[2353] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[2391] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[2353] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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[2462] | 19 | #ifndef LEMON_PR_BIPARTITE_MATCHING |
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| 20 | #define LEMON_PR_BIPARTITE_MATCHING |
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[2353] | 21 | |
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| 22 | #include <lemon/graph_utils.h> |
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| 23 | #include <lemon/iterable_maps.h> |
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| 24 | #include <iostream> |
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| 25 | #include <queue> |
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| 26 | #include <lemon/elevator.h> |
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| 27 | |
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| 28 | ///\ingroup matching |
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| 29 | ///\file |
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| 30 | ///\brief Push-prelabel maximum matching algorithms in bipartite graphs. |
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| 31 | /// |
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| 32 | namespace lemon { |
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| 33 | |
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[2462] | 34 | ///Max cardinality matching algorithm based on push-relabel principle |
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[2353] | 35 | |
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[2462] | 36 | ///\ingroup matching |
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| 37 | ///Bipartite Max Cardinality Matching algorithm. This class uses the |
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| 38 | ///push-relabel principle which in several cases has better runtime |
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| 39 | ///performance than the augmenting path solutions. |
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| 40 | /// |
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| 41 | ///\author Alpar Juttner |
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| 42 | template<class Graph> |
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| 43 | class PrBipartiteMatching { |
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[2353] | 44 | typedef typename Graph::Node Node; |
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| 45 | typedef typename Graph::ANodeIt ANodeIt; |
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| 46 | typedef typename Graph::BNodeIt BNodeIt; |
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| 47 | typedef typename Graph::UEdge UEdge; |
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[2462] | 48 | typedef typename Graph::UEdgeIt UEdgeIt; |
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[2353] | 49 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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| 50 | |
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| 51 | const Graph &_g; |
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| 52 | int _node_num; |
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[2462] | 53 | int _matching_size; |
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| 54 | int _empty_level; |
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| 55 | |
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| 56 | typename Graph::template ANodeMap<typename Graph::UEdge> _matching; |
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[2353] | 57 | Elevator<Graph,typename Graph::BNode> _levels; |
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| 58 | typename Graph::template BNodeMap<int> _cov; |
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| 59 | |
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| 60 | public: |
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[2462] | 61 | |
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[2466] | 62 | /// Constructor |
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| 63 | |
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| 64 | /// Constructor |
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| 65 | /// |
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[2462] | 66 | PrBipartiteMatching(const Graph &g) : |
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[2353] | 67 | _g(g), |
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| 68 | _node_num(countBNodes(g)), |
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[2462] | 69 | _matching(g), |
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[2353] | 70 | _levels(g,_node_num), |
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| 71 | _cov(g,0) |
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| 72 | { |
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| 73 | } |
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| 74 | |
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[2462] | 75 | /// \name Execution control |
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| 76 | /// The simplest way to execute the algorithm is to use one of the |
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| 77 | /// member functions called \c run(). \n |
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| 78 | /// If you need more control on the execution, first |
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| 79 | /// you must call \ref init() and then one variant of the start() |
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| 80 | /// member. |
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| 81 | |
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| 82 | /// @{ |
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| 83 | |
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| 84 | ///Initialize the data structures |
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| 85 | |
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| 86 | ///This function constructs a prematching first, which is a |
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| 87 | ///regular matching on the A-side of the graph, but on the B-side |
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| 88 | ///each node could cover more matching edges. After that, the |
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| 89 | ///B-nodes which multiple matched, will be pushed into the lowest |
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| 90 | ///level of the Elevator. The remaning B-nodes will be pushed to |
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| 91 | ///the consequent levels respect to a Bfs on following graph: the |
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| 92 | ///nodes are the B-nodes of the original bipartite graph and two |
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| 93 | ///nodes are adjacent if a node can pass over a matching edge to |
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| 94 | ///an other node. The source of the Bfs are the lowest level |
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| 95 | ///nodes. Last, the reached B-nodes without covered matching edge |
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| 96 | ///becomes active. |
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| 97 | void init() { |
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| 98 | _matching_size=0; |
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| 99 | _empty_level=_node_num; |
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[2353] | 100 | for(ANodeIt n(_g);n!=INVALID;++n) |
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| 101 | if((_matching[n]=IncEdgeIt(_g,n))!=INVALID) |
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[2462] | 102 | ++_cov[_g.bNode(_matching[n])]; |
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[2353] | 103 | |
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| 104 | std::queue<Node> q; |
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| 105 | _levels.initStart(); |
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| 106 | for(BNodeIt n(_g);n!=INVALID;++n) |
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| 107 | if(_cov[n]>1) { |
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| 108 | _levels.initAddItem(n); |
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| 109 | q.push(n); |
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| 110 | } |
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| 111 | int hlev=0; |
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| 112 | while(!q.empty()) { |
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| 113 | Node n=q.front(); |
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| 114 | q.pop(); |
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| 115 | int nlev=_levels[n]+1; |
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| 116 | for(IncEdgeIt e(_g,n);e!=INVALID;++e) { |
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| 117 | Node m=_g.runningNode(e); |
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| 118 | if(e==_matching[m]) { |
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| 119 | for(IncEdgeIt f(_g,m);f!=INVALID;++f) { |
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| 120 | Node r=_g.runningNode(f); |
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| 121 | if(_levels[r]>nlev) { |
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| 122 | for(;nlev>hlev;hlev++) |
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| 123 | _levels.initNewLevel(); |
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| 124 | _levels.initAddItem(r); |
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| 125 | q.push(r); |
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| 126 | } |
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| 127 | } |
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| 128 | } |
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| 129 | } |
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| 130 | } |
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| 131 | _levels.initFinish(); |
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| 132 | for(BNodeIt n(_g);n!=INVALID;++n) |
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| 133 | if(_cov[n]<1&&_levels[n]<_node_num) |
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| 134 | _levels.activate(n); |
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| 135 | } |
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| 136 | |
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[2462] | 137 | ///Start the main phase of the algorithm |
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[2353] | 138 | |
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[2462] | 139 | ///This algorithm calculates the maximum matching with the |
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| 140 | ///push-relabel principle. This function should be called just |
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| 141 | ///after the init() function which already set the initial |
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| 142 | ///prematching, the level function on the B-nodes and the active, |
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| 143 | ///ie. unmatched B-nodes. |
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| 144 | /// |
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| 145 | ///The algorithm always takes highest active B-node, and it try to |
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| 146 | ///find a B-node which is eligible to pass over one of it's |
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| 147 | ///matching edge. This condition holds when the B-node is one |
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| 148 | ///level lower, and the opposite node of it's matching edge is |
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| 149 | ///adjacent to the highest active node. In this case the current |
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| 150 | ///node steals the matching edge and becomes inactive. If there is |
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| 151 | ///not eligible node then the highest active node should be lift |
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| 152 | ///to the next proper level. |
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| 153 | /// |
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| 154 | ///The nodes should not lift higher than the number of the |
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| 155 | ///B-nodes, if a node reach this level it remains unmatched. If |
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| 156 | ///during the execution one level becomes empty the nodes above it |
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| 157 | ///can be deactivated and lift to the highest level. |
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| 158 | void start() { |
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[2353] | 159 | Node act; |
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| 160 | Node bact=INVALID; |
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| 161 | Node last_activated=INVALID; |
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| 162 | while((act=_levels.highestActive())!=INVALID) { |
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| 163 | last_activated=INVALID; |
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| 164 | int actlevel=_levels[act]; |
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| 165 | |
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| 166 | UEdge bedge=INVALID; |
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| 167 | int nlevel=_node_num; |
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| 168 | { |
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| 169 | int nnlevel; |
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| 170 | for(IncEdgeIt tbedge(_g,act); |
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| 171 | tbedge!=INVALID && nlevel>=actlevel; |
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| 172 | ++tbedge) |
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| 173 | if((nnlevel=_levels[_g.bNode(_matching[_g.runningNode(tbedge)])])< |
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| 174 | nlevel) |
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| 175 | { |
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| 176 | nlevel=nnlevel; |
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| 177 | bedge=tbedge; |
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| 178 | } |
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| 179 | } |
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| 180 | if(nlevel<_node_num) { |
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| 181 | if(nlevel>=actlevel) |
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| 182 | _levels.liftHighestActiveTo(nlevel+1); |
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| 183 | bact=_g.bNode(_matching[_g.aNode(bedge)]); |
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| 184 | if(--_cov[bact]<1) { |
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| 185 | _levels.activate(bact); |
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| 186 | last_activated=bact; |
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| 187 | } |
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| 188 | _matching[_g.aNode(bedge)]=bedge; |
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| 189 | _cov[act]=1; |
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| 190 | _levels.deactivate(act); |
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| 191 | } |
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| 192 | else { |
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| 193 | if(_node_num>actlevel) |
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| 194 | _levels.liftHighestActiveTo(_node_num); |
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| 195 | _levels.deactivate(act); |
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| 196 | } |
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| 197 | |
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| 198 | if(_levels.onLevel(actlevel)==0) |
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[2462] | 199 | _levels.liftToTop(actlevel); |
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[2353] | 200 | } |
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[2462] | 201 | |
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[2466] | 202 | for(ANodeIt n(_g);n!=INVALID;++n) { |
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| 203 | if (_matching[n]==INVALID)continue; |
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| 204 | if (_cov[_g.bNode(_matching[n])]>1) { |
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[2462] | 205 | _cov[_g.bNode(_matching[n])]--; |
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| 206 | _matching[n]=INVALID; |
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[2466] | 207 | } else { |
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| 208 | ++_matching_size; |
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[2462] | 209 | } |
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[2466] | 210 | } |
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[2353] | 211 | } |
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[2462] | 212 | |
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| 213 | ///Start the algorithm to find a perfect matching |
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| 214 | |
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| 215 | ///This function is close to identical to the simple start() |
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| 216 | ///member function but it calculates just perfect matching. |
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| 217 | ///However, the perfect property is only checked on the B-side of |
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| 218 | ///the graph |
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| 219 | /// |
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| 220 | ///The main difference between the two function is the handling of |
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| 221 | ///the empty levels. The simple start() function let the nodes |
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| 222 | ///above the empty levels unmatched while this variant if it find |
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| 223 | ///an empty level immediately terminates and gives back false |
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| 224 | ///return value. |
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| 225 | bool startPerfect() { |
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| 226 | Node act; |
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| 227 | Node bact=INVALID; |
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| 228 | Node last_activated=INVALID; |
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| 229 | while((act=_levels.highestActive())!=INVALID) { |
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| 230 | last_activated=INVALID; |
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| 231 | int actlevel=_levels[act]; |
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| 232 | |
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| 233 | UEdge bedge=INVALID; |
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| 234 | int nlevel=_node_num; |
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| 235 | { |
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| 236 | int nnlevel; |
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| 237 | for(IncEdgeIt tbedge(_g,act); |
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| 238 | tbedge!=INVALID && nlevel>=actlevel; |
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| 239 | ++tbedge) |
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| 240 | if((nnlevel=_levels[_g.bNode(_matching[_g.runningNode(tbedge)])])< |
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| 241 | nlevel) |
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| 242 | { |
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| 243 | nlevel=nnlevel; |
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| 244 | bedge=tbedge; |
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| 245 | } |
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| 246 | } |
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| 247 | if(nlevel<_node_num) { |
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| 248 | if(nlevel>=actlevel) |
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| 249 | _levels.liftHighestActiveTo(nlevel+1); |
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| 250 | bact=_g.bNode(_matching[_g.aNode(bedge)]); |
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| 251 | if(--_cov[bact]<1) { |
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| 252 | _levels.activate(bact); |
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| 253 | last_activated=bact; |
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| 254 | } |
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| 255 | _matching[_g.aNode(bedge)]=bedge; |
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| 256 | _cov[act]=1; |
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| 257 | _levels.deactivate(act); |
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| 258 | } |
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| 259 | else { |
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| 260 | if(_node_num>actlevel) |
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| 261 | _levels.liftHighestActiveTo(_node_num); |
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| 262 | _levels.deactivate(act); |
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| 263 | } |
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| 264 | |
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| 265 | if(_levels.onLevel(actlevel)==0) |
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| 266 | _empty_level=actlevel; |
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| 267 | return false; |
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| 268 | } |
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[2466] | 269 | _matching_size = _node_num; |
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[2462] | 270 | return true; |
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| 271 | } |
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| 272 | |
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| 273 | ///Runs the algorithm |
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| 274 | |
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| 275 | ///Just a shortcut for the next code: |
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| 276 | ///\code |
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| 277 | /// init(); |
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| 278 | /// start(); |
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| 279 | ///\endcode |
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| 280 | void run() { |
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| 281 | init(); |
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| 282 | start(); |
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| 283 | } |
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| 284 | |
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| 285 | ///Runs the algorithm to find a perfect matching |
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| 286 | |
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| 287 | ///Just a shortcut for the next code: |
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| 288 | ///\code |
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| 289 | /// init(); |
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| 290 | /// startPerfect(); |
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| 291 | ///\endcode |
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| 292 | /// |
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| 293 | ///\note If the two nodesets of the graph have different size then |
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| 294 | ///this algorithm checks the perfect property on the B-side. |
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| 295 | bool runPerfect() { |
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| 296 | init(); |
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| 297 | return startPerfect(); |
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| 298 | } |
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| 299 | |
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| 300 | ///Runs the algorithm to find a perfect matching |
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| 301 | |
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| 302 | ///Just a shortcut for the next code: |
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| 303 | ///\code |
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| 304 | /// init(); |
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| 305 | /// startPerfect(); |
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| 306 | ///\endcode |
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| 307 | /// |
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| 308 | ///\note It checks that the size of the two nodesets are equal. |
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| 309 | bool checkedRunPerfect() { |
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| 310 | if (countANodes(_g) != _node_num) return false; |
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| 311 | init(); |
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| 312 | return startPerfect(); |
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| 313 | } |
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| 314 | |
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| 315 | ///@} |
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| 316 | |
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| 317 | /// \name Query Functions |
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| 318 | /// The result of the %Matching algorithm can be obtained using these |
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| 319 | /// functions.\n |
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| 320 | /// Before the use of these functions, |
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| 321 | /// either run() or start() must be called. |
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| 322 | ///@{ |
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| 323 | |
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[2463] | 324 | ///Set true all matching uedge in the map. |
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| 325 | |
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| 326 | ///Set true all matching uedge in the map. It does not change the |
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| 327 | ///value mapped to the other uedges. |
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| 328 | ///\return The number of the matching edges. |
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[2462] | 329 | template <typename MatchingMap> |
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| 330 | int quickMatching(MatchingMap& mm) const { |
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| 331 | for (ANodeIt n(_g);n!=INVALID;++n) { |
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| 332 | if (_matching[n]!=INVALID) mm.set(_matching[n],true); |
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| 333 | } |
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| 334 | return _matching_size; |
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| 335 | } |
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| 336 | |
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[2463] | 337 | ///Set true all matching uedge in the map and the others to false. |
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[2462] | 338 | |
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| 339 | ///Set true all matching uedge in the map and the others to false. |
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| 340 | ///\return The number of the matching edges. |
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| 341 | template<class MatchingMap> |
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| 342 | int matching(MatchingMap& mm) const { |
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| 343 | for (UEdgeIt e(_g);e!=INVALID;++e) { |
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| 344 | mm.set(e,e==_matching[_g.aNode(e)]); |
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| 345 | } |
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| 346 | return _matching_size; |
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| 347 | } |
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| 348 | |
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[2463] | 349 | ///Gives back the matching in an ANodeMap. |
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| 350 | |
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| 351 | ///Gives back the matching in an ANodeMap. The parameter should |
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| 352 | ///be a write ANodeMap of UEdge values. |
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| 353 | ///\return The number of the matching edges. |
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| 354 | template<class MatchingMap> |
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| 355 | int aMatching(MatchingMap& mm) const { |
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| 356 | for (ANodeIt n(_g);n!=INVALID;++n) { |
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| 357 | mm.set(n,_matching[n]); |
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| 358 | } |
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| 359 | return _matching_size; |
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| 360 | } |
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| 361 | |
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| 362 | ///Gives back the matching in a BNodeMap. |
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| 363 | |
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| 364 | ///Gives back the matching in a BNodeMap. The parameter should |
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| 365 | ///be a write BNodeMap of UEdge values. |
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| 366 | ///\return The number of the matching edges. |
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| 367 | template<class MatchingMap> |
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| 368 | int bMatching(MatchingMap& mm) const { |
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| 369 | for (BNodeIt n(_g);n!=INVALID;++n) { |
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| 370 | mm.set(n,INVALID); |
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| 371 | } |
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| 372 | for (ANodeIt n(_g);n!=INVALID;++n) { |
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| 373 | if (_matching[n]!=INVALID) |
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| 374 | mm.set(_g.bNode(_matching[n]),_matching[n]); |
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| 375 | } |
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| 376 | return _matching_size; |
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| 377 | } |
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| 378 | |
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[2462] | 379 | |
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| 380 | ///Returns true if the given uedge is in the matching. |
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| 381 | |
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| 382 | ///It returns true if the given uedge is in the matching. |
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| 383 | /// |
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| 384 | bool matchingEdge(const UEdge& e) const { |
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| 385 | return _matching[_g.aNode(e)]==e; |
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| 386 | } |
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| 387 | |
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| 388 | ///Returns the matching edge from the node. |
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| 389 | |
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| 390 | ///Returns the matching edge from the node. If there is not such |
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| 391 | ///edge it gives back \c INVALID. |
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| 392 | ///\note If the parameter node is a B-node then the running time is |
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| 393 | ///propotional to the degree of the node. |
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| 394 | UEdge matchingEdge(const Node& n) const { |
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| 395 | if (_g.aNode(n)) { |
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| 396 | return _matching[n]; |
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| 397 | } else { |
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| 398 | for (IncEdgeIt e(_g,n);e!=INVALID;++e) |
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| 399 | if (e==_matching[_g.aNode(e)]) return e; |
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| 400 | return INVALID; |
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| 401 | } |
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| 402 | } |
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| 403 | |
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| 404 | ///Gives back the number of the matching edges. |
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| 405 | |
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| 406 | ///Gives back the number of the matching edges. |
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| 407 | int matchingSize() const { |
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| 408 | return _matching_size; |
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| 409 | } |
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| 410 | |
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| 411 | ///Gives back a barrier on the A-nodes |
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| 412 | |
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| 413 | ///The barrier is s subset of the nodes on the same side of the |
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| 414 | ///graph. If we tried to find a perfect matching and it failed |
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| 415 | ///then the barrier size will be greater than its neighbours. If |
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| 416 | ///the maximum matching searched then the barrier size minus its |
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| 417 | ///neighbours will be exactly the unmatched nodes on the A-side. |
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| 418 | ///\retval bar A WriteMap on the ANodes with bool value. |
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| 419 | template<class BarrierMap> |
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| 420 | void aBarrier(BarrierMap &bar) const |
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[2353] | 421 | { |
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| 422 | for(ANodeIt n(_g);n!=INVALID;++n) |
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[2462] | 423 | bar.set(n,_matching[n]==INVALID || |
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| 424 | _levels[_g.bNode(_matching[n])]<_empty_level); |
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[2353] | 425 | } |
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[2462] | 426 | |
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| 427 | ///Gives back a barrier on the B-nodes |
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| 428 | |
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| 429 | ///The barrier is s subset of the nodes on the same side of the |
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| 430 | ///graph. If we tried to find a perfect matching and it failed |
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| 431 | ///then the barrier size will be greater than its neighbours. If |
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| 432 | ///the maximum matching searched then the barrier size minus its |
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| 433 | ///neighbours will be exactly the unmatched nodes on the B-side. |
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| 434 | ///\retval bar A WriteMap on the BNodes with bool value. |
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| 435 | template<class BarrierMap> |
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| 436 | void bBarrier(BarrierMap &bar) const |
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[2353] | 437 | { |
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[2462] | 438 | for(BNodeIt n(_g);n!=INVALID;++n) bar.set(n,_levels[n]>=_empty_level); |
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| 439 | } |
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| 440 | |
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| 441 | ///Returns a minimum covering of the nodes. |
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| 442 | |
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| 443 | ///The minimum covering set problem is the dual solution of the |
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| 444 | ///maximum bipartite matching. It provides a solution for this |
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| 445 | ///problem what is proof of the optimality of the matching. |
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| 446 | ///\param covering NodeMap of bool values, the nodes of the cover |
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| 447 | ///set will set true while the others false. |
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| 448 | ///\return The size of the cover set. |
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| 449 | ///\note This function can be called just after the algorithm have |
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| 450 | ///already found a matching. |
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| 451 | template<class CoverMap> |
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| 452 | int coverSet(CoverMap& covering) const { |
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| 453 | int ret=0; |
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| 454 | for(BNodeIt n(_g);n!=INVALID;++n) { |
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| 455 | if (_levels[n]<_empty_level) { covering.set(n,true); ++ret; } |
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| 456 | else covering.set(n,false); |
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| 457 | } |
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| 458 | for(ANodeIt n(_g);n!=INVALID;++n) { |
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| 459 | if (_matching[n]!=INVALID && |
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| 460 | _levels[_g.bNode(_matching[n])]>=_empty_level) |
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| 461 | { covering.set(n,true); ++ret; } |
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| 462 | else covering.set(n,false); |
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| 463 | } |
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| 464 | return ret; |
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| 465 | } |
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| 466 | |
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| 467 | |
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| 468 | /// @} |
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| 469 | |
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[2353] | 470 | }; |
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| 471 | |
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| 472 | |
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| 473 | ///Maximum cardinality of the matchings in a bipartite graph |
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| 474 | |
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| 475 | ///\ingroup matching |
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| 476 | ///This function finds the maximum cardinality of the matchings |
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| 477 | ///in a bipartite graph \c g. |
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| 478 | ///\param g An undirected bipartite graph. |
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| 479 | ///\return The cardinality of the maximum matching. |
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| 480 | /// |
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| 481 | ///\note The the implementation is based |
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| 482 | ///on the push-relabel principle. |
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| 483 | template<class Graph> |
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[2462] | 484 | int prBipartiteMatching(const Graph &g) |
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[2353] | 485 | { |
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[2462] | 486 | PrBipartiteMatching<Graph> bpm(g); |
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| 487 | return bpm.matchingSize(); |
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[2353] | 488 | } |
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| 489 | |
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| 490 | ///Maximum cardinality matching in a bipartite graph |
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| 491 | |
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| 492 | ///\ingroup matching |
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| 493 | ///This function finds a maximum cardinality matching |
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| 494 | ///in a bipartite graph \c g. |
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| 495 | ///\param g An undirected bipartite graph. |
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[2463] | 496 | ///\retval matching A write ANodeMap of value type \c UEdge. |
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| 497 | /// The found edges will be returned in this map, |
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| 498 | /// i.e. for an \c ANode \c n the edge <tt>matching[n]</tt> is the one |
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| 499 | /// that covers the node \c n. |
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[2353] | 500 | ///\return The cardinality of the maximum matching. |
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| 501 | /// |
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| 502 | ///\note The the implementation is based |
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| 503 | ///on the push-relabel principle. |
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| 504 | template<class Graph,class MT> |
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[2462] | 505 | int prBipartiteMatching(const Graph &g,MT &matching) |
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[2353] | 506 | { |
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[2462] | 507 | PrBipartiteMatching<Graph> bpm(g); |
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| 508 | bpm.run(); |
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[2463] | 509 | bpm.aMatching(matching); |
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[2462] | 510 | return bpm.matchingSize(); |
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[2353] | 511 | } |
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| 512 | |
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| 513 | ///Maximum cardinality matching in a bipartite graph |
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| 514 | |
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| 515 | ///\ingroup matching |
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| 516 | ///This function finds a maximum cardinality matching |
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| 517 | ///in a bipartite graph \c g. |
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| 518 | ///\param g An undirected bipartite graph. |
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[2463] | 519 | ///\retval matching A write ANodeMap of value type \c UEdge. |
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| 520 | /// The found edges will be returned in this map, |
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| 521 | /// i.e. for an \c ANode \c n the edge <tt>matching[n]</tt> is the one |
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| 522 | /// that covers the node \c n. |
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[2353] | 523 | ///\retval barrier A \c bool WriteMap on the BNodes. The map will be set |
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| 524 | /// exactly once for each BNode. The nodes with \c true value represent |
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| 525 | /// a barrier \e B, i.e. the cardinality of \e B minus the number of its |
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| 526 | /// neighbor is equal to the number of the <tt>BNode</tt>s minus the |
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| 527 | /// cardinality of the maximum matching. |
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| 528 | ///\return The cardinality of the maximum matching. |
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| 529 | /// |
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| 530 | ///\note The the implementation is based |
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| 531 | ///on the push-relabel principle. |
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| 532 | template<class Graph,class MT, class GT> |
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[2462] | 533 | int prBipartiteMatching(const Graph &g,MT &matching,GT &barrier) |
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[2353] | 534 | { |
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[2462] | 535 | PrBipartiteMatching<Graph> bpm(g); |
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| 536 | bpm.run(); |
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[2463] | 537 | bpm.aMatching(matching); |
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[2462] | 538 | bpm.bBarrier(barrier); |
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| 539 | return bpm.matchingSize(); |
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[2353] | 540 | } |
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| 541 | |
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| 542 | ///Perfect matching in a bipartite graph |
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| 543 | |
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| 544 | ///\ingroup matching |
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| 545 | ///This function checks whether the bipartite graph \c g |
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| 546 | ///has a perfect matching. |
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| 547 | ///\param g An undirected bipartite graph. |
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| 548 | ///\return \c true iff \c g has a perfect matching. |
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| 549 | /// |
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| 550 | ///\note The the implementation is based |
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| 551 | ///on the push-relabel principle. |
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| 552 | template<class Graph> |
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[2462] | 553 | bool prPerfectBipartiteMatching(const Graph &g) |
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[2353] | 554 | { |
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[2462] | 555 | PrBipartiteMatching<Graph> bpm(g); |
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| 556 | return bpm.runPerfect(); |
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[2353] | 557 | } |
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| 558 | |
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| 559 | ///Perfect matching in a bipartite graph |
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| 560 | |
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| 561 | ///\ingroup matching |
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| 562 | ///This function finds a perfect matching in a bipartite graph \c g. |
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| 563 | ///\param g An undirected bipartite graph. |
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[2463] | 564 | ///\retval matching A write ANodeMap of value type \c UEdge. |
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| 565 | /// The found edges will be returned in this map, |
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| 566 | /// i.e. for an \c ANode \c n the edge <tt>matching[n]</tt> is the one |
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| 567 | /// that covers the node \c n. |
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[2462] | 568 | /// The values are unchanged if the graph |
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[2353] | 569 | /// has no perfect matching. |
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| 570 | ///\return \c true iff \c g has a perfect matching. |
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| 571 | /// |
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| 572 | ///\note The the implementation is based |
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| 573 | ///on the push-relabel principle. |
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| 574 | template<class Graph,class MT> |
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[2462] | 575 | bool prPerfectBipartiteMatching(const Graph &g,MT &matching) |
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[2353] | 576 | { |
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[2462] | 577 | PrBipartiteMatching<Graph> bpm(g); |
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[2463] | 578 | bool ret = bpm.checkedRunPerfect(); |
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| 579 | if (ret) bpm.aMatching(matching); |
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[2462] | 580 | return ret; |
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[2353] | 581 | } |
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| 582 | |
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| 583 | ///Perfect matching in a bipartite graph |
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| 584 | |
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| 585 | ///\ingroup matching |
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| 586 | ///This function finds a perfect matching in a bipartite graph \c g. |
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| 587 | ///\param g An undirected bipartite graph. |
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[2463] | 588 | ///\retval matching A write ANodeMap of value type \c UEdge. |
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| 589 | /// The found edges will be returned in this map, |
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| 590 | /// i.e. for an \c ANode \c n the edge <tt>matching[n]</tt> is the one |
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| 591 | /// that covers the node \c n. |
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[2462] | 592 | /// The values are unchanged if the graph |
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[2353] | 593 | /// has no perfect matching. |
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| 594 | ///\retval barrier A \c bool WriteMap on the BNodes. The map will only |
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| 595 | /// be set if \c g has no perfect matching. In this case it is set |
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| 596 | /// exactly once for each BNode. The nodes with \c true value represent |
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| 597 | /// a barrier, i.e. a subset \e B a of BNodes with the property that |
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[2462] | 598 | /// the cardinality of \e B is greater than the number of its neighbors. |
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[2353] | 599 | ///\return \c true iff \c g has a perfect matching. |
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| 600 | /// |
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| 601 | ///\note The the implementation is based |
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| 602 | ///on the push-relabel principle. |
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| 603 | template<class Graph,class MT, class GT> |
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[2463] | 604 | bool prPerfectBipartiteMatching(const Graph &g,MT &matching,GT &barrier) |
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[2353] | 605 | { |
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[2462] | 606 | PrBipartiteMatching<Graph> bpm(g); |
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[2463] | 607 | bool ret=bpm.checkedRunPerfect(); |
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[2462] | 608 | if(ret) |
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[2463] | 609 | bpm.aMatching(matching); |
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[2462] | 610 | else |
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| 611 | bpm.bBarrier(barrier); |
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| 612 | return ret; |
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[2353] | 613 | } |
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| 614 | } |
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| 615 | |
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| 616 | #endif |
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