[2353] | 1 | /* -*- C++ -*- |
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| 2 | * lemon/preflow_matching.h - Part of LEMON, a generic C++ optimization library |
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| 3 | * |
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| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | #ifndef LEMON_BP_MATCHING |
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| 18 | #define LEMON_BP_MATCHING |
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| 19 | |
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| 20 | #include <lemon/graph_utils.h> |
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| 21 | #include <lemon/iterable_maps.h> |
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| 22 | #include <iostream> |
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| 23 | #include <queue> |
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| 24 | #include <lemon/counter.h> |
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| 25 | #include <lemon/elevator.h> |
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| 26 | |
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| 27 | ///\ingroup matching |
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| 28 | ///\file |
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| 29 | ///\brief Push-prelabel maximum matching algorithms in bipartite graphs. |
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| 30 | /// |
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| 31 | ///\todo This file slightly conflicts with \ref lemon/bipartite_matching.h |
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| 32 | ///\todo (Re)move the XYZ_TYPEDEFS macros |
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| 33 | namespace lemon { |
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| 34 | |
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| 35 | #define BIPARTITE_TYPEDEFS(Graph) \ |
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| 36 | GRAPH_TYPEDEFS(Graph) \ |
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| 37 | typedef Graph::ANodeIt ANodeIt; \ |
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| 38 | typedef Graph::BNodeIt BNodeIt; |
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| 39 | |
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| 40 | #define UNDIRBIPARTITE_TYPEDEFS(Graph) \ |
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| 41 | UNDIRGRAPH_TYPEDEFS(Graph) \ |
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| 42 | typedef Graph::ANodeIt ANodeIt; \ |
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| 43 | typedef Graph::BNodeIt BNodeIt; |
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| 44 | |
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| 45 | template<class Graph, |
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| 46 | class MT=typename Graph::template ANodeMap<typename Graph::UEdge> > |
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| 47 | class BpMatching { |
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| 48 | typedef typename Graph::Node Node; |
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| 49 | typedef typename Graph::ANodeIt ANodeIt; |
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| 50 | typedef typename Graph::BNodeIt BNodeIt; |
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| 51 | typedef typename Graph::UEdge UEdge; |
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| 52 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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| 53 | |
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| 54 | const Graph &_g; |
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| 55 | int _node_num; |
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| 56 | MT &_matching; |
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| 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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| 61 | BpMatching(const Graph &g, MT &matching) : |
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| 62 | _g(g), |
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| 63 | _node_num(countBNodes(g)), |
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| 64 | _matching(matching), |
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| 65 | _levels(g,_node_num), |
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| 66 | _cov(g,0) |
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| 67 | { |
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| 68 | } |
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| 69 | |
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| 70 | private: |
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| 71 | void init() |
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| 72 | { |
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| 73 | // for(BNodeIt n(g);n!=INVALID;++n) cov[n]=0; |
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| 74 | for(ANodeIt n(_g);n!=INVALID;++n) |
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| 75 | if((_matching[n]=IncEdgeIt(_g,n))!=INVALID) |
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| 76 | ++_cov[_g.oppositeNode(n,_matching[n])]; |
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| 77 | |
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| 78 | std::queue<Node> q; |
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| 79 | _levels.initStart(); |
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| 80 | for(BNodeIt n(_g);n!=INVALID;++n) |
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| 81 | if(_cov[n]>1) { |
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| 82 | _levels.initAddItem(n); |
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| 83 | q.push(n); |
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| 84 | } |
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| 85 | int hlev=0; |
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| 86 | while(!q.empty()) { |
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| 87 | Node n=q.front(); |
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| 88 | q.pop(); |
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| 89 | int nlev=_levels[n]+1; |
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| 90 | for(IncEdgeIt e(_g,n);e!=INVALID;++e) { |
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| 91 | Node m=_g.runningNode(e); |
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| 92 | if(e==_matching[m]) { |
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| 93 | for(IncEdgeIt f(_g,m);f!=INVALID;++f) { |
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| 94 | Node r=_g.runningNode(f); |
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| 95 | if(_levels[r]>nlev) { |
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| 96 | for(;nlev>hlev;hlev++) |
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| 97 | _levels.initNewLevel(); |
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| 98 | _levels.initAddItem(r); |
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| 99 | q.push(r); |
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| 100 | } |
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| 101 | } |
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| 102 | } |
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| 103 | } |
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| 104 | } |
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| 105 | _levels.initFinish(); |
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| 106 | for(BNodeIt n(_g);n!=INVALID;++n) |
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| 107 | if(_cov[n]<1&&_levels[n]<_node_num) |
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| 108 | _levels.activate(n); |
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| 109 | } |
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| 110 | public: |
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| 111 | int run() |
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| 112 | { |
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| 113 | init(); |
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| 114 | |
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| 115 | Node act; |
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| 116 | Node bact=INVALID; |
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| 117 | Node last_activated=INVALID; |
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| 118 | // while((act=last_activated!=INVALID? |
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| 119 | // last_activated:_levels.highestActive()) |
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| 120 | // !=INVALID) |
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| 121 | while((act=_levels.highestActive())!=INVALID) { |
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| 122 | last_activated=INVALID; |
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| 123 | int actlevel=_levels[act]; |
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| 124 | |
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| 125 | UEdge bedge=INVALID; |
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| 126 | int nlevel=_node_num; |
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| 127 | { |
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| 128 | int nnlevel; |
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| 129 | for(IncEdgeIt tbedge(_g,act); |
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| 130 | tbedge!=INVALID && nlevel>=actlevel; |
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| 131 | ++tbedge) |
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| 132 | if((nnlevel=_levels[_g.bNode(_matching[_g.runningNode(tbedge)])])< |
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| 133 | nlevel) |
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| 134 | { |
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| 135 | nlevel=nnlevel; |
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| 136 | bedge=tbedge; |
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| 137 | } |
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| 138 | } |
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| 139 | if(nlevel<_node_num) { |
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| 140 | if(nlevel>=actlevel) |
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| 141 | _levels.liftHighestActiveTo(nlevel+1); |
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| 142 | // _levels.liftTo(act,nlevel+1); |
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| 143 | bact=_g.bNode(_matching[_g.aNode(bedge)]); |
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| 144 | if(--_cov[bact]<1) { |
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| 145 | _levels.activate(bact); |
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| 146 | last_activated=bact; |
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| 147 | } |
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| 148 | _matching[_g.aNode(bedge)]=bedge; |
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| 149 | _cov[act]=1; |
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| 150 | _levels.deactivate(act); |
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| 151 | } |
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| 152 | else { |
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| 153 | if(_node_num>actlevel) |
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| 154 | _levels.liftHighestActiveTo(_node_num); |
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| 155 | // _levels.liftTo(act,_node_num); |
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| 156 | _levels.deactivate(act); |
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| 157 | } |
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| 158 | |
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| 159 | if(_levels.onLevel(actlevel)==0) |
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| 160 | _levels.liftToTop(actlevel); |
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| 161 | } |
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| 162 | |
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| 163 | int ret=_node_num; |
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| 164 | for(ANodeIt n(_g);n!=INVALID;++n) |
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| 165 | if(_matching[n]==INVALID) ret--; |
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| 166 | else if (_cov[_g.bNode(_matching[n])]>1) { |
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| 167 | _cov[_g.bNode(_matching[n])]--; |
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| 168 | ret--; |
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| 169 | _matching[n]=INVALID; |
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| 170 | } |
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| 171 | return ret; |
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| 172 | } |
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| 173 | |
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| 174 | ///\returns -1 if there is a perfect matching, or an empty level |
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| 175 | ///if it doesn't exists |
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| 176 | int runPerfect() |
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| 177 | { |
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| 178 | init(); |
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| 179 | |
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| 180 | Node act; |
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| 181 | Node bact=INVALID; |
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| 182 | Node last_activated=INVALID; |
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| 183 | while((act=_levels.highestActive())!=INVALID) { |
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| 184 | last_activated=INVALID; |
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| 185 | int actlevel=_levels[act]; |
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| 186 | |
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| 187 | UEdge bedge=INVALID; |
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| 188 | int nlevel=_node_num; |
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| 189 | { |
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| 190 | int nnlevel; |
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| 191 | for(IncEdgeIt tbedge(_g,act); |
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| 192 | tbedge!=INVALID && nlevel>=actlevel; |
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| 193 | ++tbedge) |
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| 194 | if((nnlevel=_levels[_g.bNode(_matching[_g.runningNode(tbedge)])])< |
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| 195 | nlevel) |
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| 196 | { |
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| 197 | nlevel=nnlevel; |
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| 198 | bedge=tbedge; |
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| 199 | } |
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| 200 | } |
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| 201 | if(nlevel<_node_num) { |
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| 202 | if(nlevel>=actlevel) |
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| 203 | _levels.liftHighestActiveTo(nlevel+1); |
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| 204 | bact=_g.bNode(_matching[_g.aNode(bedge)]); |
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| 205 | if(--_cov[bact]<1) { |
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| 206 | _levels.activate(bact); |
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| 207 | last_activated=bact; |
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| 208 | } |
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| 209 | _matching[_g.aNode(bedge)]=bedge; |
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| 210 | _cov[act]=1; |
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| 211 | _levels.deactivate(act); |
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| 212 | } |
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| 213 | else { |
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| 214 | if(_node_num>actlevel) |
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| 215 | _levels.liftHighestActiveTo(_node_num); |
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| 216 | _levels.deactivate(act); |
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| 217 | } |
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| 218 | |
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| 219 | if(_levels.onLevel(actlevel)==0) |
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| 220 | return actlevel; |
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| 221 | } |
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| 222 | return -1; |
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| 223 | } |
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| 224 | |
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| 225 | template<class GT> |
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| 226 | void aBarrier(GT &bar,int empty_level=-1) |
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| 227 | { |
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| 228 | if(empty_level==-1) |
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| 229 | for(empty_level=0;_levels.onLevel(empty_level);empty_level++) ; |
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| 230 | for(ANodeIt n(_g);n!=INVALID;++n) |
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| 231 | bar[n] = _matching[n]==INVALID || |
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| 232 | _levels[_g.bNode(_matching[n])]<empty_level; |
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| 233 | } |
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| 234 | template<class GT> |
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| 235 | void bBarrier(GT &bar, int empty_level=-1) |
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| 236 | { |
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| 237 | if(empty_level==-1) |
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| 238 | for(empty_level=0;_levels.onLevel(empty_level);empty_level++) ; |
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| 239 | for(BNodeIt n(_g);n!=INVALID;++n) bar[n]=(_levels[n]>empty_level); |
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| 240 | } |
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| 241 | |
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| 242 | }; |
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| 243 | |
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| 244 | |
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| 245 | ///Maximum cardinality of the matchings in a bipartite graph |
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| 246 | |
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| 247 | ///\ingroup matching |
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| 248 | ///This function finds the maximum cardinality of the matchings |
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| 249 | ///in a bipartite graph \c g. |
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| 250 | ///\param g An undirected bipartite graph. |
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| 251 | ///\return The cardinality of the maximum matching. |
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| 252 | /// |
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| 253 | ///\note The the implementation is based |
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| 254 | ///on the push-relabel principle. |
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| 255 | template<class Graph> |
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| 256 | int maxBpMatching(const Graph &g) |
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| 257 | { |
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| 258 | typename Graph::template ANodeMap<typename Graph::UEdge> matching(g); |
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| 259 | return maxBpMatching(g,matching); |
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| 260 | } |
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| 261 | |
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| 262 | ///Maximum cardinality matching in a bipartite graph |
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| 263 | |
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| 264 | ///\ingroup matching |
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| 265 | ///This function finds a maximum cardinality matching |
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| 266 | ///in a bipartite graph \c g. |
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| 267 | ///\param g An undirected bipartite graph. |
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| 268 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
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| 269 | /// The found edges will be returned in this map, |
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| 270 | /// i.e. for an \c ANode \c n, |
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| 271 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n, or |
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| 272 | /// \ref INVALID if it is uncovered. |
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| 273 | ///\return The cardinality of the maximum matching. |
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| 274 | /// |
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| 275 | ///\note The the implementation is based |
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| 276 | ///on the push-relabel principle. |
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| 277 | template<class Graph,class MT> |
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| 278 | int maxBpMatching(const Graph &g,MT &matching) |
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| 279 | { |
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| 280 | return BpMatching<Graph,MT>(g,matching).run(); |
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| 281 | } |
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| 282 | |
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| 283 | ///Maximum cardinality matching in a bipartite graph |
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| 284 | |
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| 285 | ///\ingroup matching |
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| 286 | ///This function finds a maximum cardinality matching |
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| 287 | ///in a bipartite graph \c g. |
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| 288 | ///\param g An undirected bipartite graph. |
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| 289 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
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| 290 | /// The found edges will be returned in this map, |
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| 291 | /// i.e. for an \c ANode \c n, |
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| 292 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n, or |
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| 293 | /// \ref INVALID if it is uncovered. |
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| 294 | ///\retval barrier A \c bool WriteMap on the BNodes. The map will be set |
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| 295 | /// exactly once for each BNode. The nodes with \c true value represent |
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| 296 | /// a barrier \e B, i.e. the cardinality of \e B minus the number of its |
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| 297 | /// neighbor is equal to the number of the <tt>BNode</tt>s minus the |
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| 298 | /// cardinality of the maximum matching. |
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| 299 | ///\return The cardinality of the maximum matching. |
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| 300 | /// |
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| 301 | ///\note The the implementation is based |
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| 302 | ///on the push-relabel principle. |
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| 303 | template<class Graph,class MT, class GT> |
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| 304 | int maxBpMatching(const Graph &g,MT &matching,GT &barrier) |
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| 305 | { |
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| 306 | BpMatching<Graph,MT> bpm(g,matching); |
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| 307 | int ret=bpm.run(); |
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| 308 | bpm.barrier(barrier); |
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| 309 | return ret; |
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| 310 | } |
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| 311 | |
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| 312 | ///Perfect matching in a bipartite graph |
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| 313 | |
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| 314 | ///\ingroup matching |
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| 315 | ///This function checks whether the bipartite graph \c g |
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| 316 | ///has a perfect matching. |
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| 317 | ///\param g An undirected bipartite graph. |
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| 318 | ///\return \c true iff \c g has a perfect matching. |
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| 319 | /// |
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| 320 | ///\note The the implementation is based |
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| 321 | ///on the push-relabel principle. |
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| 322 | template<class Graph> |
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| 323 | bool perfectBpMatching(const Graph &g) |
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| 324 | { |
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| 325 | typename Graph::template ANodeMap<typename Graph::UEdge> matching(g); |
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| 326 | return perfectBpMatching(g,matching); |
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| 327 | } |
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| 328 | |
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| 329 | ///Perfect matching in a bipartite graph |
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| 330 | |
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| 331 | ///\ingroup matching |
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| 332 | ///This function finds a perfect matching in a bipartite graph \c g. |
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| 333 | ///\param g An undirected bipartite graph. |
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| 334 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
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| 335 | /// The found edges will be returned in this map, |
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| 336 | /// i.e. for an \c ANode \c n, |
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| 337 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n. |
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| 338 | /// The values are unspecified if the graph |
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| 339 | /// has no perfect matching. |
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| 340 | ///\return \c true iff \c g has a perfect matching. |
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| 341 | /// |
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| 342 | ///\note The the implementation is based |
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| 343 | ///on the push-relabel principle. |
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| 344 | template<class Graph,class MT> |
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| 345 | bool perfectBpMatching(const Graph &g,MT &matching) |
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| 346 | { |
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| 347 | return BpMatching<Graph,MT>(g,matching).runPerfect()<0; |
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| 348 | } |
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| 349 | |
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| 350 | ///Perfect matching in a bipartite graph |
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| 351 | |
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| 352 | ///\ingroup matching |
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| 353 | ///This function finds a perfect matching in a bipartite graph \c g. |
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| 354 | ///\param g An undirected bipartite graph. |
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| 355 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
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| 356 | /// The found edges will be returned in this map, |
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| 357 | /// i.e. for an \c ANode \c n, |
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| 358 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n. |
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| 359 | /// The values are unspecified if the graph |
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| 360 | /// has no perfect matching. |
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| 361 | ///\retval barrier A \c bool WriteMap on the BNodes. The map will only |
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| 362 | /// be set if \c g has no perfect matching. In this case it is set |
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| 363 | /// exactly once for each BNode. The nodes with \c true value represent |
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| 364 | /// a barrier, i.e. a subset \e B a of BNodes with the property that |
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| 365 | /// the cardinality of \e B is greater than the numner of its neighbors. |
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| 366 | ///\return \c true iff \c g has a perfect matching. |
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| 367 | /// |
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| 368 | ///\note The the implementation is based |
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| 369 | ///on the push-relabel principle. |
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| 370 | template<class Graph,class MT, class GT> |
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| 371 | int perfectBpMatching(const Graph &g,MT &matching,GT &barrier) |
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| 372 | { |
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| 373 | BpMatching<Graph,MT> bpm(g,matching); |
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| 374 | int ret=bpm.run(); |
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| 375 | if(ret>=0) |
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| 376 | bpm.barrier(barrier,ret); |
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| 377 | return ret<0; |
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| 378 | } |
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| 379 | } |
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| 380 | |
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| 381 | #endif |
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