[1077] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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[2553] | 5 | * Copyright (C) 2003-2008 |
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[1956] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[1077] | 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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[2548] | 22 | #include <vector> |
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[1077] | 23 | #include <queue> |
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[2548] | 24 | #include <set> |
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| 25 | |
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[1993] | 26 | #include <lemon/bits/invalid.h> |
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[1093] | 27 | #include <lemon/unionfind.h> |
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[1077] | 28 | #include <lemon/graph_utils.h> |
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[2548] | 29 | #include <lemon/bin_heap.h> |
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[1077] | 30 | |
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[2042] | 31 | ///\ingroup matching |
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[1077] | 32 | ///\file |
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[2549] | 33 | ///\brief Maximum matching algorithms in undirected graph. |
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[1077] | 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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[2505] | 37 | ///\ingroup matching |
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[2548] | 38 | /// |
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[2505] | 39 | ///\brief Edmonds' alternating forest maximum matching algorithm. |
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| 40 | /// |
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[1077] | 41 | ///This class provides Edmonds' alternating forest matching |
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| 42 | ///algorithm. The starting matching (if any) can be passed to the |
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[2505] | 43 | ///algorithm using some of init functions. |
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[1077] | 44 | /// |
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| 45 | ///The dual side of a matching is a map of the nodes to |
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[2505] | 46 | ///MaxMatching::DecompType, having values \c D, \c A and \c C |
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| 47 | ///showing the Gallai-Edmonds decomposition of the graph. The nodes |
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| 48 | ///in \c D induce a graph with factor-critical components, the nodes |
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| 49 | ///in \c A form the barrier, and the nodes in \c C induce a graph |
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| 50 | ///having a perfect matching. This decomposition can be attained by |
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| 51 | ///calling \c decomposition() after running the algorithm. |
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[1077] | 52 | /// |
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| 53 | ///\param Graph The undirected graph type the algorithm runs on. |
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| 54 | /// |
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| 55 | ///\author Jacint Szabo |
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| 56 | template <typename Graph> |
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| 57 | class MaxMatching { |
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[1165] | 58 | |
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| 59 | protected: |
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| 60 | |
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[1077] | 61 | typedef typename Graph::Node Node; |
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| 62 | typedef typename Graph::Edge Edge; |
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[1909] | 63 | typedef typename Graph::UEdge UEdge; |
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| 64 | typedef typename Graph::UEdgeIt UEdgeIt; |
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[1077] | 65 | typedef typename Graph::NodeIt NodeIt; |
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| 66 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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| 67 | |
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[2205] | 68 | typedef typename Graph::template NodeMap<int> UFECrossRef; |
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[2308] | 69 | typedef UnionFindEnum<UFECrossRef> UFE; |
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[2505] | 70 | typedef std::vector<Node> NV; |
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| 71 | |
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| 72 | typedef typename Graph::template NodeMap<int> EFECrossRef; |
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| 73 | typedef ExtendFindEnum<EFECrossRef> EFE; |
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[1077] | 74 | |
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| 75 | public: |
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| 76 | |
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[2505] | 77 | ///\brief Indicates the Gallai-Edmonds decomposition of the graph. |
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| 78 | /// |
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[1077] | 79 | ///Indicates the Gallai-Edmonds decomposition of the graph, which |
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| 80 | ///shows an upper bound on the size of a maximum matching. The |
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[2505] | 81 | ///nodes with DecompType \c D induce a graph with factor-critical |
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[1077] | 82 | ///components, the nodes in \c A form the canonical barrier, and the |
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| 83 | ///nodes in \c C induce a graph having a perfect matching. |
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[2505] | 84 | enum DecompType { |
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[1077] | 85 | D=0, |
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| 86 | A=1, |
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| 87 | C=2 |
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| 88 | }; |
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| 89 | |
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[1165] | 90 | protected: |
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[1077] | 91 | |
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| 92 | static const int HEUR_density=2; |
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| 93 | const Graph& g; |
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[1093] | 94 | typename Graph::template NodeMap<Node> _mate; |
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[2505] | 95 | typename Graph::template NodeMap<DecompType> position; |
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[1077] | 96 | |
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| 97 | public: |
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| 98 | |
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[2505] | 99 | MaxMatching(const Graph& _g) |
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| 100 | : g(_g), _mate(_g), position(_g) {} |
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[1077] | 101 | |
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[2505] | 102 | ///\brief Sets the actual matching to the empty matching. |
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| 103 | /// |
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| 104 | ///Sets the actual matching to the empty matching. |
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| 105 | /// |
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| 106 | void init() { |
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[1587] | 107 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[2505] | 108 | _mate.set(v,INVALID); |
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| 109 | position.set(v,C); |
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[1587] | 110 | } |
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| 111 | } |
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| 112 | |
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[2505] | 113 | ///\brief Finds a greedy matching for initial matching. |
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| 114 | /// |
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| 115 | ///For initial matchig it finds a maximal greedy matching. |
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| 116 | void greedyInit() { |
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| 117 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 118 | _mate.set(v,INVALID); |
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| 119 | position.set(v,C); |
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| 120 | } |
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[1587] | 121 | for(NodeIt v(g); v!=INVALID; ++v) |
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| 122 | if ( _mate[v]==INVALID ) { |
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| 123 | for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) { |
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| 124 | Node y=g.runningNode(e); |
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| 125 | if ( _mate[y]==INVALID && y!=v ) { |
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| 126 | _mate.set(v,y); |
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| 127 | _mate.set(y,v); |
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| 128 | break; |
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| 129 | } |
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| 130 | } |
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| 131 | } |
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| 132 | } |
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[1077] | 133 | |
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[2505] | 134 | ///\brief Initialize the matching from each nodes' mate. |
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| 135 | /// |
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| 136 | ///Initialize the matching from a \c Node valued \c Node map. This |
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| 137 | ///map must be \e symmetric, i.e. if \c map[u]==v then \c |
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| 138 | ///map[v]==u must hold, and \c uv will be an edge of the initial |
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| 139 | ///matching. |
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| 140 | template <typename MateMap> |
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| 141 | void mateMapInit(MateMap& map) { |
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| 142 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 143 | _mate.set(v,map[v]); |
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| 144 | position.set(v,C); |
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| 145 | } |
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| 146 | } |
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[1077] | 147 | |
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[2505] | 148 | ///\brief Initialize the matching from a node map with the |
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| 149 | ///incident matching edges. |
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| 150 | /// |
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| 151 | ///Initialize the matching from an \c UEdge valued \c Node map. \c |
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| 152 | ///map[v] must be an \c UEdge incident to \c v. This map must have |
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| 153 | ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c |
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| 154 | ///g.oppositeNode(v,map[v])==u holds, and now some edge joining \c |
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| 155 | ///u to \c v will be an edge of the matching. |
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| 156 | template<typename MatchingMap> |
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| 157 | void matchingMapInit(MatchingMap& map) { |
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| 158 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 159 | position.set(v,C); |
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| 160 | UEdge e=map[v]; |
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| 161 | if ( e!=INVALID ) |
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| 162 | _mate.set(v,g.oppositeNode(v,e)); |
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| 163 | else |
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| 164 | _mate.set(v,INVALID); |
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| 165 | } |
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| 166 | } |
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| 167 | |
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| 168 | ///\brief Initialize the matching from the map containing the |
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| 169 | ///undirected matching edges. |
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| 170 | /// |
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| 171 | ///Initialize the matching from a \c bool valued \c UEdge map. This |
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| 172 | ///map must have the property that there are no two incident edges |
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| 173 | ///\c e, \c f with \c map[e]==map[f]==true. The edges \c e with \c |
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| 174 | ///map[e]==true form the matching. |
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| 175 | template <typename MatchingMap> |
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| 176 | void matchingInit(MatchingMap& map) { |
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| 177 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 178 | _mate.set(v,INVALID); |
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| 179 | position.set(v,C); |
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| 180 | } |
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| 181 | for(UEdgeIt e(g); e!=INVALID; ++e) { |
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| 182 | if ( map[e] ) { |
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| 183 | Node u=g.source(e); |
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| 184 | Node v=g.target(e); |
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| 185 | _mate.set(u,v); |
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| 186 | _mate.set(v,u); |
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| 187 | } |
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| 188 | } |
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| 189 | } |
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| 190 | |
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| 191 | |
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| 192 | ///\brief Runs Edmonds' algorithm. |
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| 193 | /// |
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| 194 | ///Runs Edmonds' algorithm for sparse graphs (number of edges < |
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| 195 | ///2*number of nodes), and a heuristical Edmonds' algorithm with a |
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| 196 | ///heuristic of postponing shrinks for dense graphs. |
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| 197 | void run() { |
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| 198 | if (countUEdges(g) < HEUR_density * countNodes(g)) { |
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| 199 | greedyInit(); |
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| 200 | startSparse(); |
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| 201 | } else { |
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| 202 | init(); |
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| 203 | startDense(); |
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| 204 | } |
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| 205 | } |
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| 206 | |
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| 207 | |
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| 208 | ///\brief Starts Edmonds' algorithm. |
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| 209 | /// |
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| 210 | ///If runs the original Edmonds' algorithm. |
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| 211 | void startSparse() { |
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| 212 | |
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| 213 | typename Graph::template NodeMap<Node> ear(g,INVALID); |
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| 214 | //undefined for the base nodes of the blossoms (i.e. for the |
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| 215 | //representative elements of UFE blossom) and for the nodes in C |
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| 216 | |
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| 217 | UFECrossRef blossom_base(g); |
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| 218 | UFE blossom(blossom_base); |
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| 219 | NV rep(countNodes(g)); |
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| 220 | |
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| 221 | EFECrossRef tree_base(g); |
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| 222 | EFE tree(tree_base); |
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| 223 | |
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| 224 | //If these UFE's would be members of the class then also |
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| 225 | //blossom_base and tree_base should be a member. |
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| 226 | |
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| 227 | //We build only one tree and the other vertices uncovered by the |
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| 228 | //matching belong to C. (They can be considered as singleton |
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| 229 | //trees.) If this tree can be augmented or no more |
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| 230 | //grow/augmentation/shrink is possible then we return to this |
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| 231 | //"for" cycle. |
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| 232 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 233 | if (position[v]==C && _mate[v]==INVALID) { |
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| 234 | rep[blossom.insert(v)] = v; |
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| 235 | tree.insert(v); |
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| 236 | position.set(v,D); |
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| 237 | normShrink(v, ear, blossom, rep, tree); |
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| 238 | } |
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| 239 | } |
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| 240 | } |
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| 241 | |
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| 242 | ///\brief Starts Edmonds' algorithm. |
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| 243 | /// |
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| 244 | ///It runs Edmonds' algorithm with a heuristic of postponing |
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| 245 | ///shrinks, giving a faster algorithm for dense graphs. |
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| 246 | void startDense() { |
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| 247 | |
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| 248 | typename Graph::template NodeMap<Node> ear(g,INVALID); |
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| 249 | //undefined for the base nodes of the blossoms (i.e. for the |
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| 250 | //representative elements of UFE blossom) and for the nodes in C |
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| 251 | |
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| 252 | UFECrossRef blossom_base(g); |
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| 253 | UFE blossom(blossom_base); |
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| 254 | NV rep(countNodes(g)); |
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| 255 | |
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| 256 | EFECrossRef tree_base(g); |
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| 257 | EFE tree(tree_base); |
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| 258 | |
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| 259 | //If these UFE's would be members of the class then also |
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| 260 | //blossom_base and tree_base should be a member. |
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| 261 | |
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| 262 | //We build only one tree and the other vertices uncovered by the |
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| 263 | //matching belong to C. (They can be considered as singleton |
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| 264 | //trees.) If this tree can be augmented or no more |
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| 265 | //grow/augmentation/shrink is possible then we return to this |
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| 266 | //"for" cycle. |
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| 267 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 268 | if ( position[v]==C && _mate[v]==INVALID ) { |
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| 269 | rep[blossom.insert(v)] = v; |
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| 270 | tree.insert(v); |
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| 271 | position.set(v,D); |
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| 272 | lateShrink(v, ear, blossom, rep, tree); |
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| 273 | } |
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| 274 | } |
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| 275 | } |
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| 276 | |
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| 277 | |
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| 278 | |
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| 279 | ///\brief Returns the size of the actual matching stored. |
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| 280 | /// |
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[1077] | 281 | ///Returns the size of the actual matching stored. After \ref |
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| 282 | ///run() it returns the size of a maximum matching in the graph. |
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[1587] | 283 | int size() const { |
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| 284 | int s=0; |
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| 285 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 286 | if ( _mate[v]!=INVALID ) { |
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| 287 | ++s; |
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| 288 | } |
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| 289 | } |
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| 290 | return s/2; |
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| 291 | } |
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| 292 | |
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[1077] | 293 | |
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[2505] | 294 | ///\brief Returns the mate of a node in the actual matching. |
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[1077] | 295 | /// |
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[1093] | 296 | ///Returns the mate of a \c node in the actual matching. |
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| 297 | ///Returns INVALID if the \c node is not covered by the actual matching. |
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[2505] | 298 | Node mate(const Node& node) const { |
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[1093] | 299 | return _mate[node]; |
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| 300 | } |
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| 301 | |
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[2505] | 302 | ///\brief Returns the matching edge incident to the given node. |
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| 303 | /// |
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| 304 | ///Returns the matching edge of a \c node in the actual matching. |
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| 305 | ///Returns INVALID if the \c node is not covered by the actual matching. |
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| 306 | UEdge matchingEdge(const Node& node) const { |
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| 307 | if (_mate[node] == INVALID) return INVALID; |
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| 308 | Node n = node < _mate[node] ? node : _mate[node]; |
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| 309 | for (IncEdgeIt e(g, n); e != INVALID; ++e) { |
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| 310 | if (g.oppositeNode(n, e) == _mate[n]) { |
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| 311 | return e; |
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| 312 | } |
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| 313 | } |
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| 314 | return INVALID; |
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| 315 | } |
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[1077] | 316 | |
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[2505] | 317 | /// \brief Returns the class of the node in the Edmonds-Gallai |
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| 318 | /// decomposition. |
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| 319 | /// |
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| 320 | /// Returns the class of the node in the Edmonds-Gallai |
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| 321 | /// decomposition. |
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| 322 | DecompType decomposition(const Node& n) { |
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| 323 | return position[n] == A; |
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| 324 | } |
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| 325 | |
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| 326 | /// \brief Returns true when the node is in the barrier. |
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| 327 | /// |
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| 328 | /// Returns true when the node is in the barrier. |
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| 329 | bool barrier(const Node& n) { |
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| 330 | return position[n] == A; |
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| 331 | } |
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[1077] | 332 | |
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[2505] | 333 | ///\brief Gives back the matching in a \c Node of mates. |
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| 334 | /// |
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[1165] | 335 | ///Writes the stored matching to a \c Node valued \c Node map. The |
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[1077] | 336 | ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c |
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| 337 | ///map[v]==u will hold, and now \c uv is an edge of the matching. |
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[2505] | 338 | template <typename MateMap> |
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| 339 | void mateMap(MateMap& map) const { |
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[1077] | 340 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[1093] | 341 | map.set(v,_mate[v]); |
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[1077] | 342 | } |
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| 343 | } |
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| 344 | |
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[2505] | 345 | ///\brief Gives back the matching in an \c UEdge valued \c Node |
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| 346 | ///map. |
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| 347 | /// |
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[1909] | 348 | ///Writes the stored matching to an \c UEdge valued \c Node |
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| 349 | ///map. \c map[v] will be an \c UEdge incident to \c v. This |
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[1165] | 350 | ///map will have the property that if \c g.oppositeNode(u,map[u]) |
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| 351 | ///== v then \c map[u]==map[v] holds, and now this edge is an edge |
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| 352 | ///of the matching. |
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[2505] | 353 | template <typename MatchingMap> |
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| 354 | void matchingMap(MatchingMap& map) const { |
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[1077] | 355 | typename Graph::template NodeMap<bool> todo(g,true); |
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| 356 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[2505] | 357 | if (_mate[v]!=INVALID && v < _mate[v]) { |
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[1093] | 358 | Node u=_mate[v]; |
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[1077] | 359 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
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[1158] | 360 | if ( g.runningNode(e) == u ) { |
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[1077] | 361 | map.set(u,e); |
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| 362 | map.set(v,e); |
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| 363 | todo.set(u,false); |
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| 364 | todo.set(v,false); |
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| 365 | break; |
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| 366 | } |
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| 367 | } |
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| 368 | } |
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| 369 | } |
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| 370 | } |
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| 371 | |
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| 372 | |
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[2505] | 373 | ///\brief Gives back the matching in a \c bool valued \c UEdge |
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| 374 | ///map. |
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| 375 | /// |
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[1165] | 376 | ///Writes the matching stored to a \c bool valued \c Edge |
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| 377 | ///map. This map will have the property that there are no two |
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| 378 | ///incident edges \c e, \c f with \c map[e]==map[f]==true. The |
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| 379 | ///edges \c e with \c map[e]==true form the matching. |
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[2505] | 380 | template<typename MatchingMap> |
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| 381 | void matching(MatchingMap& map) const { |
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[1909] | 382 | for(UEdgeIt e(g); e!=INVALID; ++e) map.set(e,false); |
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[1077] | 383 | |
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| 384 | typename Graph::template NodeMap<bool> todo(g,true); |
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| 385 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[1093] | 386 | if ( todo[v] && _mate[v]!=INVALID ) { |
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| 387 | Node u=_mate[v]; |
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[1077] | 388 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
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[1158] | 389 | if ( g.runningNode(e) == u ) { |
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[1077] | 390 | map.set(e,true); |
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| 391 | todo.set(u,false); |
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| 392 | todo.set(v,false); |
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| 393 | break; |
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| 394 | } |
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| 395 | } |
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| 396 | } |
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| 397 | } |
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| 398 | } |
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| 399 | |
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| 400 | |
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[2505] | 401 | ///\brief Returns the canonical decomposition of the graph after running |
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[1077] | 402 | ///the algorithm. |
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[2505] | 403 | /// |
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[1090] | 404 | ///After calling any run methods of the class, it writes the |
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| 405 | ///Gallai-Edmonds canonical decomposition of the graph. \c map |
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[2505] | 406 | ///must be a node map of \ref DecompType 's. |
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| 407 | template <typename DecompositionMap> |
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| 408 | void decomposition(DecompositionMap& map) const { |
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| 409 | for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]); |
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| 410 | } |
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| 411 | |
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| 412 | ///\brief Returns a barrier on the nodes. |
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| 413 | /// |
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| 414 | ///After calling any run methods of the class, it writes a |
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| 415 | ///canonical barrier on the nodes. The odd component number of the |
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| 416 | ///remaining graph minus the barrier size is a lower bound for the |
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| 417 | ///uncovered nodes in the graph. The \c map must be a node map of |
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| 418 | ///bools. |
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| 419 | template <typename BarrierMap> |
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| 420 | void barrier(BarrierMap& barrier) { |
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| 421 | for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A); |
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[1077] | 422 | } |
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| 423 | |
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| 424 | private: |
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| 425 | |
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[1165] | 426 | |
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[1077] | 427 | void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
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[2505] | 428 | UFE& blossom, NV& rep, EFE& tree) { |
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| 429 | //We have one tree which we grow, and also shrink but only if it |
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| 430 | //cannot be postponed. If we augment then we return to the "for" |
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| 431 | //cycle of runEdmonds(). |
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| 432 | |
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| 433 | std::queue<Node> Q; //queue of the totally unscanned nodes |
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| 434 | Q.push(v); |
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| 435 | std::queue<Node> R; |
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| 436 | //queue of the nodes which must be scanned for a possible shrink |
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| 437 | |
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| 438 | while ( !Q.empty() ) { |
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| 439 | Node x=Q.front(); |
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| 440 | Q.pop(); |
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| 441 | for( IncEdgeIt e(g,x); e!= INVALID; ++e ) { |
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| 442 | Node y=g.runningNode(e); |
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| 443 | //growOrAugment grows if y is covered by the matching and |
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| 444 | //augments if not. In this latter case it returns 1. |
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| 445 | if (position[y]==C && |
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| 446 | growOrAugment(y, x, ear, blossom, rep, tree, Q)) return; |
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| 447 | } |
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| 448 | R.push(x); |
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| 449 | } |
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| 450 | |
---|
| 451 | while ( !R.empty() ) { |
---|
| 452 | Node x=R.front(); |
---|
| 453 | R.pop(); |
---|
| 454 | |
---|
| 455 | for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) { |
---|
| 456 | Node y=g.runningNode(e); |
---|
| 457 | |
---|
| 458 | if ( position[y] == D && blossom.find(x) != blossom.find(y) ) |
---|
| 459 | //Recall that we have only one tree. |
---|
| 460 | shrink( x, y, ear, blossom, rep, tree, Q); |
---|
| 461 | |
---|
| 462 | while ( !Q.empty() ) { |
---|
| 463 | Node z=Q.front(); |
---|
| 464 | Q.pop(); |
---|
| 465 | for( IncEdgeIt f(g,z); f!= INVALID; ++f ) { |
---|
| 466 | Node w=g.runningNode(f); |
---|
| 467 | //growOrAugment grows if y is covered by the matching and |
---|
| 468 | //augments if not. In this latter case it returns 1. |
---|
| 469 | if (position[w]==C && |
---|
| 470 | growOrAugment(w, z, ear, blossom, rep, tree, Q)) return; |
---|
| 471 | } |
---|
| 472 | R.push(z); |
---|
| 473 | } |
---|
| 474 | } //for e |
---|
| 475 | } // while ( !R.empty() ) |
---|
| 476 | } |
---|
[1077] | 477 | |
---|
[1234] | 478 | void normShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
---|
[2505] | 479 | UFE& blossom, NV& rep, EFE& tree) { |
---|
| 480 | //We have one tree, which we grow and shrink. If we augment then we |
---|
| 481 | //return to the "for" cycle of runEdmonds(). |
---|
| 482 | |
---|
| 483 | std::queue<Node> Q; //queue of the unscanned nodes |
---|
| 484 | Q.push(v); |
---|
| 485 | while ( !Q.empty() ) { |
---|
| 486 | |
---|
| 487 | Node x=Q.front(); |
---|
| 488 | Q.pop(); |
---|
| 489 | |
---|
| 490 | for( IncEdgeIt e(g,x); e!=INVALID; ++e ) { |
---|
| 491 | Node y=g.runningNode(e); |
---|
| 492 | |
---|
| 493 | switch ( position[y] ) { |
---|
| 494 | case D: //x and y must be in the same tree |
---|
| 495 | if ( blossom.find(x) != blossom.find(y)) |
---|
| 496 | //x and y are in the same tree |
---|
| 497 | shrink(x, y, ear, blossom, rep, tree, Q); |
---|
| 498 | break; |
---|
| 499 | case C: |
---|
| 500 | //growOrAugment grows if y is covered by the matching and |
---|
| 501 | //augments if not. In this latter case it returns 1. |
---|
| 502 | if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return; |
---|
| 503 | break; |
---|
| 504 | default: break; |
---|
| 505 | } |
---|
| 506 | } |
---|
| 507 | } |
---|
| 508 | } |
---|
[1077] | 509 | |
---|
[2023] | 510 | void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear, |
---|
[2505] | 511 | UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) { |
---|
| 512 | //x and y are the two adjacent vertices in two blossoms. |
---|
| 513 | |
---|
| 514 | typename Graph::template NodeMap<bool> path(g,false); |
---|
| 515 | |
---|
| 516 | Node b=rep[blossom.find(x)]; |
---|
| 517 | path.set(b,true); |
---|
| 518 | b=_mate[b]; |
---|
| 519 | while ( b!=INVALID ) { |
---|
| 520 | b=rep[blossom.find(ear[b])]; |
---|
| 521 | path.set(b,true); |
---|
| 522 | b=_mate[b]; |
---|
| 523 | } //we go until the root through bases of blossoms and odd vertices |
---|
| 524 | |
---|
| 525 | Node top=y; |
---|
| 526 | Node middle=rep[blossom.find(top)]; |
---|
| 527 | Node bottom=x; |
---|
| 528 | while ( !path[middle] ) |
---|
| 529 | shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q); |
---|
| 530 | //Until we arrive to a node on the path, we update blossom, tree |
---|
| 531 | //and the positions of the odd nodes. |
---|
| 532 | |
---|
| 533 | Node base=middle; |
---|
| 534 | top=x; |
---|
| 535 | middle=rep[blossom.find(top)]; |
---|
| 536 | bottom=y; |
---|
| 537 | Node blossom_base=rep[blossom.find(base)]; |
---|
| 538 | while ( middle!=blossom_base ) |
---|
| 539 | shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q); |
---|
| 540 | //Until we arrive to a node on the path, we update blossom, tree |
---|
| 541 | //and the positions of the odd nodes. |
---|
| 542 | |
---|
| 543 | rep[blossom.find(base)] = base; |
---|
| 544 | } |
---|
[1077] | 545 | |
---|
[1234] | 546 | void shrinkStep(Node& top, Node& middle, Node& bottom, |
---|
| 547 | typename Graph::template NodeMap<Node>& ear, |
---|
[2505] | 548 | UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) { |
---|
| 549 | //We traverse a blossom and update everything. |
---|
| 550 | |
---|
| 551 | ear.set(top,bottom); |
---|
| 552 | Node t=top; |
---|
| 553 | while ( t!=middle ) { |
---|
| 554 | Node u=_mate[t]; |
---|
| 555 | t=ear[u]; |
---|
| 556 | ear.set(t,u); |
---|
| 557 | } |
---|
| 558 | bottom=_mate[middle]; |
---|
| 559 | position.set(bottom,D); |
---|
| 560 | Q.push(bottom); |
---|
| 561 | top=ear[bottom]; |
---|
| 562 | Node oldmiddle=middle; |
---|
| 563 | middle=rep[blossom.find(top)]; |
---|
| 564 | tree.erase(bottom); |
---|
| 565 | tree.erase(oldmiddle); |
---|
| 566 | blossom.insert(bottom); |
---|
| 567 | blossom.join(bottom, oldmiddle); |
---|
| 568 | blossom.join(top, oldmiddle); |
---|
| 569 | } |
---|
| 570 | |
---|
| 571 | |
---|
[1077] | 572 | |
---|
[2023] | 573 | bool growOrAugment(Node& y, Node& x, typename Graph::template |
---|
[2505] | 574 | NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree, |
---|
| 575 | std::queue<Node>& Q) { |
---|
| 576 | //x is in a blossom in the tree, y is outside. If y is covered by |
---|
| 577 | //the matching we grow, otherwise we augment. In this case we |
---|
| 578 | //return 1. |
---|
| 579 | |
---|
| 580 | if ( _mate[y]!=INVALID ) { //grow |
---|
| 581 | ear.set(y,x); |
---|
| 582 | Node w=_mate[y]; |
---|
| 583 | rep[blossom.insert(w)] = w; |
---|
| 584 | position.set(y,A); |
---|
| 585 | position.set(w,D); |
---|
| 586 | int t = tree.find(rep[blossom.find(x)]); |
---|
| 587 | tree.insert(y,t); |
---|
| 588 | tree.insert(w,t); |
---|
| 589 | Q.push(w); |
---|
| 590 | } else { //augment |
---|
| 591 | augment(x, ear, blossom, rep, tree); |
---|
| 592 | _mate.set(x,y); |
---|
| 593 | _mate.set(y,x); |
---|
| 594 | return true; |
---|
| 595 | } |
---|
| 596 | return false; |
---|
| 597 | } |
---|
[2023] | 598 | |
---|
[1234] | 599 | void augment(Node x, typename Graph::template NodeMap<Node>& ear, |
---|
[2505] | 600 | UFE& blossom, NV& rep, EFE& tree) { |
---|
| 601 | Node v=_mate[x]; |
---|
| 602 | while ( v!=INVALID ) { |
---|
| 603 | |
---|
| 604 | Node u=ear[v]; |
---|
| 605 | _mate.set(v,u); |
---|
| 606 | Node tmp=v; |
---|
| 607 | v=_mate[u]; |
---|
| 608 | _mate.set(u,tmp); |
---|
| 609 | } |
---|
| 610 | int y = tree.find(rep[blossom.find(x)]); |
---|
| 611 | for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) { |
---|
| 612 | if ( position[tit] == D ) { |
---|
| 613 | int b = blossom.find(tit); |
---|
| 614 | for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) { |
---|
| 615 | position.set(bit, C); |
---|
| 616 | } |
---|
| 617 | blossom.eraseClass(b); |
---|
| 618 | } else position.set(tit, C); |
---|
| 619 | } |
---|
| 620 | tree.eraseClass(y); |
---|
| 621 | |
---|
| 622 | } |
---|
[1077] | 623 | |
---|
| 624 | }; |
---|
[2548] | 625 | |
---|
| 626 | /// \ingroup matching |
---|
| 627 | /// |
---|
| 628 | /// \brief Weighted matching in general undirected graphs |
---|
| 629 | /// |
---|
| 630 | /// This class provides an efficient implementation of Edmond's |
---|
| 631 | /// maximum weighted matching algorithm. The implementation is based |
---|
| 632 | /// on extensive use of priority queues and provides |
---|
| 633 | /// \f$O(nm\log(n))\f$ time complexity. |
---|
| 634 | /// |
---|
| 635 | /// The maximum weighted matching problem is to find undirected |
---|
| 636 | /// edges in the graph with maximum overall weight and no two of |
---|
| 637 | /// them shares their endpoints. The problem can be formulated with |
---|
| 638 | /// the next linear program: |
---|
| 639 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
| 640 | ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f] |
---|
| 641 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 642 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
| 643 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 644 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both endpoints in |
---|
| 645 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of |
---|
| 646 | /// the nodes. |
---|
| 647 | /// |
---|
| 648 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 649 | /// optimality. The solution of the dual problem can be used to check |
---|
| 650 | /// the result of the algorithm. The dual linear problem is the next: |
---|
| 651 | /// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f] |
---|
| 652 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
| 653 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
| 654 | /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f] |
---|
| 655 | /// |
---|
| 656 | /// The algorithm can be executed with \c run() or the \c init() and |
---|
| 657 | /// then the \c start() member functions. After it the matching can |
---|
| 658 | /// be asked with \c matching() or mate() functions. The dual |
---|
| 659 | /// solution can be get with \c nodeValue(), \c blossomNum() and \c |
---|
| 660 | /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt |
---|
| 661 | /// "BlossomIt" nested class which is able to iterate on the nodes |
---|
| 662 | /// of a blossom. If the value type is integral then the dual |
---|
| 663 | /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4". |
---|
| 664 | /// |
---|
| 665 | /// \author Balazs Dezso |
---|
| 666 | template <typename _UGraph, |
---|
| 667 | typename _WeightMap = typename _UGraph::template UEdgeMap<int> > |
---|
| 668 | class MaxWeightedMatching { |
---|
| 669 | public: |
---|
| 670 | |
---|
| 671 | typedef _UGraph UGraph; |
---|
| 672 | typedef _WeightMap WeightMap; |
---|
| 673 | typedef typename WeightMap::Value Value; |
---|
| 674 | |
---|
| 675 | /// \brief Scaling factor for dual solution |
---|
| 676 | /// |
---|
| 677 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 678 | /// according to the value type. |
---|
| 679 | static const int dualScale = |
---|
| 680 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 681 | |
---|
| 682 | typedef typename UGraph::template NodeMap<typename UGraph::Edge> |
---|
| 683 | MatchingMap; |
---|
| 684 | |
---|
| 685 | private: |
---|
| 686 | |
---|
| 687 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
| 688 | |
---|
| 689 | typedef typename UGraph::template NodeMap<Value> NodePotential; |
---|
| 690 | typedef std::vector<Node> BlossomNodeList; |
---|
| 691 | |
---|
| 692 | struct BlossomVariable { |
---|
| 693 | int begin, end; |
---|
| 694 | Value value; |
---|
| 695 | |
---|
| 696 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 697 | : begin(_begin), end(_end), value(_value) {} |
---|
| 698 | |
---|
| 699 | }; |
---|
| 700 | |
---|
| 701 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 702 | |
---|
| 703 | const UGraph& _ugraph; |
---|
| 704 | const WeightMap& _weight; |
---|
| 705 | |
---|
| 706 | MatchingMap* _matching; |
---|
| 707 | |
---|
| 708 | NodePotential* _node_potential; |
---|
| 709 | |
---|
| 710 | BlossomPotential _blossom_potential; |
---|
| 711 | BlossomNodeList _blossom_node_list; |
---|
| 712 | |
---|
| 713 | int _node_num; |
---|
| 714 | int _blossom_num; |
---|
| 715 | |
---|
| 716 | typedef typename UGraph::template NodeMap<int> NodeIntMap; |
---|
| 717 | typedef typename UGraph::template EdgeMap<int> EdgeIntMap; |
---|
| 718 | typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap; |
---|
| 719 | typedef IntegerMap<int> IntIntMap; |
---|
| 720 | |
---|
| 721 | enum Status { |
---|
| 722 | EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2 |
---|
| 723 | }; |
---|
| 724 | |
---|
| 725 | typedef HeapUnionFind<Value, NodeIntMap> BlossomSet; |
---|
| 726 | struct BlossomData { |
---|
| 727 | int tree; |
---|
| 728 | Status status; |
---|
| 729 | Edge pred, next; |
---|
| 730 | Value pot, offset; |
---|
| 731 | Node base; |
---|
| 732 | }; |
---|
| 733 | |
---|
| 734 | NodeIntMap *_blossom_index; |
---|
| 735 | BlossomSet *_blossom_set; |
---|
| 736 | IntegerMap<BlossomData>* _blossom_data; |
---|
| 737 | |
---|
| 738 | NodeIntMap *_node_index; |
---|
| 739 | EdgeIntMap *_node_heap_index; |
---|
| 740 | |
---|
| 741 | struct NodeData { |
---|
| 742 | |
---|
| 743 | NodeData(EdgeIntMap& node_heap_index) |
---|
| 744 | : heap(node_heap_index) {} |
---|
| 745 | |
---|
| 746 | int blossom; |
---|
| 747 | Value pot; |
---|
| 748 | BinHeap<Value, EdgeIntMap> heap; |
---|
| 749 | std::map<int, Edge> heap_index; |
---|
| 750 | |
---|
| 751 | int tree; |
---|
| 752 | }; |
---|
| 753 | |
---|
| 754 | IntegerMap<NodeData>* _node_data; |
---|
| 755 | |
---|
| 756 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 757 | |
---|
| 758 | IntIntMap *_tree_set_index; |
---|
| 759 | TreeSet *_tree_set; |
---|
| 760 | |
---|
| 761 | NodeIntMap *_delta1_index; |
---|
| 762 | BinHeap<Value, NodeIntMap> *_delta1; |
---|
| 763 | |
---|
| 764 | IntIntMap *_delta2_index; |
---|
| 765 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 766 | |
---|
| 767 | UEdgeIntMap *_delta3_index; |
---|
| 768 | BinHeap<Value, UEdgeIntMap> *_delta3; |
---|
| 769 | |
---|
| 770 | IntIntMap *_delta4_index; |
---|
| 771 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 772 | |
---|
| 773 | Value _delta_sum; |
---|
| 774 | |
---|
| 775 | void createStructures() { |
---|
| 776 | _node_num = countNodes(_ugraph); |
---|
| 777 | _blossom_num = _node_num * 3 / 2; |
---|
| 778 | |
---|
| 779 | if (!_matching) { |
---|
| 780 | _matching = new MatchingMap(_ugraph); |
---|
| 781 | } |
---|
| 782 | if (!_node_potential) { |
---|
| 783 | _node_potential = new NodePotential(_ugraph); |
---|
| 784 | } |
---|
| 785 | if (!_blossom_set) { |
---|
| 786 | _blossom_index = new NodeIntMap(_ugraph); |
---|
| 787 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 788 | _blossom_data = new IntegerMap<BlossomData>(_blossom_num); |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | if (!_node_index) { |
---|
| 792 | _node_index = new NodeIntMap(_ugraph); |
---|
| 793 | _node_heap_index = new EdgeIntMap(_ugraph); |
---|
| 794 | _node_data = new IntegerMap<NodeData>(_node_num, |
---|
| 795 | NodeData(*_node_heap_index)); |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | if (!_tree_set) { |
---|
| 799 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 800 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 801 | } |
---|
| 802 | if (!_delta1) { |
---|
| 803 | _delta1_index = new NodeIntMap(_ugraph); |
---|
| 804 | _delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index); |
---|
| 805 | } |
---|
| 806 | if (!_delta2) { |
---|
| 807 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 808 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
| 809 | } |
---|
| 810 | if (!_delta3) { |
---|
| 811 | _delta3_index = new UEdgeIntMap(_ugraph); |
---|
| 812 | _delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index); |
---|
| 813 | } |
---|
| 814 | if (!_delta4) { |
---|
| 815 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 816 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
| 817 | } |
---|
| 818 | } |
---|
| 819 | |
---|
| 820 | void destroyStructures() { |
---|
| 821 | _node_num = countNodes(_ugraph); |
---|
| 822 | _blossom_num = _node_num * 3 / 2; |
---|
| 823 | |
---|
| 824 | if (_matching) { |
---|
| 825 | delete _matching; |
---|
| 826 | } |
---|
| 827 | if (_node_potential) { |
---|
| 828 | delete _node_potential; |
---|
| 829 | } |
---|
| 830 | if (_blossom_set) { |
---|
| 831 | delete _blossom_index; |
---|
| 832 | delete _blossom_set; |
---|
| 833 | delete _blossom_data; |
---|
| 834 | } |
---|
| 835 | |
---|
| 836 | if (_node_index) { |
---|
| 837 | delete _node_index; |
---|
| 838 | delete _node_heap_index; |
---|
| 839 | delete _node_data; |
---|
| 840 | } |
---|
| 841 | |
---|
| 842 | if (_tree_set) { |
---|
| 843 | delete _tree_set_index; |
---|
| 844 | delete _tree_set; |
---|
| 845 | } |
---|
| 846 | if (_delta1) { |
---|
| 847 | delete _delta1_index; |
---|
| 848 | delete _delta1; |
---|
| 849 | } |
---|
| 850 | if (_delta2) { |
---|
| 851 | delete _delta2_index; |
---|
| 852 | delete _delta2; |
---|
| 853 | } |
---|
| 854 | if (_delta3) { |
---|
| 855 | delete _delta3_index; |
---|
| 856 | delete _delta3; |
---|
| 857 | } |
---|
| 858 | if (_delta4) { |
---|
| 859 | delete _delta4_index; |
---|
| 860 | delete _delta4; |
---|
| 861 | } |
---|
| 862 | } |
---|
| 863 | |
---|
| 864 | void matchedToEven(int blossom, int tree) { |
---|
| 865 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 866 | _delta2->erase(blossom); |
---|
| 867 | } |
---|
| 868 | |
---|
| 869 | if (!_blossom_set->trivial(blossom)) { |
---|
| 870 | (*_blossom_data)[blossom].pot -= |
---|
| 871 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 872 | } |
---|
| 873 | |
---|
| 874 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 875 | n != INVALID; ++n) { |
---|
| 876 | |
---|
| 877 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 878 | int ni = (*_node_index)[n]; |
---|
| 879 | |
---|
| 880 | (*_node_data)[ni].heap.clear(); |
---|
| 881 | (*_node_data)[ni].heap_index.clear(); |
---|
| 882 | |
---|
| 883 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 884 | |
---|
| 885 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 886 | |
---|
| 887 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 888 | Node v = _ugraph.source(e); |
---|
| 889 | int vb = _blossom_set->find(v); |
---|
| 890 | int vi = (*_node_index)[v]; |
---|
| 891 | |
---|
| 892 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 893 | dualScale * _weight[e]; |
---|
| 894 | |
---|
| 895 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 896 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 897 | _delta3->push(e, rw / 2); |
---|
| 898 | } |
---|
| 899 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 900 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 901 | _delta3->push(e, rw); |
---|
| 902 | } |
---|
| 903 | } else { |
---|
| 904 | typename std::map<int, Edge>::iterator it = |
---|
| 905 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 906 | |
---|
| 907 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 908 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 909 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 910 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 911 | it->second = e; |
---|
| 912 | } |
---|
| 913 | } else { |
---|
| 914 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 915 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 916 | } |
---|
| 917 | |
---|
| 918 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 919 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 920 | |
---|
| 921 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 922 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 923 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 924 | (*_blossom_data)[vb].offset); |
---|
| 925 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 926 | (*_blossom_data)[vb].offset){ |
---|
| 927 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 928 | (*_blossom_data)[vb].offset); |
---|
| 929 | } |
---|
| 930 | } |
---|
| 931 | } |
---|
| 932 | } |
---|
| 933 | } |
---|
| 934 | } |
---|
| 935 | (*_blossom_data)[blossom].offset = 0; |
---|
| 936 | } |
---|
| 937 | |
---|
| 938 | void matchedToOdd(int blossom) { |
---|
| 939 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 940 | _delta2->erase(blossom); |
---|
| 941 | } |
---|
| 942 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 943 | if (!_blossom_set->trivial(blossom)) { |
---|
| 944 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 945 | (*_blossom_data)[blossom].offset); |
---|
| 946 | } |
---|
| 947 | } |
---|
| 948 | |
---|
| 949 | void evenToMatched(int blossom, int tree) { |
---|
| 950 | if (!_blossom_set->trivial(blossom)) { |
---|
| 951 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 952 | } |
---|
| 953 | |
---|
| 954 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 955 | n != INVALID; ++n) { |
---|
| 956 | int ni = (*_node_index)[n]; |
---|
| 957 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 958 | |
---|
| 959 | _delta1->erase(n); |
---|
| 960 | |
---|
| 961 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 962 | Node v = _ugraph.source(e); |
---|
| 963 | int vb = _blossom_set->find(v); |
---|
| 964 | int vi = (*_node_index)[v]; |
---|
| 965 | |
---|
| 966 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 967 | dualScale * _weight[e]; |
---|
| 968 | |
---|
| 969 | if (vb == blossom) { |
---|
| 970 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 971 | _delta3->erase(e); |
---|
| 972 | } |
---|
| 973 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 974 | |
---|
| 975 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 976 | _delta3->erase(e); |
---|
| 977 | } |
---|
| 978 | |
---|
| 979 | int vt = _tree_set->find(vb); |
---|
| 980 | |
---|
| 981 | if (vt != tree) { |
---|
| 982 | |
---|
| 983 | Edge r = _ugraph.oppositeEdge(e); |
---|
| 984 | |
---|
| 985 | typename std::map<int, Edge>::iterator it = |
---|
| 986 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 987 | |
---|
| 988 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 989 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 990 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 991 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 992 | it->second = r; |
---|
| 993 | } |
---|
| 994 | } else { |
---|
| 995 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 996 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 997 | } |
---|
| 998 | |
---|
| 999 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1000 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1001 | |
---|
| 1002 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1003 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1004 | (*_blossom_data)[blossom].offset); |
---|
| 1005 | } else if ((*_delta2)[blossom] > |
---|
| 1006 | _blossom_set->classPrio(blossom) - |
---|
| 1007 | (*_blossom_data)[blossom].offset){ |
---|
| 1008 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1009 | (*_blossom_data)[blossom].offset); |
---|
| 1010 | } |
---|
| 1011 | } |
---|
| 1012 | } |
---|
| 1013 | |
---|
| 1014 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1015 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1016 | _delta3->erase(e); |
---|
| 1017 | } |
---|
| 1018 | } else { |
---|
| 1019 | |
---|
| 1020 | typename std::map<int, Edge>::iterator it = |
---|
| 1021 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1022 | |
---|
| 1023 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1024 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 1025 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 1026 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 1027 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 1028 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 1029 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 1030 | } |
---|
| 1031 | |
---|
| 1032 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1033 | if (_blossom_set->classPrio(vb) == |
---|
| 1034 | std::numeric_limits<Value>::max()) { |
---|
| 1035 | _delta2->erase(vb); |
---|
| 1036 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 1037 | (*_blossom_data)[vb].offset) { |
---|
| 1038 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 1039 | (*_blossom_data)[vb].offset); |
---|
| 1040 | } |
---|
| 1041 | } |
---|
| 1042 | } |
---|
| 1043 | } |
---|
| 1044 | } |
---|
| 1045 | } |
---|
| 1046 | } |
---|
| 1047 | |
---|
| 1048 | void oddToMatched(int blossom) { |
---|
| 1049 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 1050 | |
---|
| 1051 | if (_blossom_set->classPrio(blossom) != |
---|
| 1052 | std::numeric_limits<Value>::max()) { |
---|
| 1053 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1054 | (*_blossom_data)[blossom].offset); |
---|
| 1055 | } |
---|
| 1056 | |
---|
| 1057 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1058 | _delta4->erase(blossom); |
---|
| 1059 | } |
---|
| 1060 | } |
---|
| 1061 | |
---|
| 1062 | void oddToEven(int blossom, int tree) { |
---|
| 1063 | if (!_blossom_set->trivial(blossom)) { |
---|
| 1064 | _delta4->erase(blossom); |
---|
| 1065 | (*_blossom_data)[blossom].pot -= |
---|
| 1066 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 1067 | } |
---|
| 1068 | |
---|
| 1069 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1070 | n != INVALID; ++n) { |
---|
| 1071 | int ni = (*_node_index)[n]; |
---|
| 1072 | |
---|
| 1073 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1074 | |
---|
| 1075 | (*_node_data)[ni].heap.clear(); |
---|
| 1076 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1077 | (*_node_data)[ni].pot += |
---|
| 1078 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 1079 | |
---|
| 1080 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
| 1081 | |
---|
| 1082 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 1083 | Node v = _ugraph.source(e); |
---|
| 1084 | int vb = _blossom_set->find(v); |
---|
| 1085 | int vi = (*_node_index)[v]; |
---|
| 1086 | |
---|
| 1087 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1088 | dualScale * _weight[e]; |
---|
| 1089 | |
---|
| 1090 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1091 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 1092 | _delta3->push(e, rw / 2); |
---|
| 1093 | } |
---|
| 1094 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1095 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 1096 | _delta3->push(e, rw); |
---|
| 1097 | } |
---|
| 1098 | } else { |
---|
| 1099 | |
---|
| 1100 | typename std::map<int, Edge>::iterator it = |
---|
| 1101 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 1102 | |
---|
| 1103 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 1104 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 1105 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 1106 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 1107 | it->second = e; |
---|
| 1108 | } |
---|
| 1109 | } else { |
---|
| 1110 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 1111 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 1112 | } |
---|
| 1113 | |
---|
| 1114 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 1115 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 1116 | |
---|
| 1117 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 1118 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 1119 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 1120 | (*_blossom_data)[vb].offset); |
---|
| 1121 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 1122 | (*_blossom_data)[vb].offset) { |
---|
| 1123 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 1124 | (*_blossom_data)[vb].offset); |
---|
| 1125 | } |
---|
| 1126 | } |
---|
| 1127 | } |
---|
| 1128 | } |
---|
| 1129 | } |
---|
| 1130 | } |
---|
| 1131 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1132 | } |
---|
| 1133 | |
---|
| 1134 | |
---|
| 1135 | void matchedToUnmatched(int blossom) { |
---|
| 1136 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1137 | _delta2->erase(blossom); |
---|
| 1138 | } |
---|
| 1139 | |
---|
| 1140 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1141 | n != INVALID; ++n) { |
---|
| 1142 | int ni = (*_node_index)[n]; |
---|
| 1143 | |
---|
| 1144 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 1145 | |
---|
| 1146 | (*_node_data)[ni].heap.clear(); |
---|
| 1147 | (*_node_data)[ni].heap_index.clear(); |
---|
| 1148 | |
---|
| 1149 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 1150 | Node v = _ugraph.target(e); |
---|
| 1151 | int vb = _blossom_set->find(v); |
---|
| 1152 | int vi = (*_node_index)[v]; |
---|
| 1153 | |
---|
| 1154 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1155 | dualScale * _weight[e]; |
---|
| 1156 | |
---|
| 1157 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1158 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
| 1159 | _delta3->push(e, rw); |
---|
| 1160 | } |
---|
| 1161 | } |
---|
| 1162 | } |
---|
| 1163 | } |
---|
| 1164 | } |
---|
| 1165 | |
---|
| 1166 | void unmatchedToMatched(int blossom) { |
---|
| 1167 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 1168 | n != INVALID; ++n) { |
---|
| 1169 | int ni = (*_node_index)[n]; |
---|
| 1170 | |
---|
| 1171 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 1172 | Node v = _ugraph.source(e); |
---|
| 1173 | int vb = _blossom_set->find(v); |
---|
| 1174 | int vi = (*_node_index)[v]; |
---|
| 1175 | |
---|
| 1176 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 1177 | dualScale * _weight[e]; |
---|
| 1178 | |
---|
| 1179 | if (vb == blossom) { |
---|
| 1180 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1181 | _delta3->erase(e); |
---|
| 1182 | } |
---|
| 1183 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 1184 | |
---|
| 1185 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1186 | _delta3->erase(e); |
---|
| 1187 | } |
---|
| 1188 | |
---|
| 1189 | int vt = _tree_set->find(vb); |
---|
| 1190 | |
---|
| 1191 | Edge r = _ugraph.oppositeEdge(e); |
---|
| 1192 | |
---|
| 1193 | typename std::map<int, Edge>::iterator it = |
---|
| 1194 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 1195 | |
---|
| 1196 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 1197 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 1198 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 1199 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 1200 | it->second = r; |
---|
| 1201 | } |
---|
| 1202 | } else { |
---|
| 1203 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 1204 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 1205 | } |
---|
| 1206 | |
---|
| 1207 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 1208 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 1209 | |
---|
| 1210 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 1211 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1212 | (*_blossom_data)[blossom].offset); |
---|
| 1213 | } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)- |
---|
| 1214 | (*_blossom_data)[blossom].offset){ |
---|
| 1215 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 1216 | (*_blossom_data)[blossom].offset); |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | |
---|
| 1220 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
| 1221 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 1222 | _delta3->erase(e); |
---|
| 1223 | } |
---|
| 1224 | } |
---|
| 1225 | } |
---|
| 1226 | } |
---|
| 1227 | } |
---|
| 1228 | |
---|
| 1229 | void alternatePath(int even, int tree) { |
---|
| 1230 | int odd; |
---|
| 1231 | |
---|
| 1232 | evenToMatched(even, tree); |
---|
| 1233 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1234 | |
---|
| 1235 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 1236 | odd = _blossom_set->find(_ugraph.target((*_blossom_data)[even].pred)); |
---|
| 1237 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 1238 | oddToMatched(odd); |
---|
| 1239 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 1240 | |
---|
| 1241 | even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred)); |
---|
| 1242 | (*_blossom_data)[even].status = MATCHED; |
---|
| 1243 | evenToMatched(even, tree); |
---|
| 1244 | (*_blossom_data)[even].next = |
---|
| 1245 | _ugraph.oppositeEdge((*_blossom_data)[odd].pred); |
---|
| 1246 | } |
---|
| 1247 | |
---|
| 1248 | } |
---|
| 1249 | |
---|
| 1250 | void destroyTree(int tree) { |
---|
| 1251 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 1252 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 1253 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1254 | evenToMatched(b, tree); |
---|
| 1255 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 1256 | (*_blossom_data)[b].status = MATCHED; |
---|
| 1257 | oddToMatched(b); |
---|
| 1258 | } |
---|
| 1259 | } |
---|
| 1260 | _tree_set->eraseClass(tree); |
---|
| 1261 | } |
---|
| 1262 | |
---|
| 1263 | |
---|
| 1264 | void unmatchNode(const Node& node) { |
---|
| 1265 | int blossom = _blossom_set->find(node); |
---|
| 1266 | int tree = _tree_set->find(blossom); |
---|
| 1267 | |
---|
| 1268 | alternatePath(blossom, tree); |
---|
| 1269 | destroyTree(tree); |
---|
| 1270 | |
---|
| 1271 | (*_blossom_data)[blossom].status = UNMATCHED; |
---|
| 1272 | (*_blossom_data)[blossom].base = node; |
---|
| 1273 | matchedToUnmatched(blossom); |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | |
---|
| 1277 | void augmentOnEdge(const UEdge& edge) { |
---|
| 1278 | |
---|
| 1279 | int left = _blossom_set->find(_ugraph.source(edge)); |
---|
| 1280 | int right = _blossom_set->find(_ugraph.target(edge)); |
---|
| 1281 | |
---|
| 1282 | if ((*_blossom_data)[left].status == EVEN) { |
---|
| 1283 | int left_tree = _tree_set->find(left); |
---|
| 1284 | alternatePath(left, left_tree); |
---|
| 1285 | destroyTree(left_tree); |
---|
| 1286 | } else { |
---|
| 1287 | (*_blossom_data)[left].status = MATCHED; |
---|
| 1288 | unmatchedToMatched(left); |
---|
| 1289 | } |
---|
| 1290 | |
---|
| 1291 | if ((*_blossom_data)[right].status == EVEN) { |
---|
| 1292 | int right_tree = _tree_set->find(right); |
---|
| 1293 | alternatePath(right, right_tree); |
---|
| 1294 | destroyTree(right_tree); |
---|
| 1295 | } else { |
---|
| 1296 | (*_blossom_data)[right].status = MATCHED; |
---|
| 1297 | unmatchedToMatched(right); |
---|
| 1298 | } |
---|
| 1299 | |
---|
| 1300 | (*_blossom_data)[left].next = _ugraph.direct(edge, true); |
---|
| 1301 | (*_blossom_data)[right].next = _ugraph.direct(edge, false); |
---|
| 1302 | } |
---|
| 1303 | |
---|
| 1304 | void extendOnEdge(const Edge& edge) { |
---|
| 1305 | int base = _blossom_set->find(_ugraph.target(edge)); |
---|
| 1306 | int tree = _tree_set->find(base); |
---|
| 1307 | |
---|
| 1308 | int odd = _blossom_set->find(_ugraph.source(edge)); |
---|
| 1309 | _tree_set->insert(odd, tree); |
---|
| 1310 | (*_blossom_data)[odd].status = ODD; |
---|
| 1311 | matchedToOdd(odd); |
---|
| 1312 | (*_blossom_data)[odd].pred = edge; |
---|
| 1313 | |
---|
| 1314 | int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next)); |
---|
| 1315 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 1316 | _tree_set->insert(even, tree); |
---|
| 1317 | (*_blossom_data)[even].status = EVEN; |
---|
| 1318 | matchedToEven(even, tree); |
---|
| 1319 | } |
---|
| 1320 | |
---|
| 1321 | void shrinkOnEdge(const UEdge& uedge, int tree) { |
---|
| 1322 | int nca = -1; |
---|
| 1323 | std::vector<int> left_path, right_path; |
---|
| 1324 | |
---|
| 1325 | { |
---|
| 1326 | std::set<int> left_set, right_set; |
---|
| 1327 | int left = _blossom_set->find(_ugraph.source(uedge)); |
---|
| 1328 | left_path.push_back(left); |
---|
| 1329 | left_set.insert(left); |
---|
| 1330 | |
---|
| 1331 | int right = _blossom_set->find(_ugraph.target(uedge)); |
---|
| 1332 | right_path.push_back(right); |
---|
| 1333 | right_set.insert(right); |
---|
| 1334 | |
---|
| 1335 | while (true) { |
---|
| 1336 | |
---|
| 1337 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 1338 | |
---|
| 1339 | left = |
---|
| 1340 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
| 1341 | left_path.push_back(left); |
---|
| 1342 | left = |
---|
| 1343 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
| 1344 | left_path.push_back(left); |
---|
| 1345 | |
---|
| 1346 | left_set.insert(left); |
---|
| 1347 | |
---|
| 1348 | if (right_set.find(left) != right_set.end()) { |
---|
| 1349 | nca = left; |
---|
| 1350 | break; |
---|
| 1351 | } |
---|
| 1352 | |
---|
| 1353 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 1354 | |
---|
| 1355 | right = |
---|
| 1356 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
| 1357 | right_path.push_back(right); |
---|
| 1358 | right = |
---|
| 1359 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
| 1360 | right_path.push_back(right); |
---|
| 1361 | |
---|
| 1362 | right_set.insert(right); |
---|
| 1363 | |
---|
| 1364 | if (left_set.find(right) != left_set.end()) { |
---|
| 1365 | nca = right; |
---|
| 1366 | break; |
---|
| 1367 | } |
---|
| 1368 | |
---|
| 1369 | } |
---|
| 1370 | |
---|
| 1371 | if (nca == -1) { |
---|
| 1372 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 1373 | nca = right; |
---|
| 1374 | while (left_set.find(nca) == left_set.end()) { |
---|
| 1375 | nca = |
---|
| 1376 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 1377 | right_path.push_back(nca); |
---|
| 1378 | nca = |
---|
| 1379 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 1380 | right_path.push_back(nca); |
---|
| 1381 | } |
---|
| 1382 | } else { |
---|
| 1383 | nca = left; |
---|
| 1384 | while (right_set.find(nca) == right_set.end()) { |
---|
| 1385 | nca = |
---|
| 1386 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 1387 | left_path.push_back(nca); |
---|
| 1388 | nca = |
---|
| 1389 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 1390 | left_path.push_back(nca); |
---|
| 1391 | } |
---|
| 1392 | } |
---|
| 1393 | } |
---|
| 1394 | } |
---|
| 1395 | |
---|
| 1396 | std::vector<int> subblossoms; |
---|
| 1397 | Edge prev; |
---|
| 1398 | |
---|
| 1399 | prev = _ugraph.direct(uedge, true); |
---|
| 1400 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 1401 | subblossoms.push_back(left_path[i]); |
---|
| 1402 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 1403 | _tree_set->erase(left_path[i]); |
---|
| 1404 | |
---|
| 1405 | subblossoms.push_back(left_path[i + 1]); |
---|
| 1406 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 1407 | oddToEven(left_path[i + 1], tree); |
---|
| 1408 | _tree_set->erase(left_path[i + 1]); |
---|
| 1409 | prev = _ugraph.oppositeEdge((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 1410 | } |
---|
| 1411 | |
---|
| 1412 | int k = 0; |
---|
| 1413 | while (right_path[k] != nca) ++k; |
---|
| 1414 | |
---|
| 1415 | subblossoms.push_back(nca); |
---|
| 1416 | (*_blossom_data)[nca].next = prev; |
---|
| 1417 | |
---|
| 1418 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 1419 | subblossoms.push_back(right_path[i + 1]); |
---|
| 1420 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 1421 | oddToEven(right_path[i + 1], tree); |
---|
| 1422 | _tree_set->erase(right_path[i + 1]); |
---|
| 1423 | |
---|
| 1424 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 1425 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 1426 | |
---|
| 1427 | subblossoms.push_back(right_path[i]); |
---|
| 1428 | _tree_set->erase(right_path[i]); |
---|
| 1429 | } |
---|
| 1430 | |
---|
| 1431 | int surface = |
---|
| 1432 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 1433 | |
---|
| 1434 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1435 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1436 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 1437 | } |
---|
| 1438 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 1439 | } |
---|
| 1440 | |
---|
| 1441 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 1442 | (*_blossom_data)[surface].offset = 0; |
---|
| 1443 | (*_blossom_data)[surface].status = EVEN; |
---|
| 1444 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 1445 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 1446 | |
---|
| 1447 | _tree_set->insert(surface, tree); |
---|
| 1448 | _tree_set->erase(nca); |
---|
| 1449 | } |
---|
| 1450 | |
---|
| 1451 | void splitBlossom(int blossom) { |
---|
| 1452 | Edge next = (*_blossom_data)[blossom].next; |
---|
| 1453 | Edge pred = (*_blossom_data)[blossom].pred; |
---|
| 1454 | |
---|
| 1455 | int tree = _tree_set->find(blossom); |
---|
| 1456 | |
---|
| 1457 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 1458 | oddToMatched(blossom); |
---|
| 1459 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 1460 | _delta2->erase(blossom); |
---|
| 1461 | } |
---|
| 1462 | |
---|
| 1463 | std::vector<int> subblossoms; |
---|
| 1464 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1465 | |
---|
| 1466 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 1467 | int b = _blossom_set->find(_ugraph.source(pred)); |
---|
| 1468 | int d = _blossom_set->find(_ugraph.source(next)); |
---|
| 1469 | |
---|
[2549] | 1470 | int ib = -1, id = -1; |
---|
[2548] | 1471 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1472 | if (subblossoms[i] == b) ib = i; |
---|
| 1473 | if (subblossoms[i] == d) id = i; |
---|
| 1474 | |
---|
| 1475 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 1476 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 1477 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 1478 | } |
---|
| 1479 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 1480 | std::numeric_limits<Value>::max()) { |
---|
| 1481 | _delta2->push(subblossoms[i], |
---|
| 1482 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 1483 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 1484 | } |
---|
| 1485 | } |
---|
| 1486 | |
---|
| 1487 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 1488 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 1489 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1490 | int sb = subblossoms[i]; |
---|
| 1491 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1492 | (*_blossom_data)[sb].next = |
---|
| 1493 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 1494 | } |
---|
| 1495 | |
---|
| 1496 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1497 | int sb = subblossoms[i]; |
---|
| 1498 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1499 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1500 | |
---|
| 1501 | (*_blossom_data)[sb].status = ODD; |
---|
| 1502 | matchedToOdd(sb); |
---|
| 1503 | _tree_set->insert(sb, tree); |
---|
| 1504 | (*_blossom_data)[sb].pred = pred; |
---|
| 1505 | (*_blossom_data)[sb].next = |
---|
| 1506 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 1507 | |
---|
| 1508 | pred = (*_blossom_data)[ub].next; |
---|
| 1509 | |
---|
| 1510 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1511 | matchedToEven(tb, tree); |
---|
| 1512 | _tree_set->insert(tb, tree); |
---|
| 1513 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 1514 | } |
---|
| 1515 | |
---|
| 1516 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 1517 | matchedToOdd(subblossoms[id]); |
---|
| 1518 | _tree_set->insert(subblossoms[id], tree); |
---|
| 1519 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 1520 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 1521 | |
---|
| 1522 | } else { |
---|
| 1523 | |
---|
| 1524 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 1525 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 1526 | int sb = subblossoms[i]; |
---|
| 1527 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1528 | (*_blossom_data)[sb].next = |
---|
| 1529 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 1530 | } |
---|
| 1531 | |
---|
| 1532 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 1533 | int sb = subblossoms[i]; |
---|
| 1534 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 1535 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 1536 | |
---|
| 1537 | (*_blossom_data)[sb].status = ODD; |
---|
| 1538 | matchedToOdd(sb); |
---|
| 1539 | _tree_set->insert(sb, tree); |
---|
| 1540 | (*_blossom_data)[sb].next = next; |
---|
| 1541 | (*_blossom_data)[sb].pred = |
---|
| 1542 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 1543 | |
---|
| 1544 | (*_blossom_data)[tb].status = EVEN; |
---|
| 1545 | matchedToEven(tb, tree); |
---|
| 1546 | _tree_set->insert(tb, tree); |
---|
| 1547 | (*_blossom_data)[tb].pred = |
---|
| 1548 | (*_blossom_data)[tb].next = |
---|
| 1549 | _ugraph.oppositeEdge((*_blossom_data)[ub].next); |
---|
| 1550 | next = (*_blossom_data)[ub].next; |
---|
| 1551 | } |
---|
| 1552 | |
---|
| 1553 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 1554 | matchedToOdd(subblossoms[ib]); |
---|
| 1555 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 1556 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 1557 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 1558 | } |
---|
| 1559 | _tree_set->erase(blossom); |
---|
| 1560 | } |
---|
| 1561 | |
---|
| 1562 | void extractBlossom(int blossom, const Node& base, const Edge& matching) { |
---|
| 1563 | if (_blossom_set->trivial(blossom)) { |
---|
| 1564 | int bi = (*_node_index)[base]; |
---|
| 1565 | Value pot = (*_node_data)[bi].pot; |
---|
| 1566 | |
---|
| 1567 | _matching->set(base, matching); |
---|
| 1568 | _blossom_node_list.push_back(base); |
---|
| 1569 | _node_potential->set(base, pot); |
---|
| 1570 | } else { |
---|
| 1571 | |
---|
| 1572 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 1573 | int bn = _blossom_node_list.size(); |
---|
| 1574 | |
---|
| 1575 | std::vector<int> subblossoms; |
---|
| 1576 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 1577 | int b = _blossom_set->find(base); |
---|
| 1578 | int ib = -1; |
---|
| 1579 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 1580 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 1581 | } |
---|
| 1582 | |
---|
| 1583 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 1584 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 1585 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 1586 | |
---|
| 1587 | Edge m = (*_blossom_data)[tb].next; |
---|
| 1588 | extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m)); |
---|
| 1589 | extractBlossom(tb, _ugraph.source(m), m); |
---|
| 1590 | } |
---|
| 1591 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 1592 | |
---|
| 1593 | int en = _blossom_node_list.size(); |
---|
| 1594 | |
---|
| 1595 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 1596 | } |
---|
| 1597 | } |
---|
| 1598 | |
---|
| 1599 | void extractMatching() { |
---|
| 1600 | std::vector<int> blossoms; |
---|
| 1601 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 1602 | blossoms.push_back(c); |
---|
| 1603 | } |
---|
| 1604 | |
---|
| 1605 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 1606 | if ((*_blossom_data)[blossoms[i]].status == MATCHED) { |
---|
| 1607 | |
---|
| 1608 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 1609 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 1610 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 1611 | n != INVALID; ++n) { |
---|
| 1612 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 1613 | } |
---|
| 1614 | |
---|
| 1615 | Edge matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 1616 | Node base = _ugraph.source(matching); |
---|
| 1617 | extractBlossom(blossoms[i], base, matching); |
---|
| 1618 | } else { |
---|
| 1619 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
| 1620 | extractBlossom(blossoms[i], base, INVALID); |
---|
| 1621 | } |
---|
| 1622 | } |
---|
| 1623 | } |
---|
| 1624 | |
---|
| 1625 | public: |
---|
| 1626 | |
---|
| 1627 | /// \brief Constructor |
---|
| 1628 | /// |
---|
| 1629 | /// Constructor. |
---|
| 1630 | MaxWeightedMatching(const UGraph& ugraph, const WeightMap& weight) |
---|
| 1631 | : _ugraph(ugraph), _weight(weight), _matching(0), |
---|
| 1632 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 1633 | _node_num(0), _blossom_num(0), |
---|
| 1634 | |
---|
| 1635 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 1636 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 1637 | _tree_set_index(0), _tree_set(0), |
---|
| 1638 | |
---|
| 1639 | _delta1_index(0), _delta1(0), |
---|
| 1640 | _delta2_index(0), _delta2(0), |
---|
| 1641 | _delta3_index(0), _delta3(0), |
---|
| 1642 | _delta4_index(0), _delta4(0), |
---|
| 1643 | |
---|
| 1644 | _delta_sum() {} |
---|
| 1645 | |
---|
| 1646 | ~MaxWeightedMatching() { |
---|
| 1647 | destroyStructures(); |
---|
| 1648 | } |
---|
| 1649 | |
---|
| 1650 | /// \name Execution control |
---|
| 1651 | /// The simplest way to execute the algorithm is to use the member |
---|
| 1652 | /// \c run() member function. |
---|
| 1653 | |
---|
| 1654 | ///@{ |
---|
| 1655 | |
---|
| 1656 | /// \brief Initialize the algorithm |
---|
| 1657 | /// |
---|
| 1658 | /// Initialize the algorithm |
---|
| 1659 | void init() { |
---|
| 1660 | createStructures(); |
---|
| 1661 | |
---|
| 1662 | for (EdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
| 1663 | _node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP); |
---|
| 1664 | } |
---|
| 1665 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 1666 | _delta1_index->set(n, _delta1->PRE_HEAP); |
---|
| 1667 | } |
---|
| 1668 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
| 1669 | _delta3_index->set(e, _delta3->PRE_HEAP); |
---|
| 1670 | } |
---|
| 1671 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 1672 | _delta2_index->set(i, _delta2->PRE_HEAP); |
---|
| 1673 | _delta4_index->set(i, _delta4->PRE_HEAP); |
---|
| 1674 | } |
---|
| 1675 | |
---|
| 1676 | int index = 0; |
---|
| 1677 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 1678 | Value max = 0; |
---|
| 1679 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 1680 | if (_ugraph.target(e) == n) continue; |
---|
| 1681 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 1682 | max = (dualScale * _weight[e]) / 2; |
---|
| 1683 | } |
---|
| 1684 | } |
---|
| 1685 | _node_index->set(n, index); |
---|
| 1686 | (*_node_data)[index].pot = max; |
---|
| 1687 | _delta1->push(n, max); |
---|
| 1688 | int blossom = |
---|
| 1689 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 1690 | |
---|
| 1691 | _tree_set->insert(blossom); |
---|
| 1692 | |
---|
| 1693 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 1694 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 1695 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 1696 | (*_blossom_data)[blossom].pot = 0; |
---|
| 1697 | (*_blossom_data)[blossom].offset = 0; |
---|
| 1698 | ++index; |
---|
| 1699 | } |
---|
| 1700 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
| 1701 | int si = (*_node_index)[_ugraph.source(e)]; |
---|
| 1702 | int ti = (*_node_index)[_ugraph.target(e)]; |
---|
| 1703 | if (_ugraph.source(e) != _ugraph.target(e)) { |
---|
| 1704 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 1705 | dualScale * _weight[e]) / 2); |
---|
| 1706 | } |
---|
| 1707 | } |
---|
| 1708 | } |
---|
| 1709 | |
---|
| 1710 | /// \brief Starts the algorithm |
---|
| 1711 | /// |
---|
| 1712 | /// Starts the algorithm |
---|
| 1713 | void start() { |
---|
| 1714 | enum OpType { |
---|
| 1715 | D1, D2, D3, D4 |
---|
| 1716 | }; |
---|
| 1717 | |
---|
| 1718 | int unmatched = _node_num; |
---|
| 1719 | while (unmatched > 0) { |
---|
| 1720 | Value d1 = !_delta1->empty() ? |
---|
| 1721 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
| 1722 | |
---|
| 1723 | Value d2 = !_delta2->empty() ? |
---|
| 1724 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 1725 | |
---|
| 1726 | Value d3 = !_delta3->empty() ? |
---|
| 1727 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 1728 | |
---|
| 1729 | Value d4 = !_delta4->empty() ? |
---|
| 1730 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 1731 | |
---|
| 1732 | _delta_sum = d1; OpType ot = D1; |
---|
| 1733 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
| 1734 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
| 1735 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 1736 | |
---|
| 1737 | |
---|
| 1738 | switch (ot) { |
---|
| 1739 | case D1: |
---|
| 1740 | { |
---|
| 1741 | Node n = _delta1->top(); |
---|
| 1742 | unmatchNode(n); |
---|
| 1743 | --unmatched; |
---|
| 1744 | } |
---|
| 1745 | break; |
---|
| 1746 | case D2: |
---|
| 1747 | { |
---|
| 1748 | int blossom = _delta2->top(); |
---|
| 1749 | Node n = _blossom_set->classTop(blossom); |
---|
| 1750 | Edge e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 1751 | extendOnEdge(e); |
---|
| 1752 | } |
---|
| 1753 | break; |
---|
| 1754 | case D3: |
---|
| 1755 | { |
---|
| 1756 | UEdge e = _delta3->top(); |
---|
| 1757 | |
---|
| 1758 | int left_blossom = _blossom_set->find(_ugraph.source(e)); |
---|
| 1759 | int right_blossom = _blossom_set->find(_ugraph.target(e)); |
---|
| 1760 | |
---|
| 1761 | if (left_blossom == right_blossom) { |
---|
| 1762 | _delta3->pop(); |
---|
| 1763 | } else { |
---|
| 1764 | int left_tree; |
---|
| 1765 | if ((*_blossom_data)[left_blossom].status == EVEN) { |
---|
| 1766 | left_tree = _tree_set->find(left_blossom); |
---|
| 1767 | } else { |
---|
| 1768 | left_tree = -1; |
---|
| 1769 | ++unmatched; |
---|
| 1770 | } |
---|
| 1771 | int right_tree; |
---|
| 1772 | if ((*_blossom_data)[right_blossom].status == EVEN) { |
---|
| 1773 | right_tree = _tree_set->find(right_blossom); |
---|
| 1774 | } else { |
---|
| 1775 | right_tree = -1; |
---|
| 1776 | ++unmatched; |
---|
| 1777 | } |
---|
| 1778 | |
---|
| 1779 | if (left_tree == right_tree) { |
---|
| 1780 | shrinkOnEdge(e, left_tree); |
---|
| 1781 | } else { |
---|
| 1782 | augmentOnEdge(e); |
---|
| 1783 | unmatched -= 2; |
---|
| 1784 | } |
---|
| 1785 | } |
---|
| 1786 | } break; |
---|
| 1787 | case D4: |
---|
| 1788 | splitBlossom(_delta4->top()); |
---|
| 1789 | break; |
---|
| 1790 | } |
---|
| 1791 | } |
---|
| 1792 | extractMatching(); |
---|
| 1793 | } |
---|
| 1794 | |
---|
| 1795 | /// \brief Runs %MaxWeightedMatching algorithm. |
---|
| 1796 | /// |
---|
| 1797 | /// This method runs the %MaxWeightedMatching algorithm. |
---|
| 1798 | /// |
---|
| 1799 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 1800 | /// \code |
---|
| 1801 | /// mwm.init(); |
---|
| 1802 | /// mwm.start(); |
---|
| 1803 | /// \endcode |
---|
| 1804 | void run() { |
---|
| 1805 | init(); |
---|
| 1806 | start(); |
---|
| 1807 | } |
---|
| 1808 | |
---|
| 1809 | /// @} |
---|
| 1810 | |
---|
| 1811 | /// \name Primal solution |
---|
| 1812 | /// Functions for get the primal solution, ie. the matching. |
---|
| 1813 | |
---|
| 1814 | /// @{ |
---|
| 1815 | |
---|
| 1816 | /// \brief Returns the matching value. |
---|
| 1817 | /// |
---|
| 1818 | /// Returns the matching value. |
---|
| 1819 | Value matchingValue() const { |
---|
| 1820 | Value sum = 0; |
---|
| 1821 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 1822 | if ((*_matching)[n] != INVALID) { |
---|
| 1823 | sum += _weight[(*_matching)[n]]; |
---|
| 1824 | } |
---|
| 1825 | } |
---|
| 1826 | return sum /= 2; |
---|
| 1827 | } |
---|
| 1828 | |
---|
| 1829 | /// \brief Returns true when the edge is in the matching. |
---|
| 1830 | /// |
---|
| 1831 | /// Returns true when the edge is in the matching. |
---|
| 1832 | bool matching(const UEdge& edge) const { |
---|
| 1833 | return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true); |
---|
| 1834 | } |
---|
| 1835 | |
---|
| 1836 | /// \brief Returns the incident matching edge. |
---|
| 1837 | /// |
---|
| 1838 | /// Returns the incident matching edge from given node. If the |
---|
| 1839 | /// node is not matched then it gives back \c INVALID. |
---|
| 1840 | Edge matching(const Node& node) const { |
---|
| 1841 | return (*_matching)[node]; |
---|
| 1842 | } |
---|
| 1843 | |
---|
| 1844 | /// \brief Returns the mate of the node. |
---|
| 1845 | /// |
---|
| 1846 | /// Returns the adjancent node in a mathcing edge. If the node is |
---|
| 1847 | /// not matched then it gives back \c INVALID. |
---|
| 1848 | Node mate(const Node& node) const { |
---|
| 1849 | return (*_matching)[node] != INVALID ? |
---|
| 1850 | _ugraph.target((*_matching)[node]) : INVALID; |
---|
| 1851 | } |
---|
| 1852 | |
---|
| 1853 | /// @} |
---|
| 1854 | |
---|
| 1855 | /// \name Dual solution |
---|
| 1856 | /// Functions for get the dual solution. |
---|
| 1857 | |
---|
| 1858 | /// @{ |
---|
| 1859 | |
---|
| 1860 | /// \brief Returns the value of the dual solution. |
---|
| 1861 | /// |
---|
| 1862 | /// Returns the value of the dual solution. It should be equal to |
---|
| 1863 | /// the primal value scaled by \ref dualScale "dual scale". |
---|
| 1864 | Value dualValue() const { |
---|
| 1865 | Value sum = 0; |
---|
| 1866 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 1867 | sum += nodeValue(n); |
---|
| 1868 | } |
---|
| 1869 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 1870 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 1871 | } |
---|
| 1872 | return sum; |
---|
| 1873 | } |
---|
| 1874 | |
---|
| 1875 | /// \brief Returns the value of the node. |
---|
| 1876 | /// |
---|
| 1877 | /// Returns the the value of the node. |
---|
| 1878 | Value nodeValue(const Node& n) const { |
---|
| 1879 | return (*_node_potential)[n]; |
---|
| 1880 | } |
---|
| 1881 | |
---|
| 1882 | /// \brief Returns the number of the blossoms in the basis. |
---|
| 1883 | /// |
---|
| 1884 | /// Returns the number of the blossoms in the basis. |
---|
| 1885 | /// \see BlossomIt |
---|
| 1886 | int blossomNum() const { |
---|
| 1887 | return _blossom_potential.size(); |
---|
| 1888 | } |
---|
| 1889 | |
---|
| 1890 | |
---|
| 1891 | /// \brief Returns the number of the nodes in the blossom. |
---|
| 1892 | /// |
---|
| 1893 | /// Returns the number of the nodes in the blossom. |
---|
| 1894 | int blossomSize(int k) const { |
---|
| 1895 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 1896 | } |
---|
| 1897 | |
---|
| 1898 | /// \brief Returns the value of the blossom. |
---|
| 1899 | /// |
---|
| 1900 | /// Returns the the value of the blossom. |
---|
| 1901 | /// \see BlossomIt |
---|
| 1902 | Value blossomValue(int k) const { |
---|
| 1903 | return _blossom_potential[k].value; |
---|
| 1904 | } |
---|
| 1905 | |
---|
| 1906 | /// \brief Lemon iterator for get the items of the blossom. |
---|
| 1907 | /// |
---|
| 1908 | /// Lemon iterator for get the nodes of the blossom. This class |
---|
| 1909 | /// provides a common style lemon iterator which gives back a |
---|
| 1910 | /// subset of the nodes. |
---|
| 1911 | class BlossomIt { |
---|
| 1912 | public: |
---|
| 1913 | |
---|
| 1914 | /// \brief Constructor. |
---|
| 1915 | /// |
---|
| 1916 | /// Constructor for get the nodes of the variable. |
---|
| 1917 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
| 1918 | : _algorithm(&algorithm) |
---|
| 1919 | { |
---|
| 1920 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 1921 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 1922 | } |
---|
| 1923 | |
---|
| 1924 | /// \brief Invalid constructor. |
---|
| 1925 | /// |
---|
| 1926 | /// Invalid constructor. |
---|
| 1927 | BlossomIt(Invalid) : _index(-1) {} |
---|
| 1928 | |
---|
| 1929 | /// \brief Conversion to node. |
---|
| 1930 | /// |
---|
| 1931 | /// Conversion to node. |
---|
| 1932 | operator Node() const { |
---|
| 1933 | return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID; |
---|
| 1934 | } |
---|
| 1935 | |
---|
| 1936 | /// \brief Increment operator. |
---|
| 1937 | /// |
---|
| 1938 | /// Increment operator. |
---|
| 1939 | BlossomIt& operator++() { |
---|
| 1940 | ++_index; |
---|
| 1941 | if (_index == _last) { |
---|
| 1942 | _index = -1; |
---|
| 1943 | } |
---|
| 1944 | return *this; |
---|
| 1945 | } |
---|
| 1946 | |
---|
| 1947 | bool operator==(const BlossomIt& it) const { |
---|
| 1948 | return _index == it._index; |
---|
| 1949 | } |
---|
| 1950 | bool operator!=(const BlossomIt& it) const { |
---|
| 1951 | return _index != it._index; |
---|
| 1952 | } |
---|
| 1953 | |
---|
| 1954 | private: |
---|
| 1955 | const MaxWeightedMatching* _algorithm; |
---|
| 1956 | int _last; |
---|
| 1957 | int _index; |
---|
| 1958 | }; |
---|
| 1959 | |
---|
| 1960 | /// @} |
---|
| 1961 | |
---|
| 1962 | }; |
---|
| 1963 | |
---|
| 1964 | /// \ingroup matching |
---|
| 1965 | /// |
---|
| 1966 | /// \brief Weighted perfect matching in general undirected graphs |
---|
| 1967 | /// |
---|
| 1968 | /// This class provides an efficient implementation of Edmond's |
---|
| 1969 | /// maximum weighted perfecr matching algorithm. The implementation |
---|
| 1970 | /// is based on extensive use of priority queues and provides |
---|
| 1971 | /// \f$O(nm\log(n))\f$ time complexity. |
---|
| 1972 | /// |
---|
| 1973 | /// The maximum weighted matching problem is to find undirected |
---|
| 1974 | /// edges in the graph with maximum overall weight and no two of |
---|
| 1975 | /// them shares their endpoints and covers all nodes. The problem |
---|
| 1976 | /// can be formulated with the next linear program: |
---|
| 1977 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
| 1978 | ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f] |
---|
| 1979 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
| 1980 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
| 1981 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
| 1982 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both endpoints in |
---|
| 1983 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of |
---|
| 1984 | /// the nodes. |
---|
| 1985 | /// |
---|
| 1986 | /// The algorithm calculates an optimal matching and a proof of the |
---|
| 1987 | /// optimality. The solution of the dual problem can be used to check |
---|
| 1988 | /// the result of the algorithm. The dual linear problem is the next: |
---|
| 1989 | /// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f] |
---|
| 1990 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
| 1991 | /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f] |
---|
| 1992 | /// |
---|
| 1993 | /// The algorithm can be executed with \c run() or the \c init() and |
---|
| 1994 | /// then the \c start() member functions. After it the matching can |
---|
| 1995 | /// be asked with \c matching() or mate() functions. The dual |
---|
| 1996 | /// solution can be get with \c nodeValue(), \c blossomNum() and \c |
---|
| 1997 | /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt |
---|
| 1998 | /// "BlossomIt" nested class which is able to iterate on the nodes |
---|
| 1999 | /// of a blossom. If the value type is integral then the dual |
---|
| 2000 | /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4". |
---|
| 2001 | /// |
---|
| 2002 | /// \author Balazs Dezso |
---|
| 2003 | template <typename _UGraph, |
---|
| 2004 | typename _WeightMap = typename _UGraph::template UEdgeMap<int> > |
---|
| 2005 | class MaxWeightedPerfectMatching { |
---|
| 2006 | public: |
---|
| 2007 | |
---|
| 2008 | typedef _UGraph UGraph; |
---|
| 2009 | typedef _WeightMap WeightMap; |
---|
| 2010 | typedef typename WeightMap::Value Value; |
---|
| 2011 | |
---|
| 2012 | /// \brief Scaling factor for dual solution |
---|
| 2013 | /// |
---|
| 2014 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
| 2015 | /// according to the value type. |
---|
| 2016 | static const int dualScale = |
---|
| 2017 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
| 2018 | |
---|
| 2019 | typedef typename UGraph::template NodeMap<typename UGraph::Edge> |
---|
| 2020 | MatchingMap; |
---|
| 2021 | |
---|
| 2022 | private: |
---|
| 2023 | |
---|
| 2024 | UGRAPH_TYPEDEFS(typename UGraph); |
---|
| 2025 | |
---|
| 2026 | typedef typename UGraph::template NodeMap<Value> NodePotential; |
---|
| 2027 | typedef std::vector<Node> BlossomNodeList; |
---|
| 2028 | |
---|
| 2029 | struct BlossomVariable { |
---|
| 2030 | int begin, end; |
---|
| 2031 | Value value; |
---|
| 2032 | |
---|
| 2033 | BlossomVariable(int _begin, int _end, Value _value) |
---|
| 2034 | : begin(_begin), end(_end), value(_value) {} |
---|
| 2035 | |
---|
| 2036 | }; |
---|
| 2037 | |
---|
| 2038 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
| 2039 | |
---|
| 2040 | const UGraph& _ugraph; |
---|
| 2041 | const WeightMap& _weight; |
---|
| 2042 | |
---|
| 2043 | MatchingMap* _matching; |
---|
| 2044 | |
---|
| 2045 | NodePotential* _node_potential; |
---|
| 2046 | |
---|
| 2047 | BlossomPotential _blossom_potential; |
---|
| 2048 | BlossomNodeList _blossom_node_list; |
---|
| 2049 | |
---|
| 2050 | int _node_num; |
---|
| 2051 | int _blossom_num; |
---|
| 2052 | |
---|
| 2053 | typedef typename UGraph::template NodeMap<int> NodeIntMap; |
---|
| 2054 | typedef typename UGraph::template EdgeMap<int> EdgeIntMap; |
---|
| 2055 | typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap; |
---|
| 2056 | typedef IntegerMap<int> IntIntMap; |
---|
| 2057 | |
---|
| 2058 | enum Status { |
---|
| 2059 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
| 2060 | }; |
---|
| 2061 | |
---|
| 2062 | typedef HeapUnionFind<Value, NodeIntMap> BlossomSet; |
---|
| 2063 | struct BlossomData { |
---|
| 2064 | int tree; |
---|
| 2065 | Status status; |
---|
| 2066 | Edge pred, next; |
---|
| 2067 | Value pot, offset; |
---|
| 2068 | }; |
---|
| 2069 | |
---|
| 2070 | NodeIntMap *_blossom_index; |
---|
| 2071 | BlossomSet *_blossom_set; |
---|
| 2072 | IntegerMap<BlossomData>* _blossom_data; |
---|
| 2073 | |
---|
| 2074 | NodeIntMap *_node_index; |
---|
| 2075 | EdgeIntMap *_node_heap_index; |
---|
| 2076 | |
---|
| 2077 | struct NodeData { |
---|
| 2078 | |
---|
| 2079 | NodeData(EdgeIntMap& node_heap_index) |
---|
| 2080 | : heap(node_heap_index) {} |
---|
| 2081 | |
---|
| 2082 | int blossom; |
---|
| 2083 | Value pot; |
---|
| 2084 | BinHeap<Value, EdgeIntMap> heap; |
---|
| 2085 | std::map<int, Edge> heap_index; |
---|
| 2086 | |
---|
| 2087 | int tree; |
---|
| 2088 | }; |
---|
| 2089 | |
---|
| 2090 | IntegerMap<NodeData>* _node_data; |
---|
| 2091 | |
---|
| 2092 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
| 2093 | |
---|
| 2094 | IntIntMap *_tree_set_index; |
---|
| 2095 | TreeSet *_tree_set; |
---|
| 2096 | |
---|
| 2097 | IntIntMap *_delta2_index; |
---|
| 2098 | BinHeap<Value, IntIntMap> *_delta2; |
---|
| 2099 | |
---|
| 2100 | UEdgeIntMap *_delta3_index; |
---|
| 2101 | BinHeap<Value, UEdgeIntMap> *_delta3; |
---|
| 2102 | |
---|
| 2103 | IntIntMap *_delta4_index; |
---|
| 2104 | BinHeap<Value, IntIntMap> *_delta4; |
---|
| 2105 | |
---|
| 2106 | Value _delta_sum; |
---|
| 2107 | |
---|
| 2108 | void createStructures() { |
---|
| 2109 | _node_num = countNodes(_ugraph); |
---|
| 2110 | _blossom_num = _node_num * 3 / 2; |
---|
| 2111 | |
---|
| 2112 | if (!_matching) { |
---|
| 2113 | _matching = new MatchingMap(_ugraph); |
---|
| 2114 | } |
---|
| 2115 | if (!_node_potential) { |
---|
| 2116 | _node_potential = new NodePotential(_ugraph); |
---|
| 2117 | } |
---|
| 2118 | if (!_blossom_set) { |
---|
| 2119 | _blossom_index = new NodeIntMap(_ugraph); |
---|
| 2120 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
| 2121 | _blossom_data = new IntegerMap<BlossomData>(_blossom_num); |
---|
| 2122 | } |
---|
| 2123 | |
---|
| 2124 | if (!_node_index) { |
---|
| 2125 | _node_index = new NodeIntMap(_ugraph); |
---|
| 2126 | _node_heap_index = new EdgeIntMap(_ugraph); |
---|
| 2127 | _node_data = new IntegerMap<NodeData>(_node_num, |
---|
| 2128 | NodeData(*_node_heap_index)); |
---|
| 2129 | } |
---|
| 2130 | |
---|
| 2131 | if (!_tree_set) { |
---|
| 2132 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
| 2133 | _tree_set = new TreeSet(*_tree_set_index); |
---|
| 2134 | } |
---|
| 2135 | if (!_delta2) { |
---|
| 2136 | _delta2_index = new IntIntMap(_blossom_num); |
---|
| 2137 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
| 2138 | } |
---|
| 2139 | if (!_delta3) { |
---|
| 2140 | _delta3_index = new UEdgeIntMap(_ugraph); |
---|
| 2141 | _delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index); |
---|
| 2142 | } |
---|
| 2143 | if (!_delta4) { |
---|
| 2144 | _delta4_index = new IntIntMap(_blossom_num); |
---|
| 2145 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
| 2146 | } |
---|
| 2147 | } |
---|
| 2148 | |
---|
| 2149 | void destroyStructures() { |
---|
| 2150 | _node_num = countNodes(_ugraph); |
---|
| 2151 | _blossom_num = _node_num * 3 / 2; |
---|
| 2152 | |
---|
| 2153 | if (_matching) { |
---|
| 2154 | delete _matching; |
---|
| 2155 | } |
---|
| 2156 | if (_node_potential) { |
---|
| 2157 | delete _node_potential; |
---|
| 2158 | } |
---|
| 2159 | if (_blossom_set) { |
---|
| 2160 | delete _blossom_index; |
---|
| 2161 | delete _blossom_set; |
---|
| 2162 | delete _blossom_data; |
---|
| 2163 | } |
---|
| 2164 | |
---|
| 2165 | if (_node_index) { |
---|
| 2166 | delete _node_index; |
---|
| 2167 | delete _node_heap_index; |
---|
| 2168 | delete _node_data; |
---|
| 2169 | } |
---|
| 2170 | |
---|
| 2171 | if (_tree_set) { |
---|
| 2172 | delete _tree_set_index; |
---|
| 2173 | delete _tree_set; |
---|
| 2174 | } |
---|
| 2175 | if (_delta2) { |
---|
| 2176 | delete _delta2_index; |
---|
| 2177 | delete _delta2; |
---|
| 2178 | } |
---|
| 2179 | if (_delta3) { |
---|
| 2180 | delete _delta3_index; |
---|
| 2181 | delete _delta3; |
---|
| 2182 | } |
---|
| 2183 | if (_delta4) { |
---|
| 2184 | delete _delta4_index; |
---|
| 2185 | delete _delta4; |
---|
| 2186 | } |
---|
| 2187 | } |
---|
| 2188 | |
---|
| 2189 | void matchedToEven(int blossom, int tree) { |
---|
| 2190 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2191 | _delta2->erase(blossom); |
---|
| 2192 | } |
---|
| 2193 | |
---|
| 2194 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2195 | (*_blossom_data)[blossom].pot -= |
---|
| 2196 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2197 | } |
---|
| 2198 | |
---|
| 2199 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2200 | n != INVALID; ++n) { |
---|
| 2201 | |
---|
| 2202 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2203 | int ni = (*_node_index)[n]; |
---|
| 2204 | |
---|
| 2205 | (*_node_data)[ni].heap.clear(); |
---|
| 2206 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2207 | |
---|
| 2208 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2209 | |
---|
| 2210 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 2211 | Node v = _ugraph.source(e); |
---|
| 2212 | int vb = _blossom_set->find(v); |
---|
| 2213 | int vi = (*_node_index)[v]; |
---|
| 2214 | |
---|
| 2215 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2216 | dualScale * _weight[e]; |
---|
| 2217 | |
---|
| 2218 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2219 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2220 | _delta3->push(e, rw / 2); |
---|
| 2221 | } |
---|
| 2222 | } else { |
---|
| 2223 | typename std::map<int, Edge>::iterator it = |
---|
| 2224 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2225 | |
---|
| 2226 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2227 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2228 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2229 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2230 | it->second = e; |
---|
| 2231 | } |
---|
| 2232 | } else { |
---|
| 2233 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2234 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2235 | } |
---|
| 2236 | |
---|
| 2237 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2238 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2239 | |
---|
| 2240 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2241 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2242 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2243 | (*_blossom_data)[vb].offset); |
---|
| 2244 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2245 | (*_blossom_data)[vb].offset){ |
---|
| 2246 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2247 | (*_blossom_data)[vb].offset); |
---|
| 2248 | } |
---|
| 2249 | } |
---|
| 2250 | } |
---|
| 2251 | } |
---|
| 2252 | } |
---|
| 2253 | } |
---|
| 2254 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2255 | } |
---|
| 2256 | |
---|
| 2257 | void matchedToOdd(int blossom) { |
---|
| 2258 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2259 | _delta2->erase(blossom); |
---|
| 2260 | } |
---|
| 2261 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
| 2262 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2263 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
| 2264 | (*_blossom_data)[blossom].offset); |
---|
| 2265 | } |
---|
| 2266 | } |
---|
| 2267 | |
---|
| 2268 | void evenToMatched(int blossom, int tree) { |
---|
| 2269 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2270 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
| 2271 | } |
---|
| 2272 | |
---|
| 2273 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2274 | n != INVALID; ++n) { |
---|
| 2275 | int ni = (*_node_index)[n]; |
---|
| 2276 | (*_node_data)[ni].pot -= _delta_sum; |
---|
| 2277 | |
---|
| 2278 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 2279 | Node v = _ugraph.source(e); |
---|
| 2280 | int vb = _blossom_set->find(v); |
---|
| 2281 | int vi = (*_node_index)[v]; |
---|
| 2282 | |
---|
| 2283 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2284 | dualScale * _weight[e]; |
---|
| 2285 | |
---|
| 2286 | if (vb == blossom) { |
---|
| 2287 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2288 | _delta3->erase(e); |
---|
| 2289 | } |
---|
| 2290 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2291 | |
---|
| 2292 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
| 2293 | _delta3->erase(e); |
---|
| 2294 | } |
---|
| 2295 | |
---|
| 2296 | int vt = _tree_set->find(vb); |
---|
| 2297 | |
---|
| 2298 | if (vt != tree) { |
---|
| 2299 | |
---|
| 2300 | Edge r = _ugraph.oppositeEdge(e); |
---|
| 2301 | |
---|
| 2302 | typename std::map<int, Edge>::iterator it = |
---|
| 2303 | (*_node_data)[ni].heap_index.find(vt); |
---|
| 2304 | |
---|
| 2305 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
| 2306 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
| 2307 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
| 2308 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
| 2309 | it->second = r; |
---|
| 2310 | } |
---|
| 2311 | } else { |
---|
| 2312 | (*_node_data)[ni].heap.push(r, rw); |
---|
| 2313 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
| 2314 | } |
---|
| 2315 | |
---|
| 2316 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
| 2317 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
| 2318 | |
---|
| 2319 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
| 2320 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2321 | (*_blossom_data)[blossom].offset); |
---|
| 2322 | } else if ((*_delta2)[blossom] > |
---|
| 2323 | _blossom_set->classPrio(blossom) - |
---|
| 2324 | (*_blossom_data)[blossom].offset){ |
---|
| 2325 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2326 | (*_blossom_data)[blossom].offset); |
---|
| 2327 | } |
---|
| 2328 | } |
---|
| 2329 | } |
---|
| 2330 | } else { |
---|
| 2331 | |
---|
| 2332 | typename std::map<int, Edge>::iterator it = |
---|
| 2333 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2334 | |
---|
| 2335 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2336 | (*_node_data)[vi].heap.erase(it->second); |
---|
| 2337 | (*_node_data)[vi].heap_index.erase(it); |
---|
| 2338 | if ((*_node_data)[vi].heap.empty()) { |
---|
| 2339 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
| 2340 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
| 2341 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
| 2342 | } |
---|
| 2343 | |
---|
| 2344 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2345 | if (_blossom_set->classPrio(vb) == |
---|
| 2346 | std::numeric_limits<Value>::max()) { |
---|
| 2347 | _delta2->erase(vb); |
---|
| 2348 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
| 2349 | (*_blossom_data)[vb].offset) { |
---|
| 2350 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
| 2351 | (*_blossom_data)[vb].offset); |
---|
| 2352 | } |
---|
| 2353 | } |
---|
| 2354 | } |
---|
| 2355 | } |
---|
| 2356 | } |
---|
| 2357 | } |
---|
| 2358 | } |
---|
| 2359 | |
---|
| 2360 | void oddToMatched(int blossom) { |
---|
| 2361 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
| 2362 | |
---|
| 2363 | if (_blossom_set->classPrio(blossom) != |
---|
| 2364 | std::numeric_limits<Value>::max()) { |
---|
| 2365 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
| 2366 | (*_blossom_data)[blossom].offset); |
---|
| 2367 | } |
---|
| 2368 | |
---|
| 2369 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2370 | _delta4->erase(blossom); |
---|
| 2371 | } |
---|
| 2372 | } |
---|
| 2373 | |
---|
| 2374 | void oddToEven(int blossom, int tree) { |
---|
| 2375 | if (!_blossom_set->trivial(blossom)) { |
---|
| 2376 | _delta4->erase(blossom); |
---|
| 2377 | (*_blossom_data)[blossom].pot -= |
---|
| 2378 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
| 2379 | } |
---|
| 2380 | |
---|
| 2381 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
| 2382 | n != INVALID; ++n) { |
---|
| 2383 | int ni = (*_node_index)[n]; |
---|
| 2384 | |
---|
| 2385 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
| 2386 | |
---|
| 2387 | (*_node_data)[ni].heap.clear(); |
---|
| 2388 | (*_node_data)[ni].heap_index.clear(); |
---|
| 2389 | (*_node_data)[ni].pot += |
---|
| 2390 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
| 2391 | |
---|
| 2392 | for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 2393 | Node v = _ugraph.source(e); |
---|
| 2394 | int vb = _blossom_set->find(v); |
---|
| 2395 | int vi = (*_node_index)[v]; |
---|
| 2396 | |
---|
| 2397 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
| 2398 | dualScale * _weight[e]; |
---|
| 2399 | |
---|
| 2400 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
| 2401 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
| 2402 | _delta3->push(e, rw / 2); |
---|
| 2403 | } |
---|
| 2404 | } else { |
---|
| 2405 | |
---|
| 2406 | typename std::map<int, Edge>::iterator it = |
---|
| 2407 | (*_node_data)[vi].heap_index.find(tree); |
---|
| 2408 | |
---|
| 2409 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
| 2410 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
| 2411 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
| 2412 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
| 2413 | it->second = e; |
---|
| 2414 | } |
---|
| 2415 | } else { |
---|
| 2416 | (*_node_data)[vi].heap.push(e, rw); |
---|
| 2417 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
| 2418 | } |
---|
| 2419 | |
---|
| 2420 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
| 2421 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
| 2422 | |
---|
| 2423 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
| 2424 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
| 2425 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
| 2426 | (*_blossom_data)[vb].offset); |
---|
| 2427 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
| 2428 | (*_blossom_data)[vb].offset) { |
---|
| 2429 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
| 2430 | (*_blossom_data)[vb].offset); |
---|
| 2431 | } |
---|
| 2432 | } |
---|
| 2433 | } |
---|
| 2434 | } |
---|
| 2435 | } |
---|
| 2436 | } |
---|
| 2437 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2438 | } |
---|
| 2439 | |
---|
| 2440 | void alternatePath(int even, int tree) { |
---|
| 2441 | int odd; |
---|
| 2442 | |
---|
| 2443 | evenToMatched(even, tree); |
---|
| 2444 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2445 | |
---|
| 2446 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
| 2447 | odd = _blossom_set->find(_ugraph.target((*_blossom_data)[even].pred)); |
---|
| 2448 | (*_blossom_data)[odd].status = MATCHED; |
---|
| 2449 | oddToMatched(odd); |
---|
| 2450 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
| 2451 | |
---|
| 2452 | even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred)); |
---|
| 2453 | (*_blossom_data)[even].status = MATCHED; |
---|
| 2454 | evenToMatched(even, tree); |
---|
| 2455 | (*_blossom_data)[even].next = |
---|
| 2456 | _ugraph.oppositeEdge((*_blossom_data)[odd].pred); |
---|
| 2457 | } |
---|
| 2458 | |
---|
| 2459 | } |
---|
| 2460 | |
---|
| 2461 | void destroyTree(int tree) { |
---|
| 2462 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
| 2463 | if ((*_blossom_data)[b].status == EVEN) { |
---|
| 2464 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2465 | evenToMatched(b, tree); |
---|
| 2466 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
| 2467 | (*_blossom_data)[b].status = MATCHED; |
---|
| 2468 | oddToMatched(b); |
---|
| 2469 | } |
---|
| 2470 | } |
---|
| 2471 | _tree_set->eraseClass(tree); |
---|
| 2472 | } |
---|
| 2473 | |
---|
| 2474 | void augmentOnEdge(const UEdge& edge) { |
---|
| 2475 | |
---|
| 2476 | int left = _blossom_set->find(_ugraph.source(edge)); |
---|
| 2477 | int right = _blossom_set->find(_ugraph.target(edge)); |
---|
| 2478 | |
---|
| 2479 | int left_tree = _tree_set->find(left); |
---|
| 2480 | alternatePath(left, left_tree); |
---|
| 2481 | destroyTree(left_tree); |
---|
| 2482 | |
---|
| 2483 | int right_tree = _tree_set->find(right); |
---|
| 2484 | alternatePath(right, right_tree); |
---|
| 2485 | destroyTree(right_tree); |
---|
| 2486 | |
---|
| 2487 | (*_blossom_data)[left].next = _ugraph.direct(edge, true); |
---|
| 2488 | (*_blossom_data)[right].next = _ugraph.direct(edge, false); |
---|
| 2489 | } |
---|
| 2490 | |
---|
| 2491 | void extendOnEdge(const Edge& edge) { |
---|
| 2492 | int base = _blossom_set->find(_ugraph.target(edge)); |
---|
| 2493 | int tree = _tree_set->find(base); |
---|
| 2494 | |
---|
| 2495 | int odd = _blossom_set->find(_ugraph.source(edge)); |
---|
| 2496 | _tree_set->insert(odd, tree); |
---|
| 2497 | (*_blossom_data)[odd].status = ODD; |
---|
| 2498 | matchedToOdd(odd); |
---|
| 2499 | (*_blossom_data)[odd].pred = edge; |
---|
| 2500 | |
---|
| 2501 | int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next)); |
---|
| 2502 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
| 2503 | _tree_set->insert(even, tree); |
---|
| 2504 | (*_blossom_data)[even].status = EVEN; |
---|
| 2505 | matchedToEven(even, tree); |
---|
| 2506 | } |
---|
| 2507 | |
---|
| 2508 | void shrinkOnEdge(const UEdge& uedge, int tree) { |
---|
| 2509 | int nca = -1; |
---|
| 2510 | std::vector<int> left_path, right_path; |
---|
| 2511 | |
---|
| 2512 | { |
---|
| 2513 | std::set<int> left_set, right_set; |
---|
| 2514 | int left = _blossom_set->find(_ugraph.source(uedge)); |
---|
| 2515 | left_path.push_back(left); |
---|
| 2516 | left_set.insert(left); |
---|
| 2517 | |
---|
| 2518 | int right = _blossom_set->find(_ugraph.target(uedge)); |
---|
| 2519 | right_path.push_back(right); |
---|
| 2520 | right_set.insert(right); |
---|
| 2521 | |
---|
| 2522 | while (true) { |
---|
| 2523 | |
---|
| 2524 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
| 2525 | |
---|
| 2526 | left = |
---|
| 2527 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
| 2528 | left_path.push_back(left); |
---|
| 2529 | left = |
---|
| 2530 | _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred)); |
---|
| 2531 | left_path.push_back(left); |
---|
| 2532 | |
---|
| 2533 | left_set.insert(left); |
---|
| 2534 | |
---|
| 2535 | if (right_set.find(left) != right_set.end()) { |
---|
| 2536 | nca = left; |
---|
| 2537 | break; |
---|
| 2538 | } |
---|
| 2539 | |
---|
| 2540 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
| 2541 | |
---|
| 2542 | right = |
---|
| 2543 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
| 2544 | right_path.push_back(right); |
---|
| 2545 | right = |
---|
| 2546 | _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred)); |
---|
| 2547 | right_path.push_back(right); |
---|
| 2548 | |
---|
| 2549 | right_set.insert(right); |
---|
| 2550 | |
---|
| 2551 | if (left_set.find(right) != left_set.end()) { |
---|
| 2552 | nca = right; |
---|
| 2553 | break; |
---|
| 2554 | } |
---|
| 2555 | |
---|
| 2556 | } |
---|
| 2557 | |
---|
| 2558 | if (nca == -1) { |
---|
| 2559 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
| 2560 | nca = right; |
---|
| 2561 | while (left_set.find(nca) == left_set.end()) { |
---|
| 2562 | nca = |
---|
| 2563 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 2564 | right_path.push_back(nca); |
---|
| 2565 | nca = |
---|
| 2566 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 2567 | right_path.push_back(nca); |
---|
| 2568 | } |
---|
| 2569 | } else { |
---|
| 2570 | nca = left; |
---|
| 2571 | while (right_set.find(nca) == right_set.end()) { |
---|
| 2572 | nca = |
---|
| 2573 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 2574 | left_path.push_back(nca); |
---|
| 2575 | nca = |
---|
| 2576 | _blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred)); |
---|
| 2577 | left_path.push_back(nca); |
---|
| 2578 | } |
---|
| 2579 | } |
---|
| 2580 | } |
---|
| 2581 | } |
---|
| 2582 | |
---|
| 2583 | std::vector<int> subblossoms; |
---|
| 2584 | Edge prev; |
---|
| 2585 | |
---|
| 2586 | prev = _ugraph.direct(uedge, true); |
---|
| 2587 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
| 2588 | subblossoms.push_back(left_path[i]); |
---|
| 2589 | (*_blossom_data)[left_path[i]].next = prev; |
---|
| 2590 | _tree_set->erase(left_path[i]); |
---|
| 2591 | |
---|
| 2592 | subblossoms.push_back(left_path[i + 1]); |
---|
| 2593 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
| 2594 | oddToEven(left_path[i + 1], tree); |
---|
| 2595 | _tree_set->erase(left_path[i + 1]); |
---|
| 2596 | prev = _ugraph.oppositeEdge((*_blossom_data)[left_path[i + 1]].pred); |
---|
| 2597 | } |
---|
| 2598 | |
---|
| 2599 | int k = 0; |
---|
| 2600 | while (right_path[k] != nca) ++k; |
---|
| 2601 | |
---|
| 2602 | subblossoms.push_back(nca); |
---|
| 2603 | (*_blossom_data)[nca].next = prev; |
---|
| 2604 | |
---|
| 2605 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
| 2606 | subblossoms.push_back(right_path[i + 1]); |
---|
| 2607 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
| 2608 | oddToEven(right_path[i + 1], tree); |
---|
| 2609 | _tree_set->erase(right_path[i + 1]); |
---|
| 2610 | |
---|
| 2611 | (*_blossom_data)[right_path[i + 1]].next = |
---|
| 2612 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
| 2613 | |
---|
| 2614 | subblossoms.push_back(right_path[i]); |
---|
| 2615 | _tree_set->erase(right_path[i]); |
---|
| 2616 | } |
---|
| 2617 | |
---|
| 2618 | int surface = |
---|
| 2619 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
| 2620 | |
---|
| 2621 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2622 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2623 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
| 2624 | } |
---|
| 2625 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
| 2626 | } |
---|
| 2627 | |
---|
| 2628 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
| 2629 | (*_blossom_data)[surface].offset = 0; |
---|
| 2630 | (*_blossom_data)[surface].status = EVEN; |
---|
| 2631 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
| 2632 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
| 2633 | |
---|
| 2634 | _tree_set->insert(surface, tree); |
---|
| 2635 | _tree_set->erase(nca); |
---|
| 2636 | } |
---|
| 2637 | |
---|
| 2638 | void splitBlossom(int blossom) { |
---|
| 2639 | Edge next = (*_blossom_data)[blossom].next; |
---|
| 2640 | Edge pred = (*_blossom_data)[blossom].pred; |
---|
| 2641 | |
---|
| 2642 | int tree = _tree_set->find(blossom); |
---|
| 2643 | |
---|
| 2644 | (*_blossom_data)[blossom].status = MATCHED; |
---|
| 2645 | oddToMatched(blossom); |
---|
| 2646 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
| 2647 | _delta2->erase(blossom); |
---|
| 2648 | } |
---|
| 2649 | |
---|
| 2650 | std::vector<int> subblossoms; |
---|
| 2651 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2652 | |
---|
| 2653 | Value offset = (*_blossom_data)[blossom].offset; |
---|
| 2654 | int b = _blossom_set->find(_ugraph.source(pred)); |
---|
| 2655 | int d = _blossom_set->find(_ugraph.source(next)); |
---|
| 2656 | |
---|
[2549] | 2657 | int ib = -1, id = -1; |
---|
[2548] | 2658 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2659 | if (subblossoms[i] == b) ib = i; |
---|
| 2660 | if (subblossoms[i] == d) id = i; |
---|
| 2661 | |
---|
| 2662 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
| 2663 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
| 2664 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
| 2665 | } |
---|
| 2666 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
| 2667 | std::numeric_limits<Value>::max()) { |
---|
| 2668 | _delta2->push(subblossoms[i], |
---|
| 2669 | _blossom_set->classPrio(subblossoms[i]) - |
---|
| 2670 | (*_blossom_data)[subblossoms[i]].offset); |
---|
| 2671 | } |
---|
| 2672 | } |
---|
| 2673 | |
---|
| 2674 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
| 2675 | for (int i = (id + 1) % subblossoms.size(); |
---|
| 2676 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2677 | int sb = subblossoms[i]; |
---|
| 2678 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2679 | (*_blossom_data)[sb].next = |
---|
| 2680 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 2681 | } |
---|
| 2682 | |
---|
| 2683 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2684 | int sb = subblossoms[i]; |
---|
| 2685 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2686 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2687 | |
---|
| 2688 | (*_blossom_data)[sb].status = ODD; |
---|
| 2689 | matchedToOdd(sb); |
---|
| 2690 | _tree_set->insert(sb, tree); |
---|
| 2691 | (*_blossom_data)[sb].pred = pred; |
---|
| 2692 | (*_blossom_data)[sb].next = |
---|
| 2693 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 2694 | |
---|
| 2695 | pred = (*_blossom_data)[ub].next; |
---|
| 2696 | |
---|
| 2697 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2698 | matchedToEven(tb, tree); |
---|
| 2699 | _tree_set->insert(tb, tree); |
---|
| 2700 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
| 2701 | } |
---|
| 2702 | |
---|
| 2703 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
| 2704 | matchedToOdd(subblossoms[id]); |
---|
| 2705 | _tree_set->insert(subblossoms[id], tree); |
---|
| 2706 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
| 2707 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
| 2708 | |
---|
| 2709 | } else { |
---|
| 2710 | |
---|
| 2711 | for (int i = (ib + 1) % subblossoms.size(); |
---|
| 2712 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
| 2713 | int sb = subblossoms[i]; |
---|
| 2714 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2715 | (*_blossom_data)[sb].next = |
---|
| 2716 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 2717 | } |
---|
| 2718 | |
---|
| 2719 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
| 2720 | int sb = subblossoms[i]; |
---|
| 2721 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
| 2722 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
| 2723 | |
---|
| 2724 | (*_blossom_data)[sb].status = ODD; |
---|
| 2725 | matchedToOdd(sb); |
---|
| 2726 | _tree_set->insert(sb, tree); |
---|
| 2727 | (*_blossom_data)[sb].next = next; |
---|
| 2728 | (*_blossom_data)[sb].pred = |
---|
| 2729 | _ugraph.oppositeEdge((*_blossom_data)[tb].next); |
---|
| 2730 | |
---|
| 2731 | (*_blossom_data)[tb].status = EVEN; |
---|
| 2732 | matchedToEven(tb, tree); |
---|
| 2733 | _tree_set->insert(tb, tree); |
---|
| 2734 | (*_blossom_data)[tb].pred = |
---|
| 2735 | (*_blossom_data)[tb].next = |
---|
| 2736 | _ugraph.oppositeEdge((*_blossom_data)[ub].next); |
---|
| 2737 | next = (*_blossom_data)[ub].next; |
---|
| 2738 | } |
---|
| 2739 | |
---|
| 2740 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
| 2741 | matchedToOdd(subblossoms[ib]); |
---|
| 2742 | _tree_set->insert(subblossoms[ib], tree); |
---|
| 2743 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
| 2744 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
| 2745 | } |
---|
| 2746 | _tree_set->erase(blossom); |
---|
| 2747 | } |
---|
| 2748 | |
---|
| 2749 | void extractBlossom(int blossom, const Node& base, const Edge& matching) { |
---|
| 2750 | if (_blossom_set->trivial(blossom)) { |
---|
| 2751 | int bi = (*_node_index)[base]; |
---|
| 2752 | Value pot = (*_node_data)[bi].pot; |
---|
| 2753 | |
---|
| 2754 | _matching->set(base, matching); |
---|
| 2755 | _blossom_node_list.push_back(base); |
---|
| 2756 | _node_potential->set(base, pot); |
---|
| 2757 | } else { |
---|
| 2758 | |
---|
| 2759 | Value pot = (*_blossom_data)[blossom].pot; |
---|
| 2760 | int bn = _blossom_node_list.size(); |
---|
| 2761 | |
---|
| 2762 | std::vector<int> subblossoms; |
---|
| 2763 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
| 2764 | int b = _blossom_set->find(base); |
---|
| 2765 | int ib = -1; |
---|
| 2766 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
| 2767 | if (subblossoms[i] == b) { ib = i; break; } |
---|
| 2768 | } |
---|
| 2769 | |
---|
| 2770 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
| 2771 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
| 2772 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
| 2773 | |
---|
| 2774 | Edge m = (*_blossom_data)[tb].next; |
---|
| 2775 | extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m)); |
---|
| 2776 | extractBlossom(tb, _ugraph.source(m), m); |
---|
| 2777 | } |
---|
| 2778 | extractBlossom(subblossoms[ib], base, matching); |
---|
| 2779 | |
---|
| 2780 | int en = _blossom_node_list.size(); |
---|
| 2781 | |
---|
| 2782 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
| 2783 | } |
---|
| 2784 | } |
---|
| 2785 | |
---|
| 2786 | void extractMatching() { |
---|
| 2787 | std::vector<int> blossoms; |
---|
| 2788 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
| 2789 | blossoms.push_back(c); |
---|
| 2790 | } |
---|
| 2791 | |
---|
| 2792 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
| 2793 | |
---|
| 2794 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
| 2795 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
| 2796 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
| 2797 | n != INVALID; ++n) { |
---|
| 2798 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
| 2799 | } |
---|
| 2800 | |
---|
| 2801 | Edge matching = (*_blossom_data)[blossoms[i]].next; |
---|
| 2802 | Node base = _ugraph.source(matching); |
---|
| 2803 | extractBlossom(blossoms[i], base, matching); |
---|
| 2804 | } |
---|
| 2805 | } |
---|
| 2806 | |
---|
| 2807 | public: |
---|
| 2808 | |
---|
| 2809 | /// \brief Constructor |
---|
| 2810 | /// |
---|
| 2811 | /// Constructor. |
---|
| 2812 | MaxWeightedPerfectMatching(const UGraph& ugraph, const WeightMap& weight) |
---|
| 2813 | : _ugraph(ugraph), _weight(weight), _matching(0), |
---|
| 2814 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
| 2815 | _node_num(0), _blossom_num(0), |
---|
| 2816 | |
---|
| 2817 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
| 2818 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
| 2819 | _tree_set_index(0), _tree_set(0), |
---|
| 2820 | |
---|
| 2821 | _delta2_index(0), _delta2(0), |
---|
| 2822 | _delta3_index(0), _delta3(0), |
---|
| 2823 | _delta4_index(0), _delta4(0), |
---|
| 2824 | |
---|
| 2825 | _delta_sum() {} |
---|
| 2826 | |
---|
| 2827 | ~MaxWeightedPerfectMatching() { |
---|
| 2828 | destroyStructures(); |
---|
| 2829 | } |
---|
| 2830 | |
---|
| 2831 | /// \name Execution control |
---|
| 2832 | /// The simplest way to execute the algorithm is to use the member |
---|
| 2833 | /// \c run() member function. |
---|
| 2834 | |
---|
| 2835 | ///@{ |
---|
| 2836 | |
---|
| 2837 | /// \brief Initialize the algorithm |
---|
| 2838 | /// |
---|
| 2839 | /// Initialize the algorithm |
---|
| 2840 | void init() { |
---|
| 2841 | createStructures(); |
---|
| 2842 | |
---|
| 2843 | for (EdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
| 2844 | _node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP); |
---|
| 2845 | } |
---|
| 2846 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
| 2847 | _delta3_index->set(e, _delta3->PRE_HEAP); |
---|
| 2848 | } |
---|
| 2849 | for (int i = 0; i < _blossom_num; ++i) { |
---|
| 2850 | _delta2_index->set(i, _delta2->PRE_HEAP); |
---|
| 2851 | _delta4_index->set(i, _delta4->PRE_HEAP); |
---|
| 2852 | } |
---|
| 2853 | |
---|
| 2854 | int index = 0; |
---|
| 2855 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 2856 | Value max = std::numeric_limits<Value>::min(); |
---|
| 2857 | for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) { |
---|
| 2858 | if (_ugraph.target(e) == n) continue; |
---|
| 2859 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
| 2860 | max = (dualScale * _weight[e]) / 2; |
---|
| 2861 | } |
---|
| 2862 | } |
---|
| 2863 | _node_index->set(n, index); |
---|
| 2864 | (*_node_data)[index].pot = max; |
---|
| 2865 | int blossom = |
---|
| 2866 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
| 2867 | |
---|
| 2868 | _tree_set->insert(blossom); |
---|
| 2869 | |
---|
| 2870 | (*_blossom_data)[blossom].status = EVEN; |
---|
| 2871 | (*_blossom_data)[blossom].pred = INVALID; |
---|
| 2872 | (*_blossom_data)[blossom].next = INVALID; |
---|
| 2873 | (*_blossom_data)[blossom].pot = 0; |
---|
| 2874 | (*_blossom_data)[blossom].offset = 0; |
---|
| 2875 | ++index; |
---|
| 2876 | } |
---|
| 2877 | for (UEdgeIt e(_ugraph); e != INVALID; ++e) { |
---|
| 2878 | int si = (*_node_index)[_ugraph.source(e)]; |
---|
| 2879 | int ti = (*_node_index)[_ugraph.target(e)]; |
---|
| 2880 | if (_ugraph.source(e) != _ugraph.target(e)) { |
---|
| 2881 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
| 2882 | dualScale * _weight[e]) / 2); |
---|
| 2883 | } |
---|
| 2884 | } |
---|
| 2885 | } |
---|
| 2886 | |
---|
| 2887 | /// \brief Starts the algorithm |
---|
| 2888 | /// |
---|
| 2889 | /// Starts the algorithm |
---|
| 2890 | bool start() { |
---|
| 2891 | enum OpType { |
---|
| 2892 | D2, D3, D4 |
---|
| 2893 | }; |
---|
| 2894 | |
---|
| 2895 | int unmatched = _node_num; |
---|
| 2896 | while (unmatched > 0) { |
---|
| 2897 | Value d2 = !_delta2->empty() ? |
---|
| 2898 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
| 2899 | |
---|
| 2900 | Value d3 = !_delta3->empty() ? |
---|
| 2901 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
| 2902 | |
---|
| 2903 | Value d4 = !_delta4->empty() ? |
---|
| 2904 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
| 2905 | |
---|
| 2906 | _delta_sum = d2; OpType ot = D2; |
---|
| 2907 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
| 2908 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
| 2909 | |
---|
| 2910 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
| 2911 | return false; |
---|
| 2912 | } |
---|
| 2913 | |
---|
| 2914 | switch (ot) { |
---|
| 2915 | case D2: |
---|
| 2916 | { |
---|
| 2917 | int blossom = _delta2->top(); |
---|
| 2918 | Node n = _blossom_set->classTop(blossom); |
---|
| 2919 | Edge e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
| 2920 | extendOnEdge(e); |
---|
| 2921 | } |
---|
| 2922 | break; |
---|
| 2923 | case D3: |
---|
| 2924 | { |
---|
| 2925 | UEdge e = _delta3->top(); |
---|
| 2926 | |
---|
| 2927 | int left_blossom = _blossom_set->find(_ugraph.source(e)); |
---|
| 2928 | int right_blossom = _blossom_set->find(_ugraph.target(e)); |
---|
| 2929 | |
---|
| 2930 | if (left_blossom == right_blossom) { |
---|
| 2931 | _delta3->pop(); |
---|
| 2932 | } else { |
---|
| 2933 | int left_tree = _tree_set->find(left_blossom); |
---|
| 2934 | int right_tree = _tree_set->find(right_blossom); |
---|
| 2935 | |
---|
| 2936 | if (left_tree == right_tree) { |
---|
| 2937 | shrinkOnEdge(e, left_tree); |
---|
| 2938 | } else { |
---|
| 2939 | augmentOnEdge(e); |
---|
| 2940 | unmatched -= 2; |
---|
| 2941 | } |
---|
| 2942 | } |
---|
| 2943 | } break; |
---|
| 2944 | case D4: |
---|
| 2945 | splitBlossom(_delta4->top()); |
---|
| 2946 | break; |
---|
| 2947 | } |
---|
| 2948 | } |
---|
| 2949 | extractMatching(); |
---|
| 2950 | return true; |
---|
| 2951 | } |
---|
| 2952 | |
---|
| 2953 | /// \brief Runs %MaxWeightedPerfectMatching algorithm. |
---|
| 2954 | /// |
---|
| 2955 | /// This method runs the %MaxWeightedPerfectMatching algorithm. |
---|
| 2956 | /// |
---|
| 2957 | /// \note mwm.run() is just a shortcut of the following code. |
---|
| 2958 | /// \code |
---|
| 2959 | /// mwm.init(); |
---|
| 2960 | /// mwm.start(); |
---|
| 2961 | /// \endcode |
---|
| 2962 | bool run() { |
---|
| 2963 | init(); |
---|
| 2964 | return start(); |
---|
| 2965 | } |
---|
| 2966 | |
---|
| 2967 | /// @} |
---|
| 2968 | |
---|
| 2969 | /// \name Primal solution |
---|
| 2970 | /// Functions for get the primal solution, ie. the matching. |
---|
| 2971 | |
---|
| 2972 | /// @{ |
---|
| 2973 | |
---|
| 2974 | /// \brief Returns the matching value. |
---|
| 2975 | /// |
---|
| 2976 | /// Returns the matching value. |
---|
| 2977 | Value matchingValue() const { |
---|
| 2978 | Value sum = 0; |
---|
| 2979 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 2980 | if ((*_matching)[n] != INVALID) { |
---|
| 2981 | sum += _weight[(*_matching)[n]]; |
---|
| 2982 | } |
---|
| 2983 | } |
---|
| 2984 | return sum /= 2; |
---|
| 2985 | } |
---|
| 2986 | |
---|
| 2987 | /// \brief Returns true when the edge is in the matching. |
---|
| 2988 | /// |
---|
| 2989 | /// Returns true when the edge is in the matching. |
---|
| 2990 | bool matching(const UEdge& edge) const { |
---|
| 2991 | return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true); |
---|
| 2992 | } |
---|
| 2993 | |
---|
| 2994 | /// \brief Returns the incident matching edge. |
---|
| 2995 | /// |
---|
| 2996 | /// Returns the incident matching edge from given node. |
---|
| 2997 | Edge matching(const Node& node) const { |
---|
| 2998 | return (*_matching)[node]; |
---|
| 2999 | } |
---|
| 3000 | |
---|
| 3001 | /// \brief Returns the mate of the node. |
---|
| 3002 | /// |
---|
| 3003 | /// Returns the adjancent node in a mathcing edge. |
---|
| 3004 | Node mate(const Node& node) const { |
---|
| 3005 | return _ugraph.target((*_matching)[node]); |
---|
| 3006 | } |
---|
| 3007 | |
---|
| 3008 | /// @} |
---|
| 3009 | |
---|
| 3010 | /// \name Dual solution |
---|
| 3011 | /// Functions for get the dual solution. |
---|
| 3012 | |
---|
| 3013 | /// @{ |
---|
| 3014 | |
---|
| 3015 | /// \brief Returns the value of the dual solution. |
---|
| 3016 | /// |
---|
| 3017 | /// Returns the value of the dual solution. It should be equal to |
---|
| 3018 | /// the primal value scaled by \ref dualScale "dual scale". |
---|
| 3019 | Value dualValue() const { |
---|
| 3020 | Value sum = 0; |
---|
| 3021 | for (NodeIt n(_ugraph); n != INVALID; ++n) { |
---|
| 3022 | sum += nodeValue(n); |
---|
| 3023 | } |
---|
| 3024 | for (int i = 0; i < blossomNum(); ++i) { |
---|
| 3025 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
| 3026 | } |
---|
| 3027 | return sum; |
---|
| 3028 | } |
---|
| 3029 | |
---|
| 3030 | /// \brief Returns the value of the node. |
---|
| 3031 | /// |
---|
| 3032 | /// Returns the the value of the node. |
---|
| 3033 | Value nodeValue(const Node& n) const { |
---|
| 3034 | return (*_node_potential)[n]; |
---|
| 3035 | } |
---|
| 3036 | |
---|
| 3037 | /// \brief Returns the number of the blossoms in the basis. |
---|
| 3038 | /// |
---|
| 3039 | /// Returns the number of the blossoms in the basis. |
---|
| 3040 | /// \see BlossomIt |
---|
| 3041 | int blossomNum() const { |
---|
| 3042 | return _blossom_potential.size(); |
---|
| 3043 | } |
---|
| 3044 | |
---|
| 3045 | |
---|
| 3046 | /// \brief Returns the number of the nodes in the blossom. |
---|
| 3047 | /// |
---|
| 3048 | /// Returns the number of the nodes in the blossom. |
---|
| 3049 | int blossomSize(int k) const { |
---|
| 3050 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
| 3051 | } |
---|
| 3052 | |
---|
| 3053 | /// \brief Returns the value of the blossom. |
---|
| 3054 | /// |
---|
| 3055 | /// Returns the the value of the blossom. |
---|
| 3056 | /// \see BlossomIt |
---|
| 3057 | Value blossomValue(int k) const { |
---|
| 3058 | return _blossom_potential[k].value; |
---|
| 3059 | } |
---|
| 3060 | |
---|
| 3061 | /// \brief Lemon iterator for get the items of the blossom. |
---|
| 3062 | /// |
---|
| 3063 | /// Lemon iterator for get the nodes of the blossom. This class |
---|
| 3064 | /// provides a common style lemon iterator which gives back a |
---|
| 3065 | /// subset of the nodes. |
---|
| 3066 | class BlossomIt { |
---|
| 3067 | public: |
---|
| 3068 | |
---|
| 3069 | /// \brief Constructor. |
---|
| 3070 | /// |
---|
| 3071 | /// Constructor for get the nodes of the variable. |
---|
| 3072 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
| 3073 | : _algorithm(&algorithm) |
---|
| 3074 | { |
---|
| 3075 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
| 3076 | _last = _algorithm->_blossom_potential[variable].end; |
---|
| 3077 | } |
---|
| 3078 | |
---|
| 3079 | /// \brief Invalid constructor. |
---|
| 3080 | /// |
---|
| 3081 | /// Invalid constructor. |
---|
| 3082 | BlossomIt(Invalid) : _index(-1) {} |
---|
| 3083 | |
---|
| 3084 | /// \brief Conversion to node. |
---|
| 3085 | /// |
---|
| 3086 | /// Conversion to node. |
---|
| 3087 | operator Node() const { |
---|
| 3088 | return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID; |
---|
| 3089 | } |
---|
| 3090 | |
---|
| 3091 | /// \brief Increment operator. |
---|
| 3092 | /// |
---|
| 3093 | /// Increment operator. |
---|
| 3094 | BlossomIt& operator++() { |
---|
| 3095 | ++_index; |
---|
| 3096 | if (_index == _last) { |
---|
| 3097 | _index = -1; |
---|
| 3098 | } |
---|
| 3099 | return *this; |
---|
| 3100 | } |
---|
| 3101 | |
---|
| 3102 | bool operator==(const BlossomIt& it) const { |
---|
| 3103 | return _index == it._index; |
---|
| 3104 | } |
---|
| 3105 | bool operator!=(const BlossomIt& it) const { |
---|
| 3106 | return _index != it._index; |
---|
| 3107 | } |
---|
| 3108 | |
---|
| 3109 | private: |
---|
| 3110 | const MaxWeightedPerfectMatching* _algorithm; |
---|
| 3111 | int _last; |
---|
| 3112 | int _index; |
---|
| 3113 | }; |
---|
| 3114 | |
---|
| 3115 | /// @} |
---|
| 3116 | |
---|
| 3117 | }; |
---|
| 3118 | |
---|
[1077] | 3119 | |
---|
| 3120 | } //END OF NAMESPACE LEMON |
---|
| 3121 | |
---|
[1165] | 3122 | #endif //LEMON_MAX_MATCHING_H |
---|