COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/lemon/max_matching.h @ 1177:e41c2907fb49

Last change on this file since 1177:e41c2907fb49 was 1177:e41c2907fb49, checked in by Alpar Juttner, 15 years ago

Fix 'make distcheck' failure.

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1/* -*- C++ -*-
2 * src/lemon/max_matching.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Combinatorial Optimization Research Group, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_MAX_MATCHING_H
18#define LEMON_MAX_MATCHING_H
19
20#include <queue>
21#include <lemon/invalid.h>
22#include <lemon/unionfind.h>
23#include <lemon/graph_utils.h>
24
25///\ingroup galgs
26///\file
27///\brief Maximum matching algorithm.
28
29namespace lemon {
30
31  /// \addtogroup galgs
32  /// @{
33
34  ///Edmonds' alternating forest maximum matching algorithm.
35
36  ///This class provides Edmonds' alternating forest matching
37  ///algorithm. The starting matching (if any) can be passed to the
38  ///algorithm using read-in functions \ref readNMapNode, \ref
39  ///readNMapEdge or \ref readEMapBool depending on the container. The
40  ///resulting maximum matching can be attained by write-out functions
41  ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
42  ///depending on the preferred container.
43  ///
44  ///The dual side of a matching is a map of the nodes to
45  ///MaxMatching::pos_enum, having values D, A and C showing the
46  ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
47  ///a graph with factor-critical components, the nodes in A form the
48  ///barrier, and the nodes in C induce a graph having a perfect
49  ///matching. This decomposition can be attained by calling \ref
50  ///writePos after running the algorithm.
51  ///
52  ///\param Graph The undirected graph type the algorithm runs on.
53  ///
54  ///\author Jacint Szabo 
55  template <typename Graph>
56  class MaxMatching {
57
58  protected:
59
60    typedef typename Graph::Node Node;
61    typedef typename Graph::Edge Edge;
62    typedef typename Graph::UndirEdge UndirEdge;
63    typedef typename Graph::UndirEdgeIt UndirEdgeIt;
64    typedef typename Graph::NodeIt NodeIt;
65    typedef typename Graph::IncEdgeIt IncEdgeIt;
66
67    typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;
68
69  public:
70   
71    ///Indicates the Gallai-Edmonds decomposition of the graph.
72
73    ///Indicates the Gallai-Edmonds decomposition of the graph, which
74    ///shows an upper bound on the size of a maximum matching. The
75    ///nodes with pos_enum \c D induce a graph with factor-critical
76    ///components, the nodes in \c A form the canonical barrier, and the
77    ///nodes in \c C induce a graph having a perfect matching.
78    enum pos_enum {
79      D=0,
80      A=1,
81      C=2
82    };
83
84  protected:
85
86    static const int HEUR_density=2;
87    const Graph& g;
88    typename Graph::template NodeMap<Node> _mate;
89    typename Graph::template NodeMap<pos_enum> position;
90     
91  public:
92   
93    MaxMatching(const Graph& _g) : g(_g), _mate(_g,INVALID), position(_g) {}
94
95    ///Runs Edmonds' algorithm.
96
97    ///Runs Edmonds' algorithm for sparse graphs (number of edges <
98    ///2*number of nodes), and a heuristical Edmonds' algorithm with a
99    ///heuristic of postponing shrinks for dense graphs.
100    inline void run();
101
102    ///Runs Edmonds' algorithm.
103   
104    ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
105    ///Edmonds' algorithm with a heuristic of postponing shrinks,
106    ///giving a faster algorithm for dense graphs. 
107    void runEdmonds( int heur );
108
109    ///Finds a greedy matching starting from the actual matching.
110   
111    ///Starting form the actual matching stored, it finds a maximal
112    ///greedy matching.
113    void greedyMatching();
114
115    ///Returns the size of the actual matching stored.
116
117    ///Returns the size of the actual matching stored. After \ref
118    ///run() it returns the size of a maximum matching in the graph.
119    int size() const;
120
121    ///Resets the actual matching to the empty matching.
122
123    ///Resets the actual matching to the empty matching. 
124    ///
125    void resetMatching();
126
127    ///Returns the mate of a node in the actual matching.
128
129    ///Returns the mate of a \c node in the actual matching.
130    ///Returns INVALID if the \c node is not covered by the actual matching.
131    Node mate(Node& node) const {
132      return _mate[node];
133    }
134
135    ///Reads a matching from a \c Node valued \c Node map.
136
137    ///Reads a matching from a \c Node valued \c Node map. This map
138    ///must be \e symmetric, i.e. if \c map[u]==v then \c map[v]==u
139    ///must hold, and \c uv will be an edge of the matching.
140    template<typename NMapN>
141    void readNMapNode(NMapN& map) {
142      for(NodeIt v(g); v!=INVALID; ++v) {
143        _mate.set(v,map[v]);   
144      }
145    }
146   
147    ///Writes the stored matching to a \c Node valued \c Node map.
148
149    ///Writes the stored matching to a \c Node valued \c Node map. The
150    ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
151    ///map[v]==u will hold, and now \c uv is an edge of the matching.
152    template<typename NMapN>
153    void writeNMapNode (NMapN& map) const {
154      for(NodeIt v(g); v!=INVALID; ++v) {
155        map.set(v,_mate[v]);   
156      }
157    }
158
159    ///Reads a matching from an \c UndirEdge valued \c Node map.
160
161    ///Reads a matching from an \c UndirEdge valued \c Node map. \c
162    ///map[v] must be an \c UndirEdge incident to \c v. This map must
163    ///have the property that if \c g.oppositeNode(u,map[u])==v then
164    ///\c \c g.oppositeNode(v,map[v])==u holds, and now some edge
165    ///joining \c u to \c v will be an edge of the matching.
166    template<typename NMapE>
167    void readNMapEdge(NMapE& map) {
168     for(NodeIt v(g); v!=INVALID; ++v) {
169       UndirEdge e=map[v];
170        if ( e!=INVALID )
171          _mate.set(v,g.oppositeNode(v,e));
172      }
173    }
174   
175    ///Writes the matching stored to an \c UndirEdge valued \c Node map.
176
177    ///Writes the stored matching to an \c UndirEdge valued \c Node
178    ///map. \c map[v] will be an \c UndirEdge incident to \c v. This
179    ///map will have the property that if \c g.oppositeNode(u,map[u])
180    ///== v then \c map[u]==map[v] holds, and now this edge is an edge
181    ///of the matching.
182    template<typename NMapE>
183    void writeNMapEdge (NMapE& map)  const {
184      typename Graph::template NodeMap<bool> todo(g,true);
185      for(NodeIt v(g); v!=INVALID; ++v) {
186        if ( todo[v] && _mate[v]!=INVALID ) {
187          Node u=_mate[v];
188          for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
189            if ( g.runningNode(e) == u ) {
190              map.set(u,e);
191              map.set(v,e);
192              todo.set(u,false);
193              todo.set(v,false);
194              break;
195            }
196          }
197        }
198      }
199    }
200
201
202    ///Reads a matching from a \c bool valued \c Edge map.
203   
204    ///Reads a matching from a \c bool valued \c Edge map. This map
205    ///must have the property that there are no two incident edges \c
206    ///e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
207    ///map[e]==true form the matching.
208    template<typename EMapB>
209    void readEMapBool(EMapB& map) {
210      for(UndirEdgeIt e(g); e!=INVALID; ++e) {
211        if ( map[e] ) {
212          Node u=g.source(e);     
213          Node v=g.target(e);
214          _mate.set(u,v);
215          _mate.set(v,u);
216        }
217      }
218    }
219
220
221    ///Writes the matching stored to a \c bool valued \c Edge map.
222
223    ///Writes the matching stored to a \c bool valued \c Edge
224    ///map. This map will have the property that there are no two
225    ///incident edges \c e, \c f with \c map[e]==map[f]==true. The
226    ///edges \c e with \c map[e]==true form the matching.
227    template<typename EMapB>
228    void writeEMapBool (EMapB& map) const {
229      for(UndirEdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
230
231      typename Graph::template NodeMap<bool> todo(g,true);
232      for(NodeIt v(g); v!=INVALID; ++v) {
233        if ( todo[v] && _mate[v]!=INVALID ) {
234          Node u=_mate[v];
235          for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
236            if ( g.runningNode(e) == u ) {
237              map.set(e,true);
238              todo.set(u,false);
239              todo.set(v,false);
240              break;
241            }
242          }
243        }
244      }
245    }
246
247
248    ///Writes the canonical decomposition of the graph after running
249    ///the algorithm.
250
251    ///After calling any run methods of the class, it writes the
252    ///Gallai-Edmonds canonical decomposition of the graph. \c map
253    ///must be a node map of \ref pos_enum 's.
254    template<typename NMapEnum>
255    void writePos (NMapEnum& map) const {
256      for(NodeIt v(g); v!=INVALID; ++v)  map.set(v,position[v]);
257    }
258
259  private:
260
261 
262    void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, 
263                    UFE& blossom, UFE& tree);
264
265    void normShrink(Node v, typename Graph::NodeMap<Node>& ear, 
266                    UFE& blossom, UFE& tree);
267
268    bool noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear, 
269                      UFE& blossom, UFE& tree, std::queue<Node>& Q);
270
271    void shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear, 
272                    UFE& blossom, UFE& tree, std::queue<Node>& Q);
273
274    void augment(Node x, typename Graph::NodeMap<Node>& ear, 
275                 UFE& blossom, UFE& tree);
276
277  };
278
279
280  // **********************************************************************
281  //  IMPLEMENTATIONS
282  // **********************************************************************
283
284
285  template <typename Graph>
286  void MaxMatching<Graph>::run() {
287    if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) {
288      greedyMatching();
289      runEdmonds(0);
290    } else runEdmonds(1);
291  }
292
293
294  template <typename Graph>
295  void MaxMatching<Graph>::runEdmonds( int heur=1 ) {
296
297    for(NodeIt v(g); v!=INVALID; ++v)
298      position.set(v,C);     
299
300    typename Graph::template NodeMap<Node> ear(g,INVALID);
301    //undefined for the base nodes of the blossoms (i.e. for the
302    //representative elements of UFE blossom) and for the nodes in C
303
304    typename UFE::MapType blossom_base(g);
305    UFE blossom(blossom_base);
306    typename UFE::MapType tree_base(g);
307    UFE tree(tree_base);
308    //If these UFE's would be members of the class then also
309    //blossom_base and tree_base should be a member.
310
311    for(NodeIt v(g); v!=INVALID; ++v) {
312      if ( position[v]==C && _mate[v]==INVALID ) {
313        blossom.insert(v);
314        tree.insert(v);
315        position.set(v,D);
316        if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
317        else normShrink( v, ear, blossom, tree );
318      }
319    }
320  }
321
322   
323  template <typename Graph>
324  void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, 
325                                      UFE& blossom, UFE& tree) {
326
327    std::queue<Node> Q;   //queue of the totally unscanned nodes
328    Q.push(v); 
329    std::queue<Node> R;   
330    //queue of the nodes which must be scanned for a possible shrink
331     
332    while ( !Q.empty() ) {
333      Node x=Q.front();
334      Q.pop();
335      if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
336      else R.push(x);
337    }
338     
339    while ( !R.empty() ) {
340      Node x=R.front();
341      R.pop();
342       
343      for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
344        Node y=g.runningNode(e);
345
346        if ( position[y] == D && blossom.find(x) != blossom.find(y) ) {
347          //x and y must be in the same tree
348       
349          typename Graph::template NodeMap<bool> path(g,false);
350
351          Node b=blossom.find(x);
352          path.set(b,true);
353          b=_mate[b];
354          while ( b!=INVALID ) {
355            b=blossom.find(ear[b]);
356            path.set(b,true);
357            b=_mate[b];
358          } //going till the root
359       
360          Node top=y;
361          Node middle=blossom.find(top);
362          Node bottom=x;
363          while ( !path[middle] )
364            shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
365                 
366          Node base=middle;
367          top=x;
368          middle=blossom.find(top);
369          bottom=y;
370          Node blossom_base=blossom.find(base);
371          while ( middle!=blossom_base )
372            shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
373                 
374          blossom.makeRep(base);
375        } // if shrink is needed
376
377        while ( !Q.empty() ) {
378          Node x=Q.front();
379          Q.pop();
380          if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
381          else R.push(x);
382        }
383      } //for e
384    } // while ( !R.empty() )
385  }
386
387
388  template <typename Graph>
389  void MaxMatching<Graph>::normShrink(Node v, typename Graph::NodeMap<Node>& ear, 
390                                      UFE& blossom, UFE& tree) {
391
392    std::queue<Node> Q;   //queue of the unscanned nodes
393    Q.push(v); 
394    while ( !Q.empty() ) {
395
396      Node x=Q.front();
397      Q.pop();
398       
399      for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
400        Node y=g.runningNode(e);
401             
402        switch ( position[y] ) {
403        case D:          //x and y must be in the same tree
404
405          if ( blossom.find(x) != blossom.find(y) ) { //shrink
406            typename Graph::template NodeMap<bool> path(g,false);
407             
408            Node b=blossom.find(x);
409            path.set(b,true);
410            b=_mate[b];
411            while ( b!=INVALID ) {
412              b=blossom.find(ear[b]);
413              path.set(b,true);
414              b=_mate[b];
415            } //going till the root
416       
417            Node top=y;
418            Node middle=blossom.find(top);
419            Node bottom=x;
420            while ( !path[middle] )
421              shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
422               
423            Node base=middle;
424            top=x;
425            middle=blossom.find(top);
426            bottom=y;
427            Node blossom_base=blossom.find(base);
428            while ( middle!=blossom_base )
429              shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
430               
431            blossom.makeRep(base);
432          }
433          break;
434        case C:
435          if ( _mate[y]!=INVALID ) {   //grow
436
437            ear.set(y,x);
438            Node w=_mate[y];
439            blossom.insert(w);
440            position.set(y,A);
441            position.set(w,D);
442            tree.insert(y);
443            tree.insert(w);
444            tree.join(y,blossom.find(x)); 
445            tree.join(w,y); 
446            Q.push(w);
447          } else {                 //augment 
448            augment(x, ear, blossom, tree);
449            _mate.set(x,y);
450            _mate.set(y,x);
451            return;
452          } //if
453          break;
454        default: break;
455        }
456      }
457    }
458  }
459
460  template <typename Graph>
461  void MaxMatching<Graph>::greedyMatching() {
462    for(NodeIt v(g); v!=INVALID; ++v)
463      if ( _mate[v]==INVALID ) {
464        for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
465          Node y=g.runningNode(e);
466          if ( _mate[y]==INVALID && y!=v ) {
467            _mate.set(v,y);
468            _mate.set(y,v);
469            break;
470          }
471        }
472      }
473  }
474   
475  template <typename Graph>
476  int MaxMatching<Graph>::size() const {
477    int s=0;
478    for(NodeIt v(g); v!=INVALID; ++v) {
479      if ( _mate[v]!=INVALID ) {
480        ++s;
481      }
482    }
483    return s/2;
484  }
485
486  template <typename Graph>
487  void MaxMatching<Graph>::resetMatching() {
488    for(NodeIt v(g); v!=INVALID; ++v)
489      _mate.set(v,INVALID);     
490  }
491
492  template <typename Graph>
493  bool MaxMatching<Graph>::noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear, 
494                                        UFE& blossom, UFE& tree, std::queue<Node>& Q) {
495    for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
496      Node y=g.runningNode(e);
497       
498      if ( position[y]==C ) {
499        if ( _mate[y]!=INVALID ) {       //grow
500          ear.set(y,x);
501          Node w=_mate[y];
502          blossom.insert(w);
503          position.set(y,A);
504          position.set(w,D);
505          tree.insert(y);
506          tree.insert(w);
507          tree.join(y,blossom.find(x)); 
508          tree.join(w,y); 
509          Q.push(w);
510        } else {                      //augment
511          augment(x, ear, blossom, tree);
512          _mate.set(x,y);
513          _mate.set(y,x);
514          return true;
515        }
516      }
517    }
518    return false;
519  }
520
521  template <typename Graph>
522  void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear, 
523                                      UFE& blossom, UFE& tree, std::queue<Node>& Q) {
524    ear.set(top,bottom);
525    Node t=top;
526    while ( t!=middle ) {
527      Node u=_mate[t];
528      t=ear[u];
529      ear.set(t,u);
530    }
531    bottom=_mate[middle];
532    position.set(bottom,D);
533    Q.push(bottom);
534    top=ear[bottom];           
535    Node oldmiddle=middle;
536    middle=blossom.find(top);
537    tree.erase(bottom);
538    tree.erase(oldmiddle);
539    blossom.insert(bottom);
540    blossom.join(bottom, oldmiddle);
541    blossom.join(top, oldmiddle);
542  }
543
544  template <typename Graph>
545  void MaxMatching<Graph>::augment(Node x, typename Graph::NodeMap<Node>& ear, 
546                                   UFE& blossom, UFE& tree) {
547    Node v=_mate[x];
548    while ( v!=INVALID ) {
549       
550      Node u=ear[v];
551      _mate.set(v,u);
552      Node tmp=v;
553      v=_mate[u];
554      _mate.set(u,tmp);
555    }
556    typename UFE::ItemIt it;
557    for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {   
558      if ( position[it] == D ) {
559        typename UFE::ItemIt b_it;
560        for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) { 
561          position.set( b_it ,C);
562        }
563        blossom.eraseClass(it);
564      } else position.set( it ,C);
565    }
566    tree.eraseClass(x);
567
568  }
569
570  /// @}
571 
572} //END OF NAMESPACE LEMON
573
574#endif //LEMON_MAX_MATCHING_H
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