[326] | 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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[440] | 5 | * Copyright (C) 2003-2009 |
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[326] | 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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[327] | 34 | ///\brief Maximum matching algorithms in general graphs. |
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[326] | 35 | |
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| 36 | namespace lemon { |
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| 37 | |
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[327] | 38 | /// \ingroup matching |
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[326] | 39 | /// |
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[590] | 40 | /// \brief Maximum cardinality matching in general graphs |
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[326] | 41 | /// |
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[590] | 42 | /// This class implements Edmonds' alternating forest matching algorithm |
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[593] | 43 | /// for finding a maximum cardinality matching in a general undirected graph. |
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[590] | 44 | /// It can be started from an arbitrary initial matching |
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| 45 | /// (the default is the empty one). |
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[326] | 46 | /// |
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[330] | 47 | /// The dual solution of the problem is a map of the nodes to |
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[590] | 48 | /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D), |
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| 49 | /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds |
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| 50 | /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph |
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| 51 | /// with factor-critical components, the nodes in \c ODD/A form the |
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| 52 | /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having |
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| 53 | /// a perfect matching. The number of the factor-critical components |
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[327] | 54 | /// minus the number of barrier nodes is a lower bound on the |
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[330] | 55 | /// unmatched nodes, and the matching is optimal if and only if this bound is |
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[593] | 56 | /// tight. This decomposition can be obtained using \ref status() or |
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| 57 | /// \ref statusMap() after running the algorithm. |
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[326] | 58 | /// |
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[593] | 59 | /// \tparam GR The undirected graph type the algorithm runs on. |
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[559] | 60 | template <typename GR> |
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[326] | 61 | class MaxMatching { |
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[327] | 62 | public: |
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| 63 | |
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[590] | 64 | /// The graph type of the algorithm |
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[559] | 65 | typedef GR Graph; |
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[593] | 66 | /// The type of the matching map |
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[327] | 67 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
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| 68 | MatchingMap; |
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| 69 | |
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[590] | 70 | ///\brief Status constants for Gallai-Edmonds decomposition. |
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[327] | 71 | /// |
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[590] | 72 | ///These constants are used for indicating the Gallai-Edmonds |
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| 73 | ///decomposition of a graph. The nodes with status \c EVEN (or \c D) |
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| 74 | ///induce a subgraph with factor-critical components, the nodes with |
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| 75 | ///status \c ODD (or \c A) form the canonical barrier, and the nodes |
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| 76 | ///with status \c MATCHED (or \c C) induce a subgraph having a |
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| 77 | ///perfect matching. |
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[327] | 78 | enum Status { |
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[590] | 79 | EVEN = 1, ///< = 1. (\c D is an alias for \c EVEN.) |
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| 80 | D = 1, |
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| 81 | MATCHED = 0, ///< = 0. (\c C is an alias for \c MATCHED.) |
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| 82 | C = 0, |
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| 83 | ODD = -1, ///< = -1. (\c A is an alias for \c ODD.) |
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| 84 | A = -1, |
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| 85 | UNMATCHED = -2 ///< = -2. |
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[327] | 86 | }; |
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| 87 | |
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[593] | 88 | /// The type of the status map |
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[327] | 89 | typedef typename Graph::template NodeMap<Status> StatusMap; |
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| 90 | |
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| 91 | private: |
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[326] | 92 | |
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| 93 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 94 | |
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[327] | 95 | typedef UnionFindEnum<IntNodeMap> BlossomSet; |
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| 96 | typedef ExtendFindEnum<IntNodeMap> TreeSet; |
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| 97 | typedef RangeMap<Node> NodeIntMap; |
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| 98 | typedef MatchingMap EarMap; |
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| 99 | typedef std::vector<Node> NodeQueue; |
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| 100 | |
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| 101 | const Graph& _graph; |
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| 102 | MatchingMap* _matching; |
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| 103 | StatusMap* _status; |
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| 104 | |
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| 105 | EarMap* _ear; |
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| 106 | |
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| 107 | IntNodeMap* _blossom_set_index; |
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| 108 | BlossomSet* _blossom_set; |
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| 109 | NodeIntMap* _blossom_rep; |
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| 110 | |
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| 111 | IntNodeMap* _tree_set_index; |
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| 112 | TreeSet* _tree_set; |
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| 113 | |
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| 114 | NodeQueue _node_queue; |
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| 115 | int _process, _postpone, _last; |
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| 116 | |
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| 117 | int _node_num; |
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| 118 | |
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| 119 | private: |
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| 120 | |
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| 121 | void createStructures() { |
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| 122 | _node_num = countNodes(_graph); |
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| 123 | if (!_matching) { |
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| 124 | _matching = new MatchingMap(_graph); |
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| 125 | } |
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| 126 | if (!_status) { |
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| 127 | _status = new StatusMap(_graph); |
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| 128 | } |
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| 129 | if (!_ear) { |
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| 130 | _ear = new EarMap(_graph); |
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| 131 | } |
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| 132 | if (!_blossom_set) { |
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| 133 | _blossom_set_index = new IntNodeMap(_graph); |
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| 134 | _blossom_set = new BlossomSet(*_blossom_set_index); |
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| 135 | } |
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| 136 | if (!_blossom_rep) { |
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| 137 | _blossom_rep = new NodeIntMap(_node_num); |
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| 138 | } |
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| 139 | if (!_tree_set) { |
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| 140 | _tree_set_index = new IntNodeMap(_graph); |
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| 141 | _tree_set = new TreeSet(*_tree_set_index); |
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| 142 | } |
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| 143 | _node_queue.resize(_node_num); |
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| 144 | } |
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| 145 | |
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| 146 | void destroyStructures() { |
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| 147 | if (_matching) { |
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| 148 | delete _matching; |
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| 149 | } |
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| 150 | if (_status) { |
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| 151 | delete _status; |
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| 152 | } |
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| 153 | if (_ear) { |
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| 154 | delete _ear; |
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| 155 | } |
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| 156 | if (_blossom_set) { |
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| 157 | delete _blossom_set; |
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| 158 | delete _blossom_set_index; |
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| 159 | } |
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| 160 | if (_blossom_rep) { |
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| 161 | delete _blossom_rep; |
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| 162 | } |
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| 163 | if (_tree_set) { |
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| 164 | delete _tree_set_index; |
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| 165 | delete _tree_set; |
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| 166 | } |
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| 167 | } |
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| 168 | |
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| 169 | void processDense(const Node& n) { |
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| 170 | _process = _postpone = _last = 0; |
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| 171 | _node_queue[_last++] = n; |
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| 172 | |
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| 173 | while (_process != _last) { |
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| 174 | Node u = _node_queue[_process++]; |
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| 175 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 176 | Node v = _graph.target(a); |
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| 177 | if ((*_status)[v] == MATCHED) { |
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| 178 | extendOnArc(a); |
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| 179 | } else if ((*_status)[v] == UNMATCHED) { |
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| 180 | augmentOnArc(a); |
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| 181 | return; |
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| 182 | } |
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| 183 | } |
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| 184 | } |
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| 185 | |
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| 186 | while (_postpone != _last) { |
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| 187 | Node u = _node_queue[_postpone++]; |
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| 188 | |
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| 189 | for (OutArcIt a(_graph, u); a != INVALID ; ++a) { |
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| 190 | Node v = _graph.target(a); |
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| 191 | |
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| 192 | if ((*_status)[v] == EVEN) { |
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| 193 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 194 | shrinkOnEdge(a); |
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| 195 | } |
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| 196 | } |
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| 197 | |
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| 198 | while (_process != _last) { |
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| 199 | Node w = _node_queue[_process++]; |
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| 200 | for (OutArcIt b(_graph, w); b != INVALID; ++b) { |
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| 201 | Node x = _graph.target(b); |
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| 202 | if ((*_status)[x] == MATCHED) { |
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| 203 | extendOnArc(b); |
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| 204 | } else if ((*_status)[x] == UNMATCHED) { |
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| 205 | augmentOnArc(b); |
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| 206 | return; |
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| 207 | } |
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| 208 | } |
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| 209 | } |
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| 210 | } |
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| 211 | } |
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| 212 | } |
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| 213 | |
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| 214 | void processSparse(const Node& n) { |
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| 215 | _process = _last = 0; |
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| 216 | _node_queue[_last++] = n; |
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| 217 | while (_process != _last) { |
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| 218 | Node u = _node_queue[_process++]; |
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| 219 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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| 220 | Node v = _graph.target(a); |
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| 221 | |
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| 222 | if ((*_status)[v] == EVEN) { |
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| 223 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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| 224 | shrinkOnEdge(a); |
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| 225 | } |
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| 226 | } else if ((*_status)[v] == MATCHED) { |
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| 227 | extendOnArc(a); |
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| 228 | } else if ((*_status)[v] == UNMATCHED) { |
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| 229 | augmentOnArc(a); |
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| 230 | return; |
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| 231 | } |
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| 232 | } |
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| 233 | } |
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| 234 | } |
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| 235 | |
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| 236 | void shrinkOnEdge(const Edge& e) { |
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| 237 | Node nca = INVALID; |
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| 238 | |
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| 239 | { |
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| 240 | std::set<Node> left_set, right_set; |
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| 241 | |
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| 242 | Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))]; |
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| 243 | left_set.insert(left); |
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| 244 | |
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| 245 | Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))]; |
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| 246 | right_set.insert(right); |
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| 247 | |
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| 248 | while (true) { |
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| 249 | if ((*_matching)[left] == INVALID) break; |
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| 250 | left = _graph.target((*_matching)[left]); |
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| 251 | left = (*_blossom_rep)[_blossom_set-> |
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| 252 | find(_graph.target((*_ear)[left]))]; |
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| 253 | if (right_set.find(left) != right_set.end()) { |
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| 254 | nca = left; |
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| 255 | break; |
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| 256 | } |
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| 257 | left_set.insert(left); |
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| 258 | |
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| 259 | if ((*_matching)[right] == INVALID) break; |
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| 260 | right = _graph.target((*_matching)[right]); |
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| 261 | right = (*_blossom_rep)[_blossom_set-> |
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| 262 | find(_graph.target((*_ear)[right]))]; |
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| 263 | if (left_set.find(right) != left_set.end()) { |
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| 264 | nca = right; |
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| 265 | break; |
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| 266 | } |
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| 267 | right_set.insert(right); |
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| 268 | } |
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| 269 | |
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| 270 | if (nca == INVALID) { |
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| 271 | if ((*_matching)[left] == INVALID) { |
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| 272 | nca = right; |
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| 273 | while (left_set.find(nca) == left_set.end()) { |
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| 274 | nca = _graph.target((*_matching)[nca]); |
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| 275 | nca =(*_blossom_rep)[_blossom_set-> |
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| 276 | find(_graph.target((*_ear)[nca]))]; |
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| 277 | } |
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| 278 | } else { |
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| 279 | nca = left; |
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| 280 | while (right_set.find(nca) == right_set.end()) { |
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| 281 | nca = _graph.target((*_matching)[nca]); |
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| 282 | nca = (*_blossom_rep)[_blossom_set-> |
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| 283 | find(_graph.target((*_ear)[nca]))]; |
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| 284 | } |
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| 285 | } |
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| 286 | } |
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| 287 | } |
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| 288 | |
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| 289 | { |
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| 290 | |
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| 291 | Node node = _graph.u(e); |
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| 292 | Arc arc = _graph.direct(e, true); |
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| 293 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 294 | |
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| 295 | while (base != nca) { |
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[581] | 296 | (*_ear)[node] = arc; |
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[327] | 297 | |
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| 298 | Node n = node; |
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| 299 | while (n != base) { |
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| 300 | n = _graph.target((*_matching)[n]); |
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| 301 | Arc a = (*_ear)[n]; |
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| 302 | n = _graph.target(a); |
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[581] | 303 | (*_ear)[n] = _graph.oppositeArc(a); |
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[327] | 304 | } |
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| 305 | node = _graph.target((*_matching)[base]); |
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| 306 | _tree_set->erase(base); |
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| 307 | _tree_set->erase(node); |
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| 308 | _blossom_set->insert(node, _blossom_set->find(base)); |
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[581] | 309 | (*_status)[node] = EVEN; |
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[327] | 310 | _node_queue[_last++] = node; |
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| 311 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 312 | node = _graph.target((*_ear)[node]); |
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| 313 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 314 | _blossom_set->join(_graph.target(arc), base); |
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| 315 | } |
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| 316 | } |
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| 317 | |
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[581] | 318 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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[327] | 319 | |
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| 320 | { |
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| 321 | |
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| 322 | Node node = _graph.v(e); |
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| 323 | Arc arc = _graph.direct(e, false); |
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| 324 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 325 | |
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| 326 | while (base != nca) { |
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[581] | 327 | (*_ear)[node] = arc; |
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[327] | 328 | |
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| 329 | Node n = node; |
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| 330 | while (n != base) { |
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| 331 | n = _graph.target((*_matching)[n]); |
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| 332 | Arc a = (*_ear)[n]; |
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| 333 | n = _graph.target(a); |
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[581] | 334 | (*_ear)[n] = _graph.oppositeArc(a); |
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[327] | 335 | } |
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| 336 | node = _graph.target((*_matching)[base]); |
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| 337 | _tree_set->erase(base); |
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| 338 | _tree_set->erase(node); |
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| 339 | _blossom_set->insert(node, _blossom_set->find(base)); |
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[581] | 340 | (*_status)[node] = EVEN; |
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[327] | 341 | _node_queue[_last++] = node; |
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| 342 | arc = _graph.oppositeArc((*_ear)[node]); |
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| 343 | node = _graph.target((*_ear)[node]); |
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| 344 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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| 345 | _blossom_set->join(_graph.target(arc), base); |
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| 346 | } |
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| 347 | } |
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| 348 | |
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[581] | 349 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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[327] | 350 | } |
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| 351 | |
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| 352 | void extendOnArc(const Arc& a) { |
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| 353 | Node base = _graph.source(a); |
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| 354 | Node odd = _graph.target(a); |
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| 355 | |
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[581] | 356 | (*_ear)[odd] = _graph.oppositeArc(a); |
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[327] | 357 | Node even = _graph.target((*_matching)[odd]); |
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[581] | 358 | (*_blossom_rep)[_blossom_set->insert(even)] = even; |
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| 359 | (*_status)[odd] = ODD; |
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| 360 | (*_status)[even] = EVEN; |
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[327] | 361 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]); |
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| 362 | _tree_set->insert(odd, tree); |
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| 363 | _tree_set->insert(even, tree); |
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| 364 | _node_queue[_last++] = even; |
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| 365 | |
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| 366 | } |
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| 367 | |
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| 368 | void augmentOnArc(const Arc& a) { |
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| 369 | Node even = _graph.source(a); |
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| 370 | Node odd = _graph.target(a); |
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| 371 | |
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| 372 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]); |
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| 373 | |
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[581] | 374 | (*_matching)[odd] = _graph.oppositeArc(a); |
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| 375 | (*_status)[odd] = MATCHED; |
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[327] | 376 | |
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| 377 | Arc arc = (*_matching)[even]; |
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[581] | 378 | (*_matching)[even] = a; |
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[327] | 379 | |
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| 380 | while (arc != INVALID) { |
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| 381 | odd = _graph.target(arc); |
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| 382 | arc = (*_ear)[odd]; |
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| 383 | even = _graph.target(arc); |
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[581] | 384 | (*_matching)[odd] = arc; |
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[327] | 385 | arc = (*_matching)[even]; |
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[581] | 386 | (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]); |
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[327] | 387 | } |
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| 388 | |
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| 389 | for (typename TreeSet::ItemIt it(*_tree_set, tree); |
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| 390 | it != INVALID; ++it) { |
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| 391 | if ((*_status)[it] == ODD) { |
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[581] | 392 | (*_status)[it] = MATCHED; |
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[327] | 393 | } else { |
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| 394 | int blossom = _blossom_set->find(it); |
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| 395 | for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom); |
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| 396 | jt != INVALID; ++jt) { |
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[581] | 397 | (*_status)[jt] = MATCHED; |
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[327] | 398 | } |
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| 399 | _blossom_set->eraseClass(blossom); |
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| 400 | } |
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| 401 | } |
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| 402 | _tree_set->eraseClass(tree); |
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| 403 | |
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| 404 | } |
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[326] | 405 | |
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| 406 | public: |
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| 407 | |
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[327] | 408 | /// \brief Constructor |
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[326] | 409 | /// |
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[327] | 410 | /// Constructor. |
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| 411 | MaxMatching(const Graph& graph) |
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| 412 | : _graph(graph), _matching(0), _status(0), _ear(0), |
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| 413 | _blossom_set_index(0), _blossom_set(0), _blossom_rep(0), |
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| 414 | _tree_set_index(0), _tree_set(0) {} |
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| 415 | |
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| 416 | ~MaxMatching() { |
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| 417 | destroyStructures(); |
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| 418 | } |
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| 419 | |
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[590] | 420 | /// \name Execution Control |
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[330] | 421 | /// The simplest way to execute the algorithm is to use the |
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[590] | 422 | /// \c run() member function.\n |
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| 423 | /// If you need better control on the execution, you have to call |
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| 424 | /// one of the functions \ref init(), \ref greedyInit() or |
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| 425 | /// \ref matchingInit() first, then you can start the algorithm with |
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| 426 | /// \ref startSparse() or \ref startDense(). |
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[327] | 427 | |
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| 428 | ///@{ |
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| 429 | |
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[590] | 430 | /// \brief Set the initial matching to the empty matching. |
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[326] | 431 | /// |
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[590] | 432 | /// This function sets the initial matching to the empty matching. |
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[326] | 433 | void init() { |
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[327] | 434 | createStructures(); |
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| 435 | for(NodeIt n(_graph); n != INVALID; ++n) { |
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[581] | 436 | (*_matching)[n] = INVALID; |
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| 437 | (*_status)[n] = UNMATCHED; |
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[326] | 438 | } |
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| 439 | } |
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| 440 | |
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[590] | 441 | /// \brief Find an initial matching in a greedy way. |
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[326] | 442 | /// |
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[590] | 443 | /// This function finds an initial matching in a greedy way. |
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[326] | 444 | void greedyInit() { |
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[327] | 445 | createStructures(); |
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| 446 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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[581] | 447 | (*_matching)[n] = INVALID; |
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| 448 | (*_status)[n] = UNMATCHED; |
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[326] | 449 | } |
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[327] | 450 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 451 | if ((*_matching)[n] == INVALID) { |
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| 452 | for (OutArcIt a(_graph, n); a != INVALID ; ++a) { |
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| 453 | Node v = _graph.target(a); |
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| 454 | if ((*_matching)[v] == INVALID && v != n) { |
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[581] | 455 | (*_matching)[n] = a; |
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| 456 | (*_status)[n] = MATCHED; |
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| 457 | (*_matching)[v] = _graph.oppositeArc(a); |
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| 458 | (*_status)[v] = MATCHED; |
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[326] | 459 | break; |
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| 460 | } |
---|
| 461 | } |
---|
| 462 | } |
---|
| 463 | } |
---|
| 464 | } |
---|
| 465 | |
---|
[327] | 466 | |
---|
[590] | 467 | /// \brief Initialize the matching from a map. |
---|
[326] | 468 | /// |
---|
[590] | 469 | /// This function initializes the matching from a \c bool valued edge |
---|
| 470 | /// map. This map should have the property that there are no two incident |
---|
| 471 | /// edges with \c true value, i.e. it really contains a matching. |
---|
[559] | 472 | /// \return \c true if the map contains a matching. |
---|
[327] | 473 | template <typename MatchingMap> |
---|
| 474 | bool matchingInit(const MatchingMap& matching) { |
---|
| 475 | createStructures(); |
---|
| 476 | |
---|
| 477 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[581] | 478 | (*_matching)[n] = INVALID; |
---|
| 479 | (*_status)[n] = UNMATCHED; |
---|
[326] | 480 | } |
---|
[327] | 481 | for(EdgeIt e(_graph); e!=INVALID; ++e) { |
---|
| 482 | if (matching[e]) { |
---|
| 483 | |
---|
| 484 | Node u = _graph.u(e); |
---|
| 485 | if ((*_matching)[u] != INVALID) return false; |
---|
[581] | 486 | (*_matching)[u] = _graph.direct(e, true); |
---|
| 487 | (*_status)[u] = MATCHED; |
---|
[327] | 488 | |
---|
| 489 | Node v = _graph.v(e); |
---|
| 490 | if ((*_matching)[v] != INVALID) return false; |
---|
[581] | 491 | (*_matching)[v] = _graph.direct(e, false); |
---|
| 492 | (*_status)[v] = MATCHED; |
---|
[327] | 493 | } |
---|
| 494 | } |
---|
| 495 | return true; |
---|
[326] | 496 | } |
---|
| 497 | |
---|
[590] | 498 | /// \brief Start Edmonds' algorithm |
---|
[326] | 499 | /// |
---|
[590] | 500 | /// This function runs the original Edmonds' algorithm. |
---|
| 501 | /// |
---|
[651] | 502 | /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be |
---|
[590] | 503 | /// called before using this function. |
---|
[327] | 504 | void startSparse() { |
---|
| 505 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 506 | if ((*_status)[n] == UNMATCHED) { |
---|
| 507 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 508 | _tree_set->insert(n); |
---|
[581] | 509 | (*_status)[n] = EVEN; |
---|
[327] | 510 | processSparse(n); |
---|
[326] | 511 | } |
---|
| 512 | } |
---|
| 513 | } |
---|
| 514 | |
---|
[590] | 515 | /// \brief Start Edmonds' algorithm with a heuristic improvement |
---|
| 516 | /// for dense graphs |
---|
[326] | 517 | /// |
---|
[590] | 518 | /// This function runs Edmonds' algorithm with a heuristic of postponing |
---|
[330] | 519 | /// shrinks, therefore resulting in a faster algorithm for dense graphs. |
---|
[590] | 520 | /// |
---|
[651] | 521 | /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be |
---|
[590] | 522 | /// called before using this function. |
---|
[327] | 523 | void startDense() { |
---|
| 524 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 525 | if ((*_status)[n] == UNMATCHED) { |
---|
| 526 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
| 527 | _tree_set->insert(n); |
---|
[581] | 528 | (*_status)[n] = EVEN; |
---|
[327] | 529 | processDense(n); |
---|
| 530 | } |
---|
| 531 | } |
---|
| 532 | } |
---|
| 533 | |
---|
| 534 | |
---|
[590] | 535 | /// \brief Run Edmonds' algorithm |
---|
[327] | 536 | /// |
---|
[590] | 537 | /// This function runs Edmonds' algorithm. An additional heuristic of |
---|
| 538 | /// postponing shrinks is used for relatively dense graphs |
---|
| 539 | /// (for which <tt>m>=2*n</tt> holds). |
---|
[326] | 540 | void run() { |
---|
[327] | 541 | if (countEdges(_graph) < 2 * countNodes(_graph)) { |
---|
[326] | 542 | greedyInit(); |
---|
| 543 | startSparse(); |
---|
| 544 | } else { |
---|
| 545 | init(); |
---|
| 546 | startDense(); |
---|
| 547 | } |
---|
| 548 | } |
---|
| 549 | |
---|
[327] | 550 | /// @} |
---|
| 551 | |
---|
[590] | 552 | /// \name Primal Solution |
---|
| 553 | /// Functions to get the primal solution, i.e. the maximum matching. |
---|
[327] | 554 | |
---|
| 555 | /// @{ |
---|
[326] | 556 | |
---|
[590] | 557 | /// \brief Return the size (cardinality) of the matching. |
---|
[326] | 558 | /// |
---|
[590] | 559 | /// This function returns the size (cardinality) of the current matching. |
---|
| 560 | /// After run() it returns the size of the maximum matching in the graph. |
---|
[327] | 561 | int matchingSize() const { |
---|
| 562 | int size = 0; |
---|
| 563 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 564 | if ((*_matching)[n] != INVALID) { |
---|
| 565 | ++size; |
---|
[326] | 566 | } |
---|
| 567 | } |
---|
[327] | 568 | return size / 2; |
---|
[326] | 569 | } |
---|
| 570 | |
---|
[590] | 571 | /// \brief Return \c true if the given edge is in the matching. |
---|
[327] | 572 | /// |
---|
[590] | 573 | /// This function returns \c true if the given edge is in the current |
---|
| 574 | /// matching. |
---|
[327] | 575 | bool matching(const Edge& edge) const { |
---|
| 576 | return edge == (*_matching)[_graph.u(edge)]; |
---|
| 577 | } |
---|
| 578 | |
---|
[590] | 579 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[327] | 580 | /// |
---|
[590] | 581 | /// This function returns the matching arc (or edge) incident to the |
---|
| 582 | /// given node in the current matching or \c INVALID if the node is |
---|
| 583 | /// not covered by the matching. |
---|
[327] | 584 | Arc matching(const Node& n) const { |
---|
| 585 | return (*_matching)[n]; |
---|
| 586 | } |
---|
[326] | 587 | |
---|
[593] | 588 | /// \brief Return a const reference to the matching map. |
---|
| 589 | /// |
---|
| 590 | /// This function returns a const reference to a node map that stores |
---|
| 591 | /// the matching arc (or edge) incident to each node. |
---|
| 592 | const MatchingMap& matchingMap() const { |
---|
| 593 | return *_matching; |
---|
| 594 | } |
---|
| 595 | |
---|
[590] | 596 | /// \brief Return the mate of the given node. |
---|
[326] | 597 | /// |
---|
[590] | 598 | /// This function returns the mate of the given node in the current |
---|
| 599 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
[327] | 600 | Node mate(const Node& n) const { |
---|
| 601 | return (*_matching)[n] != INVALID ? |
---|
| 602 | _graph.target((*_matching)[n]) : INVALID; |
---|
[326] | 603 | } |
---|
| 604 | |
---|
[327] | 605 | /// @} |
---|
| 606 | |
---|
[590] | 607 | /// \name Dual Solution |
---|
| 608 | /// Functions to get the dual solution, i.e. the Gallai-Edmonds |
---|
| 609 | /// decomposition. |
---|
[327] | 610 | |
---|
| 611 | /// @{ |
---|
[326] | 612 | |
---|
[590] | 613 | /// \brief Return the status of the given node in the Edmonds-Gallai |
---|
[326] | 614 | /// decomposition. |
---|
| 615 | /// |
---|
[590] | 616 | /// This function returns the \ref Status "status" of the given node |
---|
| 617 | /// in the Edmonds-Gallai decomposition. |
---|
[593] | 618 | Status status(const Node& n) const { |
---|
[327] | 619 | return (*_status)[n]; |
---|
[326] | 620 | } |
---|
| 621 | |
---|
[593] | 622 | /// \brief Return a const reference to the status map, which stores |
---|
| 623 | /// the Edmonds-Gallai decomposition. |
---|
| 624 | /// |
---|
| 625 | /// This function returns a const reference to a node map that stores the |
---|
| 626 | /// \ref Status "status" of each node in the Edmonds-Gallai decomposition. |
---|
| 627 | const StatusMap& statusMap() const { |
---|
| 628 | return *_status; |
---|
| 629 | } |
---|
| 630 | |
---|
[590] | 631 | /// \brief Return \c true if the given node is in the barrier. |
---|
[326] | 632 | /// |
---|
[590] | 633 | /// This function returns \c true if the given node is in the barrier. |
---|
[327] | 634 | bool barrier(const Node& n) const { |
---|
| 635 | return (*_status)[n] == ODD; |
---|
[326] | 636 | } |
---|
| 637 | |
---|
[327] | 638 | /// @} |
---|
[326] | 639 | |
---|
| 640 | }; |
---|
| 641 | |
---|
| 642 | /// \ingroup matching |
---|
| 643 | /// |
---|
| 644 | /// \brief Weighted matching in general graphs |
---|
| 645 | /// |
---|
| 646 | /// This class provides an efficient implementation of Edmond's |
---|
| 647 | /// maximum weighted matching algorithm. The implementation is based |
---|
| 648 | /// on extensive use of priority queues and provides |
---|
[559] | 649 | /// \f$O(nm\log n)\f$ time complexity. |
---|
[326] | 650 | /// |
---|
[590] | 651 | /// The maximum weighted matching problem is to find a subset of the |
---|
| 652 | /// edges in an undirected graph with maximum overall weight for which |
---|
| 653 | /// each node has at most one incident edge. |
---|
| 654 | /// It can be formulated with the following linear program. |
---|
[326] | 655 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
[327] | 656 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 657 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[326] | 658 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 659 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[327] | 660 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 661 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 662 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 663 | /// subsets of the nodes. |
---|
[326] | 664 | /// |
---|
| 665 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 666 | /// optimality. The solution of the dual problem can be used to check |
---|
[327] | 667 | /// the result of the algorithm. The dual linear problem is the |
---|
[590] | 668 | /// following. |
---|
[327] | 669 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)} |
---|
| 670 | z_B \ge w_{uv} \quad \forall uv\in E\f] */ |
---|
[326] | 671 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
| 672 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[327] | 673 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 674 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[326] | 675 | /// |
---|
[590] | 676 | /// The algorithm can be executed with the run() function. |
---|
| 677 | /// After it the matching (the primal solution) and the dual solution |
---|
| 678 | /// can be obtained using the query functions and the |
---|
| 679 | /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class, |
---|
| 680 | /// which is able to iterate on the nodes of a blossom. |
---|
| 681 | /// If the value type is integer, then the dual solution is multiplied |
---|
| 682 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
| 683 | /// |
---|
[593] | 684 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
[590] | 685 | /// \tparam WM The type edge weight map. The default type is |
---|
| 686 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 687 | #ifdef DOXYGEN |
---|
| 688 | template <typename GR, typename WM> |
---|
| 689 | #else |
---|
[559] | 690 | template <typename GR, |
---|
| 691 | typename WM = typename GR::template EdgeMap<int> > |
---|
[590] | 692 | #endif |
---|
[326] | 693 | class MaxWeightedMatching { |
---|
| 694 | public: |
---|
| 695 | |
---|
[590] | 696 | /// The graph type of the algorithm |
---|
[559] | 697 | typedef GR Graph; |
---|
[590] | 698 | /// The type of the edge weight map |
---|
[559] | 699 | typedef WM WeightMap; |
---|
[590] | 700 | /// The value type of the edge weights |
---|
[326] | 701 | typedef typename WeightMap::Value Value; |
---|
| 702 | |
---|
[593] | 703 | /// The type of the matching map |
---|
[590] | 704 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 705 | MatchingMap; |
---|
| 706 | |
---|
[326] | 707 | /// \brief Scaling factor for dual solution |
---|
| 708 | /// |
---|
[590] | 709 | /// Scaling factor for dual solution. It is equal to 4 or 1 |
---|
[326] | 710 | /// according to the value type. |
---|
| 711 | static const int dualScale = |
---|
| 712 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 713 | |
---|
| 714 | private: |
---|
| 715 | |
---|
| 716 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 717 | |
---|
| 718 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 719 | typedef std::vector<Node> BlossomNodeList; |
---|
| 720 | |
---|
| 721 | struct BlossomVariable { |
---|
| 722 | int begin, end; |
---|
| 723 | Value value; |
---|
| 724 | |
---|
| 725 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 726 | : begin(_begin), end(_end), value(_value) {} |
---|
| 727 | |
---|
| 728 | }; |
---|
| 729 | |
---|
| 730 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 731 | |
---|
| 732 | const Graph& _graph; |
---|
| 733 | const WeightMap& _weight; |
---|
| 734 | |
---|
| 735 | MatchingMap* _matching; |
---|
| 736 | |
---|
| 737 | NodePotential* _node_potential; |
---|
| 738 | |
---|
| 739 | BlossomPotential _blossom_potential; |
---|
| 740 | BlossomNodeList _blossom_node_list; |
---|
| 741 | |
---|
| 742 | int _node_num; |
---|
| 743 | int _blossom_num; |
---|
| 744 | |
---|
| 745 | typedef RangeMap<int> IntIntMap; |
---|
| 746 | |
---|
| 747 | enum Status { |
---|
| 748 | EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2 |
---|
| 749 | }; |
---|
| 750 | |
---|
[327] | 751 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[326] | 752 | struct BlossomData { |
---|
| 753 | int tree; |
---|
| 754 | Status status; |
---|
| 755 | Arc pred, next; |
---|
| 756 | Value pot, offset; |
---|
| 757 | Node base; |
---|
| 758 | }; |
---|
| 759 | |
---|
[327] | 760 | IntNodeMap *_blossom_index; |
---|
[326] | 761 | BlossomSet *_blossom_set; |
---|
| 762 | RangeMap<BlossomData>* _blossom_data; |
---|
| 763 | |
---|
[327] | 764 | IntNodeMap *_node_index; |
---|
| 765 | IntArcMap *_node_heap_index; |
---|
[326] | 766 | |
---|
| 767 | struct NodeData { |
---|
| 768 | |
---|
[327] | 769 | NodeData(IntArcMap& node_heap_index) |
---|
[326] | 770 | : heap(node_heap_index) {} |
---|
| 771 | |
---|
| 772 | int blossom; |
---|
| 773 | Value pot; |
---|
[327] | 774 | BinHeap<Value, IntArcMap> heap; |
---|
[326] | 775 | std::map<int, Arc> heap_index; |
---|
| 776 | |
---|
| 777 | int tree; |
---|
| 778 | }; |
---|
| 779 | |
---|
| 780 | RangeMap<NodeData>* _node_data; |
---|
| 781 | |
---|
| 782 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 783 | |
---|
| 784 | IntIntMap *_tree_set_index; |
---|
| 785 | TreeSet *_tree_set; |
---|
| 786 | |
---|
[327] | 787 | IntNodeMap *_delta1_index; |
---|
| 788 | BinHeap<Value, IntNodeMap> *_delta1; |
---|
[326] | 789 | |
---|
| 790 | IntIntMap *_delta2_index; |
---|
| 791 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 792 | |
---|
[327] | 793 | IntEdgeMap *_delta3_index; |
---|
| 794 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[326] | 795 | |
---|
| 796 | IntIntMap *_delta4_index; |
---|
| 797 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 798 | |
---|
| 799 | Value _delta_sum; |
---|
| 800 | |
---|
| 801 | void createStructures() { |
---|
| 802 | _node_num = countNodes(_graph); |
---|
| 803 | _blossom_num = _node_num * 3 / 2; |
---|
| 804 | |
---|
| 805 | if (!_matching) { |
---|
| 806 | _matching = new MatchingMap(_graph); |
---|
| 807 | } |
---|
| 808 | if (!_node_potential) { |
---|
| 809 | _node_potential = new NodePotential(_graph); |
---|
| 810 | } |
---|
| 811 | if (!_blossom_set) { |
---|
[327] | 812 | _blossom_index = new IntNodeMap(_graph); |
---|
[326] | 813 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 814 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
| 815 | } |
---|
| 816 | |
---|
| 817 | if (!_node_index) { |
---|
[327] | 818 | _node_index = new IntNodeMap(_graph); |
---|
| 819 | _node_heap_index = new IntArcMap(_graph); |
---|
[326] | 820 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
| 821 | NodeData(*_node_heap_index)); |
---|
| 822 | } |
---|
| 823 | |
---|
| 824 | if (!_tree_set) { |
---|
| 825 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 826 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 827 | } |
---|
| 828 | if (!_delta1) { |
---|
[327] | 829 | _delta1_index = new IntNodeMap(_graph); |
---|
| 830 | _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index); |
---|
[326] | 831 | } |
---|
| 832 | if (!_delta2) { |
---|
| 833 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 834 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
| 835 | } |
---|
| 836 | if (!_delta3) { |
---|
[327] | 837 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 838 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[326] | 839 | } |
---|
| 840 | if (!_delta4) { |
---|
| 841 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 842 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
| 843 | } |
---|
| 844 | } |
---|
| 845 | |
---|
| 846 | void destroyStructures() { |
---|
| 847 | _node_num = countNodes(_graph); |
---|
| 848 | _blossom_num = _node_num * 3 / 2; |
---|
| 849 | |
---|
| 850 | if (_matching) { |
---|
| 851 | delete _matching; |
---|
| 852 | } |
---|
| 853 | if (_node_potential) { |
---|
| 854 | delete _node_potential; |
---|
| 855 | } |
---|
| 856 | if (_blossom_set) { |
---|
| 857 | delete _blossom_index; |
---|
| 858 | delete _blossom_set; |
---|
| 859 | delete _blossom_data; |
---|
| 860 | } |
---|
| 861 | |
---|
| 862 | if (_node_index) { |
---|
| 863 | delete _node_index; |
---|
| 864 | delete _node_heap_index; |
---|
| 865 | delete _node_data; |
---|
| 866 | } |
---|
| 867 | |
---|
| 868 | if (_tree_set) { |
---|
| 869 | delete _tree_set_index; |
---|
| 870 | delete _tree_set; |
---|
| 871 | } |
---|
| 872 | if (_delta1) { |
---|
| 873 | delete _delta1_index; |
---|
| 874 | delete _delta1; |
---|
| 875 | } |
---|
| 876 | if (_delta2) { |
---|
| 877 | delete _delta2_index; |
---|
| 878 | delete _delta2; |
---|
| 879 | } |
---|
| 880 | if (_delta3) { |
---|
| 881 | delete _delta3_index; |
---|
| 882 | delete _delta3; |
---|
| 883 | } |
---|
| 884 | if (_delta4) { |
---|
| 885 | delete _delta4_index; |
---|
| 886 | delete _delta4; |
---|
| 887 | } |
---|
| 888 | } |
---|
| 889 | |
---|
| 890 | void matchedToEven(int blossom, int tree) { |
---|
| 891 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 892 | _delta2->erase(blossom); |
---|
| 893 | } |
---|
| 894 | |
---|
| 895 | if (!_blossom_set->trivial(blossom)) { |
---|
| 896 | (*_blossom_data)[blossom].pot -= |
---|
| 897 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 898 | } |
---|
| 899 | |
---|
| 900 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 901 | n != INVALID; ++n) { |
---|
| 902 | |
---|
| 903 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 904 | int ni = (*_node_index)[n]; |
---|
| 905 | |
---|
| 906 | (*_node_data)[ni].heap.clear(); |
---|
| 907 | (*_node_data)[ni].heap_index.clear(); |
---|
| 908 | |
---|
| 909 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 910 | |
---|
| 911 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 912 | |
---|
| 913 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 914 | Node v = _graph.source(e); |
---|
| 915 | int vb = _blossom_set->find(v); |
---|
| 916 | int vi = (*_node_index)[v]; |
---|
| 917 | |
---|
| 918 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 919 | dualScale * _weight[e]; |
---|
| 920 | |
---|
| 921 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 922 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 923 | _delta3->push(e, rw / 2); |
---|
| 924 | } |
---|
| 925 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 926 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 927 | _delta3->push(e, rw); |
---|
| 928 | } |
---|
| 929 | } else { |
---|
| 930 | typename std::map<int, Arc>::iterator it = |
---|
| 931 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 932 | |
---|
| 933 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 934 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 935 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 936 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 937 | it->second = e; |
---|
| 938 | } |
---|
| 939 | } else { |
---|
| 940 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 941 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 942 | } |
---|
| 943 | |
---|
| 944 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 945 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 946 | |
---|
| 947 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 948 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 949 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 950 | (*_blossom_data)[vb].offset); |
---|
| 951 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 952 | (*_blossom_data)[vb].offset){ |
---|
| 953 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 954 | (*_blossom_data)[vb].offset); |
---|
| 955 | } |
---|
| 956 | } |
---|
| 957 | } |
---|
| 958 | } |
---|
| 959 | } |
---|
| 960 | } |
---|
| 961 | (*_blossom_data)[blossom].offset = 0; |
---|
| 962 | } |
---|
| 963 | |
---|
| 964 | void matchedToOdd(int blossom) { |
---|
| 965 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 966 | _delta2->erase(blossom); |
---|
| 967 | } |
---|
| 968 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 969 | if (!_blossom_set->trivial(blossom)) { |
---|
| 970 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 971 | (*_blossom_data)[blossom].offset); |
---|
| 972 | } |
---|
| 973 | } |
---|
| 974 | |
---|
| 975 | void evenToMatched(int blossom, int tree) { |
---|
| 976 | if (!_blossom_set->trivial(blossom)) { |
---|
| 977 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 978 | } |
---|
| 979 | |
---|
| 980 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 981 | n != INVALID; ++n) { |
---|
| 982 | int ni = (*_node_index)[n]; |
---|
| 983 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 984 | |
---|
| 985 | _delta1->erase(n); |
---|
| 986 | |
---|
| 987 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 988 | Node v = _graph.source(e); |
---|
| 989 | int vb = _blossom_set->find(v); |
---|
| 990 | int vi = (*_node_index)[v]; |
---|
| 991 | |
---|
| 992 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 993 | dualScale * _weight[e]; |
---|
| 994 | |
---|
| 995 | if (vb == blossom) { |
---|
| 996 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 997 | _delta3->erase(e); |
---|
| 998 | } |
---|
| 999 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1000 | |
---|
| 1001 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1002 | _delta3->erase(e); |
---|
| 1003 | } |
---|
| 1004 | |
---|
| 1005 | int vt = _tree_set->find(vb); |
---|
| 1006 | |
---|
| 1007 | if (vt != tree) { |
---|
| 1008 | |
---|
| 1009 | Arc r = _graph.oppositeArc(e); |
---|
| 1010 | |
---|
| 1011 | typename std::map<int, Arc>::iterator it = |
---|
| 1012 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1013 | |
---|
| 1014 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1015 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1016 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 1017 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 1018 | it->second = r; |
---|
| 1019 | } |
---|
| 1020 | } else { |
---|
| 1021 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 1022 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 1023 | } |
---|
| 1024 | |
---|
| 1025 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1026 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1027 | |
---|
| 1028 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1029 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1030 | (*_blossom_data)[blossom].offset); |
---|
| 1031 | } else if ((*_delta2)[blossom] > |
---|
| 1032 | _blossom_set->classPrio(blossom) - |
---|
| 1033 | (*_blossom_data)[blossom].offset){ |
---|
| 1034 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1035 | (*_blossom_data)[blossom].offset); |
---|
| 1036 | } |
---|
| 1037 | } |
---|
| 1038 | } |
---|
| 1039 | |
---|
| 1040 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1041 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1042 | _delta3->erase(e); |
---|
| 1043 | } |
---|
| 1044 | } else { |
---|
| 1045 | |
---|
| 1046 | typename std::map<int, Arc>::iterator it = |
---|
| 1047 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1048 | |
---|
| 1049 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1050 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 1051 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 1052 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 1053 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 1054 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 1055 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 1056 | } |
---|
| 1057 | |
---|
| 1058 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1059 | if (_blossom_set->classPrio(vb) == |
---|
| 1060 | std::numeric_limits<Value>::max()) { |
---|
| 1061 | _delta2->erase(vb); |
---|
| 1062 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 1063 | (*_blossom_data)[vb].offset) { |
---|
| 1064 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 1065 | (*_blossom_data)[vb].offset); |
---|
| 1066 | } |
---|
| 1067 | } |
---|
| 1068 | } |
---|
| 1069 | } |
---|
| 1070 | } |
---|
| 1071 | } |
---|
| 1072 | } |
---|
| 1073 | |
---|
| 1074 | void oddToMatched(int blossom) { |
---|
| 1075 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 1076 | |
---|
| 1077 | if (_blossom_set->classPrio(blossom) != |
---|
| 1078 | std::numeric_limits<Value>::max()) { |
---|
| 1079 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1080 | (*_blossom_data)[blossom].offset); |
---|
| 1081 | } |
---|
| 1082 | |
---|
| 1083 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1084 | _delta4->erase(blossom); |
---|
| 1085 | } |
---|
| 1086 | } |
---|
| 1087 | |
---|
| 1088 | void oddToEven(int blossom, int tree) { |
---|
| 1089 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1090 | _delta4->erase(blossom); |
---|
| 1091 | (*_blossom_data)[blossom].pot -= |
---|
| 1092 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 1093 | } |
---|
| 1094 | |
---|
| 1095 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1096 | n != INVALID; ++n) { |
---|
| 1097 | int ni = (*_node_index)[n]; |
---|
| 1098 | |
---|
| 1099 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1100 | |
---|
| 1101 | (*_node_data)[ni].heap.clear(); |
---|
| 1102 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1103 | (*_node_data)[ni].pot += |
---|
| 1104 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 1105 | |
---|
| 1106 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 1107 | |
---|
| 1108 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1109 | Node v = _graph.source(e); |
---|
| 1110 | int vb = _blossom_set->find(v); |
---|
| 1111 | int vi = (*_node_index)[v]; |
---|
| 1112 | |
---|
| 1113 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1114 | dualScale * _weight[e]; |
---|
| 1115 | |
---|
| 1116 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1117 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 1118 | _delta3->push(e, rw / 2); |
---|
| 1119 | } |
---|
| 1120 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1121 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 1122 | _delta3->push(e, rw); |
---|
| 1123 | } |
---|
| 1124 | } else { |
---|
| 1125 | |
---|
| 1126 | typename std::map<int, Arc>::iterator it = |
---|
| 1127 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1128 | |
---|
| 1129 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1130 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 1131 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 1132 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 1133 | it->second = e; |
---|
| 1134 | } |
---|
| 1135 | } else { |
---|
| 1136 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 1137 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 1138 | } |
---|
| 1139 | |
---|
| 1140 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 1141 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 1142 | |
---|
| 1143 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1144 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 1145 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 1146 | (*_blossom_data)[vb].offset); |
---|
| 1147 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 1148 | (*_blossom_data)[vb].offset) { |
---|
| 1149 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 1150 | (*_blossom_data)[vb].offset); |
---|
| 1151 | } |
---|
| 1152 | } |
---|
| 1153 | } |
---|
| 1154 | } |
---|
| 1155 | } |
---|
| 1156 | } |
---|
| 1157 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1158 | } |
---|
| 1159 | |
---|
| 1160 | |
---|
| 1161 | void matchedToUnmatched(int blossom) { |
---|
| 1162 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1163 | _delta2->erase(blossom); |
---|
| 1164 | } |
---|
| 1165 | |
---|
| 1166 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1167 | n != INVALID; ++n) { |
---|
| 1168 | int ni = (*_node_index)[n]; |
---|
| 1169 | |
---|
| 1170 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1171 | |
---|
| 1172 | (*_node_data)[ni].heap.clear(); |
---|
| 1173 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1174 | |
---|
| 1175 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1176 | Node v = _graph.target(e); |
---|
| 1177 | int vb = _blossom_set->find(v); |
---|
| 1178 | int vi = (*_node_index)[v]; |
---|
| 1179 | |
---|
| 1180 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1181 | dualScale * _weight[e]; |
---|
| 1182 | |
---|
| 1183 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1184 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 1185 | _delta3->push(e, rw); |
---|
| 1186 | } |
---|
| 1187 | } |
---|
| 1188 | } |
---|
| 1189 | } |
---|
| 1190 | } |
---|
| 1191 | |
---|
| 1192 | void unmatchedToMatched(int blossom) { |
---|
| 1193 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1194 | n != INVALID; ++n) { |
---|
| 1195 | int ni = (*_node_index)[n]; |
---|
| 1196 | |
---|
| 1197 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1198 | Node v = _graph.source(e); |
---|
| 1199 | int vb = _blossom_set->find(v); |
---|
| 1200 | int vi = (*_node_index)[v]; |
---|
| 1201 | |
---|
| 1202 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1203 | dualScale * _weight[e]; |
---|
| 1204 | |
---|
| 1205 | if (vb == blossom) { |
---|
| 1206 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1207 | _delta3->erase(e); |
---|
| 1208 | } |
---|
| 1209 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1210 | |
---|
| 1211 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1212 | _delta3->erase(e); |
---|
| 1213 | } |
---|
| 1214 | |
---|
| 1215 | int vt = _tree_set->find(vb); |
---|
| 1216 | |
---|
| 1217 | Arc r = _graph.oppositeArc(e); |
---|
| 1218 | |
---|
| 1219 | typename std::map<int, Arc>::iterator it = |
---|
| 1220 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1221 | |
---|
| 1222 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1223 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1224 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 1225 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 1226 | it->second = r; |
---|
| 1227 | } |
---|
| 1228 | } else { |
---|
| 1229 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 1230 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 1231 | } |
---|
| 1232 | |
---|
| 1233 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1234 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1235 | |
---|
| 1236 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1237 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1238 | (*_blossom_data)[blossom].offset); |
---|
| 1239 | } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)- |
---|
| 1240 | (*_blossom_data)[blossom].offset){ |
---|
| 1241 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1242 | (*_blossom_data)[blossom].offset); |
---|
| 1243 | } |
---|
| 1244 | } |
---|
| 1245 | |
---|
| 1246 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1247 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1248 | _delta3->erase(e); |
---|
| 1249 | } |
---|
| 1250 | } |
---|
| 1251 | } |
---|
| 1252 | } |
---|
| 1253 | } |
---|
| 1254 | |
---|
| 1255 | void alternatePath(int even, int tree) { |
---|
| 1256 | int odd; |
---|
| 1257 | |
---|
| 1258 | evenToMatched(even, tree); |
---|
| 1259 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1260 | |
---|
| 1261 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 1262 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 1263 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 1264 | oddToMatched(odd); |
---|
| 1265 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 1266 | |
---|
| 1267 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 1268 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1269 | evenToMatched(even, tree); |
---|
| 1270 | (*_blossom_data)[even].next = |
---|
| 1271 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 1272 | } |
---|
| 1273 | |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | void destroyTree(int tree) { |
---|
| 1277 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 1278 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 1279 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1280 | evenToMatched(b, tree); |
---|
| 1281 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 1282 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1283 | oddToMatched(b); |
---|
| 1284 | } |
---|
| 1285 | } |
---|
| 1286 | _tree_set->eraseClass(tree); |
---|
| 1287 | } |
---|
| 1288 | |
---|
| 1289 | |
---|
| 1290 | void unmatchNode(const Node& node) { |
---|
| 1291 | int blossom = _blossom_set->find(node); |
---|
| 1292 | int tree = _tree_set->find(blossom); |
---|
| 1293 | |
---|
| 1294 | alternatePath(blossom, tree); |
---|
| 1295 | destroyTree(tree); |
---|
| 1296 | |
---|
| 1297 | (*_blossom_data)[blossom].status = UNMATCHED; |
---|
| 1298 | (*_blossom_data)[blossom].base = node; |
---|
| 1299 | matchedToUnmatched(blossom); |
---|
| 1300 | } |
---|
| 1301 | |
---|
| 1302 | |
---|
[327] | 1303 | void augmentOnEdge(const Edge& edge) { |
---|
| 1304 | |
---|
| 1305 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1306 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[326] | 1307 | |
---|
| 1308 | if ((*_blossom_data)[left].status == EVEN) { |
---|
| 1309 | int left_tree = _tree_set->find(left); |
---|
| 1310 | alternatePath(left, left_tree); |
---|
| 1311 | destroyTree(left_tree); |
---|
| 1312 | } else { |
---|
| 1313 | (*_blossom_data)[left].status = MATCHED; |
---|
| 1314 | unmatchedToMatched(left); |
---|
| 1315 | } |
---|
| 1316 | |
---|
| 1317 | if ((*_blossom_data)[right].status == EVEN) { |
---|
| 1318 | int right_tree = _tree_set->find(right); |
---|
| 1319 | alternatePath(right, right_tree); |
---|
| 1320 | destroyTree(right_tree); |
---|
| 1321 | } else { |
---|
| 1322 | (*_blossom_data)[right].status = MATCHED; |
---|
| 1323 | unmatchedToMatched(right); |
---|
| 1324 | } |
---|
| 1325 | |
---|
[327] | 1326 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 1327 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[326] | 1328 | } |
---|
| 1329 | |
---|
| 1330 | void extendOnArc(const Arc& arc) { |
---|
| 1331 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 1332 | int tree = _tree_set->find(base); |
---|
| 1333 | |
---|
| 1334 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 1335 | _tree_set->insert(odd, tree); |
---|
| 1336 | (*_blossom_data)[odd].status = ODD; |
---|
| 1337 | matchedToOdd(odd); |
---|
| 1338 | (*_blossom_data)[odd].pred = arc; |
---|
| 1339 | |
---|
| 1340 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 1341 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 1342 | _tree_set->insert(even, tree); |
---|
| 1343 | (*_blossom_data)[even].status = EVEN; |
---|
| 1344 | matchedToEven(even, tree); |
---|
| 1345 | } |
---|
| 1346 | |
---|
[327] | 1347 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[326] | 1348 | int nca = -1; |
---|
| 1349 | std::vector<int> left_path, right_path; |
---|
| 1350 | |
---|
| 1351 | { |
---|
| 1352 | std::set<int> left_set, right_set; |
---|
| 1353 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 1354 | left_path.push_back(left); |
---|
| 1355 | left_set.insert(left); |
---|
| 1356 | |
---|
| 1357 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 1358 | right_path.push_back(right); |
---|
| 1359 | right_set.insert(right); |
---|
| 1360 | |
---|
| 1361 | while (true) { |
---|
| 1362 | |
---|
| 1363 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 1364 | |
---|
| 1365 | left = |
---|
| 1366 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1367 | left_path.push_back(left); |
---|
| 1368 | left = |
---|
| 1369 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 1370 | left_path.push_back(left); |
---|
| 1371 | |
---|
| 1372 | left_set.insert(left); |
---|
| 1373 | |
---|
| 1374 | if (right_set.find(left) != right_set.end()) { |
---|
| 1375 | nca = left; |
---|
| 1376 | break; |
---|
| 1377 | } |
---|
| 1378 | |
---|
| 1379 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 1380 | |
---|
| 1381 | right = |
---|
| 1382 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1383 | right_path.push_back(right); |
---|
| 1384 | right = |
---|
| 1385 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 1386 | right_path.push_back(right); |
---|
| 1387 | |
---|
| 1388 | right_set.insert(right); |
---|
| 1389 | |
---|
| 1390 | if (left_set.find(right) != left_set.end()) { |
---|
| 1391 | nca = right; |
---|
| 1392 | break; |
---|
| 1393 | } |
---|
| 1394 | |
---|
| 1395 | } |
---|
| 1396 | |
---|
| 1397 | if (nca == -1) { |
---|
| 1398 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 1399 | nca = right; |
---|
| 1400 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1401 | nca = |
---|
| 1402 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1403 | right_path.push_back(nca); |
---|
| 1404 | nca = |
---|
| 1405 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1406 | right_path.push_back(nca); |
---|
| 1407 | } |
---|
| 1408 | } else { |
---|
| 1409 | nca = left; |
---|
| 1410 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1411 | nca = |
---|
| 1412 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1413 | left_path.push_back(nca); |
---|
| 1414 | nca = |
---|
| 1415 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 1416 | left_path.push_back(nca); |
---|
| 1417 | } |
---|
| 1418 | } |
---|
| 1419 | } |
---|
| 1420 | } |
---|
| 1421 | |
---|
| 1422 | std::vector<int> subblossoms; |
---|
| 1423 | Arc prev; |
---|
| 1424 | |
---|
| 1425 | prev = _graph.direct(edge, true); |
---|
| 1426 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1427 | subblossoms.push_back(left_path[i]); |
---|
| 1428 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 1429 | _tree_set->erase(left_path[i]); |
---|
| 1430 | |
---|
| 1431 | subblossoms.push_back(left_path[i + 1]); |
---|
| 1432 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 1433 | oddToEven(left_path[i + 1], tree); |
---|
| 1434 | _tree_set->erase(left_path[i + 1]); |
---|
| 1435 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 1436 | } |
---|
| 1437 | |
---|
| 1438 | int k = 0; |
---|
| 1439 | while (right_path[k] != nca) ++k; |
---|
| 1440 | |
---|
| 1441 | subblossoms.push_back(nca); |
---|
| 1442 | (*_blossom_data)[nca].next = prev; |
---|
| 1443 | |
---|
| 1444 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 1445 | subblossoms.push_back(right_path[i + 1]); |
---|
| 1446 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 1447 | oddToEven(right_path[i + 1], tree); |
---|
| 1448 | _tree_set->erase(right_path[i + 1]); |
---|
| 1449 | |
---|
| 1450 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 1451 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 1452 | |
---|
| 1453 | subblossoms.push_back(right_path[i]); |
---|
| 1454 | _tree_set->erase(right_path[i]); |
---|
| 1455 | } |
---|
| 1456 | |
---|
| 1457 | int surface = |
---|
| 1458 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1459 | |
---|
| 1460 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1461 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1462 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 1463 | } |
---|
| 1464 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 1465 | } |
---|
| 1466 | |
---|
| 1467 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 1468 | (*_blossom_data)[surface].offset = 0; |
---|
| 1469 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1470 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 1471 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 1472 | |
---|
| 1473 | _tree_set->insert(surface, tree); |
---|
| 1474 | _tree_set->erase(nca); |
---|
| 1475 | } |
---|
| 1476 | |
---|
| 1477 | void splitBlossom(int blossom) { |
---|
| 1478 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 1479 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 1480 | |
---|
| 1481 | int tree = _tree_set->find(blossom); |
---|
| 1482 | |
---|
| 1483 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1484 | oddToMatched(blossom); |
---|
| 1485 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1486 | _delta2->erase(blossom); |
---|
| 1487 | } |
---|
| 1488 | |
---|
| 1489 | std::vector<int> subblossoms; |
---|
| 1490 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1491 | |
---|
| 1492 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 1493 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 1494 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 1495 | |
---|
| 1496 | int ib = -1, id = -1; |
---|
| 1497 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1498 | if (subblossoms[i] == b) ib = i; |
---|
| 1499 | if (subblossoms[i] == d) id = i; |
---|
| 1500 | |
---|
| 1501 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 1502 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1503 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 1504 | } |
---|
| 1505 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 1506 | std::numeric_limits<Value>::max()) { |
---|
| 1507 | _delta2->push(subblossoms[i], |
---|
| 1508 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 1509 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 1510 | } |
---|
| 1511 | } |
---|
| 1512 | |
---|
| 1513 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 1514 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 1515 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1516 | int sb = subblossoms[i]; |
---|
| 1517 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1518 | (*_blossom_data)[sb].next = |
---|
| 1519 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1520 | } |
---|
| 1521 | |
---|
| 1522 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1523 | int sb = subblossoms[i]; |
---|
| 1524 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1525 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1526 | |
---|
| 1527 | (*_blossom_data)[sb].status = ODD; |
---|
| 1528 | matchedToOdd(sb); |
---|
| 1529 | _tree_set->insert(sb, tree); |
---|
| 1530 | (*_blossom_data)[sb].pred = pred; |
---|
| 1531 | (*_blossom_data)[sb].next = |
---|
| 1532 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1533 | |
---|
| 1534 | pred = (*_blossom_data)[ub].next; |
---|
| 1535 | |
---|
| 1536 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1537 | matchedToEven(tb, tree); |
---|
| 1538 | _tree_set->insert(tb, tree); |
---|
| 1539 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 1540 | } |
---|
| 1541 | |
---|
| 1542 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 1543 | matchedToOdd(subblossoms[id]); |
---|
| 1544 | _tree_set->insert(subblossoms[id], tree); |
---|
| 1545 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 1546 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 1547 | |
---|
| 1548 | } else { |
---|
| 1549 | |
---|
| 1550 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 1551 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1552 | int sb = subblossoms[i]; |
---|
| 1553 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1554 | (*_blossom_data)[sb].next = |
---|
| 1555 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1556 | } |
---|
| 1557 | |
---|
| 1558 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1559 | int sb = subblossoms[i]; |
---|
| 1560 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1561 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1562 | |
---|
| 1563 | (*_blossom_data)[sb].status = ODD; |
---|
| 1564 | matchedToOdd(sb); |
---|
| 1565 | _tree_set->insert(sb, tree); |
---|
| 1566 | (*_blossom_data)[sb].next = next; |
---|
| 1567 | (*_blossom_data)[sb].pred = |
---|
| 1568 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 1569 | |
---|
| 1570 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1571 | matchedToEven(tb, tree); |
---|
| 1572 | _tree_set->insert(tb, tree); |
---|
| 1573 | (*_blossom_data)[tb].pred = |
---|
| 1574 | (*_blossom_data)[tb].next = |
---|
| 1575 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 1576 | next = (*_blossom_data)[ub].next; |
---|
| 1577 | } |
---|
| 1578 | |
---|
| 1579 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 1580 | matchedToOdd(subblossoms[ib]); |
---|
| 1581 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 1582 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 1583 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 1584 | } |
---|
| 1585 | _tree_set->erase(blossom); |
---|
| 1586 | } |
---|
| 1587 | |
---|
| 1588 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 1589 | if (_blossom_set->trivial(blossom)) { |
---|
| 1590 | int bi = (*_node_index)[base]; |
---|
| 1591 | Value pot = (*_node_data)[bi].pot; |
---|
| 1592 | |
---|
[581] | 1593 | (*_matching)[base] = matching; |
---|
[326] | 1594 | _blossom_node_list.push_back(base); |
---|
[581] | 1595 | (*_node_potential)[base] = pot; |
---|
[326] | 1596 | } else { |
---|
| 1597 | |
---|
| 1598 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 1599 | int bn = _blossom_node_list.size(); |
---|
| 1600 | |
---|
| 1601 | std::vector<int> subblossoms; |
---|
| 1602 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1603 | int b = _blossom_set->find(base); |
---|
| 1604 | int ib = -1; |
---|
| 1605 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1606 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 1607 | } |
---|
| 1608 | |
---|
| 1609 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 1610 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 1611 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 1612 | |
---|
| 1613 | Arc m = (*_blossom_data)[tb].next; |
---|
| 1614 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 1615 | extractBlossom(tb, _graph.source(m), m); |
---|
| 1616 | } |
---|
| 1617 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 1618 | |
---|
| 1619 | int en = _blossom_node_list.size(); |
---|
| 1620 | |
---|
| 1621 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 1622 | } |
---|
| 1623 | } |
---|
| 1624 | |
---|
| 1625 | void extractMatching() { |
---|
| 1626 | std::vector<int> blossoms; |
---|
| 1627 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 1628 | blossoms.push_back(c); |
---|
| 1629 | } |
---|
| 1630 | |
---|
| 1631 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 1632 | if ((*_blossom_data)[blossoms[i]].status == MATCHED) { |
---|
| 1633 | |
---|
| 1634 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 1635 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 1636 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 1637 | n != INVALID; ++n) { |
---|
| 1638 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 1639 | } |
---|
| 1640 | |
---|
| 1641 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 1642 | Node base = _graph.source(matching); |
---|
| 1643 | extractBlossom(blossoms[i], base, matching); |
---|
| 1644 | } else { |
---|
| 1645 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
| 1646 | extractBlossom(blossoms[i], base, INVALID); |
---|
| 1647 | } |
---|
| 1648 | } |
---|
| 1649 | } |
---|
| 1650 | |
---|
| 1651 | public: |
---|
| 1652 | |
---|
| 1653 | /// \brief Constructor |
---|
| 1654 | /// |
---|
| 1655 | /// Constructor. |
---|
| 1656 | MaxWeightedMatching(const Graph& graph, const WeightMap& weight) |
---|
| 1657 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 1658 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 1659 | _node_num(0), _blossom_num(0), |
---|
| 1660 | |
---|
| 1661 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 1662 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 1663 | _tree_set_index(0), _tree_set(0), |
---|
| 1664 | |
---|
| 1665 | _delta1_index(0), _delta1(0), |
---|
| 1666 | _delta2_index(0), _delta2(0), |
---|
| 1667 | _delta3_index(0), _delta3(0), |
---|
| 1668 | _delta4_index(0), _delta4(0), |
---|
| 1669 | |
---|
| 1670 | _delta_sum() {} |
---|
| 1671 | |
---|
| 1672 | ~MaxWeightedMatching() { |
---|
| 1673 | destroyStructures(); |
---|
| 1674 | } |
---|
| 1675 | |
---|
[590] | 1676 | /// \name Execution Control |
---|
[330] | 1677 | /// The simplest way to execute the algorithm is to use the |
---|
[590] | 1678 | /// \ref run() member function. |
---|
[326] | 1679 | |
---|
| 1680 | ///@{ |
---|
| 1681 | |
---|
| 1682 | /// \brief Initialize the algorithm |
---|
| 1683 | /// |
---|
[590] | 1684 | /// This function initializes the algorithm. |
---|
[326] | 1685 | void init() { |
---|
| 1686 | createStructures(); |
---|
| 1687 | |
---|
| 1688 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[581] | 1689 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
[326] | 1690 | } |
---|
| 1691 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
[581] | 1692 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
[326] | 1693 | } |
---|
| 1694 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
[581] | 1695 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
[326] | 1696 | } |
---|
| 1697 | for (int i = 0; i < _blossom_num; ++i) { |
---|
[581] | 1698 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 1699 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
[326] | 1700 | } |
---|
| 1701 | |
---|
| 1702 | int index = 0; |
---|
| 1703 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1704 | Value max = 0; |
---|
| 1705 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 1706 | if (_graph.target(e) == n) continue; |
---|
| 1707 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 1708 | max = (dualScale * _weight[e]) / 2; |
---|
| 1709 | } |
---|
| 1710 | } |
---|
[581] | 1711 | (*_node_index)[n] = index; |
---|
[326] | 1712 | (*_node_data)[index].pot = max; |
---|
| 1713 | _delta1->push(n, max); |
---|
| 1714 | int blossom = |
---|
| 1715 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1716 | |
---|
| 1717 | _tree_set->insert(blossom); |
---|
| 1718 | |
---|
| 1719 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 1720 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1721 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 1722 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1723 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1724 | ++index; |
---|
| 1725 | } |
---|
| 1726 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 1727 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 1728 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 1729 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 1730 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1731 | dualScale * _weight[e]) / 2); |
---|
| 1732 | } |
---|
| 1733 | } |
---|
| 1734 | } |
---|
| 1735 | |
---|
[590] | 1736 | /// \brief Start the algorithm |
---|
[326] | 1737 | /// |
---|
[590] | 1738 | /// This function starts the algorithm. |
---|
| 1739 | /// |
---|
| 1740 | /// \pre \ref init() must be called before using this function. |
---|
[326] | 1741 | void start() { |
---|
| 1742 | enum OpType { |
---|
| 1743 | D1, D2, D3, D4 |
---|
| 1744 | }; |
---|
| 1745 | |
---|
| 1746 | int unmatched = _node_num; |
---|
| 1747 | while (unmatched > 0) { |
---|
| 1748 | Value d1 = !_delta1->empty() ? |
---|
| 1749 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
| 1750 | |
---|
| 1751 | Value d2 = !_delta2->empty() ? |
---|
| 1752 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 1753 | |
---|
| 1754 | Value d3 = !_delta3->empty() ? |
---|
| 1755 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 1756 | |
---|
| 1757 | Value d4 = !_delta4->empty() ? |
---|
| 1758 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 1759 | |
---|
| 1760 | _delta_sum = d1; OpType ot = D1; |
---|
| 1761 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
| 1762 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
| 1763 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 1764 | |
---|
| 1765 | |
---|
| 1766 | switch (ot) { |
---|
| 1767 | case D1: |
---|
| 1768 | { |
---|
| 1769 | Node n = _delta1->top(); |
---|
| 1770 | unmatchNode(n); |
---|
| 1771 | --unmatched; |
---|
| 1772 | } |
---|
| 1773 | break; |
---|
| 1774 | case D2: |
---|
| 1775 | { |
---|
| 1776 | int blossom = _delta2->top(); |
---|
| 1777 | Node n = _blossom_set->classTop(blossom); |
---|
| 1778 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 1779 | extendOnArc(e); |
---|
| 1780 | } |
---|
| 1781 | break; |
---|
| 1782 | case D3: |
---|
| 1783 | { |
---|
| 1784 | Edge e = _delta3->top(); |
---|
| 1785 | |
---|
| 1786 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 1787 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 1788 | |
---|
| 1789 | if (left_blossom == right_blossom) { |
---|
| 1790 | _delta3->pop(); |
---|
| 1791 | } else { |
---|
| 1792 | int left_tree; |
---|
| 1793 | if ((*_blossom_data)[left_blossom].status == EVEN) { |
---|
| 1794 | left_tree = _tree_set->find(left_blossom); |
---|
| 1795 | } else { |
---|
| 1796 | left_tree = -1; |
---|
| 1797 | ++unmatched; |
---|
| 1798 | } |
---|
| 1799 | int right_tree; |
---|
| 1800 | if ((*_blossom_data)[right_blossom].status == EVEN) { |
---|
| 1801 | right_tree = _tree_set->find(right_blossom); |
---|
| 1802 | } else { |
---|
| 1803 | right_tree = -1; |
---|
| 1804 | ++unmatched; |
---|
| 1805 | } |
---|
| 1806 | |
---|
| 1807 | if (left_tree == right_tree) { |
---|
[327] | 1808 | shrinkOnEdge(e, left_tree); |
---|
[326] | 1809 | } else { |
---|
[327] | 1810 | augmentOnEdge(e); |
---|
[326] | 1811 | unmatched -= 2; |
---|
| 1812 | } |
---|
| 1813 | } |
---|
| 1814 | } break; |
---|
| 1815 | case D4: |
---|
| 1816 | splitBlossom(_delta4->top()); |
---|
| 1817 | break; |
---|
| 1818 | } |
---|
| 1819 | } |
---|
| 1820 | extractMatching(); |
---|
| 1821 | } |
---|
| 1822 | |
---|
[590] | 1823 | /// \brief Run the algorithm. |
---|
[326] | 1824 | /// |
---|
[590] | 1825 | /// This method runs the \c %MaxWeightedMatching algorithm. |
---|
[326] | 1826 | /// |
---|
| 1827 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 1828 | /// \code |
---|
| 1829 | /// mwm.init(); |
---|
| 1830 | /// mwm.start(); |
---|
| 1831 | /// \endcode |
---|
| 1832 | void run() { |
---|
| 1833 | init(); |
---|
| 1834 | start(); |
---|
| 1835 | } |
---|
| 1836 | |
---|
| 1837 | /// @} |
---|
| 1838 | |
---|
[590] | 1839 | /// \name Primal Solution |
---|
| 1840 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
| 1841 | /// matching.\n |
---|
| 1842 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1843 | /// using them. |
---|
[326] | 1844 | |
---|
| 1845 | /// @{ |
---|
| 1846 | |
---|
[590] | 1847 | /// \brief Return the weight of the matching. |
---|
[326] | 1848 | /// |
---|
[590] | 1849 | /// This function returns the weight of the found matching. |
---|
| 1850 | /// |
---|
| 1851 | /// \pre Either run() or start() must be called before using this function. |
---|
[593] | 1852 | Value matchingWeight() const { |
---|
[326] | 1853 | Value sum = 0; |
---|
| 1854 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1855 | if ((*_matching)[n] != INVALID) { |
---|
| 1856 | sum += _weight[(*_matching)[n]]; |
---|
| 1857 | } |
---|
| 1858 | } |
---|
| 1859 | return sum /= 2; |
---|
| 1860 | } |
---|
| 1861 | |
---|
[590] | 1862 | /// \brief Return the size (cardinality) of the matching. |
---|
[326] | 1863 | /// |
---|
[590] | 1864 | /// This function returns the size (cardinality) of the found matching. |
---|
| 1865 | /// |
---|
| 1866 | /// \pre Either run() or start() must be called before using this function. |
---|
[327] | 1867 | int matchingSize() const { |
---|
| 1868 | int num = 0; |
---|
| 1869 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1870 | if ((*_matching)[n] != INVALID) { |
---|
| 1871 | ++num; |
---|
| 1872 | } |
---|
| 1873 | } |
---|
| 1874 | return num /= 2; |
---|
| 1875 | } |
---|
| 1876 | |
---|
[590] | 1877 | /// \brief Return \c true if the given edge is in the matching. |
---|
[327] | 1878 | /// |
---|
[590] | 1879 | /// This function returns \c true if the given edge is in the found |
---|
| 1880 | /// matching. |
---|
| 1881 | /// |
---|
| 1882 | /// \pre Either run() or start() must be called before using this function. |
---|
[327] | 1883 | bool matching(const Edge& edge) const { |
---|
| 1884 | return edge == (*_matching)[_graph.u(edge)]; |
---|
[326] | 1885 | } |
---|
| 1886 | |
---|
[590] | 1887 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[326] | 1888 | /// |
---|
[590] | 1889 | /// This function returns the matching arc (or edge) incident to the |
---|
| 1890 | /// given node in the found matching or \c INVALID if the node is |
---|
| 1891 | /// not covered by the matching. |
---|
| 1892 | /// |
---|
| 1893 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 1894 | Arc matching(const Node& node) const { |
---|
| 1895 | return (*_matching)[node]; |
---|
| 1896 | } |
---|
| 1897 | |
---|
[593] | 1898 | /// \brief Return a const reference to the matching map. |
---|
| 1899 | /// |
---|
| 1900 | /// This function returns a const reference to a node map that stores |
---|
| 1901 | /// the matching arc (or edge) incident to each node. |
---|
| 1902 | const MatchingMap& matchingMap() const { |
---|
| 1903 | return *_matching; |
---|
| 1904 | } |
---|
| 1905 | |
---|
[590] | 1906 | /// \brief Return the mate of the given node. |
---|
[326] | 1907 | /// |
---|
[590] | 1908 | /// This function returns the mate of the given node in the found |
---|
| 1909 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
| 1910 | /// |
---|
| 1911 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 1912 | Node mate(const Node& node) const { |
---|
| 1913 | return (*_matching)[node] != INVALID ? |
---|
| 1914 | _graph.target((*_matching)[node]) : INVALID; |
---|
| 1915 | } |
---|
| 1916 | |
---|
| 1917 | /// @} |
---|
| 1918 | |
---|
[590] | 1919 | /// \name Dual Solution |
---|
| 1920 | /// Functions to get the dual solution.\n |
---|
| 1921 | /// Either \ref run() or \ref start() function should be called before |
---|
| 1922 | /// using them. |
---|
[326] | 1923 | |
---|
| 1924 | /// @{ |
---|
| 1925 | |
---|
[590] | 1926 | /// \brief Return the value of the dual solution. |
---|
[326] | 1927 | /// |
---|
[590] | 1928 | /// This function returns the value of the dual solution. |
---|
| 1929 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
| 1930 | /// "dual scale". |
---|
| 1931 | /// |
---|
| 1932 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 1933 | Value dualValue() const { |
---|
| 1934 | Value sum = 0; |
---|
| 1935 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1936 | sum += nodeValue(n); |
---|
| 1937 | } |
---|
| 1938 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 1939 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 1940 | } |
---|
| 1941 | return sum; |
---|
| 1942 | } |
---|
| 1943 | |
---|
[590] | 1944 | /// \brief Return the dual value (potential) of the given node. |
---|
[326] | 1945 | /// |
---|
[590] | 1946 | /// This function returns the dual value (potential) of the given node. |
---|
| 1947 | /// |
---|
| 1948 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 1949 | Value nodeValue(const Node& n) const { |
---|
| 1950 | return (*_node_potential)[n]; |
---|
| 1951 | } |
---|
| 1952 | |
---|
[590] | 1953 | /// \brief Return the number of the blossoms in the basis. |
---|
[326] | 1954 | /// |
---|
[590] | 1955 | /// This function returns the number of the blossoms in the basis. |
---|
| 1956 | /// |
---|
| 1957 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 1958 | /// \see BlossomIt |
---|
| 1959 | int blossomNum() const { |
---|
| 1960 | return _blossom_potential.size(); |
---|
| 1961 | } |
---|
| 1962 | |
---|
[590] | 1963 | /// \brief Return the number of the nodes in the given blossom. |
---|
[326] | 1964 | /// |
---|
[590] | 1965 | /// This function returns the number of the nodes in the given blossom. |
---|
| 1966 | /// |
---|
| 1967 | /// \pre Either run() or start() must be called before using this function. |
---|
| 1968 | /// \see BlossomIt |
---|
[326] | 1969 | int blossomSize(int k) const { |
---|
| 1970 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 1971 | } |
---|
| 1972 | |
---|
[590] | 1973 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
[326] | 1974 | /// |
---|
[590] | 1975 | /// This function returns the dual value (ptential) of the given blossom. |
---|
| 1976 | /// |
---|
| 1977 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 1978 | Value blossomValue(int k) const { |
---|
| 1979 | return _blossom_potential[k].value; |
---|
| 1980 | } |
---|
| 1981 | |
---|
[590] | 1982 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
[326] | 1983 | /// |
---|
[590] | 1984 | /// This class provides an iterator for obtaining the nodes of the |
---|
| 1985 | /// given blossom. It lists a subset of the nodes. |
---|
| 1986 | /// Before using this iterator, you must allocate a |
---|
| 1987 | /// MaxWeightedMatching class and execute it. |
---|
[326] | 1988 | class BlossomIt { |
---|
| 1989 | public: |
---|
| 1990 | |
---|
| 1991 | /// \brief Constructor. |
---|
| 1992 | /// |
---|
[590] | 1993 | /// Constructor to get the nodes of the given variable. |
---|
| 1994 | /// |
---|
| 1995 | /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or |
---|
| 1996 | /// \ref MaxWeightedMatching::start() "algorithm.start()" must be |
---|
| 1997 | /// called before initializing this iterator. |
---|
[326] | 1998 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
| 1999 | : _algorithm(&algorithm) |
---|
| 2000 | { |
---|
| 2001 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 2002 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 2003 | } |
---|
| 2004 | |
---|
[590] | 2005 | /// \brief Conversion to \c Node. |
---|
[326] | 2006 | /// |
---|
[590] | 2007 | /// Conversion to \c Node. |
---|
[326] | 2008 | operator Node() const { |
---|
[327] | 2009 | return _algorithm->_blossom_node_list[_index]; |
---|
[326] | 2010 | } |
---|
| 2011 | |
---|
| 2012 | /// \brief Increment operator. |
---|
| 2013 | /// |
---|
| 2014 | /// Increment operator. |
---|
| 2015 | BlossomIt& operator++() { |
---|
| 2016 | ++_index; |
---|
| 2017 | return *this; |
---|
| 2018 | } |
---|
| 2019 | |
---|
[327] | 2020 | /// \brief Validity checking |
---|
| 2021 | /// |
---|
| 2022 | /// Checks whether the iterator is invalid. |
---|
| 2023 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 2024 | |
---|
| 2025 | /// \brief Validity checking |
---|
| 2026 | /// |
---|
| 2027 | /// Checks whether the iterator is valid. |
---|
| 2028 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[326] | 2029 | |
---|
| 2030 | private: |
---|
| 2031 | const MaxWeightedMatching* _algorithm; |
---|
| 2032 | int _last; |
---|
| 2033 | int _index; |
---|
| 2034 | }; |
---|
| 2035 | |
---|
| 2036 | /// @} |
---|
| 2037 | |
---|
| 2038 | }; |
---|
| 2039 | |
---|
| 2040 | /// \ingroup matching |
---|
| 2041 | /// |
---|
| 2042 | /// \brief Weighted perfect matching in general graphs |
---|
| 2043 | /// |
---|
| 2044 | /// This class provides an efficient implementation of Edmond's |
---|
[327] | 2045 | /// maximum weighted perfect matching algorithm. The implementation |
---|
[326] | 2046 | /// is based on extensive use of priority queues and provides |
---|
[559] | 2047 | /// \f$O(nm\log n)\f$ time complexity. |
---|
[326] | 2048 | /// |
---|
[590] | 2049 | /// The maximum weighted perfect matching problem is to find a subset of |
---|
| 2050 | /// the edges in an undirected graph with maximum overall weight for which |
---|
| 2051 | /// each node has exactly one incident edge. |
---|
| 2052 | /// It can be formulated with the following linear program. |
---|
[326] | 2053 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
[327] | 2054 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
| 2055 | \quad \forall B\in\mathcal{O}\f] */ |
---|
[326] | 2056 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 2057 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
[327] | 2058 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 2059 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
| 2060 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
| 2061 | /// subsets of the nodes. |
---|
[326] | 2062 | /// |
---|
| 2063 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 2064 | /// optimality. The solution of the dual problem can be used to check |
---|
[327] | 2065 | /// the result of the algorithm. The dual linear problem is the |
---|
[590] | 2066 | /// following. |
---|
[327] | 2067 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge |
---|
| 2068 | w_{uv} \quad \forall uv\in E\f] */ |
---|
[326] | 2069 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
[327] | 2070 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
| 2071 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
[326] | 2072 | /// |
---|
[590] | 2073 | /// The algorithm can be executed with the run() function. |
---|
| 2074 | /// After it the matching (the primal solution) and the dual solution |
---|
| 2075 | /// can be obtained using the query functions and the |
---|
| 2076 | /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class, |
---|
| 2077 | /// which is able to iterate on the nodes of a blossom. |
---|
| 2078 | /// If the value type is integer, then the dual solution is multiplied |
---|
| 2079 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
| 2080 | /// |
---|
[593] | 2081 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
[590] | 2082 | /// \tparam WM The type edge weight map. The default type is |
---|
| 2083 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
| 2084 | #ifdef DOXYGEN |
---|
| 2085 | template <typename GR, typename WM> |
---|
| 2086 | #else |
---|
[559] | 2087 | template <typename GR, |
---|
| 2088 | typename WM = typename GR::template EdgeMap<int> > |
---|
[590] | 2089 | #endif |
---|
[326] | 2090 | class MaxWeightedPerfectMatching { |
---|
| 2091 | public: |
---|
| 2092 | |
---|
[590] | 2093 | /// The graph type of the algorithm |
---|
[559] | 2094 | typedef GR Graph; |
---|
[590] | 2095 | /// The type of the edge weight map |
---|
[559] | 2096 | typedef WM WeightMap; |
---|
[590] | 2097 | /// The value type of the edge weights |
---|
[326] | 2098 | typedef typename WeightMap::Value Value; |
---|
| 2099 | |
---|
| 2100 | /// \brief Scaling factor for dual solution |
---|
| 2101 | /// |
---|
| 2102 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 2103 | /// according to the value type. |
---|
| 2104 | static const int dualScale = |
---|
| 2105 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 2106 | |
---|
[593] | 2107 | /// The type of the matching map |
---|
[326] | 2108 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
| 2109 | MatchingMap; |
---|
| 2110 | |
---|
| 2111 | private: |
---|
| 2112 | |
---|
| 2113 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
| 2114 | |
---|
| 2115 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
| 2116 | typedef std::vector<Node> BlossomNodeList; |
---|
| 2117 | |
---|
| 2118 | struct BlossomVariable { |
---|
| 2119 | int begin, end; |
---|
| 2120 | Value value; |
---|
| 2121 | |
---|
| 2122 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 2123 | : begin(_begin), end(_end), value(_value) {} |
---|
| 2124 | |
---|
| 2125 | }; |
---|
| 2126 | |
---|
| 2127 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 2128 | |
---|
| 2129 | const Graph& _graph; |
---|
| 2130 | const WeightMap& _weight; |
---|
| 2131 | |
---|
| 2132 | MatchingMap* _matching; |
---|
| 2133 | |
---|
| 2134 | NodePotential* _node_potential; |
---|
| 2135 | |
---|
| 2136 | BlossomPotential _blossom_potential; |
---|
| 2137 | BlossomNodeList _blossom_node_list; |
---|
| 2138 | |
---|
| 2139 | int _node_num; |
---|
| 2140 | int _blossom_num; |
---|
| 2141 | |
---|
| 2142 | typedef RangeMap<int> IntIntMap; |
---|
| 2143 | |
---|
| 2144 | enum Status { |
---|
| 2145 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
| 2146 | }; |
---|
| 2147 | |
---|
[327] | 2148 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
[326] | 2149 | struct BlossomData { |
---|
| 2150 | int tree; |
---|
| 2151 | Status status; |
---|
| 2152 | Arc pred, next; |
---|
| 2153 | Value pot, offset; |
---|
| 2154 | }; |
---|
| 2155 | |
---|
[327] | 2156 | IntNodeMap *_blossom_index; |
---|
[326] | 2157 | BlossomSet *_blossom_set; |
---|
| 2158 | RangeMap<BlossomData>* _blossom_data; |
---|
| 2159 | |
---|
[327] | 2160 | IntNodeMap *_node_index; |
---|
| 2161 | IntArcMap *_node_heap_index; |
---|
[326] | 2162 | |
---|
| 2163 | struct NodeData { |
---|
| 2164 | |
---|
[327] | 2165 | NodeData(IntArcMap& node_heap_index) |
---|
[326] | 2166 | : heap(node_heap_index) {} |
---|
| 2167 | |
---|
| 2168 | int blossom; |
---|
| 2169 | Value pot; |
---|
[327] | 2170 | BinHeap<Value, IntArcMap> heap; |
---|
[326] | 2171 | std::map<int, Arc> heap_index; |
---|
| 2172 | |
---|
| 2173 | int tree; |
---|
| 2174 | }; |
---|
| 2175 | |
---|
| 2176 | RangeMap<NodeData>* _node_data; |
---|
| 2177 | |
---|
| 2178 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 2179 | |
---|
| 2180 | IntIntMap *_tree_set_index; |
---|
| 2181 | TreeSet *_tree_set; |
---|
| 2182 | |
---|
| 2183 | IntIntMap *_delta2_index; |
---|
| 2184 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 2185 | |
---|
[327] | 2186 | IntEdgeMap *_delta3_index; |
---|
| 2187 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
[326] | 2188 | |
---|
| 2189 | IntIntMap *_delta4_index; |
---|
| 2190 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 2191 | |
---|
| 2192 | Value _delta_sum; |
---|
| 2193 | |
---|
| 2194 | void createStructures() { |
---|
| 2195 | _node_num = countNodes(_graph); |
---|
| 2196 | _blossom_num = _node_num * 3 / 2; |
---|
| 2197 | |
---|
| 2198 | if (!_matching) { |
---|
| 2199 | _matching = new MatchingMap(_graph); |
---|
| 2200 | } |
---|
| 2201 | if (!_node_potential) { |
---|
| 2202 | _node_potential = new NodePotential(_graph); |
---|
| 2203 | } |
---|
| 2204 | if (!_blossom_set) { |
---|
[327] | 2205 | _blossom_index = new IntNodeMap(_graph); |
---|
[326] | 2206 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 2207 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
| 2208 | } |
---|
| 2209 | |
---|
| 2210 | if (!_node_index) { |
---|
[327] | 2211 | _node_index = new IntNodeMap(_graph); |
---|
| 2212 | _node_heap_index = new IntArcMap(_graph); |
---|
[326] | 2213 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
[327] | 2214 | NodeData(*_node_heap_index)); |
---|
[326] | 2215 | } |
---|
| 2216 | |
---|
| 2217 | if (!_tree_set) { |
---|
| 2218 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 2219 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 2220 | } |
---|
| 2221 | if (!_delta2) { |
---|
| 2222 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 2223 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
| 2224 | } |
---|
| 2225 | if (!_delta3) { |
---|
[327] | 2226 | _delta3_index = new IntEdgeMap(_graph); |
---|
| 2227 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
[326] | 2228 | } |
---|
| 2229 | if (!_delta4) { |
---|
| 2230 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 2231 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
| 2232 | } |
---|
| 2233 | } |
---|
| 2234 | |
---|
| 2235 | void destroyStructures() { |
---|
| 2236 | _node_num = countNodes(_graph); |
---|
| 2237 | _blossom_num = _node_num * 3 / 2; |
---|
| 2238 | |
---|
| 2239 | if (_matching) { |
---|
| 2240 | delete _matching; |
---|
| 2241 | } |
---|
| 2242 | if (_node_potential) { |
---|
| 2243 | delete _node_potential; |
---|
| 2244 | } |
---|
| 2245 | if (_blossom_set) { |
---|
| 2246 | delete _blossom_index; |
---|
| 2247 | delete _blossom_set; |
---|
| 2248 | delete _blossom_data; |
---|
| 2249 | } |
---|
| 2250 | |
---|
| 2251 | if (_node_index) { |
---|
| 2252 | delete _node_index; |
---|
| 2253 | delete _node_heap_index; |
---|
| 2254 | delete _node_data; |
---|
| 2255 | } |
---|
| 2256 | |
---|
| 2257 | if (_tree_set) { |
---|
| 2258 | delete _tree_set_index; |
---|
| 2259 | delete _tree_set; |
---|
| 2260 | } |
---|
| 2261 | if (_delta2) { |
---|
| 2262 | delete _delta2_index; |
---|
| 2263 | delete _delta2; |
---|
| 2264 | } |
---|
| 2265 | if (_delta3) { |
---|
| 2266 | delete _delta3_index; |
---|
| 2267 | delete _delta3; |
---|
| 2268 | } |
---|
| 2269 | if (_delta4) { |
---|
| 2270 | delete _delta4_index; |
---|
| 2271 | delete _delta4; |
---|
| 2272 | } |
---|
| 2273 | } |
---|
| 2274 | |
---|
| 2275 | void matchedToEven(int blossom, int tree) { |
---|
| 2276 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2277 | _delta2->erase(blossom); |
---|
| 2278 | } |
---|
| 2279 | |
---|
| 2280 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2281 | (*_blossom_data)[blossom].pot -= |
---|
| 2282 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2283 | } |
---|
| 2284 | |
---|
| 2285 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2286 | n != INVALID; ++n) { |
---|
| 2287 | |
---|
| 2288 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2289 | int ni = (*_node_index)[n]; |
---|
| 2290 | |
---|
| 2291 | (*_node_data)[ni].heap.clear(); |
---|
| 2292 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2293 | |
---|
| 2294 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2295 | |
---|
| 2296 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2297 | Node v = _graph.source(e); |
---|
| 2298 | int vb = _blossom_set->find(v); |
---|
| 2299 | int vi = (*_node_index)[v]; |
---|
| 2300 | |
---|
| 2301 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2302 | dualScale * _weight[e]; |
---|
| 2303 | |
---|
| 2304 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2305 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2306 | _delta3->push(e, rw / 2); |
---|
| 2307 | } |
---|
| 2308 | } else { |
---|
| 2309 | typename std::map<int, Arc>::iterator it = |
---|
| 2310 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2311 | |
---|
| 2312 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2313 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2314 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2315 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2316 | it->second = e; |
---|
| 2317 | } |
---|
| 2318 | } else { |
---|
| 2319 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2320 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2321 | } |
---|
| 2322 | |
---|
| 2323 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2324 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2325 | |
---|
| 2326 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2327 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2328 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2329 | (*_blossom_data)[vb].offset); |
---|
| 2330 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2331 | (*_blossom_data)[vb].offset){ |
---|
| 2332 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2333 | (*_blossom_data)[vb].offset); |
---|
| 2334 | } |
---|
| 2335 | } |
---|
| 2336 | } |
---|
| 2337 | } |
---|
| 2338 | } |
---|
| 2339 | } |
---|
| 2340 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2341 | } |
---|
| 2342 | |
---|
| 2343 | void matchedToOdd(int blossom) { |
---|
| 2344 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2345 | _delta2->erase(blossom); |
---|
| 2346 | } |
---|
| 2347 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 2348 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2349 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 2350 | (*_blossom_data)[blossom].offset); |
---|
| 2351 | } |
---|
| 2352 | } |
---|
| 2353 | |
---|
| 2354 | void evenToMatched(int blossom, int tree) { |
---|
| 2355 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2356 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 2357 | } |
---|
| 2358 | |
---|
| 2359 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2360 | n != INVALID; ++n) { |
---|
| 2361 | int ni = (*_node_index)[n]; |
---|
| 2362 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 2363 | |
---|
| 2364 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2365 | Node v = _graph.source(e); |
---|
| 2366 | int vb = _blossom_set->find(v); |
---|
| 2367 | int vi = (*_node_index)[v]; |
---|
| 2368 | |
---|
| 2369 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2370 | dualScale * _weight[e]; |
---|
| 2371 | |
---|
| 2372 | if (vb == blossom) { |
---|
| 2373 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2374 | _delta3->erase(e); |
---|
| 2375 | } |
---|
| 2376 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2377 | |
---|
| 2378 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2379 | _delta3->erase(e); |
---|
| 2380 | } |
---|
| 2381 | |
---|
| 2382 | int vt = _tree_set->find(vb); |
---|
| 2383 | |
---|
| 2384 | if (vt != tree) { |
---|
| 2385 | |
---|
| 2386 | Arc r = _graph.oppositeArc(e); |
---|
| 2387 | |
---|
| 2388 | typename std::map<int, Arc>::iterator it = |
---|
| 2389 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 2390 | |
---|
| 2391 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 2392 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 2393 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 2394 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 2395 | it->second = r; |
---|
| 2396 | } |
---|
| 2397 | } else { |
---|
| 2398 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 2399 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 2400 | } |
---|
| 2401 | |
---|
| 2402 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 2403 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 2404 | |
---|
| 2405 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 2406 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2407 | (*_blossom_data)[blossom].offset); |
---|
| 2408 | } else if ((*_delta2)[blossom] > |
---|
| 2409 | _blossom_set->classPrio(blossom) - |
---|
| 2410 | (*_blossom_data)[blossom].offset){ |
---|
| 2411 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2412 | (*_blossom_data)[blossom].offset); |
---|
| 2413 | } |
---|
| 2414 | } |
---|
| 2415 | } |
---|
| 2416 | } else { |
---|
| 2417 | |
---|
| 2418 | typename std::map<int, Arc>::iterator it = |
---|
| 2419 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2420 | |
---|
| 2421 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2422 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 2423 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 2424 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 2425 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 2426 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 2427 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 2428 | } |
---|
| 2429 | |
---|
| 2430 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2431 | if (_blossom_set->classPrio(vb) == |
---|
| 2432 | std::numeric_limits<Value>::max()) { |
---|
| 2433 | _delta2->erase(vb); |
---|
| 2434 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 2435 | (*_blossom_data)[vb].offset) { |
---|
| 2436 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 2437 | (*_blossom_data)[vb].offset); |
---|
| 2438 | } |
---|
| 2439 | } |
---|
| 2440 | } |
---|
| 2441 | } |
---|
| 2442 | } |
---|
| 2443 | } |
---|
| 2444 | } |
---|
| 2445 | |
---|
| 2446 | void oddToMatched(int blossom) { |
---|
| 2447 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 2448 | |
---|
| 2449 | if (_blossom_set->classPrio(blossom) != |
---|
| 2450 | std::numeric_limits<Value>::max()) { |
---|
| 2451 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2452 | (*_blossom_data)[blossom].offset); |
---|
| 2453 | } |
---|
| 2454 | |
---|
| 2455 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2456 | _delta4->erase(blossom); |
---|
| 2457 | } |
---|
| 2458 | } |
---|
| 2459 | |
---|
| 2460 | void oddToEven(int blossom, int tree) { |
---|
| 2461 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2462 | _delta4->erase(blossom); |
---|
| 2463 | (*_blossom_data)[blossom].pot -= |
---|
| 2464 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2465 | } |
---|
| 2466 | |
---|
| 2467 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2468 | n != INVALID; ++n) { |
---|
| 2469 | int ni = (*_node_index)[n]; |
---|
| 2470 | |
---|
| 2471 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2472 | |
---|
| 2473 | (*_node_data)[ni].heap.clear(); |
---|
| 2474 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2475 | (*_node_data)[ni].pot += |
---|
| 2476 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2477 | |
---|
| 2478 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2479 | Node v = _graph.source(e); |
---|
| 2480 | int vb = _blossom_set->find(v); |
---|
| 2481 | int vi = (*_node_index)[v]; |
---|
| 2482 | |
---|
| 2483 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2484 | dualScale * _weight[e]; |
---|
| 2485 | |
---|
| 2486 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2487 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2488 | _delta3->push(e, rw / 2); |
---|
| 2489 | } |
---|
| 2490 | } else { |
---|
| 2491 | |
---|
| 2492 | typename std::map<int, Arc>::iterator it = |
---|
| 2493 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2494 | |
---|
| 2495 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2496 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2497 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2498 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2499 | it->second = e; |
---|
| 2500 | } |
---|
| 2501 | } else { |
---|
| 2502 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2503 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2504 | } |
---|
| 2505 | |
---|
| 2506 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2507 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2508 | |
---|
| 2509 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2510 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2511 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2512 | (*_blossom_data)[vb].offset); |
---|
| 2513 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2514 | (*_blossom_data)[vb].offset) { |
---|
| 2515 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2516 | (*_blossom_data)[vb].offset); |
---|
| 2517 | } |
---|
| 2518 | } |
---|
| 2519 | } |
---|
| 2520 | } |
---|
| 2521 | } |
---|
| 2522 | } |
---|
| 2523 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2524 | } |
---|
| 2525 | |
---|
| 2526 | void alternatePath(int even, int tree) { |
---|
| 2527 | int odd; |
---|
| 2528 | |
---|
| 2529 | evenToMatched(even, tree); |
---|
| 2530 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2531 | |
---|
| 2532 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 2533 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
| 2534 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 2535 | oddToMatched(odd); |
---|
| 2536 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 2537 | |
---|
| 2538 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
| 2539 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2540 | evenToMatched(even, tree); |
---|
| 2541 | (*_blossom_data)[even].next = |
---|
| 2542 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
| 2543 | } |
---|
| 2544 | |
---|
| 2545 | } |
---|
| 2546 | |
---|
| 2547 | void destroyTree(int tree) { |
---|
| 2548 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 2549 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 2550 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2551 | evenToMatched(b, tree); |
---|
| 2552 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 2553 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2554 | oddToMatched(b); |
---|
| 2555 | } |
---|
| 2556 | } |
---|
| 2557 | _tree_set->eraseClass(tree); |
---|
| 2558 | } |
---|
| 2559 | |
---|
[327] | 2560 | void augmentOnEdge(const Edge& edge) { |
---|
| 2561 | |
---|
| 2562 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2563 | int right = _blossom_set->find(_graph.v(edge)); |
---|
[326] | 2564 | |
---|
| 2565 | int left_tree = _tree_set->find(left); |
---|
| 2566 | alternatePath(left, left_tree); |
---|
| 2567 | destroyTree(left_tree); |
---|
| 2568 | |
---|
| 2569 | int right_tree = _tree_set->find(right); |
---|
| 2570 | alternatePath(right, right_tree); |
---|
| 2571 | destroyTree(right_tree); |
---|
| 2572 | |
---|
[327] | 2573 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
| 2574 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
[326] | 2575 | } |
---|
| 2576 | |
---|
| 2577 | void extendOnArc(const Arc& arc) { |
---|
| 2578 | int base = _blossom_set->find(_graph.target(arc)); |
---|
| 2579 | int tree = _tree_set->find(base); |
---|
| 2580 | |
---|
| 2581 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
| 2582 | _tree_set->insert(odd, tree); |
---|
| 2583 | (*_blossom_data)[odd].status = ODD; |
---|
| 2584 | matchedToOdd(odd); |
---|
| 2585 | (*_blossom_data)[odd].pred = arc; |
---|
| 2586 | |
---|
| 2587 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
| 2588 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 2589 | _tree_set->insert(even, tree); |
---|
| 2590 | (*_blossom_data)[even].status = EVEN; |
---|
| 2591 | matchedToEven(even, tree); |
---|
| 2592 | } |
---|
| 2593 | |
---|
[327] | 2594 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
[326] | 2595 | int nca = -1; |
---|
| 2596 | std::vector<int> left_path, right_path; |
---|
| 2597 | |
---|
| 2598 | { |
---|
| 2599 | std::set<int> left_set, right_set; |
---|
| 2600 | int left = _blossom_set->find(_graph.u(edge)); |
---|
| 2601 | left_path.push_back(left); |
---|
| 2602 | left_set.insert(left); |
---|
| 2603 | |
---|
| 2604 | int right = _blossom_set->find(_graph.v(edge)); |
---|
| 2605 | right_path.push_back(right); |
---|
| 2606 | right_set.insert(right); |
---|
| 2607 | |
---|
| 2608 | while (true) { |
---|
| 2609 | |
---|
| 2610 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 2611 | |
---|
| 2612 | left = |
---|
| 2613 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2614 | left_path.push_back(left); |
---|
| 2615 | left = |
---|
| 2616 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
| 2617 | left_path.push_back(left); |
---|
| 2618 | |
---|
| 2619 | left_set.insert(left); |
---|
| 2620 | |
---|
| 2621 | if (right_set.find(left) != right_set.end()) { |
---|
| 2622 | nca = left; |
---|
| 2623 | break; |
---|
| 2624 | } |
---|
| 2625 | |
---|
| 2626 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 2627 | |
---|
| 2628 | right = |
---|
| 2629 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2630 | right_path.push_back(right); |
---|
| 2631 | right = |
---|
| 2632 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
| 2633 | right_path.push_back(right); |
---|
| 2634 | |
---|
| 2635 | right_set.insert(right); |
---|
| 2636 | |
---|
| 2637 | if (left_set.find(right) != left_set.end()) { |
---|
| 2638 | nca = right; |
---|
| 2639 | break; |
---|
| 2640 | } |
---|
| 2641 | |
---|
| 2642 | } |
---|
| 2643 | |
---|
| 2644 | if (nca == -1) { |
---|
| 2645 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 2646 | nca = right; |
---|
| 2647 | while (left_set.find(nca) == left_set.end()) { |
---|
| 2648 | nca = |
---|
| 2649 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2650 | right_path.push_back(nca); |
---|
| 2651 | nca = |
---|
| 2652 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2653 | right_path.push_back(nca); |
---|
| 2654 | } |
---|
| 2655 | } else { |
---|
| 2656 | nca = left; |
---|
| 2657 | while (right_set.find(nca) == right_set.end()) { |
---|
| 2658 | nca = |
---|
| 2659 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2660 | left_path.push_back(nca); |
---|
| 2661 | nca = |
---|
| 2662 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
| 2663 | left_path.push_back(nca); |
---|
| 2664 | } |
---|
| 2665 | } |
---|
| 2666 | } |
---|
| 2667 | } |
---|
| 2668 | |
---|
| 2669 | std::vector<int> subblossoms; |
---|
| 2670 | Arc prev; |
---|
| 2671 | |
---|
| 2672 | prev = _graph.direct(edge, true); |
---|
| 2673 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 2674 | subblossoms.push_back(left_path[i]); |
---|
| 2675 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 2676 | _tree_set->erase(left_path[i]); |
---|
| 2677 | |
---|
| 2678 | subblossoms.push_back(left_path[i + 1]); |
---|
| 2679 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 2680 | oddToEven(left_path[i + 1], tree); |
---|
| 2681 | _tree_set->erase(left_path[i + 1]); |
---|
| 2682 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 2683 | } |
---|
| 2684 | |
---|
| 2685 | int k = 0; |
---|
| 2686 | while (right_path[k] != nca) ++k; |
---|
| 2687 | |
---|
| 2688 | subblossoms.push_back(nca); |
---|
| 2689 | (*_blossom_data)[nca].next = prev; |
---|
| 2690 | |
---|
| 2691 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 2692 | subblossoms.push_back(right_path[i + 1]); |
---|
| 2693 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 2694 | oddToEven(right_path[i + 1], tree); |
---|
| 2695 | _tree_set->erase(right_path[i + 1]); |
---|
| 2696 | |
---|
| 2697 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 2698 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 2699 | |
---|
| 2700 | subblossoms.push_back(right_path[i]); |
---|
| 2701 | _tree_set->erase(right_path[i]); |
---|
| 2702 | } |
---|
| 2703 | |
---|
| 2704 | int surface = |
---|
| 2705 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 2706 | |
---|
| 2707 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2708 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2709 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 2710 | } |
---|
| 2711 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 2712 | } |
---|
| 2713 | |
---|
| 2714 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 2715 | (*_blossom_data)[surface].offset = 0; |
---|
| 2716 | (*_blossom_data)[surface].status = EVEN; |
---|
| 2717 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 2718 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 2719 | |
---|
| 2720 | _tree_set->insert(surface, tree); |
---|
| 2721 | _tree_set->erase(nca); |
---|
| 2722 | } |
---|
| 2723 | |
---|
| 2724 | void splitBlossom(int blossom) { |
---|
| 2725 | Arc next = (*_blossom_data)[blossom].next; |
---|
| 2726 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
| 2727 | |
---|
| 2728 | int tree = _tree_set->find(blossom); |
---|
| 2729 | |
---|
| 2730 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 2731 | oddToMatched(blossom); |
---|
| 2732 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2733 | _delta2->erase(blossom); |
---|
| 2734 | } |
---|
| 2735 | |
---|
| 2736 | std::vector<int> subblossoms; |
---|
| 2737 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2738 | |
---|
| 2739 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 2740 | int b = _blossom_set->find(_graph.source(pred)); |
---|
| 2741 | int d = _blossom_set->find(_graph.source(next)); |
---|
| 2742 | |
---|
| 2743 | int ib = -1, id = -1; |
---|
| 2744 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2745 | if (subblossoms[i] == b) ib = i; |
---|
| 2746 | if (subblossoms[i] == d) id = i; |
---|
| 2747 | |
---|
| 2748 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 2749 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2750 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 2751 | } |
---|
| 2752 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 2753 | std::numeric_limits<Value>::max()) { |
---|
| 2754 | _delta2->push(subblossoms[i], |
---|
| 2755 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 2756 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 2757 | } |
---|
| 2758 | } |
---|
| 2759 | |
---|
| 2760 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 2761 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 2762 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2763 | int sb = subblossoms[i]; |
---|
| 2764 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2765 | (*_blossom_data)[sb].next = |
---|
| 2766 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2767 | } |
---|
| 2768 | |
---|
| 2769 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2770 | int sb = subblossoms[i]; |
---|
| 2771 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2772 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2773 | |
---|
| 2774 | (*_blossom_data)[sb].status = ODD; |
---|
| 2775 | matchedToOdd(sb); |
---|
| 2776 | _tree_set->insert(sb, tree); |
---|
| 2777 | (*_blossom_data)[sb].pred = pred; |
---|
| 2778 | (*_blossom_data)[sb].next = |
---|
| 2779 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2780 | |
---|
| 2781 | pred = (*_blossom_data)[ub].next; |
---|
| 2782 | |
---|
| 2783 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2784 | matchedToEven(tb, tree); |
---|
| 2785 | _tree_set->insert(tb, tree); |
---|
| 2786 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 2787 | } |
---|
| 2788 | |
---|
| 2789 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 2790 | matchedToOdd(subblossoms[id]); |
---|
| 2791 | _tree_set->insert(subblossoms[id], tree); |
---|
| 2792 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 2793 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 2794 | |
---|
| 2795 | } else { |
---|
| 2796 | |
---|
| 2797 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 2798 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2799 | int sb = subblossoms[i]; |
---|
| 2800 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2801 | (*_blossom_data)[sb].next = |
---|
| 2802 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2803 | } |
---|
| 2804 | |
---|
| 2805 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2806 | int sb = subblossoms[i]; |
---|
| 2807 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2808 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2809 | |
---|
| 2810 | (*_blossom_data)[sb].status = ODD; |
---|
| 2811 | matchedToOdd(sb); |
---|
| 2812 | _tree_set->insert(sb, tree); |
---|
| 2813 | (*_blossom_data)[sb].next = next; |
---|
| 2814 | (*_blossom_data)[sb].pred = |
---|
| 2815 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
| 2816 | |
---|
| 2817 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2818 | matchedToEven(tb, tree); |
---|
| 2819 | _tree_set->insert(tb, tree); |
---|
| 2820 | (*_blossom_data)[tb].pred = |
---|
| 2821 | (*_blossom_data)[tb].next = |
---|
| 2822 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
| 2823 | next = (*_blossom_data)[ub].next; |
---|
| 2824 | } |
---|
| 2825 | |
---|
| 2826 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 2827 | matchedToOdd(subblossoms[ib]); |
---|
| 2828 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 2829 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 2830 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 2831 | } |
---|
| 2832 | _tree_set->erase(blossom); |
---|
| 2833 | } |
---|
| 2834 | |
---|
| 2835 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
| 2836 | if (_blossom_set->trivial(blossom)) { |
---|
| 2837 | int bi = (*_node_index)[base]; |
---|
| 2838 | Value pot = (*_node_data)[bi].pot; |
---|
| 2839 | |
---|
[581] | 2840 | (*_matching)[base] = matching; |
---|
[326] | 2841 | _blossom_node_list.push_back(base); |
---|
[581] | 2842 | (*_node_potential)[base] = pot; |
---|
[326] | 2843 | } else { |
---|
| 2844 | |
---|
| 2845 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 2846 | int bn = _blossom_node_list.size(); |
---|
| 2847 | |
---|
| 2848 | std::vector<int> subblossoms; |
---|
| 2849 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2850 | int b = _blossom_set->find(base); |
---|
| 2851 | int ib = -1; |
---|
| 2852 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2853 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 2854 | } |
---|
| 2855 | |
---|
| 2856 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 2857 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 2858 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 2859 | |
---|
| 2860 | Arc m = (*_blossom_data)[tb].next; |
---|
| 2861 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
| 2862 | extractBlossom(tb, _graph.source(m), m); |
---|
| 2863 | } |
---|
| 2864 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 2865 | |
---|
| 2866 | int en = _blossom_node_list.size(); |
---|
| 2867 | |
---|
| 2868 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 2869 | } |
---|
| 2870 | } |
---|
| 2871 | |
---|
| 2872 | void extractMatching() { |
---|
| 2873 | std::vector<int> blossoms; |
---|
| 2874 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 2875 | blossoms.push_back(c); |
---|
| 2876 | } |
---|
| 2877 | |
---|
| 2878 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 2879 | |
---|
| 2880 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 2881 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 2882 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 2883 | n != INVALID; ++n) { |
---|
| 2884 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 2885 | } |
---|
| 2886 | |
---|
| 2887 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 2888 | Node base = _graph.source(matching); |
---|
| 2889 | extractBlossom(blossoms[i], base, matching); |
---|
| 2890 | } |
---|
| 2891 | } |
---|
| 2892 | |
---|
| 2893 | public: |
---|
| 2894 | |
---|
| 2895 | /// \brief Constructor |
---|
| 2896 | /// |
---|
| 2897 | /// Constructor. |
---|
| 2898 | MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight) |
---|
| 2899 | : _graph(graph), _weight(weight), _matching(0), |
---|
| 2900 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 2901 | _node_num(0), _blossom_num(0), |
---|
| 2902 | |
---|
| 2903 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 2904 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 2905 | _tree_set_index(0), _tree_set(0), |
---|
| 2906 | |
---|
| 2907 | _delta2_index(0), _delta2(0), |
---|
| 2908 | _delta3_index(0), _delta3(0), |
---|
| 2909 | _delta4_index(0), _delta4(0), |
---|
| 2910 | |
---|
| 2911 | _delta_sum() {} |
---|
| 2912 | |
---|
| 2913 | ~MaxWeightedPerfectMatching() { |
---|
| 2914 | destroyStructures(); |
---|
| 2915 | } |
---|
| 2916 | |
---|
[590] | 2917 | /// \name Execution Control |
---|
[330] | 2918 | /// The simplest way to execute the algorithm is to use the |
---|
[590] | 2919 | /// \ref run() member function. |
---|
[326] | 2920 | |
---|
| 2921 | ///@{ |
---|
| 2922 | |
---|
| 2923 | /// \brief Initialize the algorithm |
---|
| 2924 | /// |
---|
[590] | 2925 | /// This function initializes the algorithm. |
---|
[326] | 2926 | void init() { |
---|
| 2927 | createStructures(); |
---|
| 2928 | |
---|
| 2929 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
[581] | 2930 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
[326] | 2931 | } |
---|
| 2932 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
[581] | 2933 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
[326] | 2934 | } |
---|
| 2935 | for (int i = 0; i < _blossom_num; ++i) { |
---|
[581] | 2936 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
| 2937 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
[326] | 2938 | } |
---|
| 2939 | |
---|
| 2940 | int index = 0; |
---|
| 2941 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 2942 | Value max = - std::numeric_limits<Value>::max(); |
---|
| 2943 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
| 2944 | if (_graph.target(e) == n) continue; |
---|
| 2945 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 2946 | max = (dualScale * _weight[e]) / 2; |
---|
| 2947 | } |
---|
| 2948 | } |
---|
[581] | 2949 | (*_node_index)[n] = index; |
---|
[326] | 2950 | (*_node_data)[index].pot = max; |
---|
| 2951 | int blossom = |
---|
| 2952 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 2953 | |
---|
| 2954 | _tree_set->insert(blossom); |
---|
| 2955 | |
---|
| 2956 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 2957 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 2958 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 2959 | (*_blossom_data)[blossom].pot = 0; |
---|
| 2960 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2961 | ++index; |
---|
| 2962 | } |
---|
| 2963 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 2964 | int si = (*_node_index)[_graph.u(e)]; |
---|
| 2965 | int ti = (*_node_index)[_graph.v(e)]; |
---|
| 2966 | if (_graph.u(e) != _graph.v(e)) { |
---|
| 2967 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 2968 | dualScale * _weight[e]) / 2); |
---|
| 2969 | } |
---|
| 2970 | } |
---|
| 2971 | } |
---|
| 2972 | |
---|
[590] | 2973 | /// \brief Start the algorithm |
---|
[326] | 2974 | /// |
---|
[590] | 2975 | /// This function starts the algorithm. |
---|
| 2976 | /// |
---|
| 2977 | /// \pre \ref init() must be called before using this function. |
---|
[326] | 2978 | bool start() { |
---|
| 2979 | enum OpType { |
---|
| 2980 | D2, D3, D4 |
---|
| 2981 | }; |
---|
| 2982 | |
---|
| 2983 | int unmatched = _node_num; |
---|
| 2984 | while (unmatched > 0) { |
---|
| 2985 | Value d2 = !_delta2->empty() ? |
---|
| 2986 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 2987 | |
---|
| 2988 | Value d3 = !_delta3->empty() ? |
---|
| 2989 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 2990 | |
---|
| 2991 | Value d4 = !_delta4->empty() ? |
---|
| 2992 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 2993 | |
---|
| 2994 | _delta_sum = d2; OpType ot = D2; |
---|
| 2995 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
| 2996 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 2997 | |
---|
| 2998 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
| 2999 | return false; |
---|
| 3000 | } |
---|
| 3001 | |
---|
| 3002 | switch (ot) { |
---|
| 3003 | case D2: |
---|
| 3004 | { |
---|
| 3005 | int blossom = _delta2->top(); |
---|
| 3006 | Node n = _blossom_set->classTop(blossom); |
---|
| 3007 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 3008 | extendOnArc(e); |
---|
| 3009 | } |
---|
| 3010 | break; |
---|
| 3011 | case D3: |
---|
| 3012 | { |
---|
| 3013 | Edge e = _delta3->top(); |
---|
| 3014 | |
---|
| 3015 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
| 3016 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
| 3017 | |
---|
| 3018 | if (left_blossom == right_blossom) { |
---|
| 3019 | _delta3->pop(); |
---|
| 3020 | } else { |
---|
| 3021 | int left_tree = _tree_set->find(left_blossom); |
---|
| 3022 | int right_tree = _tree_set->find(right_blossom); |
---|
| 3023 | |
---|
| 3024 | if (left_tree == right_tree) { |
---|
[327] | 3025 | shrinkOnEdge(e, left_tree); |
---|
[326] | 3026 | } else { |
---|
[327] | 3027 | augmentOnEdge(e); |
---|
[326] | 3028 | unmatched -= 2; |
---|
| 3029 | } |
---|
| 3030 | } |
---|
| 3031 | } break; |
---|
| 3032 | case D4: |
---|
| 3033 | splitBlossom(_delta4->top()); |
---|
| 3034 | break; |
---|
| 3035 | } |
---|
| 3036 | } |
---|
| 3037 | extractMatching(); |
---|
| 3038 | return true; |
---|
| 3039 | } |
---|
| 3040 | |
---|
[590] | 3041 | /// \brief Run the algorithm. |
---|
[326] | 3042 | /// |
---|
[590] | 3043 | /// This method runs the \c %MaxWeightedPerfectMatching algorithm. |
---|
[326] | 3044 | /// |
---|
[590] | 3045 | /// \note mwpm.run() is just a shortcut of the following code. |
---|
[326] | 3046 | /// \code |
---|
[590] | 3047 | /// mwpm.init(); |
---|
| 3048 | /// mwpm.start(); |
---|
[326] | 3049 | /// \endcode |
---|
| 3050 | bool run() { |
---|
| 3051 | init(); |
---|
| 3052 | return start(); |
---|
| 3053 | } |
---|
| 3054 | |
---|
| 3055 | /// @} |
---|
| 3056 | |
---|
[590] | 3057 | /// \name Primal Solution |
---|
| 3058 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
| 3059 | /// perfect matching.\n |
---|
| 3060 | /// Either \ref run() or \ref start() function should be called before |
---|
| 3061 | /// using them. |
---|
[326] | 3062 | |
---|
| 3063 | /// @{ |
---|
| 3064 | |
---|
[590] | 3065 | /// \brief Return the weight of the matching. |
---|
[326] | 3066 | /// |
---|
[590] | 3067 | /// This function returns the weight of the found matching. |
---|
| 3068 | /// |
---|
| 3069 | /// \pre Either run() or start() must be called before using this function. |
---|
[593] | 3070 | Value matchingWeight() const { |
---|
[326] | 3071 | Value sum = 0; |
---|
| 3072 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3073 | if ((*_matching)[n] != INVALID) { |
---|
| 3074 | sum += _weight[(*_matching)[n]]; |
---|
| 3075 | } |
---|
| 3076 | } |
---|
| 3077 | return sum /= 2; |
---|
| 3078 | } |
---|
| 3079 | |
---|
[590] | 3080 | /// \brief Return \c true if the given edge is in the matching. |
---|
[326] | 3081 | /// |
---|
[590] | 3082 | /// This function returns \c true if the given edge is in the found |
---|
| 3083 | /// matching. |
---|
| 3084 | /// |
---|
| 3085 | /// \pre Either run() or start() must be called before using this function. |
---|
[327] | 3086 | bool matching(const Edge& edge) const { |
---|
| 3087 | return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge; |
---|
[326] | 3088 | } |
---|
| 3089 | |
---|
[590] | 3090 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
[326] | 3091 | /// |
---|
[590] | 3092 | /// This function returns the matching arc (or edge) incident to the |
---|
| 3093 | /// given node in the found matching or \c INVALID if the node is |
---|
| 3094 | /// not covered by the matching. |
---|
| 3095 | /// |
---|
| 3096 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 3097 | Arc matching(const Node& node) const { |
---|
| 3098 | return (*_matching)[node]; |
---|
| 3099 | } |
---|
| 3100 | |
---|
[593] | 3101 | /// \brief Return a const reference to the matching map. |
---|
| 3102 | /// |
---|
| 3103 | /// This function returns a const reference to a node map that stores |
---|
| 3104 | /// the matching arc (or edge) incident to each node. |
---|
| 3105 | const MatchingMap& matchingMap() const { |
---|
| 3106 | return *_matching; |
---|
| 3107 | } |
---|
| 3108 | |
---|
[590] | 3109 | /// \brief Return the mate of the given node. |
---|
[326] | 3110 | /// |
---|
[590] | 3111 | /// This function returns the mate of the given node in the found |
---|
| 3112 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
| 3113 | /// |
---|
| 3114 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 3115 | Node mate(const Node& node) const { |
---|
| 3116 | return _graph.target((*_matching)[node]); |
---|
| 3117 | } |
---|
| 3118 | |
---|
| 3119 | /// @} |
---|
| 3120 | |
---|
[590] | 3121 | /// \name Dual Solution |
---|
| 3122 | /// Functions to get the dual solution.\n |
---|
| 3123 | /// Either \ref run() or \ref start() function should be called before |
---|
| 3124 | /// using them. |
---|
[326] | 3125 | |
---|
| 3126 | /// @{ |
---|
| 3127 | |
---|
[590] | 3128 | /// \brief Return the value of the dual solution. |
---|
[326] | 3129 | /// |
---|
[590] | 3130 | /// This function returns the value of the dual solution. |
---|
| 3131 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
| 3132 | /// "dual scale". |
---|
| 3133 | /// |
---|
| 3134 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 3135 | Value dualValue() const { |
---|
| 3136 | Value sum = 0; |
---|
| 3137 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 3138 | sum += nodeValue(n); |
---|
| 3139 | } |
---|
| 3140 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 3141 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 3142 | } |
---|
| 3143 | return sum; |
---|
| 3144 | } |
---|
| 3145 | |
---|
[590] | 3146 | /// \brief Return the dual value (potential) of the given node. |
---|
[326] | 3147 | /// |
---|
[590] | 3148 | /// This function returns the dual value (potential) of the given node. |
---|
| 3149 | /// |
---|
| 3150 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 3151 | Value nodeValue(const Node& n) const { |
---|
| 3152 | return (*_node_potential)[n]; |
---|
| 3153 | } |
---|
| 3154 | |
---|
[590] | 3155 | /// \brief Return the number of the blossoms in the basis. |
---|
[326] | 3156 | /// |
---|
[590] | 3157 | /// This function returns the number of the blossoms in the basis. |
---|
| 3158 | /// |
---|
| 3159 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 3160 | /// \see BlossomIt |
---|
| 3161 | int blossomNum() const { |
---|
| 3162 | return _blossom_potential.size(); |
---|
| 3163 | } |
---|
| 3164 | |
---|
[590] | 3165 | /// \brief Return the number of the nodes in the given blossom. |
---|
[326] | 3166 | /// |
---|
[590] | 3167 | /// This function returns the number of the nodes in the given blossom. |
---|
| 3168 | /// |
---|
| 3169 | /// \pre Either run() or start() must be called before using this function. |
---|
| 3170 | /// \see BlossomIt |
---|
[326] | 3171 | int blossomSize(int k) const { |
---|
| 3172 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 3173 | } |
---|
| 3174 | |
---|
[590] | 3175 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
[326] | 3176 | /// |
---|
[590] | 3177 | /// This function returns the dual value (ptential) of the given blossom. |
---|
| 3178 | /// |
---|
| 3179 | /// \pre Either run() or start() must be called before using this function. |
---|
[326] | 3180 | Value blossomValue(int k) const { |
---|
| 3181 | return _blossom_potential[k].value; |
---|
| 3182 | } |
---|
| 3183 | |
---|
[590] | 3184 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
[326] | 3185 | /// |
---|
[590] | 3186 | /// This class provides an iterator for obtaining the nodes of the |
---|
| 3187 | /// given blossom. It lists a subset of the nodes. |
---|
| 3188 | /// Before using this iterator, you must allocate a |
---|
| 3189 | /// MaxWeightedPerfectMatching class and execute it. |
---|
[326] | 3190 | class BlossomIt { |
---|
| 3191 | public: |
---|
| 3192 | |
---|
| 3193 | /// \brief Constructor. |
---|
| 3194 | /// |
---|
[590] | 3195 | /// Constructor to get the nodes of the given variable. |
---|
| 3196 | /// |
---|
| 3197 | /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()" |
---|
| 3198 | /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()" |
---|
| 3199 | /// must be called before initializing this iterator. |
---|
[326] | 3200 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
| 3201 | : _algorithm(&algorithm) |
---|
| 3202 | { |
---|
| 3203 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 3204 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 3205 | } |
---|
| 3206 | |
---|
[590] | 3207 | /// \brief Conversion to \c Node. |
---|
[326] | 3208 | /// |
---|
[590] | 3209 | /// Conversion to \c Node. |
---|
[326] | 3210 | operator Node() const { |
---|
[327] | 3211 | return _algorithm->_blossom_node_list[_index]; |
---|
[326] | 3212 | } |
---|
| 3213 | |
---|
| 3214 | /// \brief Increment operator. |
---|
| 3215 | /// |
---|
| 3216 | /// Increment operator. |
---|
| 3217 | BlossomIt& operator++() { |
---|
| 3218 | ++_index; |
---|
| 3219 | return *this; |
---|
| 3220 | } |
---|
| 3221 | |
---|
[327] | 3222 | /// \brief Validity checking |
---|
| 3223 | /// |
---|
[590] | 3224 | /// This function checks whether the iterator is invalid. |
---|
[327] | 3225 | bool operator==(Invalid) const { return _index == _last; } |
---|
| 3226 | |
---|
| 3227 | /// \brief Validity checking |
---|
| 3228 | /// |
---|
[590] | 3229 | /// This function checks whether the iterator is valid. |
---|
[327] | 3230 | bool operator!=(Invalid) const { return _index != _last; } |
---|
[326] | 3231 | |
---|
| 3232 | private: |
---|
| 3233 | const MaxWeightedPerfectMatching* _algorithm; |
---|
| 3234 | int _last; |
---|
| 3235 | int _index; |
---|
| 3236 | }; |
---|
| 3237 | |
---|
| 3238 | /// @} |
---|
| 3239 | |
---|
| 3240 | }; |
---|
| 3241 | |
---|
| 3242 | } //END OF NAMESPACE LEMON |
---|
| 3243 | |
---|
| 3244 | #endif //LEMON_MAX_MATCHING_H |
---|