source: lemon-0.x/src/lemon/max_matching.h @ 1090:9e9195331ea6

/* -*- C++ -*-
 * src/lemon/max_matching.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_MAX_MATCHING_H
#define LEMON_MAX_MATCHING_H

#include <queue>
#include <invalid.h>
#include <unionfind.h>
#include <lemon/graph_utils.h>

///\ingroup galgs
///\file
///\brief Maximum matching algorithm.

namespace lemon {

  /// \addtogroup galgs
  /// @{

  ///Edmonds' alternating forest maximum matching algorithm.

  ///This class provides Edmonds' alternating forest matching
  ///algorithm. The starting matching (if any) can be passed to the
  ///algorithm using read-in functions \ref readNMapNode, \ref
  ///readNMapEdge or \ref readEMapBool depending on the container. The
  ///resulting maximum matching can be attained by write-out functions
  ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
  ///depending on the preferred container. 
  ///
  ///The dual side of a matching is a map of the nodes to
  ///MaxMatching::pos_enum, having values D, A and C showing the
  ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
  ///a graph with factor-critical components, the nodes in A form the
  ///barrier, and the nodes in C induce a graph having a perfect
  ///matching. This decomposition can be attained by calling \ref
  ///writePos after running the algorithm. 
  ///
  ///\param Graph The undirected graph type the algorithm runs on.
  ///
  ///\author Jacint Szabo  
  template <typename Graph>
  class MaxMatching {
    typedef typename Graph::Node Node;
    typedef typename Graph::Edge Edge;
    typedef typename Graph::UndirEdgeIt UndirEdgeIt;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::IncEdgeIt IncEdgeIt;

    typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;

  public:
    
    ///Indicates the Gallai-Edmonds decomposition of the graph.

    ///Indicates the Gallai-Edmonds decomposition of the graph, which
    ///shows an upper bound on the size of a maximum matching. The
    ///nodes with pos_enum \c D induce a graph with factor-critical
    ///components, the nodes in \c A form the canonical barrier, and the
    ///nodes in \c C induce a graph having a perfect matching. 
    enum pos_enum {
      D=0,
      A=1,
      C=2
    }; 

  private:

    static const int HEUR_density=2;
    const Graph& g;
    typename Graph::template NodeMap<Node> mate;
    typename Graph::template NodeMap<pos_enum> position;
     
  public:
    
    MaxMatching(const Graph& _g) : g(_g), mate(_g,INVALID), position(_g) {}

    ///Runs Edmonds' algorithm.

    ///Runs Edmonds' algorithm for sparse graphs (number of edges <
    ///2*number of nodes), and a heuristical Edmonds' algorithm with a
    ///heuristic of postponing shrinks for dense graphs. 
    inline void run();

    ///Runs Edmonds' algorithm.
    
    ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
    ///Edmonds' algorithm with a heuristic of postponing shrinks,
    ///giving a faster algorithm for dense graphs.  
    void runEdmonds( int heur );

    ///Finds a greedy matching starting from the actual matching.
    
    ///Starting form the actual matching stored, it finds a maximal
    ///greedy matching.
    void greedyMatching();

    ///Returns the size of the actual matching stored.

    ///Returns the size of the actual matching stored. After \ref
    ///run() it returns the size of a maximum matching in the graph.
    int size() const;

    ///Resets the actual matching to the empty matching.

    ///Resets the actual matching to the empty matching.  
    ///
    void resetMatching();

    ///Reads a matching from a \c Node map of \c Nodes.

    ///Reads a matching from a \c Node map of \c Nodes. This map must be \e
    ///symmetric, i.e. if \c map[u]==v then \c map[v]==u must hold, and
    ///\c uv will be an edge of the matching.
    template<typename NMapN>
    void readNMapNode(NMapN& map) {
      for(NodeIt v(g); v!=INVALID; ++v) {
        mate.set(v,map[v]);   
      } 
    } 
    
    ///Writes the stored matching to a \c Node map of \c Nodes.

    ///Writes the stored matching to a \c Node map of \c Nodes. The
    ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
    ///map[v]==u will hold, and now \c uv is an edge of the matching.
    template<typename NMapN>
    void writeNMapNode (NMapN& map) const {
      for(NodeIt v(g); v!=INVALID; ++v) {
        map.set(v,mate[v]);   
      } 
    } 

    ///Reads a matching from a \c Node map of \c Edges.

    ///Reads a matching from a \c Node map of incident \c Edges. This
    ///map must have the property that if \c G.target(map[u])==v then \c
    ///G.target(map[v])==u must hold, and now this edge is an edge of
    ///the matching.
    template<typename NMapE>
    void readNMapEdge(NMapE& map) {
     for(NodeIt v(g); v!=INVALID; ++v) {
        Edge e=map[v];
        if ( g.valid(e) )
          g.source(e) == v ? mate.set(v,g.target(e)) : mate.set(v,g.source(e)); 
      } 
    } 
    
    ///Writes the matching stored to a \c Node map of \c Edges.

    ///Writes the stored matching to a \c Node map of incident \c
    ///Edges. This map will have the property that if \c
    ///g.target(map[u])==v then \c g.target(map[v])==u holds, and now this
    ///edge is an edge of the matching.
    template<typename NMapE>
    void writeNMapEdge (NMapE& map)  const {
      typename Graph::template NodeMap<bool> todo(g,true); 
      for(NodeIt v(g); v!=INVALID; ++v) {
        if ( todo[v] && mate[v]!=INVALID ) {
          Node u=mate[v];
          for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
            if ( g.target(e) == u ) {
              map.set(u,e);
              map.set(v,e);
              todo.set(u,false);
              todo.set(v,false);
              break;
            }
          }
        }
      } 
    }


    ///Reads a matching from an \c Edge map of \c bools.
    
    ///Reads a matching from an \c Edge map of \c bools. This map must
    ///have the property that there are no two adjacent edges \c e, \c
    ///f with \c map[e]==map[f]==true. The edges \c e with \c
    ///map[e]==true form the matching.
    template<typename EMapB>
    void readEMapBool(EMapB& map) {
      for(UndirEdgeIt e(g); e!=INVALID; ++e) {
        if ( map[e] ) {
          Node u=g.source(e);     
          Node v=g.target(e);
          mate.set(u,v);
          mate.set(v,u);
        } 
      } 
    }


    ///Writes the matching stored to an \c Edge map of \c bools.

    ///Writes the matching stored to an \c Edge map of \c bools. This
    ///map will have the property that there are no two adjacent edges
    ///\c e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
    ///map[e]==true form the matching.
    template<typename EMapB>
    void writeEMapBool (EMapB& map) const {
      for(UndirEdgeIt e(g); e!=INVALID; ++e) map.set(e,false);

      typename Graph::template NodeMap<bool> todo(g,true); 
      for(NodeIt v(g); v!=INVALID; ++v) {
        if ( todo[v] && mate[v]!=INVALID ) {
          Node u=mate[v];
          for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
            if ( g.target(e) == u ) {
              map.set(e,true);
              todo.set(u,false);
              todo.set(v,false);
              break;
            }
          }
        }
      } 
    }


    ///Writes the canonical decomposition of the graph after running
    ///the algorithm.

    ///After calling any run methods of the class, it writes the
    ///Gallai-Edmonds canonical decomposition of the graph. \c map
    ///must be a node map of \ref pos_enum 's.
    template<typename NMapEnum>
    void writePos (NMapEnum& map) const {
      for(NodeIt v(g); v!=INVALID; ++v)  map.set(v,position[v]);
    }

  private: 

    void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
                    UFE& blossom, UFE& tree);

    void normShrink(Node v, typename Graph::NodeMap<Node>& ear,  
                    UFE& blossom, UFE& tree);

    bool noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,  
                      UFE& blossom, UFE& tree, std::queue<Node>& Q);

    void shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,  
                    UFE& blossom, UFE& tree, std::queue<Node>& Q);

    void augment(Node x, typename Graph::NodeMap<Node>& ear,  
                 UFE& blossom, UFE& tree);

  };


  // **********************************************************************
  //  IMPLEMENTATIONS
  // **********************************************************************


  template <typename Graph>
  void MaxMatching<Graph>::run() {
    if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) {
      greedyMatching();
      runEdmonds(0);
    } else runEdmonds(1);
  }


  template <typename Graph>
  void MaxMatching<Graph>::runEdmonds( int heur=1 ) {

    for(NodeIt v(g); v!=INVALID; ++v)
      position.set(v,C);      

    typename Graph::template NodeMap<Node> ear(g,INVALID); 
    //undefined for the base nodes of the blossoms (i.e. for the
    //representative elements of UFE blossom) and for the nodes in C
 
    typename UFE::MapType blossom_base(g);
    UFE blossom(blossom_base);
    typename UFE::MapType tree_base(g);
    UFE tree(tree_base);

    for(NodeIt v(g); v!=INVALID; ++v) {
      if ( position[v]==C && mate[v]==INVALID ) {
        blossom.insert(v);
        tree.insert(v); 
        position.set(v,D);
        if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
        else normShrink( v, ear, blossom, tree );
      }
    }
  }

    
  template <typename Graph>
  void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
                                      UFE& blossom, UFE& tree) {

    std::queue<Node> Q;   //queue of the totally unscanned nodes
    Q.push(v);  
    std::queue<Node> R;   
    //queue of the nodes which must be scanned for a possible shrink
      
    while ( !Q.empty() ) {
      Node x=Q.front();
      Q.pop();
      if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
      else R.push(x);
    }
      
    while ( !R.empty() ) {
      Node x=R.front();
      R.pop();
        
      for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
        Node y=g.target(e);

        if ( position[y] == D && blossom.find(x) != blossom.find(y) ) { 
          //x and y must be in the same tree
        
          typename Graph::template NodeMap<bool> path(g,false);

          Node b=blossom.find(x);
          path.set(b,true);
          b=mate[b];
          while ( b!=INVALID ) { 
            b=blossom.find(ear[b]);
            path.set(b,true);
            b=mate[b];
          } //going till the root
        
          Node top=y;
          Node middle=blossom.find(top);
          Node bottom=x;
          while ( !path[middle] )
            shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
                  
          Node base=middle;
          top=x;
          middle=blossom.find(top);
          bottom=y;
          Node blossom_base=blossom.find(base);
          while ( middle!=blossom_base )
            shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
                  
          blossom.makeRep(base);
        } // if shrink is needed

        while ( !Q.empty() ) {
          Node x=Q.front();
          Q.pop();
          if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
          else R.push(x);
        }
      } //for e
    } // while ( !R.empty() )
  }


  template <typename Graph>
  void MaxMatching<Graph>::normShrink(Node v, typename Graph::NodeMap<Node>& ear,  
                                      UFE& blossom, UFE& tree) {

    std::queue<Node> Q;   //queue of the unscanned nodes
    Q.push(v);  
    while ( !Q.empty() ) {

      Node x=Q.front();
      Q.pop();
        
      for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
        Node y=g.target(e);
              
        switch ( position[y] ) {
        case D:          //x and y must be in the same tree

          if ( blossom.find(x) != blossom.find(y) ) { //shrink
            typename Graph::template NodeMap<bool> path(g,false);
              
            Node b=blossom.find(x);
            path.set(b,true);
            b=mate[b];
            while ( b!=INVALID ) { 
              b=blossom.find(ear[b]);
              path.set(b,true);
              b=mate[b];
            } //going till the root
        
            Node top=y;
            Node middle=blossom.find(top);
            Node bottom=x;
            while ( !path[middle] )
              shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
                
            Node base=middle;
            top=x;
            middle=blossom.find(top);
            bottom=y;
            Node blossom_base=blossom.find(base);
            while ( middle!=blossom_base )
              shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
                
            blossom.makeRep(base);
          }
          break;
        case C:
          if ( mate[y]!=INVALID ) {   //grow

            ear.set(y,x);
            Node w=mate[y];
            blossom.insert(w);
            position.set(y,A); 
            position.set(w,D); 
            tree.insert(y);
            tree.insert(w);
            tree.join(y,blossom.find(x));  
            tree.join(w,y);  
            Q.push(w);
          } else {                 //augment  
            augment(x, ear, blossom, tree);
            mate.set(x,y);
            mate.set(y,x);
            return;
          } //if 
          break;
        default: break;
        }
      }
    }
  }

  template <typename Graph>
  void MaxMatching<Graph>::greedyMatching() {
    for(NodeIt v(g); v!=INVALID; ++v)
      if ( mate[v]==INVALID ) {
        for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
          Node y=g.target(e);
          if ( mate[y]==INVALID && y!=v ) {
            mate.set(v,y);
            mate.set(y,v);
            break;
          }
        }
      } 
  }
   
  template <typename Graph>
  int MaxMatching<Graph>::size() const {
    int s=0;
    for(NodeIt v(g); v!=INVALID; ++v) {
      if ( mate[v]!=INVALID ) {
        ++s;
      }
    }
    return (int)s/2;
  }

  template <typename Graph>
  void MaxMatching<Graph>::resetMatching() {
    for(NodeIt v(g); v!=INVALID; ++v)
      mate.set(v,INVALID);      
  }

  template <typename Graph>
  bool MaxMatching<Graph>::noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,  
                                        UFE& blossom, UFE& tree, std::queue<Node>& Q) {
    for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
      Node y=g.target(e);
        
      if ( position[y]==C ) {
        if ( mate[y]!=INVALID ) {       //grow
          ear.set(y,x);
          Node w=mate[y];
          blossom.insert(w);
          position.set(y,A);
          position.set(w,D);
          tree.insert(y);
          tree.insert(w);
          tree.join(y,blossom.find(x));  
          tree.join(w,y);  
          Q.push(w);
        } else {                      //augment 
          augment(x, ear, blossom, tree);
          mate.set(x,y);
          mate.set(y,x);
          return true;
        }
      }
    }
    return false;
  }

  template <typename Graph>
  void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,  
                                      UFE& blossom, UFE& tree, std::queue<Node>& Q) {
    ear.set(top,bottom);
    Node t=top;
    while ( t!=middle ) {
      Node u=mate[t];
      t=ear[u];
      ear.set(t,u);
    } 
    bottom=mate[middle];
    position.set(bottom,D);
    Q.push(bottom);
    top=ear[bottom];            
    Node oldmiddle=middle;
    middle=blossom.find(top);
    tree.erase(bottom);
    tree.erase(oldmiddle);
    blossom.insert(bottom);
    blossom.join(bottom, oldmiddle);
    blossom.join(top, oldmiddle);
  }

  template <typename Graph>
  void MaxMatching<Graph>::augment(Node x, typename Graph::NodeMap<Node>& ear,  
                                   UFE& blossom, UFE& tree) { 
    Node v=mate[x];
    while ( v!=INVALID ) {
        
      Node u=ear[v];
      mate.set(v,u);
      Node tmp=v;
      v=mate[u];
      mate.set(u,tmp);
    }
    typename UFE::ItemIt it;
    for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {   
      if ( position[it] == D ) {
        typename UFE::ItemIt b_it;
        for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {  
          position.set( b_it ,C);
        }
        blossom.eraseClass(it);
      } else position.set( it ,C);
    }
    tree.eraseClass(x);

  }

  /// @}
  
} //END OF NAMESPACE LEMON

#endif //EDMONDS_H