
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| 238 | if ((*_matching)[left] == INVALID) break; |
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| 239 | left = _graph.target((*_matching)[left]); |
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| 240 | left = (*_blossom_rep)[_blossom_set-> |
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| 241 | find(_graph.target((*_ear)[left]))]; |
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| 242 | if (right_set.find(left) != right_set.end()) { |
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| 243 | nca = left; |
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| 244 | break; |
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| 245 | } |
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| 246 | left_set.insert(left); |
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| 247 | |
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| 248 | if ((*_matching)[right] == INVALID) break; |
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| 249 | right = _graph.target((*_matching)[right]); |
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| 250 | right = (*_blossom_rep)[_blossom_set-> |
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| 251 | find(_graph.target((*_ear)[right]))]; |
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| 252 | if (left_set.find(right) != left_set.end()) { |
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| 253 | nca = right; |
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| 254 | break; |
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| 255 | } |
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| 256 | right_set.insert(right); |
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| 257 | } |
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| 258 | |
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| 259 | if (nca == INVALID) { |
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| 260 | if ((*_matching)[left] == INVALID) { |
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| 261 | nca = right; |
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| 262 | while (left_set.find(nca) == left_set.end()) { |
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| 263 | nca = _graph.target((*_matching)[nca]); |
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| 264 | nca =(*_blossom_rep)[_blossom_set-> |
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| 265 | find(_graph.target((*_ear)[nca]))]; |
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| 266 | } |
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| 267 | } else { |
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| 268 | nca = left; |
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| 269 | while (right_set.find(nca) == right_set.end()) { |
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| 270 | nca = _graph.target((*_matching)[nca]); |
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| 271 | nca = (*_blossom_rep)[_blossom_set-> |
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| 272 | find(_graph.target((*_ear)[nca]))]; |
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| 273 | } |
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| 274 | } |
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| 275 | } |
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| 276 | } |
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| 277 | |
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| 278 | { |
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| 279 | |
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| 280 | Node node = _graph.u(e); |
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| 281 | Arc arc = _graph.direct(e, true); |
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| 282 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 283 | |
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| 284 | while (base != nca) { |
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| 285 | _ear->set(node, arc); |
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| 286 | |
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| 287 | Node n = node; |
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| 288 | while (n != base) { |
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| 289 | n = _graph.target((*_matching)[n]); |
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| 290 | Arc a = (*_ear)[n]; |
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| 291 | n = _graph.target(a); |
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| 292 | _ear->set(n, _graph.oppositeArc(a)); |
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| 293 | } |
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| 294 | node = _graph.target((*_matching)[base]); |
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| 295 | _tree_set->erase(base); |
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| 296 | _tree_set->erase(node); |
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| 297 | _blossom_set->insert(node, _blossom_set->find(base)); |
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| 298 | _status->set(node, EVEN); |
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| 299 | _node_queue[_last++] = node; |
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| 300 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 301 | node = _graph.target((*_ear)[node]); |
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| 302 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 303 | _blossom_set->join(_graph.target(arc), base); |
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| 304 | } |
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| 305 | } |
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| 306 | |
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| 307 | _blossom_rep->set(_blossom_set->find(nca), nca); |
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| 308 | |
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| 309 | { |
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| 310 | |
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| 311 | Node node = _graph.v(e); |
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| 312 | Arc arc = _graph.direct(e, false); |
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| 313 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 314 | |
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| 315 | while (base != nca) { |
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| 316 | _ear->set(node, arc); |
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| 317 | |
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| 318 | Node n = node; |
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| 319 | while (n != base) { |
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| 320 | n = _graph.target((*_matching)[n]); |
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| 321 | Arc a = (*_ear)[n]; |
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| 322 | n = _graph.target(a); |
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| 323 | _ear->set(n, _graph.oppositeArc(a)); |
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| 324 | } |
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| 325 | node = _graph.target((*_matching)[base]); |
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| 326 | _tree_set->erase(base); |
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| 327 | _tree_set->erase(node); |
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| 328 | _blossom_set->insert(node, _blossom_set->find(base)); |
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| 329 | _status->set(node, EVEN); |
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| 330 | _node_queue[_last++] = node; |
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| 331 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 332 | node = _graph.target((*_ear)[node]); |
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| 333 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 334 | _blossom_set->join(_graph.target(arc), base); |
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| 335 | } |
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| 336 | } |
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| 337 | |
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| 338 | _blossom_rep->set(_blossom_set->find(nca), nca); |
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| 339 | } |
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| 340 | |
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| 341 | |
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| 342 | |
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| 343 | void extendOnArc(const Arc& a) { |
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| 344 | Node base = _graph.source(a); |
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| 345 | Node odd = _graph.target(a); |
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| 346 | |
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| 347 | _ear->set(odd, _graph.oppositeArc(a)); |
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| 348 | Node even = _graph.target((*_matching)[odd]); |
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| 349 | _blossom_rep->set(_blossom_set->insert(even), even); |
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| 350 | _status->set(odd, ODD); |
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| 351 | _status->set(even, EVEN); |
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| 352 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]); |
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| 353 | _tree_set->insert(odd, tree); |
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| 354 | _tree_set->insert(even, tree); |
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| 355 | _node_queue[_last++] = even; |
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| 356 | |
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| 357 | } |
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| 358 | |
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| 359 | void augmentOnArc(const Arc& a) { |
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| 360 | Node even = _graph.source(a); |
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| 361 | Node odd = _graph.target(a); |
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| 362 | |
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| 363 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]); |
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| 364 | |
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| 365 | _matching->set(odd, _graph.oppositeArc(a)); |
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| 366 | _status->set(odd, MATCHED); |
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| 367 | |
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| 368 | Arc arc = (*_matching)[even]; |
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| 369 | _matching->set(even, a); |
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| 370 | |
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| 371 | while (arc != INVALID) { |
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| 372 | odd = _graph.target(arc); |
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| 373 | arc = (*_ear)[odd]; |
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| 374 | even = _graph.target(arc); |
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| 375 | _matching->set(odd, arc); |
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| 376 | arc = (*_matching)[even]; |
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| 377 | _matching->set(even, _graph.oppositeArc((*_matching)[odd])); |
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| 378 | } |
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| 379 | |
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| 380 | for (typename TreeSet::ItemIt it(*_tree_set, tree); |
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| 381 | it != INVALID; ++it) { |
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| 382 | if ((*_status)[it] == ODD) { |
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| 383 | _status->set(it, MATCHED); |
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| 384 | } else { |
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| 385 | int blossom = _blossom_set->find(it); |
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| 386 | for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom); |
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| 387 | jt != INVALID; ++jt) { |
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| 388 | _status->set(jt, MATCHED); |
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| 389 | } |
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| 390 | _blossom_set->eraseClass(blossom); |
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| 391 | } |
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| 392 | } |
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| 393 | _tree_set->eraseClass(tree); |
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| 394 | |
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| 395 | } |
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[338] | 396 | |
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| 397 | public: |
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| 398 | |
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[339] | 399 | /// \brief Constructor |
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[338] | 400 | /// |
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[339] | 401 | /// Constructor. |
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| 402 | MaxMatching(const Graph& graph) |
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| 403 | : _graph(graph), _matching(0), _status(0), _ear(0), |
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| 404 | _blossom_set_index(0), _blossom_set(0), _blossom_rep(0), |
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| 405 | _tree_set_index(0), _tree_set(0) {} |
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| 406 | |
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| 407 | ~MaxMatching() { |
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| 408 | destroyStructures(); |
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| 409 | } |
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| 410 | |
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| 411 | /// \name Execution control |
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[342] | 412 | /// The simplest way to execute the algorithm is to use the |
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[339] | 413 | /// \c run() member function. |
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| 414 | /// \n |
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| 415 | |
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[342] | 416 | /// If you need better control on the execution, you must call |
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[339] | 417 | /// \ref init(), \ref greedyInit() or \ref matchingInit() |
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[342] | 418 | /// functions first, then you can start the algorithm with the \ref |
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[444] | 419 | /// startSparse() or startDense() functions. |
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[339] | 420 | |
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| 421 | ///@{ |
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| 422 | |
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| 423 | /// \brief Sets the actual matching to the empty matching. |
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[338] | 424 | /// |
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[339] | 425 | /// Sets the actual matching to the empty matching. |
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[338] | 426 | /// |
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| 427 | void init() { |
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[339] | 428 | createStructures(); |
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| 429 | for(NodeIt n(_graph); n != INVALID; ++n) { |
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| 430 | _matching->set(n, INVALID); |
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| 431 | _status->set(n, UNMATCHED); |
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[338] | 432 | } |
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| 433 | } |
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| 434 | |
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[342] | 435 | ///\brief Finds an initial matching in a greedy way |
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[338] | 436 | /// |
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[342] | 437 | ///It finds an initial matching in a greedy way. |
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[338] | 438 | void greedyInit() { |
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[339] | 439 | createStructures(); |
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| 440 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 441 | _matching->set(n, INVALID); |
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| 442 | _status->set(n, UNMATCHED); |
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[338] | 443 | } |
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[339] | 444 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 445 | if ((*_matching)[n] == INVALID) { |
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| 446 | for (OutArcIt a(_graph, n); a != INVALID ; ++a) { |
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| 447 | Node v = _graph.target(a); |
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| 448 | if ((*_matching)[v] == INVALID && v != n) { |
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| 449 | _matching->set(n, a); |
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| 450 | _status->set(n, MATCHED); |
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| 451 | _matching->set(v, _graph.oppositeArc(a)); |
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| 452 | _status->set(v, MATCHED); |
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[338] | 453 | break; |
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| 454 | } |
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| 455 | } |
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| 456 | } |
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| 457 | } |
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| 458 | } |
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| 459 | |
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[339] | 460 | |
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[342] | 461 | /// \brief Initialize the matching from a map containing. |
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[338] | 462 | /// |
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[339] | 463 | /// Initialize the matching from a \c bool valued \c Edge map. This |
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| 464 | /// map must have the property that there are no two incident edges |
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| 465 | /// with true value, ie. it contains a matching. |
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| 466 | /// \return %True if the map contains a matching. |
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| 467 | template <typename MatchingMap> |
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| 468 | bool matchingInit(const MatchingMap& matching) { |
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| 469 | createStructures(); |
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| 470 | |
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| 471 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 472 | _matching->set(n, INVALID); |
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| 473 | _status->set(n, UNMATCHED); |
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[338] | 474 | } |
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[339] | 475 | for(EdgeIt e(_graph); e!=INVALID; ++e) { |
---|
| 476 | if (matching[e]) { |
---|
| 477 | |
---|
| 478 | Node u = _graph.u(e); |
---|
| 479 | if ((*_matching)[u] != INVALID) return false; |
---|
| 480 | _matching->set(u, _graph.direct(e, true)); |
---|
| 481 | _status->set(u, MATCHED); |
---|
| 482 | |
---|
| 483 | Node v = _graph.v(e); |
---|
| 484 | if ((*_matching)[v] != INVALID) return false; |
---|
| 485 | _matching->set(v, _graph.direct(e, false)); |
---|
| 486 | _status->set(v, MATCHED); |
---|
| 487 | } |
---|
| 488 | } |
---|
| 489 | return true; |
---|
[338] | 490 | } |
---|
| 491 | |
---|
[339] | 492 | /// \brief Starts Edmonds' algorithm |
---|
[338] | 493 | /// |
---|
[339] | 494 | /// If runs the original Edmonds' algorithm. |
---|
| 495 | void startSparse() { |
---|
| 496 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 497 | if ((*_status)[n] == UNMATCHED) { |
---|
| 498 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 499 | _tree_set->insert(n); |
---|
| 500 | _status->set(n, EVEN); |
---|
| 501 | processSparse(n); |
---|
[338] | 502 | } |
---|
| 503 | } |
---|
| 504 | } |
---|
| 505 | |
---|
[339] | 506 | /// \brief Starts Edmonds' algorithm. |
---|
[338] | 507 | /// |
---|
[339] | 508 | /// It runs Edmonds' algorithm with a heuristic of postponing |
---|
[342] | 509 | /// shrinks, therefore resulting in a faster algorithm for dense graphs. |
---|
[339] | 510 | void startDense() { |
---|
| 511 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 512 | if ((*_status)[n] == UNMATCHED) { |
---|
| 513 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 514 | _tree_set->insert(n); |
---|
| 515 | _status->set(n, EVEN); |
---|
| 516 | processDense(n); |
---|
| 517 | } |
---|
| 518 | } |
---|
| 519 | } |
---|
| 520 | |
---|
| 521 | |
---|
| 522 | /// \brief Runs Edmonds' algorithm |
---|
| 523 | /// |
---|
| 524 | /// Runs Edmonds' algorithm for sparse graphs (<tt>m<2*n</tt>) |
---|
| 525 | /// or Edmonds' algorithm with a heuristic of |
---|
| 526 | /// postponing shrinks for dense graphs. |
---|
[338] | 527 | void run() { |
---|
[339] | 528 | if (countEdges(_graph) < 2 * countNodes(_graph)) { |
---|
[338] | 529 | greedyInit(); |
---|
| 530 | startSparse(); |
---|
| 531 | } else { |
---|
| 532 | init(); |
---|
| 533 | startDense(); |
---|
| 534 | } |
---|
| 535 | } |
---|
| 536 | |
---|
[339] | 537 | /// @} |
---|
| 538 | |
---|
| 539 | /// \name Primal solution |
---|
[342] | 540 | /// Functions to get the primal solution, ie. the matching. |
---|
[339] | 541 | |
---|
| 542 | /// @{ |
---|
[338] | 543 | |
---|
[342] | 544 | ///\brief Returns the size of the current matching. |
---|
[338] | 545 | /// |
---|
[342] | 546 | ///Returns the size of the current matching. After \ref |
---|
[339] | 547 | ///run() it returns the size of the maximum matching in the graph. |
---|
| 548 | int matchingSize() const { |
---|
| 549 | int size = 0; |
---|
| 550 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 551 | if ((*_matching)[n] != INVALID) { |
---|
| 552 | ++size; |
---|
[338] | 553 | } |
---|
| 554 | } |
---|
[339] | 555 | return size / 2; |
---|
[338] | 556 | } |
---|
| 557 | |
---|
[339] | 558 | /// \brief Returns true when the edge is in the matching. |
---|
| 559 | /// |
---|
| 560 | /// Returns true when the edge is in the matching. |
---|
| 561 | bool matching(const Edge& edge) const { |
---|
| 562 | return edge == (*_matching)[_graph.u(edge)]; |
---|
| 563 | } |
---|
| 564 | |
---|
| 565 | /// \brief Returns the matching edge incident to the given node. |
---|
| 566 | /// |
---|
| 567 | /// Returns the matching edge of a \c node in the actual matching or |
---|
| 568 | /// INVALID if the \c node is not covered by the actual matching. |
---|
| 569 | Arc matching(const Node& n) const { |
---|
| 570 | return (*_matching)[n]; |
---|
| 571 | } |
---|
[338] | 572 | |
---|
| 573 | ///\brief Returns the mate of a node in the actual matching. |
---|
| 574 | /// |
---|
[339] | 575 | ///Returns the mate of a \c node in the actual matching or |
---|
| 576 | ///INVALID if the \c node is not covered by the actual matching. |
---|
| 577 | Node mate(const Node& n) const { |
---|
| 578 | return (*_matching)[n] != INVALID ? |
---|
| 579 | _graph.target((*_matching)[n]) : INVALID; |
---|
[338] | 580 | } |
---|
| 581 | |
---|
[339] | 582 | /// @} |
---|
| 583 | |
---|
| 584 | /// \name Dual solution |
---|
[342] | 585 | /// Functions to get the dual solution, ie. the decomposition. |
---|
[339] | 586 | |
---|
| 587 | /// @{ |
---|
[338] | 588 | |
---|
| 589 | /// \brief Returns the class of the node in the Edmonds-Gallai |
---|
| 590 | /// decomposition. |
---|
| 591 | /// |
---|
| 592 | /// Returns the class of the node in the Edmonds-Gallai |
---|
| 593 | /// decomposition. |
---|
[339] | 594 | Status decomposition(const Node& n) const { |
---|
| 595 | return (*_status)[n]; |
---|
[338] | 596 | } |
---|
| 597 | |
---|
| 598 | /// \brief Returns true when the node is in the barrier. |
---|
| 599 | /// |
---|
| 600 | /// Returns true when the node is in the barrier. |
---|
[339] | 601 | bool barrier(const Node& n) const { |
---|
| 602 | return (*_status)[n] == ODD; |
---|
[338] | 603 | } |
---|
| 604 | |
---|
[339] | 605 | /// @} |
---|
[338] | 606 | |
---|
| 607 | }; |
---|
| 608 | |
---|
| 609 | /// \ingroup matching |
---|
| 610 | /// |
---|
| 611 | /// \brief Weighted matching in general graphs |
---|
| 612 | /// |
---|
| 613 | /// This class provides an efficient implementation of Edmond's |
---|
| 614 | /// maximum weighted matching algorithm. The implementation is based |
---|
| 615 | /// on extensive use of priority queues and provides |
---|
| 616 | /// \f$O(nm\log(n))\f$ time complexity. |
---|
| 617 | /// |
---|
| 618 | /// The maximum weighted matching problem is to find undirected |
---|
[339] | 619 | /// edges in the graph with maximum overall weight and no two of |
---|
| 620 | /// them shares their ends. The problem can be formulated with the |
---|
| 621 | /// following linear program. |
---|
[338] | 622 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
[339] | 623 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 624 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[338] | 625 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 626 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[339] | 627 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 628 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 629 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 630 | /// subsets of the nodes. |
---|
[338] | 631 | /// |
---|
| 632 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 633 | /// optimality. The solution of the dual problem can be used to check |
---|
[339] | 634 | /// the result of the algorithm. The dual linear problem is the |
---|
| 635 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)} |
---|
| 636 | z_B \ge w_{uv} \quad \forall uv\in E\f] */ |
---|
[338] | 637 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
| 638 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[339] | 639 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 640 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[338] | 641 | /// |
---|
| 642 | /// The algorithm can be executed with \c run() or the \c init() and |
---|
| 643 | /// then the \c start() member functions. After it the matching can |
---|
| 644 | /// be asked with \c matching() or mate() functions. The dual |
---|
| 645 | /// solution can be get with \c nodeValue(), \c blossomNum() and \c |
---|
| 646 | /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt |
---|
[342] | 647 | /// "BlossomIt" nested class, which is able to iterate on the nodes |
---|
[338] | 648 | /// of a blossom. If the value type is integral then the dual |
---|
| 649 | /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4". |
---|
| 650 | template <typename _Graph, |
---|
| 651 | typename _WeightMap = typename _Graph::template EdgeMap<int> > |
---|
| 652 | class MaxWeightedMatching { |
---|
| 653 | public: |
---|
| 654 | |
---|
| 655 | typedef _Graph Graph; |
---|
| 656 | typedef _WeightMap WeightMap; |
---|
| 657 | typedef typename WeightMap::Value Value; |
---|
| 658 | |
---|
| 659 | /// \brief Scaling factor for dual solution |
---|
| 660 | /// |
---|
| 661 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 662 | /// according to the value type. |
---|
| 663 | static const int dualScale = |
---|
| 664 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 665 | |
---|
| 666 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 667 | MatchingMap; |
---|
| 668 | |
---|
| 669 | private: |
---|
| 670 | |
---|
| 671 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 672 | |
---|
| 673 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 674 | typedef std::vector<Node> BlossomNodeList; |
---|
| 675 | |
---|
| 676 | struct BlossomVariable { |
---|
| 677 | int begin, end; |
---|
| 678 | Value value; |
---|
| 679 | |
---|
| 680 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 681 | : begin(_begin), end(_end), value(_value) {} |
---|
| 682 | |
---|
| 683 | }; |
---|
| 684 | |
---|
| 685 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 686 | |
---|
| 687 | const Graph& _graph; |
---|
| 688 | const WeightMap& _weight; |
---|
| 689 | |
---|
| 690 | MatchingMap* _matching; |
---|
| 691 | |
---|
| 692 | NodePotential* _node_potential; |
---|
| 693 | |
---|
| 694 | BlossomPotential _blossom_potential; |
---|
| 695 | BlossomNodeList _blossom_node_list; |
---|
| 696 | |
---|
| 697 | int _node_num; |
---|
| 698 | int _blossom_num; |
---|
| 699 | |
---|
| 700 | typedef RangeMap<int> IntIntMap; |
---|
| 701 | |
---|
| 702 | enum Status { |
---|
| 703 | EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2 |
---|
| 704 | }; |
---|
| 705 | |
---|
[339] | 706 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[338] | 707 | struct BlossomData { |
---|
| 708 | int tree; |
---|
| 709 | Status status; |
---|
| 710 | Arc pred, next; |
---|
| 711 | Value pot, offset; |
---|
| 712 | Node base; |
---|
| 713 | }; |
---|
| 714 | |
---|
[339] | 715 | IntNodeMap *_blossom_index; |
---|
[338] | 716 | BlossomSet *_blossom_set; |
---|
| 717 | RangeMap<BlossomData>* _blossom_data; |
---|
| 718 | |
---|
[339] | 719 | IntNodeMap *_node_index; |
---|
| 720 | IntArcMap *_node_heap_index; |
---|
[338] | 721 | |
---|
| 722 | struct NodeData { |
---|
| 723 | |
---|
[339] | 724 | NodeData(IntArcMap& node_heap_index) |
---|
[338] | 725 | : heap(node_heap_index) {} |
---|
| 726 | |
---|
| 727 | int blossom; |
---|
| 728 | Value pot; |
---|
[339] | 729 | BinHeap<Value, IntArcMap> heap; |
---|
[338] | 730 | std::map<int, Arc> heap_index; |
---|
| 731 | |
---|
| 732 | int tree; |
---|
| 733 | }; |
---|
| 734 | |
---|
| 735 | RangeMap<NodeData>* _node_data; |
---|
| 736 | |
---|
| 737 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 738 | |
---|
| 739 | IntIntMap *_tree_set_index; |
---|
| 740 | TreeSet *_tree_set; |
---|
| 741 | |
---|
[339] | 742 | IntNodeMap *_delta1_index; |
---|
| 743 | BinHeap<Value, IntNodeMap> *_delta1; |
---|
[338] | 744 | |
---|
| 745 | IntIntMap *_delta2_index; |
---|
| 746 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 747 | |
---|
[339] | 748 | IntEdgeMap *_delta3_index; |
---|
| 749 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[338] | 750 | |
---|
| 751 | IntIntMap *_delta4_index; |
---|
| 752 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 753 | |
---|
| 754 | Value _delta_sum; |
---|
| 755 | |
---|
| 756 | void createStructures() { |
---|
| 757 | _node_num = countNodes(_graph); |
---|
| 758 | _blossom_num = _node_num * 3 / 2; |
---|
| 759 | |
---|
| 760 | if (!_matching) { |
---|
| 761 | _matching = new MatchingMap(_graph); |
---|
| 762 | } |
---|
| 763 | if (!_node_potential) { |
---|
| 764 | _node_potential = new NodePotential(_graph); |
---|
| 765 | } |
---|
| 766 | if (!_blossom_set) { |
---|
[339] | 767 | _blossom_index = new IntNodeMap(_graph); |
---|
[338] | 768 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 769 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
| 770 | } |
---|
| 771 | |
---|
| 772 | if (!_node_index) { |
---|
[339] | 773 | _node_index = new IntNodeMap(_graph); |
---|
| 774 | _node_heap_index = new IntArcMap(_graph); |
---|
[338] | 775 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
| 776 | NodeData(*_node_heap_index)); |
---|
| 777 | } |
---|
| 778 | |
---|
| 779 | if (!_tree_set) { |
---|
| 780 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 781 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 782 | } |
---|
| 783 | if (!_delta1) { |
---|
[339] | 784 | _delta1_index = new IntNodeMap(_graph); |
---|
| 785 | _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index); |
---|
[338] | 786 | } |
---|
| 787 | if (!_delta2) { |
---|
| 788 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 789 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
| 790 | } |
---|
| 791 | if (!_delta3) { |
---|
[339] | 792 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 793 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[338] | 794 | } |
---|
| 795 | if (!_delta4) { |
---|
| 796 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 797 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
| 798 | } |
---|
| 799 | } |
---|
| 800 | |
---|
| 801 | void destroyStructures() { |
---|
| 802 | _node_num = countNodes(_graph); |
---|
| 803 | _blossom_num = _node_num * 3 / 2; |
---|
| 804 | |
---|
| 805 | if (_matching) { |
---|
| 806 | delete _matching; |
---|
| 807 | } |
---|
| 808 | if (_node_potential) { |
---|
| 809 | delete _node_potential; |
---|
| 810 | } |
---|
| 811 | if (_blossom_set) { |
---|
| 812 | delete _blossom_index; |
---|
| 813 | delete _blossom_set; |
---|
| 814 | delete _blossom_data; |
---|
| 815 | } |
---|
| 816 | |
---|
| 817 | if (_node_index) { |
---|
| 818 | delete _node_index; |
---|
| 819 | delete _node_heap_index; |
---|
| 820 | delete _node_data; |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | if (_tree_set) { |
---|
| 824 | delete _tree_set_index; |
---|
| 825 | delete _tree_set; |
---|
| 826 | } |
---|
| 827 | if (_delta1) { |
---|
| 828 | delete _delta1_index; |
---|
| 829 | delete _delta1; |
---|
| 830 | } |
---|
| 831 | if (_delta2) { |
---|
| 832 | delete _delta2_index; |
---|
| 833 | delete _delta2; |
---|
| 834 | } |
---|
| 835 | if (_delta3) { |
---|
| 836 | delete _delta3_index; |
---|
| 837 | delete _delta3; |
---|
| 838 | } |
---|
| 839 | if (_delta4) { |
---|
| 840 | delete _delta4_index; |
---|
| 841 | delete _delta4; |
---|
| 842 | } |
---|
| 843 | } |
---|
| 844 | |
---|
| 845 | void matchedToEven(int blossom, int tree) { |
---|
| 846 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 847 | _delta2->erase(blossom); |
---|
| 848 | } |
---|
| 849 | |
---|
| 850 | if (!_blossom_set->trivial(blossom)) { |
---|
| 851 | (*_blossom_data)[blossom].pot -= |
---|
| 852 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 853 | } |
---|
| 854 | |
---|
| 855 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 856 | n != INVALID; ++n) { |
---|
| 857 | |
---|
| 858 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 859 | int ni = (*_node_index)[n]; |
---|
| 860 | |
---|
| 861 | (*_node_data)[ni].heap.clear(); |
---|
| 862 | (*_node_data)[ni].heap_index.clear(); |
---|
| 863 | |
---|
| 864 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 865 | |
---|
| 866 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 867 | |
---|
| 868 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 869 | Node v = _graph.source(e); |
---|
| 870 | int vb = _blossom_set->find(v); |
---|
| 871 | int vi = (*_node_index)[v]; |
---|
| 872 | |
---|
| 873 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 874 | dualScale * _weight[e]; |
---|
| 875 | |
---|
| 876 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 877 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 878 | _delta3->push(e, rw / 2); |
---|
| 879 | } |
---|
| 880 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 881 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 882 | _delta3->push(e, rw); |
---|
| 883 | } |
---|
| 884 | } else { |
---|
| 885 | typename std::map<int, Arc>::iterator it = |
---|
| 886 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 887 | |
---|
| 888 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 889 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 890 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 891 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 892 | it->second = e; |
---|
| 893 | } |
---|
| 894 | } else { |
---|
| 895 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 896 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 897 | } |
---|
| 898 | |
---|
| 899 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 900 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 901 | |
---|
| 902 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 903 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 904 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 905 | (*_blossom_data)[vb].offset); |
---|
| 906 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 907 | (*_blossom_data)[vb].offset){ |
---|
| 908 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 909 | (*_blossom_data)[vb].offset); |
---|
| 910 | } |
---|
| 911 | } |
---|
| 912 | } |
---|
| 913 | } |
---|
| 914 | } |
---|
| 915 | } |
---|
| 916 | (*_blossom_data)[blossom].offset = 0; |
---|
| 917 | } |
---|
| 918 | |
---|
| 919 | void matchedToOdd(int blossom) { |
---|
| 920 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 921 | _delta2->erase(blossom); |
---|
| 922 | } |
---|
| 923 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 924 | if (!_blossom_set->trivial(blossom)) { |
---|
| 925 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 926 | (*_blossom_data)[blossom].offset); |
---|
| 927 | } |
---|
| 928 | } |
---|
| 929 | |
---|
| 930 | void evenToMatched(int blossom, int tree) { |
---|
| 931 | if (!_blossom_set->trivial(blossom)) { |
---|
| 932 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 933 | } |
---|
| 934 | |
---|
| 935 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 936 | n != INVALID; ++n) { |
---|
| 937 | int ni = (*_node_index)[n]; |
---|
| 938 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 939 | |
---|
| 940 | _delta1->erase(n); |
---|
| 941 | |
---|
| 942 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 943 | Node v = _graph.source(e); |
---|
| 944 | int vb = _blossom_set->find(v); |
---|
| 945 | int vi = (*_node_index)[v]; |
---|
| 946 | |
---|
| 947 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 948 | dualScale * _weight[e]; |
---|
| 949 | |
---|
| 950 | if (vb == blossom) { |
---|
| 951 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 952 | _delta3->erase(e); |
---|
| 953 | } |
---|
| 954 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 955 | |
---|
| 956 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 957 | _delta3->erase(e); |
---|
| 958 | } |
---|
| 959 | |
---|
| 960 | int vt = _tree_set->find(vb); |
---|
| 961 | |
---|
| 962 | if (vt != tree) { |
---|
| 963 | |
---|
| 964 | Arc r = _graph.oppositeArc(e); |
---|
| 965 | |
---|
| 966 | typename std::map<int, Arc>::iterator it = |
---|
| 967 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 968 | |
---|
| 969 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 970 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 971 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 972 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 973 | it->second = r; |
---|
| 974 | } |
---|
| 975 | } else { |
---|
| 976 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 977 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 978 | } |
---|
| 979 | |
---|
| 980 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 981 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 982 | |
---|
| 983 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 984 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 985 | (*_blossom_data)[blossom].offset); |
---|
| 986 | } else if ((*_delta2)[blossom] > |
---|
| 987 | _blossom_set->classPrio(blossom) - |
---|
| 988 | (*_blossom_data)[blossom].offset){ |
---|
| 989 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 990 | (*_blossom_data)[blossom].offset); |
---|
| 991 | } |
---|
| 992 | } |
---|
| 993 | } |
---|
| 994 | |
---|
| 995 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 996 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 997 | _delta3->erase(e); |
---|
| 998 | } |
---|
| 999 | } else { |
---|
| 1000 | |
---|
| 1001 | typename std::map<int, Arc>::iterator it = |
---|
| 1002 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1003 | |
---|
| 1004 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1005 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 1006 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 1007 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 1008 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 1009 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 1010 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1014 | if (_blossom_set->classPrio(vb) == |
---|
| 1015 | std::numeric_limits<Value>::max()) { |
---|
| 1016 | _delta2->erase(vb); |
---|
| 1017 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 1018 | (*_blossom_data)[vb].offset) { |
---|
| 1019 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 1020 | (*_blossom_data)[vb].offset); |
---|
| 1021 | } |
---|
| 1022 | } |
---|
| 1023 | } |
---|
| 1024 | } |
---|
| 1025 | } |
---|
| 1026 | } |
---|
| 1027 | } |
---|
| 1028 | |
---|
| 1029 | void oddToMatched(int blossom) { |
---|
| 1030 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 1031 | |
---|
| 1032 | if (_blossom_set->classPrio(blossom) != |
---|
| 1033 | std::numeric_limits<Value>::max()) { |
---|
| 1034 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1035 | (*_blossom_data)[blossom].offset); |
---|
| 1036 | } |
---|
| 1037 | |
---|
| 1038 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1039 | _delta4->erase(blossom); |
---|
| 1040 | } |
---|
| 1041 | } |
---|
| 1042 | |
---|
| 1043 | void oddToEven(int blossom, int tree) { |
---|
| 1044 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1045 | _delta4->erase(blossom); |
---|
| 1046 | (*_blossom_data)[blossom].pot -= |
---|
| 1047 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 1048 | } |
---|
| 1049 | |
---|
| 1050 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1051 | n != INVALID; ++n) { |
---|
| 1052 | int ni = (*_node_index)[n]; |
---|
| 1053 | |
---|
| 1054 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1055 | |
---|
| 1056 | (*_node_data)[ni].heap.clear(); |
---|
| 1057 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1058 | (*_node_data)[ni].pot += |
---|
| 1059 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 1060 | |
---|
| 1061 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 1062 | |
---|
| 1063 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1064 | Node v = _graph.source(e); |
---|
| 1065 | int vb = _blossom_set->find(v); |
---|
| 1066 | int vi = (*_node_index)[v]; |
---|
| 1067 | |
---|
| 1068 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1069 | dualScale * _weight[e]; |
---|
| 1070 | |
---|
| 1071 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1072 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 1073 | _delta3->push(e, rw / 2); |
---|
| 1074 | } |
---|
| 1075 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1076 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 1077 | _delta3->push(e, rw); |
---|
| 1078 | } |
---|
| 1079 | } else { |
---|
| 1080 | |
---|
| 1081 | typename std::map<int, Arc>::iterator it = |
---|
| 1082 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1083 | |
---|
| 1084 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1085 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 1086 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 1087 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 1088 | it->second = e; |
---|
| 1089 | } |
---|
| 1090 | } else { |
---|
| 1091 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 1092 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 1093 | } |
---|
| 1094 | |
---|
| 1095 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 1096 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 1097 | |
---|
| 1098 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1099 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 1100 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 1101 | (*_blossom_data)[vb].offset); |
---|
| 1102 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 1103 | (*_blossom_data)[vb].offset) { |
---|
| 1104 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 1105 | (*_blossom_data)[vb].offset); |
---|
| 1106 | } |
---|
| 1107 | } |
---|
| 1108 | } |
---|
| 1109 | } |
---|
| 1110 | } |
---|
| 1111 | } |
---|
| 1112 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1113 | } |
---|
| 1114 | |
---|
| 1115 | |
---|
| 1116 | void matchedToUnmatched(int blossom) { |
---|
| 1117 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1118 | _delta2->erase(blossom); |
---|
| 1119 | } |
---|
| 1120 | |
---|
| 1121 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1122 | n != INVALID; ++n) { |
---|
| 1123 | int ni = (*_node_index)[n]; |
---|
| 1124 | |
---|
| 1125 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1126 | |
---|
| 1127 | (*_node_data)[ni].heap.clear(); |
---|
| 1128 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1129 | |
---|
| 1130 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1131 | Node v = _graph.target(e); |
---|
| 1132 | int vb = _blossom_set->find(v); |
---|
| 1133 | int vi = (*_node_index)[v]; |
---|
| 1134 | |
---|
| 1135 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1136 | dualScale * _weight[e]; |
---|
| 1137 | |
---|
| 1138 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1139 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 1140 | _delta3->push(e, rw); |
---|
| 1141 | } |
---|
| 1142 | } |
---|
| 1143 | } |
---|
| 1144 | } |
---|
| 1145 | } |
---|
| 1146 | |
---|
| 1147 | void unmatchedToMatched(int blossom) { |
---|
| 1148 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1149 | n != INVALID; ++n) { |
---|
| 1150 | int ni = (*_node_index)[n]; |
---|
| 1151 | |
---|
| 1152 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1153 | Node v = _graph.source(e); |
---|
| 1154 | int vb = _blossom_set->find(v); |
---|
| 1155 | int vi = (*_node_index)[v]; |
---|
| 1156 | |
---|
| 1157 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1158 | dualScale * _weight[e]; |
---|
| 1159 | |
---|
| 1160 | if (vb == blossom) { |
---|
| 1161 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1162 | _delta3->erase(e); |
---|
| 1163 | } |
---|
| 1164 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1165 | |
---|
| 1166 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1167 | _delta3->erase(e); |
---|
| 1168 | } |
---|
| 1169 | |
---|
| 1170 | int vt = _tree_set->find(vb); |
---|
| 1171 | |
---|
| 1172 | Arc r = _graph.oppositeArc(e); |
---|
| 1173 | |
---|
| 1174 | typename std::map<int, Arc>::iterator it = |
---|
| 1175 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1176 | |
---|
| 1177 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1178 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1179 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 1180 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 1181 | it->second = r; |
---|
| 1182 | } |
---|
| 1183 | } else { |
---|
| 1184 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 1185 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 1186 | } |
---|
| 1187 | |
---|
| 1188 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1189 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1190 | |
---|
| 1191 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1192 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1193 | (*_blossom_data)[blossom].offset); |
---|
| 1194 | } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)- |
---|
| 1195 | (*_blossom_data)[blossom].offset){ |
---|
| 1196 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1197 | (*_blossom_data)[blossom].offset); |
---|
| 1198 | } |
---|
| 1199 | } |
---|
| 1200 | |
---|
| 1201 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1202 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1203 | _delta3->erase(e); |
---|
| 1204 | } |
---|
| 1205 | } |
---|
| 1206 | } |
---|
| 1207 | } |
---|
| 1208 | } |
---|
| 1209 | |
---|
| 1210 | void alternatePath(int even, int tree) { |
---|
| 1211 | int odd; |
---|
| 1212 | |
---|
| 1213 | evenToMatched(even, tree); |
---|
| 1214 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1215 | |
---|
| 1216 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 1217 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 1218 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 1219 | oddToMatched(odd); |
---|
| 1220 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 1221 | |
---|
| 1222 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 1223 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1224 | evenToMatched(even, tree); |
---|
| 1225 | (*_blossom_data)[even].next = |
---|
| 1226 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 1227 | } |
---|
| 1228 | |
---|
| 1229 | } |
---|
| 1230 | |
---|
| 1231 | void destroyTree(int tree) { |
---|
| 1232 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 1233 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 1234 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1235 | evenToMatched(b, tree); |
---|
| 1236 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 1237 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1238 | oddToMatched(b); |
---|
| 1239 | } |
---|
| 1240 | } |
---|
| 1241 | _tree_set->eraseClass(tree); |
---|
| 1242 | } |
---|
| 1243 | |
---|
| 1244 | |
---|
| 1245 | void unmatchNode(const Node& node) { |
---|
| 1246 | int blossom = _blossom_set->find(node); |
---|
| 1247 | int tree = _tree_set->find(blossom); |
---|
| 1248 | |
---|
| 1249 | alternatePath(blossom, tree); |
---|
| 1250 | destroyTree(tree); |
---|
| 1251 | |
---|
| 1252 | (*_blossom_data)[blossom].status = UNMATCHED; |
---|
| 1253 | (*_blossom_data)[blossom].base = node; |
---|
| 1254 | matchedToUnmatched(blossom); |
---|
| 1255 | } |
---|
| 1256 | |
---|
| 1257 | |
---|
[339] | 1258 | void augmentOnEdge(const Edge& edge) { |
---|
| 1259 | |
---|
| 1260 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1261 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[338] | 1262 | |
---|
| 1263 | if ((*_blossom_data)[left].status == EVEN) { |
---|
| 1264 | int left_tree = _tree_set->find(left); |
---|
| 1265 | alternatePath(left, left_tree); |
---|
| 1266 | destroyTree(left_tree); |
---|
| 1267 | } else { |
---|
| 1268 | (*_blossom_data)[left].status = MATCHED; |
---|
| 1269 | unmatchedToMatched(left); |
---|
| 1270 | } |
---|
| 1271 | |
---|
| 1272 | if ((*_blossom_data)[right].status == EVEN) { |
---|
| 1273 | int right_tree = _tree_set->find(right); |
---|
| 1274 | alternatePath(right, right_tree); |
---|
| 1275 | destroyTree(right_tree); |
---|
| 1276 | } else { |
---|
| 1277 | (*_blossom_data)[right].status = MATCHED; |
---|
| 1278 | unmatchedToMatched(right); |
---|
| 1279 | } |
---|
| 1280 | |
---|
[339] | 1281 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 1282 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[338] | 1283 | } |
---|
| 1284 | |
---|
| 1285 | void extendOnArc(const Arc& arc) { |
---|
| 1286 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 1287 | int tree = _tree_set->find(base); |
---|
| 1288 | |
---|
| 1289 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 1290 | _tree_set->insert(odd, tree); |
---|
| 1291 | (*_blossom_data)[odd].status = ODD; |
---|
| 1292 | matchedToOdd(odd); |
---|
| 1293 | (*_blossom_data)[odd].pred = arc; |
---|
| 1294 | |
---|
| 1295 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 1296 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 1297 | _tree_set->insert(even, tree); |
---|
| 1298 | (*_blossom_data)[even].status = EVEN; |
---|
| 1299 | matchedToEven(even, tree); |
---|
| 1300 | } |
---|
| 1301 | |
---|
[339] | 1302 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[338] | 1303 | int nca = -1; |
---|
| 1304 | std::vector<int> left_path, right_path; |
---|
| 1305 | |
---|
| 1306 | { |
---|
| 1307 | std::set<int> left_set, right_set; |
---|
| 1308 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1309 | left_path.push_back(left); |
---|
| 1310 | left_set.insert(left); |
---|
| 1311 | |
---|
| 1312 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 1313 | right_path.push_back(right); |
---|
| 1314 | right_set.insert(right); |
---|
| 1315 | |
---|
| 1316 | while (true) { |
---|
| 1317 | |
---|
| 1318 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 1319 | |
---|
| 1320 | left = |
---|
| 1321 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1322 | left_path.push_back(left); |
---|
| 1323 | left = |
---|
| 1324 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1325 | left_path.push_back(left); |
---|
| 1326 | |
---|
| 1327 | left_set.insert(left); |
---|
| 1328 | |
---|
| 1329 | if (right_set.find(left) != right_set.end()) { |
---|
| 1330 | nca = left; |
---|
| 1331 | break; |
---|
| 1332 | } |
---|
| 1333 | |
---|
| 1334 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 1335 | |
---|
| 1336 | right = |
---|
| 1337 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1338 | right_path.push_back(right); |
---|
| 1339 | right = |
---|
| 1340 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1341 | right_path.push_back(right); |
---|
| 1342 | |
---|
| 1343 | right_set.insert(right); |
---|
| 1344 | |
---|
| 1345 | if (left_set.find(right) != left_set.end()) { |
---|
| 1346 | nca = right; |
---|
| 1347 | break; |
---|
| 1348 | } |
---|
| 1349 | |
---|
| 1350 | } |
---|
| 1351 | |
---|
| 1352 | if (nca == -1) { |
---|
| 1353 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 1354 | nca = right; |
---|
| 1355 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1356 | nca = |
---|
| 1357 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1358 | right_path.push_back(nca); |
---|
| 1359 | nca = |
---|
| 1360 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1361 | right_path.push_back(nca); |
---|
| 1362 | } |
---|
| 1363 | } else { |
---|
| 1364 | nca = left; |
---|
| 1365 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1366 | nca = |
---|
| 1367 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1368 | left_path.push_back(nca); |
---|
| 1369 | nca = |
---|
| 1370 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1371 | left_path.push_back(nca); |
---|
| 1372 | } |
---|
| 1373 | } |
---|
| 1374 | } |
---|
| 1375 | } |
---|
| 1376 | |
---|
| 1377 | std::vector<int> subblossoms; |
---|
| 1378 | Arc prev; |
---|
| 1379 | |
---|
| 1380 | prev = _graph.direct(edge, true); |
---|
| 1381 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1382 | subblossoms.push_back(left_path[i]); |
---|
| 1383 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 1384 | _tree_set->erase(left_path[i]); |
---|
| 1385 | |
---|
| 1386 | subblossoms.push_back(left_path[i + 1]); |
---|
| 1387 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 1388 | oddToEven(left_path[i + 1], tree); |
---|
| 1389 | _tree_set->erase(left_path[i + 1]); |
---|
| 1390 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 1391 | } |
---|
| 1392 | |
---|
| 1393 | int k = 0; |
---|
| 1394 | while (right_path[k] != nca) ++k; |
---|
| 1395 | |
---|
| 1396 | subblossoms.push_back(nca); |
---|
| 1397 | (*_blossom_data)[nca].next = prev; |
---|
| 1398 | |
---|
| 1399 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 1400 | subblossoms.push_back(right_path[i + 1]); |
---|
| 1401 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 1402 | oddToEven(right_path[i + 1], tree); |
---|
| 1403 | _tree_set->erase(right_path[i + 1]); |
---|
| 1404 | |
---|
| 1405 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 1406 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 1407 | |
---|
| 1408 | subblossoms.push_back(right_path[i]); |
---|
| 1409 | _tree_set->erase(right_path[i]); |
---|
| 1410 | } |
---|
| 1411 | |
---|
| 1412 | int surface = |
---|
| 1413 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1414 | |
---|
| 1415 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1416 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1417 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 1418 | } |
---|
| 1419 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 1420 | } |
---|
| 1421 | |
---|
| 1422 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 1423 | (*_blossom_data)[surface].offset = 0; |
---|
| 1424 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1425 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 1426 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 1427 | |
---|
| 1428 | _tree_set->insert(surface, tree); |
---|
| 1429 | _tree_set->erase(nca); |
---|
| 1430 | } |
---|
| 1431 | |
---|
| 1432 | void splitBlossom(int blossom) { |
---|
| 1433 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 1434 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 1435 | |
---|
| 1436 | int tree = _tree_set->find(blossom); |
---|
| 1437 | |
---|
| 1438 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1439 | oddToMatched(blossom); |
---|
| 1440 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1441 | _delta2->erase(blossom); |
---|
| 1442 | } |
---|
| 1443 | |
---|
| 1444 | std::vector<int> subblossoms; |
---|
| 1445 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1446 | |
---|
| 1447 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 1448 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 1449 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 1450 | |
---|
| 1451 | int ib = -1, id = -1; |
---|
| 1452 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1453 | if (subblossoms[i] == b) ib = i; |
---|
| 1454 | if (subblossoms[i] == d) id = i; |
---|
| 1455 | |
---|
| 1456 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 1457 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1458 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 1459 | } |
---|
| 1460 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 1461 | std::numeric_limits<Value>::max()) { |
---|
| 1462 | _delta2->push(subblossoms[i], |
---|
| 1463 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 1464 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 1465 | } |
---|
| 1466 | } |
---|
| 1467 | |
---|
| 1468 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 1469 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 1470 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1471 | int sb = subblossoms[i]; |
---|
| 1472 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1473 | (*_blossom_data)[sb].next = |
---|
| 1474 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1475 | } |
---|
| 1476 | |
---|
| 1477 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1478 | int sb = subblossoms[i]; |
---|
| 1479 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1480 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1481 | |
---|
| 1482 | (*_blossom_data)[sb].status = ODD; |
---|
| 1483 | matchedToOdd(sb); |
---|
| 1484 | _tree_set->insert(sb, tree); |
---|
| 1485 | (*_blossom_data)[sb].pred = pred; |
---|
| 1486 | (*_blossom_data)[sb].next = |
---|
| 1487 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1488 | |
---|
| 1489 | pred = (*_blossom_data)[ub].next; |
---|
| 1490 | |
---|
| 1491 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1492 | matchedToEven(tb, tree); |
---|
| 1493 | _tree_set->insert(tb, tree); |
---|
| 1494 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 1495 | } |
---|
| 1496 | |
---|
| 1497 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 1498 | matchedToOdd(subblossoms[id]); |
---|
| 1499 | _tree_set->insert(subblossoms[id], tree); |
---|
| 1500 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 1501 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 1502 | |
---|
| 1503 | } else { |
---|
| 1504 | |
---|
| 1505 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 1506 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1507 | int sb = subblossoms[i]; |
---|
| 1508 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1509 | (*_blossom_data)[sb].next = |
---|
| 1510 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1511 | } |
---|
| 1512 | |
---|
| 1513 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1514 | int sb = subblossoms[i]; |
---|
| 1515 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1516 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1517 | |
---|
| 1518 | (*_blossom_data)[sb].status = ODD; |
---|
| 1519 | matchedToOdd(sb); |
---|
| 1520 | _tree_set->insert(sb, tree); |
---|
| 1521 | (*_blossom_data)[sb].next = next; |
---|
| 1522 | (*_blossom_data)[sb].pred = |
---|
| 1523 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1524 | |
---|
| 1525 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1526 | matchedToEven(tb, tree); |
---|
| 1527 | _tree_set->insert(tb, tree); |
---|
| 1528 | (*_blossom_data)[tb].pred = |
---|
| 1529 | (*_blossom_data)[tb].next = |
---|
| 1530 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 1531 | next = (*_blossom_data)[ub].next; |
---|
| 1532 | } |
---|
| 1533 | |
---|
| 1534 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 1535 | matchedToOdd(subblossoms[ib]); |
---|
| 1536 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 1537 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 1538 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 1539 | } |
---|
| 1540 | _tree_set->erase(blossom); |
---|
| 1541 | } |
---|
| 1542 | |
---|
| 1543 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 1544 | if (_blossom_set->trivial(blossom)) { |
---|
| 1545 | int bi = (*_node_index)[base]; |
---|
| 1546 | Value pot = (*_node_data)[bi].pot; |
---|
| 1547 | |
---|
| 1548 | _matching->set(base, matching); |
---|
| 1549 | _blossom_node_list.push_back(base); |
---|
| 1550 | _node_potential->set(base, pot); |
---|
| 1551 | } else { |
---|
| 1552 | |
---|
| 1553 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 1554 | int bn = _blossom_node_list.size(); |
---|
| 1555 | |
---|
| 1556 | std::vector<int> subblossoms; |
---|
| 1557 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1558 | int b = _blossom_set->find(base); |
---|
| 1559 | int ib = -1; |
---|
| 1560 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1561 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 1562 | } |
---|
| 1563 | |
---|
| 1564 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 1565 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 1566 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 1567 | |
---|
| 1568 | Arc m = (*_blossom_data)[tb].next; |
---|
| 1569 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 1570 | extractBlossom(tb, _graph.source(m), m); |
---|
| 1571 | } |
---|
| 1572 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 1573 | |
---|
| 1574 | int en = _blossom_node_list.size(); |
---|
| 1575 | |
---|
| 1576 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 1577 | } |
---|
| 1578 | } |
---|
| 1579 | |
---|
| 1580 | void extractMatching() { |
---|
| 1581 | std::vector<int> blossoms; |
---|
| 1582 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 1583 | blossoms.push_back(c); |
---|
| 1584 | } |
---|
| 1585 | |
---|
| 1586 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 1587 | if ((*_blossom_data)[blossoms[i]].status == MATCHED) { |
---|
| 1588 | |
---|
| 1589 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 1590 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 1591 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 1592 | n != INVALID; ++n) { |
---|
| 1593 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 1594 | } |
---|
| 1595 | |
---|
| 1596 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 1597 | Node base = _graph.source(matching); |
---|
| 1598 | extractBlossom(blossoms[i], base, matching); |
---|
| 1599 | } else { |
---|
| 1600 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
| 1601 | extractBlossom(blossoms[i], base, INVALID); |
---|
| 1602 | } |
---|
| 1603 | } |
---|
| 1604 | } |
---|
| 1605 | |
---|
| 1606 | public: |
---|
| 1607 | |
---|
| 1608 | /// \brief Constructor |
---|
| 1609 | /// |
---|
| 1610 | /// Constructor. |
---|
| 1611 | MaxWeightedMatching(const Graph& graph, const WeightMap& weight) |
---|
| 1612 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 1613 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 1614 | _node_num(0), _blossom_num(0), |
---|
| 1615 | |
---|
| 1616 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 1617 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 1618 | _tree_set_index(0), _tree_set(0), |
---|
| 1619 | |
---|
| 1620 | _delta1_index(0), _delta1(0), |
---|
| 1621 | _delta2_index(0), _delta2(0), |
---|
| 1622 | _delta3_index(0), _delta3(0), |
---|
| 1623 | _delta4_index(0), _delta4(0), |
---|
| 1624 | |
---|
| 1625 | _delta_sum() {} |
---|
| 1626 | |
---|
| 1627 | ~MaxWeightedMatching() { |
---|
| 1628 | destroyStructures(); |
---|
| 1629 | } |
---|
| 1630 | |
---|
| 1631 | /// \name Execution control |
---|
[342] | 1632 | /// The simplest way to execute the algorithm is to use the |
---|
[338] | 1633 | /// \c run() member function. |
---|
| 1634 | |
---|
| 1635 | ///@{ |
---|
| 1636 | |
---|
| 1637 | /// \brief Initialize the algorithm |
---|
| 1638 | /// |
---|
| 1639 | /// Initialize the algorithm |
---|
| 1640 | void init() { |
---|
| 1641 | createStructures(); |
---|
| 1642 | |
---|
| 1643 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[339] | 1644 | _node_heap_index->set(e, BinHeap<Value, IntArcMap>::PRE_HEAP); |
---|
[338] | 1645 | } |
---|
| 1646 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1647 | _delta1_index->set(n, _delta1->PRE_HEAP); |
---|
| 1648 | } |
---|
| 1649 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1650 | _delta3_index->set(e, _delta3->PRE_HEAP); |
---|
| 1651 | } |
---|
| 1652 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 1653 | _delta2_index->set(i, _delta2->PRE_HEAP); |
---|
| 1654 | _delta4_index->set(i, _delta4->PRE_HEAP); |
---|
| 1655 | } |
---|
| 1656 | |
---|
| 1657 | int index = 0; |
---|
| 1658 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1659 | Value max = 0; |
---|
| 1660 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1661 | if (_graph.target(e) == n) continue; |
---|
| 1662 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 1663 | max = (dualScale * _weight[e]) / 2; |
---|
| 1664 | } |
---|
| 1665 | } |
---|
| 1666 | _node_index->set(n, index); |
---|
| 1667 | (*_node_data)[index].pot = max; |
---|
| 1668 | _delta1->push(n, max); |
---|
| 1669 | int blossom = |
---|
| 1670 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1671 | |
---|
| 1672 | _tree_set->insert(blossom); |
---|
| 1673 | |
---|
| 1674 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 1675 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1676 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 1677 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1678 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1679 | ++index; |
---|
| 1680 | } |
---|
| 1681 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1682 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 1683 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 1684 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 1685 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1686 | dualScale * _weight[e]) / 2); |
---|
| 1687 | } |
---|
| 1688 | } |
---|
| 1689 | } |
---|
| 1690 | |
---|
| 1691 | /// \brief Starts the algorithm |
---|
| 1692 | /// |
---|
| 1693 | /// Starts the algorithm |
---|
| 1694 | void start() { |
---|
| 1695 | enum OpType { |
---|
| 1696 | D1, D2, D3, D4 |
---|
| 1697 | }; |
---|
| 1698 | |
---|
| 1699 | int unmatched = _node_num; |
---|
| 1700 | while (unmatched > 0) { |
---|
| 1701 | Value d1 = !_delta1->empty() ? |
---|
| 1702 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
| 1703 | |
---|
| 1704 | Value d2 = !_delta2->empty() ? |
---|
| 1705 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 1706 | |
---|
| 1707 | Value d3 = !_delta3->empty() ? |
---|
| 1708 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 1709 | |
---|
| 1710 | Value d4 = !_delta4->empty() ? |
---|
| 1711 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 1712 | |
---|
| 1713 | _delta_sum = d1; OpType ot = D1; |
---|
| 1714 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
| 1715 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
| 1716 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 1717 | |
---|
| 1718 | |
---|
| 1719 | switch (ot) { |
---|
| 1720 | case D1: |
---|
| 1721 | { |
---|
| 1722 | Node n = _delta1->top(); |
---|
| 1723 | unmatchNode(n); |
---|
| 1724 | --unmatched; |
---|
| 1725 | } |
---|
| 1726 | break; |
---|
| 1727 | case D2: |
---|
| 1728 | { |
---|
| 1729 | int blossom = _delta2->top(); |
---|
| 1730 | Node n = _blossom_set->classTop(blossom); |
---|
| 1731 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 1732 | extendOnArc(e); |
---|
| 1733 | } |
---|
| 1734 | break; |
---|
| 1735 | case D3: |
---|
| 1736 | { |
---|
| 1737 | Edge e = _delta3->top(); |
---|
| 1738 | |
---|
| 1739 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 1740 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 1741 | |
---|
| 1742 | if (left_blossom == right_blossom) { |
---|
| 1743 | _delta3->pop(); |
---|
| 1744 | } else { |
---|
| 1745 | int left_tree; |
---|
| 1746 | if ((*_blossom_data)[left_blossom].status == EVEN) { |
---|
| 1747 | left_tree = _tree_set->find(left_blossom); |
---|
| 1748 | } else { |
---|
| 1749 | left_tree = -1; |
---|
| 1750 | ++unmatched; |
---|
| 1751 | } |
---|
| 1752 | int right_tree; |
---|
| 1753 | if ((*_blossom_data)[right_blossom].status == EVEN) { |
---|
| 1754 | right_tree = _tree_set->find(right_blossom); |
---|
| 1755 | } else { |
---|
| 1756 | right_tree = -1; |
---|
| 1757 | ++unmatched; |
---|
| 1758 | } |
---|
| 1759 | |
---|
| 1760 | if (left_tree == right_tree) { |
---|
[339] | 1761 | shrinkOnEdge(e, left_tree); |
---|
[338] | 1762 | } else { |
---|
[339] | 1763 | augmentOnEdge(e); |
---|
[338] | 1764 | unmatched -= 2; |
---|
| 1765 | } |
---|
| 1766 | } |
---|
| 1767 | } break; |
---|
| 1768 | case D4: |
---|
| 1769 | splitBlossom(_delta4->top()); |
---|
| 1770 | break; |
---|
| 1771 | } |
---|
| 1772 | } |
---|
| 1773 | extractMatching(); |
---|
| 1774 | } |
---|
| 1775 | |
---|
| 1776 | /// \brief Runs %MaxWeightedMatching algorithm. |
---|
| 1777 | /// |
---|
| 1778 | /// This method runs the %MaxWeightedMatching algorithm. |
---|
| 1779 | /// |
---|
| 1780 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 1781 | /// \code |
---|
| 1782 | /// mwm.init(); |
---|
| 1783 | /// mwm.start(); |
---|
| 1784 | /// \endcode |
---|
| 1785 | void run() { |
---|
| 1786 | init(); |
---|
| 1787 | start(); |
---|
| 1788 | } |
---|
| 1789 | |
---|
| 1790 | /// @} |
---|
| 1791 | |
---|
| 1792 | /// \name Primal solution |
---|
[342] | 1793 | /// Functions to get the primal solution, ie. the matching. |
---|
[338] | 1794 | |
---|
| 1795 | /// @{ |
---|
| 1796 | |
---|
[342] | 1797 | /// \brief Returns the weight of the matching. |
---|
[338] | 1798 | /// |
---|
[342] | 1799 | /// Returns the weight of the matching. |
---|
[338] | 1800 | Value matchingValue() const { |
---|
| 1801 | Value sum = 0; |
---|
| 1802 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1803 | if ((*_matching)[n] != INVALID) { |
---|
| 1804 | sum += _weight[(*_matching)[n]]; |
---|
| 1805 | } |
---|
| 1806 | } |
---|
| 1807 | return sum /= 2; |
---|
| 1808 | } |
---|
| 1809 | |
---|
[339] | 1810 | /// \brief Returns the cardinality of the matching. |
---|
[338] | 1811 | /// |
---|
[339] | 1812 | /// Returns the cardinality of the matching. |
---|
| 1813 | int matchingSize() const { |
---|
| 1814 | int num = 0; |
---|
| 1815 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1816 | if ((*_matching)[n] != INVALID) { |
---|
| 1817 | ++num; |
---|
| 1818 | } |
---|
| 1819 | } |
---|
| 1820 | return num /= 2; |
---|
| 1821 | } |
---|
| 1822 | |
---|
| 1823 | /// \brief Returns true when the edge is in the matching. |
---|
| 1824 | /// |
---|
| 1825 | /// Returns true when the edge is in the matching. |
---|
| 1826 | bool matching(const Edge& edge) const { |
---|
| 1827 | return edge == (*_matching)[_graph.u(edge)]; |
---|
[338] | 1828 | } |
---|
| 1829 | |
---|
| 1830 | /// \brief Returns the incident matching arc. |
---|
| 1831 | /// |
---|
| 1832 | /// Returns the incident matching arc from given node. If the |
---|
| 1833 | /// node is not matched then it gives back \c INVALID. |
---|
| 1834 | Arc matching(const Node& node) const { |
---|
| 1835 | return (*_matching)[node]; |
---|
| 1836 | } |
---|
| 1837 | |
---|
| 1838 | /// \brief Returns the mate of the node. |
---|
| 1839 | /// |
---|
| 1840 | /// Returns the adjancent node in a mathcing arc. If the node is |
---|
| 1841 | /// not matched then it gives back \c INVALID. |
---|
| 1842 | Node mate(const Node& node) const { |
---|
| 1843 | return (*_matching)[node] != INVALID ? |
---|
| 1844 | _graph.target((*_matching)[node]) : INVALID; |
---|
| 1845 | } |
---|
| 1846 | |
---|
| 1847 | /// @} |
---|
| 1848 | |
---|
| 1849 | /// \name Dual solution |
---|
[342] | 1850 | /// Functions to get the dual solution. |
---|
[338] | 1851 | |
---|
| 1852 | /// @{ |
---|
| 1853 | |
---|
| 1854 | /// \brief Returns the value of the dual solution. |
---|
| 1855 | /// |
---|
| 1856 | /// Returns the value of the dual solution. It should be equal to |
---|
| 1857 | /// the primal value scaled by \ref dualScale "dual scale". |
---|
| 1858 | Value dualValue() const { |
---|
| 1859 | Value sum = 0; |
---|
| 1860 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1861 | sum += nodeValue(n); |
---|
| 1862 | } |
---|
| 1863 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 1864 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 1865 | } |
---|
| 1866 | return sum; |
---|
| 1867 | } |
---|
| 1868 | |
---|
| 1869 | /// \brief Returns the value of the node. |
---|
| 1870 | /// |
---|
| 1871 | /// Returns the the value of the node. |
---|
| 1872 | Value nodeValue(const Node& n) const { |
---|
| 1873 | return (*_node_potential)[n]; |
---|
| 1874 | } |
---|
| 1875 | |
---|
| 1876 | /// \brief Returns the number of the blossoms in the basis. |
---|
| 1877 | /// |
---|
| 1878 | /// Returns the number of the blossoms in the basis. |
---|
| 1879 | /// \see BlossomIt |
---|
| 1880 | int blossomNum() const { |
---|
| 1881 | return _blossom_potential.size(); |
---|
| 1882 | } |
---|
| 1883 | |
---|
| 1884 | |
---|
| 1885 | /// \brief Returns the number of the nodes in the blossom. |
---|
| 1886 | /// |
---|
| 1887 | /// Returns the number of the nodes in the blossom. |
---|
| 1888 | int blossomSize(int k) const { |
---|
| 1889 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 1890 | } |
---|
| 1891 | |
---|
| 1892 | /// \brief Returns the value of the blossom. |
---|
| 1893 | /// |
---|
| 1894 | /// Returns the the value of the blossom. |
---|
| 1895 | /// \see BlossomIt |
---|
| 1896 | Value blossomValue(int k) const { |
---|
| 1897 | return _blossom_potential[k].value; |
---|
| 1898 | } |
---|
| 1899 | |
---|
[342] | 1900 | /// \brief Iterator for obtaining the nodes of the blossom. |
---|
[338] | 1901 | /// |
---|
[342] | 1902 | /// Iterator for obtaining the nodes of the blossom. This class |
---|
| 1903 | /// provides a common lemon style iterator for listing a |
---|
[338] | 1904 | /// subset of the nodes. |
---|
| 1905 | class BlossomIt { |
---|
| 1906 | public: |
---|
| 1907 | |
---|
| 1908 | /// \brief Constructor. |
---|
| 1909 | /// |
---|
[342] | 1910 | /// Constructor to get the nodes of the variable. |
---|
[338] | 1911 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
| 1912 | : _algorithm(&algorithm) |
---|
| 1913 | { |
---|
| 1914 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 1915 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 1916 | } |
---|
| 1917 | |
---|
| 1918 | /// \brief Conversion to node. |
---|
| 1919 | /// |
---|
| 1920 | /// Conversion to node. |
---|
| 1921 | operator Node() const { |
---|
[339] | 1922 | return _algorithm->_blossom_node_list[_index]; |
---|
[338] | 1923 | } |
---|
| 1924 | |
---|
| 1925 | /// \brief Increment operator. |
---|
| 1926 | /// |
---|
| 1927 | /// Increment operator. |
---|
| 1928 | BlossomIt& operator++() { |
---|
| 1929 | ++_index; |
---|
| 1930 | return *this; |
---|
| 1931 | } |
---|
| 1932 | |
---|
[339] | 1933 | /// \brief Validity checking |
---|
| 1934 | /// |
---|
| 1935 | /// Checks whether the iterator is invalid. |
---|
| 1936 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 1937 | |
---|
| 1938 | /// \brief Validity checking |
---|
| 1939 | /// |
---|
| 1940 | /// Checks whether the iterator is valid. |
---|
| 1941 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[338] | 1942 | |
---|
| 1943 | private: |
---|
| 1944 | const MaxWeightedMatching* _algorithm; |
---|
| 1945 | int _last; |
---|
| 1946 | int _index; |
---|
| 1947 | }; |
---|
| 1948 | |
---|
| 1949 | /// @} |
---|
| 1950 | |
---|
| 1951 | }; |
---|
| 1952 | |
---|
| 1953 | /// \ingroup matching |
---|
| 1954 | /// |
---|
| 1955 | /// \brief Weighted perfect matching in general graphs |
---|
| 1956 | /// |
---|
| 1957 | /// This class provides an efficient implementation of Edmond's |
---|
[339] | 1958 | /// maximum weighted perfect matching algorithm. The implementation |
---|
[338] | 1959 | /// is based on extensive use of priority queues and provides |
---|
| 1960 | /// \f$O(nm\log(n))\f$ time complexity. |
---|
| 1961 | /// |
---|
| 1962 | /// The maximum weighted matching problem is to find undirected |
---|
[339] | 1963 | /// edges in the graph with maximum overall weight and no two of |
---|
| 1964 | /// them shares their ends and covers all nodes. The problem can be |
---|
| 1965 | /// formulated with the following linear program. |
---|
[338] | 1966 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
[339] | 1967 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 1968 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[338] | 1969 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 1970 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[339] | 1971 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 1972 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 1973 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 1974 | /// subsets of the nodes. |
---|
[338] | 1975 | /// |
---|
| 1976 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 1977 | /// optimality. The solution of the dual problem can be used to check |
---|
[339] | 1978 | /// the result of the algorithm. The dual linear problem is the |
---|
| 1979 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge |
---|
| 1980 | w_{uv} \quad \forall uv\in E\f] */ |
---|
[338] | 1981 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[339] | 1982 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 1983 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[338] | 1984 | /// |
---|
| 1985 | /// The algorithm can be executed with \c run() or the \c init() and |
---|
| 1986 | /// then the \c start() member functions. After it the matching can |
---|
| 1987 | /// be asked with \c matching() or mate() functions. The dual |
---|
| 1988 | /// solution can be get with \c nodeValue(), \c blossomNum() and \c |
---|
| 1989 | /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt |
---|
| 1990 | /// "BlossomIt" nested class which is able to iterate on the nodes |
---|
| 1991 | /// of a blossom. If the value type is integral then the dual |
---|
| 1992 | /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4". |
---|
| 1993 | template <typename _Graph, |
---|
| 1994 | typename _WeightMap = typename _Graph::template EdgeMap<int> > |
---|
| 1995 | class MaxWeightedPerfectMatching { |
---|
| 1996 | public: |
---|
| 1997 | |
---|
| 1998 | typedef _Graph Graph; |
---|
| 1999 | typedef _WeightMap WeightMap; |
---|
| 2000 | typedef typename WeightMap::Value Value; |
---|
| 2001 | |
---|
| 2002 | /// \brief Scaling factor for dual solution |
---|
| 2003 | /// |
---|
| 2004 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 2005 | /// according to the value type. |
---|
| 2006 | static const int dualScale = |
---|
| 2007 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 2008 | |
---|
| 2009 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 2010 | MatchingMap; |
---|
| 2011 | |
---|
| 2012 | private: |
---|
| 2013 | |
---|
| 2014 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 2015 | |
---|
| 2016 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 2017 | typedef std::vector<Node> BlossomNodeList; |
---|
| 2018 | |
---|
| 2019 | struct BlossomVariable { |
---|
| 2020 | int begin, end; |
---|
| 2021 | Value value; |
---|
| 2022 | |
---|
| 2023 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 2024 | : begin(_begin), end(_end), value(_value) {} |
---|
| 2025 | |
---|
| 2026 | }; |
---|
| 2027 | |
---|
| 2028 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 2029 | |
---|
| 2030 | const Graph& _graph; |
---|
| 2031 | const WeightMap& _weight; |
---|
| 2032 | |
---|
| 2033 | MatchingMap* _matching; |
---|
| 2034 | |
---|
| 2035 | NodePotential* _node_potential; |
---|
| 2036 | |
---|
| 2037 | BlossomPotential _blossom_potential; |
---|
| 2038 | BlossomNodeList _blossom_node_list; |
---|
| 2039 | |
---|
| 2040 | int _node_num; |
---|
| 2041 | int _blossom_num; |
---|
| 2042 | |
---|
| 2043 | typedef RangeMap<int> IntIntMap; |
---|
| 2044 | |
---|
| 2045 | enum Status { |
---|
| 2046 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
| 2047 | }; |
---|
| 2048 | |
---|
[339] | 2049 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[338] | 2050 | struct BlossomData { |
---|
| 2051 | int tree; |
---|
| 2052 | Status status; |
---|
| 2053 | Arc pred, next; |
---|
| 2054 | Value pot, offset; |
---|
| 2055 | }; |
---|
| 2056 | |
---|
[339] | 2057 | IntNodeMap *_blossom_index; |
---|
[338] | 2058 | BlossomSet *_blossom_set; |
---|
| 2059 | RangeMap<BlossomData>* _blossom_data; |
---|
| 2060 | |
---|
[339] | 2061 | IntNodeMap *_node_index; |
---|
| 2062 | IntArcMap *_node_heap_index; |
---|
[338] | 2063 | |
---|
| 2064 | struct NodeData { |
---|
| 2065 | |
---|
[339] | 2066 | NodeData(IntArcMap& node_heap_index) |
---|
[338] | 2067 | : heap(node_heap_index) {} |
---|
| 2068 | |
---|
| 2069 | int blossom; |
---|
| 2070 | Value pot; |
---|
[339] | 2071 | BinHeap<Value, IntArcMap> heap; |
---|
[338] | 2072 | std::map<int, Arc> heap_index; |
---|
| 2073 | |
---|
| 2074 | int tree; |
---|
| 2075 | }; |
---|
| 2076 | |
---|
| 2077 | RangeMap<NodeData>* _node_data; |
---|
| 2078 | |
---|
| 2079 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 2080 | |
---|
| 2081 | IntIntMap *_tree_set_index; |
---|
| 2082 | TreeSet *_tree_set; |
---|
| 2083 | |
---|
| 2084 | IntIntMap *_delta2_index; |
---|
| 2085 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 2086 | |
---|
[339] | 2087 | IntEdgeMap *_delta3_index; |
---|
| 2088 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[338] | 2089 | |
---|
| 2090 | IntIntMap *_delta4_index; |
---|
| 2091 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 2092 | |
---|
| 2093 | Value _delta_sum; |
---|
| 2094 | |
---|
| 2095 | void createStructures() { |
---|
| 2096 | _node_num = countNodes(_graph); |
---|
| 2097 | _blossom_num = _node_num * 3 / 2; |
---|
| 2098 | |
---|
| 2099 | if (!_matching) { |
---|
| 2100 | _matching = new MatchingMap(_graph); |
---|
| 2101 | } |
---|
| 2102 | if (!_node_potential) { |
---|
| 2103 | _node_potential = new NodePotential(_graph); |
---|
| 2104 | } |
---|
| 2105 | if (!_blossom_set) { |
---|
[339] | 2106 | _blossom_index = new IntNodeMap(_graph); |
---|
[338] | 2107 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 2108 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
| 2109 | } |
---|
| 2110 | |
---|
| 2111 | if (!_node_index) { |
---|
[339] | 2112 | _node_index = new IntNodeMap(_graph); |
---|
| 2113 | _node_heap_index = new IntArcMap(_graph); |
---|
[338] | 2114 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
[339] | 2115 | NodeData(*_node_heap_index)); |
---|
[338] | 2116 | } |
---|
| 2117 | |
---|
| 2118 | if (!_tree_set) { |
---|
| 2119 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 2120 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 2121 | } |
---|
| 2122 | if (!_delta2) { |
---|
| 2123 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 2124 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
| 2125 | } |
---|
| 2126 | if (!_delta3) { |
---|
[339] | 2127 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 2128 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[338] | 2129 | } |
---|
| 2130 | if (!_delta4) { |
---|
| 2131 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 2132 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
| 2133 | } |
---|
| 2134 | } |
---|
| 2135 | |
---|
| 2136 | void destroyStructures() { |
---|
| 2137 | _node_num = countNodes(_graph); |
---|
| 2138 | _blossom_num = _node_num * 3 / 2; |
---|
| 2139 | |
---|
| 2140 | if (_matching) { |
---|
| 2141 | delete _matching; |
---|
| 2142 | } |
---|
| 2143 | if (_node_potential) { |
---|
| 2144 | delete _node_potential; |
---|
| 2145 | } |
---|
| 2146 | if (_blossom_set) { |
---|
| 2147 | delete _blossom_index; |
---|
| 2148 | delete _blossom_set; |
---|
| 2149 | delete _blossom_data; |
---|
| 2150 | } |
---|
| 2151 | |
---|
| 2152 | if (_node_index) { |
---|
| 2153 | delete _node_index; |
---|
| 2154 | delete _node_heap_index; |
---|
| 2155 | delete _node_data; |
---|
| 2156 | } |
---|
| 2157 | |
---|
| 2158 | if (_tree_set) { |
---|
| 2159 | delete _tree_set_index; |
---|
| 2160 | delete _tree_set; |
---|
| 2161 | } |
---|
| 2162 | if (_delta2) { |
---|
| 2163 | delete _delta2_index; |
---|
| 2164 | delete _delta2; |
---|
| 2165 | } |
---|
| 2166 | if (_delta3) { |
---|
| 2167 | delete _delta3_index; |
---|
| 2168 | delete _delta3; |
---|
| 2169 | } |
---|
| 2170 | if (_delta4) { |
---|
| 2171 | delete _delta4_index; |
---|
| 2172 | delete _delta4; |
---|
| 2173 | } |
---|
| 2174 | } |
---|
| 2175 | |
---|
| 2176 | void matchedToEven(int blossom, int tree) { |
---|
| 2177 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2178 | _delta2->erase(blossom); |
---|
| 2179 | } |
---|
| 2180 | |
---|
| 2181 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2182 | (*_blossom_data)[blossom].pot -= |
---|
| 2183 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2184 | } |
---|
| 2185 | |
---|
| 2186 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2187 | n != INVALID; ++n) { |
---|
| 2188 | |
---|
| 2189 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2190 | int ni = (*_node_index)[n]; |
---|
| 2191 | |
---|
| 2192 | (*_node_data)[ni].heap.clear(); |
---|
| 2193 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2194 | |
---|
| 2195 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2196 | |
---|
| 2197 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2198 | Node v = _graph.source(e); |
---|
| 2199 | int vb = _blossom_set->find(v); |
---|
| 2200 | int vi = (*_node_index)[v]; |
---|
| 2201 | |
---|
| 2202 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2203 | dualScale * _weight[e]; |
---|
| 2204 | |
---|
| 2205 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2206 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2207 | _delta3->push(e, rw / 2); |
---|
| 2208 | } |
---|
| 2209 | } else { |
---|
| 2210 | typename std::map<int, Arc>::iterator it = |
---|
| 2211 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2212 | |
---|
| 2213 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2214 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2215 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2216 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2217 | it->second = e; |
---|
| 2218 | } |
---|
| 2219 | } else { |
---|
| 2220 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2221 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2222 | } |
---|
| 2223 | |
---|
| 2224 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2225 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2226 | |
---|
| 2227 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2228 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2229 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2230 | (*_blossom_data)[vb].offset); |
---|
| 2231 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2232 | (*_blossom_data)[vb].offset){ |
---|
| 2233 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2234 | (*_blossom_data)[vb].offset); |
---|
| 2235 | } |
---|
| 2236 | } |
---|
| 2237 | } |
---|
| 2238 | } |
---|
| 2239 | } |
---|
| 2240 | } |
---|
| 2241 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2242 | } |
---|
| 2243 | |
---|
| 2244 | void matchedToOdd(int blossom) { |
---|
| 2245 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2246 | _delta2->erase(blossom); |
---|
| 2247 | } |
---|
| 2248 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 2249 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2250 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 2251 | (*_blossom_data)[blossom].offset); |
---|
| 2252 | } |
---|
| 2253 | } |
---|
| 2254 | |
---|
| 2255 | void evenToMatched(int blossom, int tree) { |
---|
| 2256 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2257 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 2258 | } |
---|
| 2259 | |
---|
| 2260 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2261 | n != INVALID; ++n) { |
---|
| 2262 | int ni = (*_node_index)[n]; |
---|
| 2263 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 2264 | |
---|
| 2265 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2266 | Node v = _graph.source(e); |
---|
| 2267 | int vb = _blossom_set->find(v); |
---|
| 2268 | int vi = (*_node_index)[v]; |
---|
| 2269 | |
---|
| 2270 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2271 | dualScale * _weight[e]; |
---|
| 2272 | |
---|
| 2273 | if (vb == blossom) { |
---|
| 2274 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2275 | _delta3->erase(e); |
---|
| 2276 | } |
---|
| 2277 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2278 | |
---|
| 2279 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2280 | _delta3->erase(e); |
---|
| 2281 | } |
---|
| 2282 | |
---|
| 2283 | int vt = _tree_set->find(vb); |
---|
| 2284 | |
---|
| 2285 | if (vt != tree) { |
---|
| 2286 | |
---|
| 2287 | Arc r = _graph.oppositeArc(e); |
---|
| 2288 | |
---|
| 2289 | typename std::map<int, Arc>::iterator it = |
---|
| 2290 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 2291 | |
---|
| 2292 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 2293 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 2294 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 2295 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 2296 | it->second = r; |
---|
| 2297 | } |
---|
| 2298 | } else { |
---|
| 2299 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 2300 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 2301 | } |
---|
| 2302 | |
---|
| 2303 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 2304 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 2305 | |
---|
| 2306 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 2307 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2308 | (*_blossom_data)[blossom].offset); |
---|
| 2309 | } else if ((*_delta2)[blossom] > |
---|
| 2310 | _blossom_set->classPrio(blossom) - |
---|
| 2311 | (*_blossom_data)[blossom].offset){ |
---|
| 2312 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2313 | (*_blossom_data)[blossom].offset); |
---|
| 2314 | } |
---|
| 2315 | } |
---|
| 2316 | } |
---|
| 2317 | } else { |
---|
| 2318 | |
---|
| 2319 | typename std::map<int, Arc>::iterator it = |
---|
| 2320 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2321 | |
---|
| 2322 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2323 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 2324 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 2325 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 2326 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 2327 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 2328 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 2329 | } |
---|
| 2330 | |
---|
| 2331 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2332 | if (_blossom_set->classPrio(vb) == |
---|
| 2333 | std::numeric_limits<Value>::max()) { |
---|
| 2334 | _delta2->erase(vb); |
---|
| 2335 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 2336 | (*_blossom_data)[vb].offset) { |
---|
| 2337 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 2338 | (*_blossom_data)[vb].offset); |
---|
| 2339 | } |
---|
| 2340 | } |
---|
| 2341 | } |
---|
| 2342 | } |
---|
| 2343 | } |
---|
| 2344 | } |
---|
| 2345 | } |
---|
| 2346 | |
---|
| 2347 | void oddToMatched(int blossom) { |
---|
| 2348 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 2349 | |
---|
| 2350 | if (_blossom_set->classPrio(blossom) != |
---|
| 2351 | std::numeric_limits<Value>::max()) { |
---|
| 2352 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2353 | (*_blossom_data)[blossom].offset); |
---|
| 2354 | } |
---|
| 2355 | |
---|
| 2356 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2357 | _delta4->erase(blossom); |
---|
| 2358 | } |
---|
| 2359 | } |
---|
| 2360 | |
---|
| 2361 | void oddToEven(int blossom, int tree) { |
---|
| 2362 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2363 | _delta4->erase(blossom); |
---|
| 2364 | (*_blossom_data)[blossom].pot -= |
---|
| 2365 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2366 | } |
---|
| 2367 | |
---|
| 2368 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2369 | n != INVALID; ++n) { |
---|
| 2370 | int ni = (*_node_index)[n]; |
---|
| 2371 | |
---|
| 2372 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2373 | |
---|
| 2374 | (*_node_data)[ni].heap.clear(); |
---|
| 2375 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2376 | (*_node_data)[ni].pot += |
---|
| 2377 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2378 | |
---|
| 2379 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2380 | Node v = _graph.source(e); |
---|
| 2381 | int vb = _blossom_set->find(v); |
---|
| 2382 | int vi = (*_node_index)[v]; |
---|
| 2383 | |
---|
| 2384 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2385 | dualScale * _weight[e]; |
---|
| 2386 | |
---|
| 2387 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2388 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2389 | _delta3->push(e, rw / 2); |
---|
| 2390 | } |
---|
| 2391 | } else { |
---|
| 2392 | |
---|
| 2393 | typename std::map<int, Arc>::iterator it = |
---|
| 2394 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2395 | |
---|
| 2396 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2397 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2398 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2399 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2400 | it->second = e; |
---|
| 2401 | } |
---|
| 2402 | } else { |
---|
| 2403 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2404 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2405 | } |
---|
| 2406 | |
---|
| 2407 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2408 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2409 | |
---|
| 2410 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2411 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2412 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2413 | (*_blossom_data)[vb].offset); |
---|
| 2414 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2415 | (*_blossom_data)[vb].offset) { |
---|
| 2416 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2417 | (*_blossom_data)[vb].offset); |
---|
| 2418 | } |
---|
| 2419 | } |
---|
| 2420 | } |
---|
| 2421 | } |
---|
| 2422 | } |
---|
| 2423 | } |
---|
| 2424 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2425 | } |
---|
| 2426 | |
---|
| 2427 | void alternatePath(int even, int tree) { |
---|
| 2428 | int odd; |
---|
| 2429 | |
---|
| 2430 | evenToMatched(even, tree); |
---|
| 2431 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2432 | |
---|
| 2433 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 2434 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 2435 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 2436 | oddToMatched(odd); |
---|
| 2437 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 2438 | |
---|
| 2439 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 2440 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2441 | evenToMatched(even, tree); |
---|
| 2442 | (*_blossom_data)[even].next = |
---|
| 2443 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 2444 | } |
---|
| 2445 | |
---|
| 2446 | } |
---|
| 2447 | |
---|
| 2448 | void destroyTree(int tree) { |
---|
| 2449 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 2450 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 2451 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2452 | evenToMatched(b, tree); |
---|
| 2453 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 2454 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2455 | oddToMatched(b); |
---|
| 2456 | } |
---|
| 2457 | } |
---|
| 2458 | _tree_set->eraseClass(tree); |
---|
| 2459 | } |
---|
| 2460 | |
---|
[339] | 2461 | void augmentOnEdge(const Edge& edge) { |
---|
| 2462 | |
---|
| 2463 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2464 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[338] | 2465 | |
---|
| 2466 | int left_tree = _tree_set->find(left); |
---|
| 2467 | alternatePath(left, left_tree); |
---|
| 2468 | destroyTree(left_tree); |
---|
| 2469 | |
---|
| 2470 | int right_tree = _tree_set->find(right); |
---|
| 2471 | alternatePath(right, right_tree); |
---|
| 2472 | destroyTree(right_tree); |
---|
| 2473 | |
---|
[339] | 2474 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 2475 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[338] | 2476 | } |
---|
| 2477 | |
---|
| 2478 | void extendOnArc(const Arc& arc) { |
---|
| 2479 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 2480 | int tree = _tree_set->find(base); |
---|
| 2481 | |
---|
| 2482 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 2483 | _tree_set->insert(odd, tree); |
---|
| 2484 | (*_blossom_data)[odd].status = ODD; |
---|
| 2485 | matchedToOdd(odd); |
---|
| 2486 | (*_blossom_data)[odd].pred = arc; |
---|
| 2487 | |
---|
| 2488 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 2489 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 2490 | _tree_set->insert(even, tree); |
---|
| 2491 | (*_blossom_data)[even].status = EVEN; |
---|
| 2492 | matchedToEven(even, tree); |
---|
| 2493 | } |
---|
| 2494 | |
---|
[339] | 2495 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[338] | 2496 | int nca = -1; |
---|
| 2497 | std::vector<int> left_path, right_path; |
---|
| 2498 | |
---|
| 2499 | { |
---|
| 2500 | std::set<int> left_set, right_set; |
---|
| 2501 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2502 | left_path.push_back(left); |
---|
| 2503 | left_set.insert(left); |
---|
| 2504 | |
---|
| 2505 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 2506 | right_path.push_back(right); |
---|
| 2507 | right_set.insert(right); |
---|
| 2508 | |
---|
| 2509 | while (true) { |
---|
| 2510 | |
---|
| 2511 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 2512 | |
---|
| 2513 | left = |
---|
| 2514 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2515 | left_path.push_back(left); |
---|
| 2516 | left = |
---|
| 2517 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2518 | left_path.push_back(left); |
---|
| 2519 | |
---|
| 2520 | left_set.insert(left); |
---|
| 2521 | |
---|
| 2522 | if (right_set.find(left) != right_set.end()) { |
---|
| 2523 | nca = left; |
---|
| 2524 | break; |
---|
| 2525 | } |
---|
| 2526 | |
---|
| 2527 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 2528 | |
---|
| 2529 | right = |
---|
| 2530 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2531 | right_path.push_back(right); |
---|
| 2532 | right = |
---|
| 2533 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2534 | right_path.push_back(right); |
---|
| 2535 | |
---|
| 2536 | right_set.insert(right); |
---|
| 2537 | |
---|
| 2538 | if (left_set.find(right) != left_set.end()) { |
---|
| 2539 | nca = right; |
---|
| 2540 | break; |
---|
| 2541 | } |
---|
| 2542 | |
---|
| 2543 | } |
---|
| 2544 | |
---|
| 2545 | if (nca == -1) { |
---|
| 2546 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 2547 | nca = right; |
---|
| 2548 | while (left_set.find(nca) == left_set.end()) { |
---|
| 2549 | nca = |
---|
| 2550 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2551 | right_path.push_back(nca); |
---|
| 2552 | nca = |
---|
| 2553 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2554 | right_path.push_back(nca); |
---|
| 2555 | } |
---|
| 2556 | } else { |
---|
| 2557 | nca = left; |
---|
| 2558 | while (right_set.find(nca) == right_set.end()) { |
---|
| 2559 | nca = |
---|
| 2560 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2561 | left_path.push_back(nca); |
---|
| 2562 | nca = |
---|
| 2563 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2564 | left_path.push_back(nca); |
---|
| 2565 | } |
---|
| 2566 | } |
---|
| 2567 | } |
---|
| 2568 | } |
---|
| 2569 | |
---|
| 2570 | std::vector<int> subblossoms; |
---|
| 2571 | Arc prev; |
---|
| 2572 | |
---|
| 2573 | prev = _graph.direct(edge, true); |
---|
| 2574 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 2575 | subblossoms.push_back(left_path[i]); |
---|
| 2576 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 2577 | _tree_set->erase(left_path[i]); |
---|
| 2578 | |
---|
| 2579 | subblossoms.push_back(left_path[i + 1]); |
---|
| 2580 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 2581 | oddToEven(left_path[i + 1], tree); |
---|
| 2582 | _tree_set->erase(left_path[i + 1]); |
---|
| 2583 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 2584 | } |
---|
| 2585 | |
---|
| 2586 | int k = 0; |
---|
| 2587 | while (right_path[k] != nca) ++k; |
---|
| 2588 | |
---|
| 2589 | subblossoms.push_back(nca); |
---|
| 2590 | (*_blossom_data)[nca].next = prev; |
---|
| 2591 | |
---|
| 2592 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 2593 | subblossoms.push_back(right_path[i + 1]); |
---|
| 2594 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 2595 | oddToEven(right_path[i + 1], tree); |
---|
| 2596 | _tree_set->erase(right_path[i + 1]); |
---|
| 2597 | |
---|
| 2598 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 2599 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 2600 | |
---|
| 2601 | subblossoms.push_back(right_path[i]); |
---|
| 2602 | _tree_set->erase(right_path[i]); |
---|
| 2603 | } |
---|
| 2604 | |
---|
| 2605 | int surface = |
---|
| 2606 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 2607 | |
---|
| 2608 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2609 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2610 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 2611 | } |
---|
| 2612 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 2613 | } |
---|
| 2614 | |
---|
| 2615 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 2616 | (*_blossom_data)[surface].offset = 0; |
---|
| 2617 | (*_blossom_data)[surface].status = EVEN; |
---|
| 2618 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 2619 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 2620 | |
---|
| 2621 | _tree_set->insert(surface, tree); |
---|
| 2622 | _tree_set->erase(nca); |
---|
| 2623 | } |
---|
| 2624 | |
---|
| 2625 | void splitBlossom(int blossom) { |
---|
| 2626 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 2627 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 2628 | |
---|
| 2629 | int tree = _tree_set->find(blossom); |
---|
| 2630 | |
---|
| 2631 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 2632 | oddToMatched(blossom); |
---|
| 2633 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2634 | _delta2->erase(blossom); |
---|
| 2635 | } |
---|
| 2636 | |
---|
| 2637 | std::vector<int> subblossoms; |
---|
| 2638 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2639 | |
---|
| 2640 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 2641 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 2642 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 2643 | |
---|
| 2644 | int ib = -1, id = -1; |
---|
| 2645 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2646 | if (subblossoms[i] == b) ib = i; |
---|
| 2647 | if (subblossoms[i] == d) id = i; |
---|
| 2648 | |
---|
| 2649 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 2650 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2651 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 2652 | } |
---|
| 2653 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 2654 | std::numeric_limits<Value>::max()) { |
---|
| 2655 | _delta2->push(subblossoms[i], |
---|
| 2656 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 2657 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 2658 | } |
---|
| 2659 | } |
---|
| 2660 | |
---|
| 2661 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 2662 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 2663 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2664 | int sb = subblossoms[i]; |
---|
| 2665 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2666 | (*_blossom_data)[sb].next = |
---|
| 2667 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2668 | } |
---|
| 2669 | |
---|
| 2670 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2671 | int sb = subblossoms[i]; |
---|
| 2672 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2673 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2674 | |
---|
| 2675 | (*_blossom_data)[sb].status = ODD; |
---|
| 2676 | matchedToOdd(sb); |
---|
| 2677 | _tree_set->insert(sb, tree); |
---|
| 2678 | (*_blossom_data)[sb].pred = pred; |
---|
| 2679 | (*_blossom_data)[sb].next = |
---|
| 2680 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2681 | |
---|
| 2682 | pred = (*_blossom_data)[ub].next; |
---|
| 2683 | |
---|
| 2684 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2685 | matchedToEven(tb, tree); |
---|
| 2686 | _tree_set->insert(tb, tree); |
---|
| 2687 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 2688 | } |
---|
| 2689 | |
---|
| 2690 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 2691 | matchedToOdd(subblossoms[id]); |
---|
| 2692 | _tree_set->insert(subblossoms[id], tree); |
---|
| 2693 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 2694 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 2695 | |
---|
| 2696 | } else { |
---|
| 2697 | |
---|
| 2698 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 2699 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2700 | int sb = subblossoms[i]; |
---|
| 2701 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2702 | (*_blossom_data)[sb].next = |
---|
| 2703 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2704 | } |
---|
| 2705 | |
---|
| 2706 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2707 | int sb = subblossoms[i]; |
---|
| 2708 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2709 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2710 | |
---|
| 2711 | (*_blossom_data)[sb].status = ODD; |
---|
| 2712 | matchedToOdd(sb); |
---|
| 2713 | _tree_set->insert(sb, tree); |
---|
| 2714 | (*_blossom_data)[sb].next = next; |
---|
| 2715 | (*_blossom_data)[sb].pred = |
---|
| 2716 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2717 | |
---|
| 2718 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2719 | matchedToEven(tb, tree); |
---|
| 2720 | _tree_set->insert(tb, tree); |
---|
| 2721 | (*_blossom_data)[tb].pred = |
---|
| 2722 | (*_blossom_data)[tb].next = |
---|
| 2723 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 2724 | next = (*_blossom_data)[ub].next; |
---|
| 2725 | } |
---|
| 2726 | |
---|
| 2727 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 2728 | matchedToOdd(subblossoms[ib]); |
---|
| 2729 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 2730 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 2731 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 2732 | } |
---|
| 2733 | _tree_set->erase(blossom); |
---|
| 2734 | } |
---|
| 2735 | |
---|
| 2736 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 2737 | if (_blossom_set->trivial(blossom)) { |
---|
| 2738 | int bi = (*_node_index)[base]; |
---|
| 2739 | Value pot = (*_node_data)[bi].pot; |
---|
| 2740 | |
---|
| 2741 | _matching->set(base, matching); |
---|
| 2742 | _blossom_node_list.push_back(base); |
---|
| 2743 | _node_potential->set(base, pot); |
---|
| 2744 | } else { |
---|
| 2745 | |
---|
| 2746 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 2747 | int bn = _blossom_node_list.size(); |
---|
| 2748 | |
---|
| 2749 | std::vector<int> subblossoms; |
---|
| 2750 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2751 | int b = _blossom_set->find(base); |
---|
| 2752 | int ib = -1; |
---|
| 2753 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2754 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 2755 | } |
---|
| 2756 | |
---|
| 2757 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 2758 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 2759 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 2760 | |
---|
| 2761 | Arc m = (*_blossom_data)[tb].next; |
---|
| 2762 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 2763 | extractBlossom(tb, _graph.source(m), m); |
---|
| 2764 | } |
---|
| 2765 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 2766 | |
---|
| 2767 | int en = _blossom_node_list.size(); |
---|
| 2768 | |
---|
| 2769 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 2770 | } |
---|
| 2771 | } |
---|
| 2772 | |
---|
| 2773 | void extractMatching() { |
---|
| 2774 | std::vector<int> blossoms; |
---|
| 2775 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 2776 | blossoms.push_back(c); |
---|
| 2777 | } |
---|
| 2778 | |
---|
| 2779 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 2780 | |
---|
| 2781 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 2782 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 2783 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 2784 | n != INVALID; ++n) { |
---|
| 2785 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 2786 | } |
---|
| 2787 | |
---|
| 2788 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 2789 | Node base = _graph.source(matching); |
---|
| 2790 | extractBlossom(blossoms[i], base, matching); |
---|
| 2791 | } |
---|
| 2792 | } |
---|
| 2793 | |
---|
| 2794 | public: |
---|
| 2795 | |
---|
| 2796 | /// \brief Constructor |
---|
| 2797 | /// |
---|
| 2798 | /// Constructor. |
---|
| 2799 | MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight) |
---|
| 2800 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 2801 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 2802 | _node_num(0), _blossom_num(0), |
---|
| 2803 | |
---|
| 2804 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 2805 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 2806 | _tree_set_index(0), _tree_set(0), |
---|
| 2807 | |
---|
| 2808 | _delta2_index(0), _delta2(0), |
---|
| 2809 | _delta3_index(0), _delta3(0), |
---|
| 2810 | _delta4_index(0), _delta4(0), |
---|
| 2811 | |
---|
| 2812 | _delta_sum() {} |
---|
| 2813 | |
---|
| 2814 | ~MaxWeightedPerfectMatching() { |
---|
| 2815 | destroyStructures(); |
---|
| 2816 | } |
---|
| 2817 | |
---|
| 2818 | /// \name Execution control |
---|
[342] | 2819 | /// The simplest way to execute the algorithm is to use the |
---|
[338] | 2820 | /// \c run() member function. |
---|
| 2821 | |
---|
| 2822 | ///@{ |
---|
| 2823 | |
---|
| 2824 | /// \brief Initialize the algorithm |
---|
| 2825 | /// |
---|
| 2826 | /// Initialize the algorithm |
---|
| 2827 | void init() { |
---|
| 2828 | createStructures(); |
---|
| 2829 | |
---|
| 2830 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[339] | 2831 | _node_heap_index->set(e, BinHeap<Value, IntArcMap>::PRE_HEAP); |
---|
[338] | 2832 | } |
---|
| 2833 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 2834 | _delta3_index->set(e, _delta3->PRE_HEAP); |
---|
| 2835 | } |
---|
| 2836 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 2837 | _delta2_index->set(i, _delta2->PRE_HEAP); |
---|
| 2838 | _delta4_index->set(i, _delta4->PRE_HEAP); |
---|
| 2839 | } |
---|
| 2840 | |
---|
| 2841 | int index = 0; |
---|
| 2842 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2843 | Value max = - std::numeric_limits<Value>::max(); |
---|
| 2844 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2845 | if (_graph.target(e) == n) continue; |
---|
| 2846 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 2847 | max = (dualScale * _weight[e]) / 2; |
---|
| 2848 | } |
---|
| 2849 | } |
---|
| 2850 | _node_index->set(n, index); |
---|
| 2851 | (*_node_data)[index].pot = max; |
---|
| 2852 | int blossom = |
---|
| 2853 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 2854 | |
---|
| 2855 | _tree_set->insert(blossom); |
---|
| 2856 | |
---|
| 2857 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 2858 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 2859 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 2860 | (*_blossom_data)[blossom].pot = 0; |
---|
| 2861 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2862 | ++index; |
---|
| 2863 | } |
---|
| 2864 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 2865 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 2866 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 2867 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 2868 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 2869 | dualScale * _weight[e]) / 2); |
---|
| 2870 | } |
---|
| 2871 | } |
---|
| 2872 | } |
---|
| 2873 | |
---|
| 2874 | /// \brief Starts the algorithm |
---|
| 2875 | /// |
---|
| 2876 | /// Starts the algorithm |
---|
| 2877 | bool start() { |
---|
| 2878 | enum OpType { |
---|
| 2879 | D2, D3, D4 |
---|
| 2880 | }; |
---|
| 2881 | |
---|
| 2882 | int unmatched = _node_num; |
---|
| 2883 | while (unmatched > 0) { |
---|
| 2884 | Value d2 = !_delta2->empty() ? |
---|
| 2885 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 2886 | |
---|
| 2887 | Value d3 = !_delta3->empty() ? |
---|
| 2888 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 2889 | |
---|
| 2890 | Value d4 = !_delta4->empty() ? |
---|
| 2891 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 2892 | |
---|
| 2893 | _delta_sum = d2; OpType ot = D2; |
---|
| 2894 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
| 2895 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 2896 | |
---|
| 2897 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
| 2898 | return false; |
---|
| 2899 | } |
---|
| 2900 | |
---|
| 2901 | switch (ot) { |
---|
| 2902 | case D2: |
---|
| 2903 | { |
---|
| 2904 | int blossom = _delta2->top(); |
---|
| 2905 | Node n = _blossom_set->classTop(blossom); |
---|
| 2906 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 2907 | extendOnArc(e); |
---|
| 2908 | } |
---|
| 2909 | break; |
---|
| 2910 | case D3: |
---|
| 2911 | { |
---|
| 2912 | Edge e = _delta3->top(); |
---|
| 2913 | |
---|
| 2914 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 2915 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 2916 | |
---|
| 2917 | if (left_blossom == right_blossom) { |
---|
| 2918 | _delta3->pop(); |
---|
| 2919 | } else { |
---|
| 2920 | int left_tree = _tree_set->find(left_blossom); |
---|
| 2921 | int right_tree = _tree_set->find(right_blossom); |
---|
| 2922 | |
---|
| 2923 | if (left_tree == right_tree) { |
---|
[339] | 2924 | shrinkOnEdge(e, left_tree); |
---|
[338] | 2925 | } else { |
---|
[339] | 2926 | augmentOnEdge(e); |
---|
[338] | 2927 | unmatched -= 2; |
---|
| 2928 | } |
---|
| 2929 | } |
---|
| 2930 | } break; |
---|
| 2931 | case D4: |
---|
| 2932 | splitBlossom(_delta4->top()); |
---|
| 2933 | break; |
---|
| 2934 | } |
---|
| 2935 | } |
---|
| 2936 | extractMatching(); |
---|
| 2937 | return true; |
---|
| 2938 | } |
---|
| 2939 | |
---|
| 2940 | /// \brief Runs %MaxWeightedPerfectMatching algorithm. |
---|
| 2941 | /// |
---|
| 2942 | /// This method runs the %MaxWeightedPerfectMatching algorithm. |
---|
| 2943 | /// |
---|
| 2944 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 2945 | /// \code |
---|
| 2946 | /// mwm.init(); |
---|
| 2947 | /// mwm.start(); |
---|
| 2948 | /// \endcode |
---|
| 2949 | bool run() { |
---|
| 2950 | init(); |
---|
| 2951 | return start(); |
---|
| 2952 | } |
---|
| 2953 | |
---|
| 2954 | /// @} |
---|
| 2955 | |
---|
| 2956 | /// \name Primal solution |
---|
[342] | 2957 | /// Functions to get the primal solution, ie. the matching. |
---|
[338] | 2958 | |
---|
| 2959 | /// @{ |
---|
| 2960 | |
---|
| 2961 | /// \brief Returns the matching value. |
---|
| 2962 | /// |
---|
| 2963 | /// Returns the matching value. |
---|
| 2964 | Value matchingValue() const { |
---|
| 2965 | Value sum = 0; |
---|
| 2966 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2967 | if ((*_matching)[n] != INVALID) { |
---|
| 2968 | sum += _weight[(*_matching)[n]]; |
---|
| 2969 | } |
---|
| 2970 | } |
---|
| 2971 | return sum /= 2; |
---|
| 2972 | } |
---|
| 2973 | |
---|
[339] | 2974 | /// \brief Returns true when the edge is in the matching. |
---|
[338] | 2975 | /// |
---|
[339] | 2976 | /// Returns true when the edge is in the matching. |
---|
| 2977 | bool matching(const Edge& edge) const { |
---|
| 2978 | return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge; |
---|
[338] | 2979 | } |
---|
| 2980 | |
---|
[339] | 2981 | /// \brief Returns the incident matching edge. |
---|
[338] | 2982 | /// |
---|
[339] | 2983 | /// Returns the incident matching arc from given edge. |
---|
[338] | 2984 | Arc matching(const Node& node) const { |
---|
| 2985 | return (*_matching)[node]; |
---|
| 2986 | } |
---|
| 2987 | |
---|
| 2988 | /// \brief Returns the mate of the node. |
---|
| 2989 | /// |
---|
| 2990 | /// Returns the adjancent node in a mathcing arc. |
---|
| 2991 | Node mate(const Node& node) const { |
---|
| 2992 | return _graph.target((*_matching)[node]); |
---|
| 2993 | } |
---|
| 2994 | |
---|
| 2995 | /// @} |
---|
| 2996 | |
---|
| 2997 | /// \name Dual solution |
---|
[342] | 2998 | /// Functions to get the dual solution. |
---|
[338] | 2999 | |
---|
| 3000 | /// @{ |
---|
| 3001 | |
---|
| 3002 | /// \brief Returns the value of the dual solution. |
---|
| 3003 | /// |
---|
| 3004 | /// Returns the value of the dual solution. It should be equal to |
---|
| 3005 | /// the primal value scaled by \ref dualScale "dual scale". |
---|
| 3006 | Value dualValue() const { |
---|
| 3007 | Value sum = 0; |
---|
| 3008 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3009 | sum += nodeValue(n); |
---|
| 3010 | } |
---|
| 3011 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 3012 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 3013 | } |
---|
| 3014 | return sum; |
---|
| 3015 | } |
---|
| 3016 | |
---|
| 3017 | /// \brief Returns the value of the node. |
---|
| 3018 | /// |
---|
| 3019 | /// Returns the the value of the node. |
---|
| 3020 | Value nodeValue(const Node& n) const { |
---|
| 3021 | return (*_node_potential)[n]; |
---|
| 3022 | } |
---|
| 3023 | |
---|
| 3024 | /// \brief Returns the number of the blossoms in the basis. |
---|
| 3025 | /// |
---|
| 3026 | /// Returns the number of the blossoms in the basis. |
---|
| 3027 | /// \see BlossomIt |
---|
| 3028 | int blossomNum() const { |
---|
| 3029 | return _blossom_potential.size(); |
---|
| 3030 | } |
---|
| 3031 | |
---|
| 3032 | |
---|
| 3033 | /// \brief Returns the number of the nodes in the blossom. |
---|
| 3034 | /// |
---|
| 3035 | /// Returns the number of the nodes in the blossom. |
---|
| 3036 | int blossomSize(int k) const { |
---|
| 3037 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 3038 | } |
---|
| 3039 | |
---|
| 3040 | /// \brief Returns the value of the blossom. |
---|
| 3041 | /// |
---|
| 3042 | /// Returns the the value of the blossom. |
---|
| 3043 | /// \see BlossomIt |
---|
| 3044 | Value blossomValue(int k) const { |
---|
| 3045 | return _blossom_potential[k].value; |
---|
| 3046 | } |
---|
| 3047 | |
---|
[342] | 3048 | /// \brief Iterator for obtaining the nodes of the blossom. |
---|
[338] | 3049 | /// |
---|
[342] | 3050 | /// Iterator for obtaining the nodes of the blossom. This class |
---|
| 3051 | /// provides a common lemon style iterator for listing a |
---|
[338] | 3052 | /// subset of the nodes. |
---|
| 3053 | class BlossomIt { |
---|
| 3054 | public: |
---|
| 3055 | |
---|
| 3056 | /// \brief Constructor. |
---|
| 3057 | /// |
---|
[342] | 3058 | /// Constructor to get the nodes of the variable. |
---|
[338] | 3059 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
| 3060 | : _algorithm(&algorithm) |
---|
| 3061 | { |
---|
| 3062 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 3063 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 3064 | } |
---|
| 3065 | |
---|
| 3066 | /// \brief Conversion to node. |
---|
| 3067 | /// |
---|
| 3068 | /// Conversion to node. |
---|
| 3069 | operator Node() const { |
---|
[339] | 3070 | return _algorithm->_blossom_node_list[_index]; |
---|
[338] | 3071 | } |
---|
| 3072 | |
---|
| 3073 | /// \brief Increment operator. |
---|
| 3074 | /// |
---|
| 3075 | /// Increment operator. |
---|
| 3076 | BlossomIt& operator++() { |
---|
| 3077 | ++_index; |
---|
| 3078 | return *this; |
---|
| 3079 | } |
---|
| 3080 | |
---|
[339] | 3081 | /// \brief Validity checking |
---|
| 3082 | /// |
---|
| 3083 | /// Checks whether the iterator is invalid. |
---|
| 3084 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 3085 | |
---|
| 3086 | /// \brief Validity checking |
---|
| 3087 | /// |
---|
| 3088 | /// Checks whether the iterator is valid. |
---|
| 3089 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[338] | 3090 | |
---|
| 3091 | private: |
---|
| 3092 | const MaxWeightedPerfectMatching* _algorithm; |
---|
| 3093 | int _last; |
---|
| 3094 | int _index; |
---|
| 3095 | }; |
---|
| 3096 | |
---|
| 3097 | /// @} |
---|
| 3098 | |
---|
| 3099 | }; |
---|
| 3100 | |
---|
| 3101 | |
---|
| 3102 | } //END OF NAMESPACE LEMON |
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| 3103 | |
---|
| 3104 | #endif //LEMON_MAX_MATCHING_H |
---|