jacint@1077: /* -*- C++ -*-
jacint@1077:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@2553:  * Copyright (C) 2003-2008
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
jacint@1077:  *
jacint@1077:  * Permission to use, modify and distribute this software is granted
jacint@1077:  * provided that this copyright notice appears in all copies. For
jacint@1077:  * precise terms see the accompanying LICENSE file.
jacint@1077:  *
jacint@1077:  * This software is provided "AS IS" with no warranty of any kind,
jacint@1077:  * express or implied, and with no claim as to its suitability for any
jacint@1077:  * purpose.
jacint@1077:  *
jacint@1077:  */
jacint@1077: 
jacint@1077: #ifndef LEMON_MAX_MATCHING_H
jacint@1077: #define LEMON_MAX_MATCHING_H
jacint@1077: 
deba@2548: #include <vector>
jacint@1077: #include <queue>
deba@2548: #include <set>
deba@2548: 
deba@1993: #include <lemon/bits/invalid.h>
jacint@1093: #include <lemon/unionfind.h>
jacint@1077: #include <lemon/graph_utils.h>
deba@2548: #include <lemon/bin_heap.h>
jacint@1077: 
deba@2042: ///\ingroup matching
jacint@1077: ///\file
deba@2549: ///\brief Maximum matching algorithms in undirected graph.
jacint@1077: 
jacint@1077: namespace lemon {
jacint@1077: 
deba@2505:   ///\ingroup matching
deba@2548:   ///
deba@2505:   ///\brief Edmonds' alternating forest maximum matching algorithm.
deba@2505:   ///
jacint@1077:   ///This class provides Edmonds' alternating forest matching
jacint@1077:   ///algorithm. The starting matching (if any) can be passed to the
deba@2505:   ///algorithm using some of init functions.
jacint@1077:   ///
jacint@1077:   ///The dual side of a matching is a map of the nodes to
deba@2505:   ///MaxMatching::DecompType, having values \c D, \c A and \c C
deba@2505:   ///showing the Gallai-Edmonds decomposition of the graph. The nodes
deba@2505:   ///in \c D induce a graph with factor-critical components, the nodes
deba@2505:   ///in \c A form the barrier, and the nodes in \c C induce a graph
deba@2505:   ///having a perfect matching. This decomposition can be attained by
deba@2505:   ///calling \c decomposition() after running the algorithm.
jacint@1077:   ///
jacint@1077:   ///\param Graph The undirected graph type the algorithm runs on.
jacint@1077:   ///
jacint@1077:   ///\author Jacint Szabo  
jacint@1077:   template <typename Graph>
jacint@1077:   class MaxMatching {
jacint@1165: 
jacint@1165:   protected:
jacint@1165: 
jacint@1077:     typedef typename Graph::Node Node;
jacint@1077:     typedef typename Graph::Edge Edge;
klao@1909:     typedef typename Graph::UEdge UEdge;
klao@1909:     typedef typename Graph::UEdgeIt UEdgeIt;
jacint@1077:     typedef typename Graph::NodeIt NodeIt;
jacint@1077:     typedef typename Graph::IncEdgeIt IncEdgeIt;
jacint@1077: 
deba@2205:     typedef typename Graph::template NodeMap<int> UFECrossRef;
deba@2308:     typedef UnionFindEnum<UFECrossRef> UFE;
deba@2505:     typedef std::vector<Node> NV;
deba@2505: 
deba@2505:     typedef typename Graph::template NodeMap<int> EFECrossRef;
deba@2505:     typedef ExtendFindEnum<EFECrossRef> EFE;
jacint@1077: 
jacint@1077:   public:
jacint@1077:     
deba@2505:     ///\brief Indicates the Gallai-Edmonds decomposition of the graph.
deba@2505:     ///
jacint@1077:     ///Indicates the Gallai-Edmonds decomposition of the graph, which
jacint@1077:     ///shows an upper bound on the size of a maximum matching. The
deba@2505:     ///nodes with DecompType \c D induce a graph with factor-critical
jacint@1077:     ///components, the nodes in \c A form the canonical barrier, and the
jacint@1077:     ///nodes in \c C induce a graph having a perfect matching. 
deba@2505:     enum DecompType {
jacint@1077:       D=0,
jacint@1077:       A=1,
jacint@1077:       C=2
jacint@1077:     }; 
jacint@1077: 
jacint@1165:   protected:
jacint@1077: 
jacint@1077:     static const int HEUR_density=2;
jacint@1077:     const Graph& g;
jacint@1093:     typename Graph::template NodeMap<Node> _mate;
deba@2505:     typename Graph::template NodeMap<DecompType> position;
jacint@1077:      
jacint@1077:   public:
jacint@1077:     
deba@2505:     MaxMatching(const Graph& _g) 
deba@2505:       : g(_g), _mate(_g), position(_g) {}
jacint@1077: 
deba@2505:     ///\brief Sets the actual matching to the empty matching.
deba@2505:     ///
deba@2505:     ///Sets the actual matching to the empty matching.  
deba@2505:     ///
deba@2505:     void init() {
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,INVALID);      
deba@2505: 	position.set(v,C);
alpar@1587:       }
alpar@1587:     }
alpar@1587: 
deba@2505:     ///\brief Finds a greedy matching for initial matching.
deba@2505:     ///
deba@2505:     ///For initial matchig it finds a maximal greedy matching.
deba@2505:     void greedyInit() {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,INVALID);      
deba@2505: 	position.set(v,C);
deba@2505:       }
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v)
alpar@1587: 	if ( _mate[v]==INVALID ) {
alpar@1587: 	  for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
alpar@1587: 	    Node y=g.runningNode(e);
alpar@1587: 	    if ( _mate[y]==INVALID && y!=v ) {
alpar@1587: 	      _mate.set(v,y);
alpar@1587: 	      _mate.set(y,v);
alpar@1587: 	      break;
alpar@1587: 	    }
alpar@1587: 	  }
alpar@1587: 	} 
alpar@1587:     }
jacint@1077: 
deba@2505:     ///\brief Initialize the matching from each nodes' mate.
deba@2505:     ///
deba@2505:     ///Initialize the matching from a \c Node valued \c Node map. This
deba@2505:     ///map must be \e symmetric, i.e. if \c map[u]==v then \c
deba@2505:     ///map[v]==u must hold, and \c uv will be an edge of the initial
deba@2505:     ///matching.
deba@2505:     template <typename MateMap>
deba@2505:     void mateMapInit(MateMap& map) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,map[v]);
deba@2505: 	position.set(v,C);
deba@2505:       } 
deba@2505:     }
jacint@1077: 
deba@2505:     ///\brief Initialize the matching from a node map with the
deba@2505:     ///incident matching edges.
deba@2505:     ///
deba@2505:     ///Initialize the matching from an \c UEdge valued \c Node map. \c
deba@2505:     ///map[v] must be an \c UEdge incident to \c v. This map must have
deba@2505:     ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c
deba@2505:     ///g.oppositeNode(v,map[v])==u holds, and now some edge joining \c
deba@2505:     ///u to \c v will be an edge of the matching.
deba@2505:     template<typename MatchingMap>
deba@2505:     void matchingMapInit(MatchingMap& map) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	position.set(v,C);
deba@2505: 	UEdge e=map[v];
deba@2505: 	if ( e!=INVALID )
deba@2505: 	  _mate.set(v,g.oppositeNode(v,e));
deba@2505: 	else 
deba@2505: 	  _mate.set(v,INVALID);
deba@2505:       } 
deba@2505:     } 
deba@2505: 
deba@2505:     ///\brief Initialize the matching from the map containing the
deba@2505:     ///undirected matching edges.
deba@2505:     ///
deba@2505:     ///Initialize the matching from a \c bool valued \c UEdge map. This
deba@2505:     ///map must have the property that there are no two incident edges
deba@2505:     ///\c e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
deba@2505:     ///map[e]==true form the matching.
deba@2505:     template <typename MatchingMap>
deba@2505:     void matchingInit(MatchingMap& map) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,INVALID);      
deba@2505: 	position.set(v,C);
deba@2505:       }
deba@2505:       for(UEdgeIt e(g); e!=INVALID; ++e) {
deba@2505: 	if ( map[e] ) {
deba@2505: 	  Node u=g.source(e);	  
deba@2505: 	  Node v=g.target(e);
deba@2505: 	  _mate.set(u,v);
deba@2505: 	  _mate.set(v,u);
deba@2505: 	} 
deba@2505:       } 
deba@2505:     }
deba@2505: 
deba@2505: 
deba@2505:     ///\brief Runs Edmonds' algorithm.
deba@2505:     ///
deba@2505:     ///Runs Edmonds' algorithm for sparse graphs (number of edges <
deba@2505:     ///2*number of nodes), and a heuristical Edmonds' algorithm with a
deba@2505:     ///heuristic of postponing shrinks for dense graphs. 
deba@2505:     void run() {
deba@2505:       if (countUEdges(g) < HEUR_density * countNodes(g)) {
deba@2505: 	greedyInit();
deba@2505: 	startSparse();
deba@2505:       } else {
deba@2505: 	init();
deba@2505: 	startDense();
deba@2505:       }
deba@2505:     }
deba@2505: 
deba@2505: 
deba@2505:     ///\brief Starts Edmonds' algorithm.
deba@2505:     /// 
deba@2505:     ///If runs the original Edmonds' algorithm.  
deba@2505:     void startSparse() {
deba@2505:             
deba@2505:       typename Graph::template NodeMap<Node> ear(g,INVALID); 
deba@2505:       //undefined for the base nodes of the blossoms (i.e. for the
deba@2505:       //representative elements of UFE blossom) and for the nodes in C 
deba@2505:       
deba@2505:       UFECrossRef blossom_base(g);
deba@2505:       UFE blossom(blossom_base);
deba@2505:       NV rep(countNodes(g));
deba@2505: 
deba@2505:       EFECrossRef tree_base(g);
deba@2505:       EFE tree(tree_base);
deba@2505: 
deba@2505:       //If these UFE's would be members of the class then also
deba@2505:       //blossom_base and tree_base should be a member.
deba@2505:       
deba@2505:       //We build only one tree and the other vertices uncovered by the
deba@2505:       //matching belong to C. (They can be considered as singleton
deba@2505:       //trees.) If this tree can be augmented or no more
deba@2505:       //grow/augmentation/shrink is possible then we return to this
deba@2505:       //"for" cycle.
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	if (position[v]==C && _mate[v]==INVALID) {
deba@2505: 	  rep[blossom.insert(v)] = v;
deba@2505: 	  tree.insert(v); 
deba@2505: 	  position.set(v,D);
deba@2505: 	  normShrink(v, ear, blossom, rep, tree);
deba@2505: 	}
deba@2505:       }
deba@2505:     }
deba@2505: 
deba@2505:     ///\brief Starts Edmonds' algorithm.
deba@2505:     /// 
deba@2505:     ///It runs Edmonds' algorithm with a heuristic of postponing
deba@2505:     ///shrinks, giving a faster algorithm for dense graphs.
deba@2505:     void startDense() {
deba@2505:             
deba@2505:       typename Graph::template NodeMap<Node> ear(g,INVALID); 
deba@2505:       //undefined for the base nodes of the blossoms (i.e. for the
deba@2505:       //representative elements of UFE blossom) and for the nodes in C 
deba@2505:       
deba@2505:       UFECrossRef blossom_base(g);
deba@2505:       UFE blossom(blossom_base);
deba@2505:       NV rep(countNodes(g));
deba@2505: 
deba@2505:       EFECrossRef tree_base(g);
deba@2505:       EFE tree(tree_base);
deba@2505: 
deba@2505:       //If these UFE's would be members of the class then also
deba@2505:       //blossom_base and tree_base should be a member.
deba@2505:       
deba@2505:       //We build only one tree and the other vertices uncovered by the
deba@2505:       //matching belong to C. (They can be considered as singleton
deba@2505:       //trees.) If this tree can be augmented or no more
deba@2505:       //grow/augmentation/shrink is possible then we return to this
deba@2505:       //"for" cycle.
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	if ( position[v]==C && _mate[v]==INVALID ) {
deba@2505: 	  rep[blossom.insert(v)] = v;
deba@2505: 	  tree.insert(v); 
deba@2505: 	  position.set(v,D);
deba@2505: 	  lateShrink(v, ear, blossom, rep, tree);
deba@2505: 	}
deba@2505:       }
deba@2505:     }
deba@2505: 
deba@2505: 
deba@2505: 
deba@2505:     ///\brief Returns the size of the actual matching stored.
deba@2505:     ///
jacint@1077:     ///Returns the size of the actual matching stored. After \ref
jacint@1077:     ///run() it returns the size of a maximum matching in the graph.
alpar@1587:     int size() const {
alpar@1587:       int s=0;
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v) {
alpar@1587: 	if ( _mate[v]!=INVALID ) {
alpar@1587: 	  ++s;
alpar@1587: 	}
alpar@1587:       }
alpar@1587:       return s/2;
alpar@1587:     }
alpar@1587: 
jacint@1077: 
deba@2505:     ///\brief Returns the mate of a node in the actual matching.
jacint@1077:     ///
jacint@1093:     ///Returns the mate of a \c node in the actual matching. 
jacint@1093:     ///Returns INVALID if the \c node is not covered by the actual matching. 
deba@2505:     Node mate(const Node& node) const {
jacint@1093:       return _mate[node];
jacint@1093:     } 
jacint@1093: 
deba@2505:     ///\brief Returns the matching edge incident to the given node.
deba@2505:     ///
deba@2505:     ///Returns the matching edge of a \c node in the actual matching. 
deba@2505:     ///Returns INVALID if the \c node is not covered by the actual matching. 
deba@2505:     UEdge matchingEdge(const Node& node) const {
deba@2505:       if (_mate[node] == INVALID) return INVALID;
deba@2505:       Node n = node < _mate[node] ? node : _mate[node];
deba@2505:       for (IncEdgeIt e(g, n); e != INVALID; ++e) {
deba@2505: 	if (g.oppositeNode(n, e) == _mate[n]) {
deba@2505: 	  return e;
deba@2505: 	}
deba@2505:       }
deba@2505:       return INVALID;
deba@2505:     } 
jacint@1077: 
deba@2505:     /// \brief Returns the class of the node in the Edmonds-Gallai
deba@2505:     /// decomposition.
deba@2505:     ///
deba@2505:     /// Returns the class of the node in the Edmonds-Gallai
deba@2505:     /// decomposition.
deba@2505:     DecompType decomposition(const Node& n) {
deba@2505:       return position[n] == A;
deba@2505:     }
deba@2505: 
deba@2505:     /// \brief Returns true when the node is in the barrier.
deba@2505:     ///
deba@2505:     /// Returns true when the node is in the barrier.
deba@2505:     bool barrier(const Node& n) {
deba@2505:       return position[n] == A;
deba@2505:     }
jacint@1077:     
deba@2505:     ///\brief Gives back the matching in a \c Node of mates.
deba@2505:     ///
jacint@1165:     ///Writes the stored matching to a \c Node valued \c Node map. The
jacint@1077:     ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
jacint@1077:     ///map[v]==u will hold, and now \c uv is an edge of the matching.
deba@2505:     template <typename MateMap>
deba@2505:     void mateMap(MateMap& map) const {
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	map.set(v,_mate[v]);   
jacint@1077:       } 
jacint@1077:     } 
jacint@1077:     
deba@2505:     ///\brief Gives back the matching in an \c UEdge valued \c Node
deba@2505:     ///map.
deba@2505:     ///
klao@1909:     ///Writes the stored matching to an \c UEdge valued \c Node
klao@1909:     ///map. \c map[v] will be an \c UEdge incident to \c v. This
jacint@1165:     ///map will have the property that if \c g.oppositeNode(u,map[u])
jacint@1165:     ///== v then \c map[u]==map[v] holds, and now this edge is an edge
jacint@1165:     ///of the matching.
deba@2505:     template <typename MatchingMap>
deba@2505:     void matchingMap(MatchingMap& map)  const {
jacint@1077:       typename Graph::template NodeMap<bool> todo(g,true); 
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	if (_mate[v]!=INVALID && v < _mate[v]) {
jacint@1093: 	  Node u=_mate[v];
jacint@1077: 	  for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
klao@1158: 	    if ( g.runningNode(e) == u ) {
jacint@1077: 	      map.set(u,e);
jacint@1077: 	      map.set(v,e);
jacint@1077: 	      todo.set(u,false);
jacint@1077: 	      todo.set(v,false);
jacint@1077: 	      break;
jacint@1077: 	    }
jacint@1077: 	  }
jacint@1077: 	}
jacint@1077:       } 
jacint@1077:     }
jacint@1077: 
jacint@1077: 
deba@2505:     ///\brief Gives back the matching in a \c bool valued \c UEdge
deba@2505:     ///map.
deba@2505:     ///
jacint@1165:     ///Writes the matching stored to a \c bool valued \c Edge
jacint@1165:     ///map. This map will have the property that there are no two
jacint@1165:     ///incident edges \c e, \c f with \c map[e]==map[f]==true. The
jacint@1165:     ///edges \c e with \c map[e]==true form the matching.
deba@2505:     template<typename MatchingMap>
deba@2505:     void matching(MatchingMap& map) const {
klao@1909:       for(UEdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
jacint@1077: 
jacint@1077:       typename Graph::template NodeMap<bool> todo(g,true); 
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	if ( todo[v] && _mate[v]!=INVALID ) {
jacint@1093: 	  Node u=_mate[v];
jacint@1077: 	  for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
klao@1158: 	    if ( g.runningNode(e) == u ) {
jacint@1077: 	      map.set(e,true);
jacint@1077: 	      todo.set(u,false);
jacint@1077: 	      todo.set(v,false);
jacint@1077: 	      break;
jacint@1077: 	    }
jacint@1077: 	  }
jacint@1077: 	}
jacint@1077:       } 
jacint@1077:     }
jacint@1077: 
jacint@1077: 
deba@2505:     ///\brief Returns the canonical decomposition of the graph after running
jacint@1077:     ///the algorithm.
deba@2505:     ///
jacint@1090:     ///After calling any run methods of the class, it writes the
jacint@1090:     ///Gallai-Edmonds canonical decomposition of the graph. \c map
deba@2505:     ///must be a node map of \ref DecompType 's.
deba@2505:     template <typename DecompositionMap>
deba@2505:     void decomposition(DecompositionMap& map) const {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
deba@2505:     }
deba@2505: 
deba@2505:     ///\brief Returns a barrier on the nodes.
deba@2505:     ///
deba@2505:     ///After calling any run methods of the class, it writes a
deba@2505:     ///canonical barrier on the nodes. The odd component number of the
deba@2505:     ///remaining graph minus the barrier size is a lower bound for the
deba@2505:     ///uncovered nodes in the graph. The \c map must be a node map of
deba@2505:     ///bools.
deba@2505:     template <typename BarrierMap>
deba@2505:     void barrier(BarrierMap& barrier) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A);    
jacint@1077:     }
jacint@1077: 
jacint@1077:   private: 
jacint@1077: 
jacint@1165:  
jacint@1077:     void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		    UFE& blossom, NV& rep, EFE& tree) {
deba@2505:       //We have one tree which we grow, and also shrink but only if it
deba@2505:       //cannot be postponed. If we augment then we return to the "for"
deba@2505:       //cycle of runEdmonds().
deba@2505: 
deba@2505:       std::queue<Node> Q;   //queue of the totally unscanned nodes
deba@2505:       Q.push(v);  
deba@2505:       std::queue<Node> R;   
deba@2505:       //queue of the nodes which must be scanned for a possible shrink
deba@2505:       
deba@2505:       while ( !Q.empty() ) {
deba@2505: 	Node x=Q.front();
deba@2505: 	Q.pop();
deba@2505: 	for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
deba@2505: 	  Node y=g.runningNode(e);
deba@2505: 	  //growOrAugment grows if y is covered by the matching and
deba@2505: 	  //augments if not. In this latter case it returns 1.
deba@2505: 	  if (position[y]==C && 
deba@2505: 	      growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
deba@2505: 	}
deba@2505: 	R.push(x);
deba@2505:       }
deba@2505:       
deba@2505:       while ( !R.empty() ) {
deba@2505: 	Node x=R.front();
deba@2505: 	R.pop();
deba@2505: 	
deba@2505: 	for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
deba@2505: 	  Node y=g.runningNode(e);
deba@2505: 
deba@2505: 	  if ( position[y] == D && blossom.find(x) != blossom.find(y) )  
deba@2505: 	    //Recall that we have only one tree.
deba@2505: 	    shrink( x, y, ear, blossom, rep, tree, Q);	
deba@2505: 	
deba@2505: 	  while ( !Q.empty() ) {
deba@2505: 	    Node z=Q.front();
deba@2505: 	    Q.pop();
deba@2505: 	    for( IncEdgeIt f(g,z); f!= INVALID; ++f ) {
deba@2505: 	      Node w=g.runningNode(f);
deba@2505: 	      //growOrAugment grows if y is covered by the matching and
deba@2505: 	      //augments if not. In this latter case it returns 1.
deba@2505: 	      if (position[w]==C && 
deba@2505: 		  growOrAugment(w, z, ear, blossom, rep, tree, Q)) return;
deba@2505: 	    }
deba@2505: 	    R.push(z);
deba@2505: 	  }
deba@2505: 	} //for e
deba@2505:       } // while ( !R.empty() )
deba@2505:     }
jacint@1077: 
alpar@1234:     void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		    UFE& blossom, NV& rep, EFE& tree) {
deba@2505:       //We have one tree, which we grow and shrink. If we augment then we
deba@2505:       //return to the "for" cycle of runEdmonds().
deba@2505:     
deba@2505:       std::queue<Node> Q;   //queue of the unscanned nodes
deba@2505:       Q.push(v);  
deba@2505:       while ( !Q.empty() ) {
deba@2505: 
deba@2505: 	Node x=Q.front();
deba@2505: 	Q.pop();
deba@2505: 	
deba@2505: 	for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
deba@2505: 	  Node y=g.runningNode(e);
deba@2505: 	      
deba@2505: 	  switch ( position[y] ) {
deba@2505: 	  case D:          //x and y must be in the same tree
deba@2505: 	    if ( blossom.find(x) != blossom.find(y))
deba@2505: 	      //x and y are in the same tree
deba@2505: 	      shrink(x, y, ear, blossom, rep, tree, Q);
deba@2505: 	    break;
deba@2505: 	  case C:
deba@2505: 	    //growOrAugment grows if y is covered by the matching and
deba@2505: 	    //augments if not. In this latter case it returns 1.
deba@2505: 	    if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
deba@2505: 	    break;
deba@2505: 	  default: break;
deba@2505: 	  }
deba@2505: 	}
deba@2505:       }
deba@2505:     }
jacint@1077: 
jacint@2023:     void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) {
deba@2505:       //x and y are the two adjacent vertices in two blossoms.
deba@2505:    
deba@2505:       typename Graph::template NodeMap<bool> path(g,false);
deba@2505:     
deba@2505:       Node b=rep[blossom.find(x)];
deba@2505:       path.set(b,true);
deba@2505:       b=_mate[b];
deba@2505:       while ( b!=INVALID ) { 
deba@2505: 	b=rep[blossom.find(ear[b])];
deba@2505: 	path.set(b,true);
deba@2505: 	b=_mate[b];
deba@2505:       } //we go until the root through bases of blossoms and odd vertices
deba@2505:     
deba@2505:       Node top=y;
deba@2505:       Node middle=rep[blossom.find(top)];
deba@2505:       Node bottom=x;
deba@2505:       while ( !path[middle] )
deba@2505: 	shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
deba@2505:       //Until we arrive to a node on the path, we update blossom, tree
deba@2505:       //and the positions of the odd nodes.
deba@2505:     
deba@2505:       Node base=middle;
deba@2505:       top=x;
deba@2505:       middle=rep[blossom.find(top)];
deba@2505:       bottom=y;
deba@2505:       Node blossom_base=rep[blossom.find(base)];
deba@2505:       while ( middle!=blossom_base )
deba@2505: 	shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
deba@2505:       //Until we arrive to a node on the path, we update blossom, tree
deba@2505:       //and the positions of the odd nodes.
deba@2505:     
deba@2505:       rep[blossom.find(base)] = base;
deba@2505:     }
jacint@1077: 
alpar@1234:     void shrinkStep(Node& top, Node& middle, Node& bottom,
alpar@1234: 		    typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		    UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) {
deba@2505:       //We traverse a blossom and update everything.
deba@2505:     
deba@2505:       ear.set(top,bottom);
deba@2505:       Node t=top;
deba@2505:       while ( t!=middle ) {
deba@2505: 	Node u=_mate[t];
deba@2505: 	t=ear[u];
deba@2505: 	ear.set(t,u);
deba@2505:       } 
deba@2505:       bottom=_mate[middle];
deba@2505:       position.set(bottom,D);
deba@2505:       Q.push(bottom);
deba@2505:       top=ear[bottom];		
deba@2505:       Node oldmiddle=middle;
deba@2505:       middle=rep[blossom.find(top)];
deba@2505:       tree.erase(bottom);
deba@2505:       tree.erase(oldmiddle);
deba@2505:       blossom.insert(bottom);
deba@2505:       blossom.join(bottom, oldmiddle);
deba@2505:       blossom.join(top, oldmiddle);
deba@2505:     }
deba@2505: 
deba@2505: 
jacint@1077: 
jacint@2023:     bool growOrAugment(Node& y, Node& x, typename Graph::template 
deba@2505: 		       NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree, 
deba@2505: 		       std::queue<Node>& Q) {
deba@2505:       //x is in a blossom in the tree, y is outside. If y is covered by
deba@2505:       //the matching we grow, otherwise we augment. In this case we
deba@2505:       //return 1.
deba@2505:     
deba@2505:       if ( _mate[y]!=INVALID ) {       //grow
deba@2505: 	ear.set(y,x);
deba@2505: 	Node w=_mate[y];
deba@2505: 	rep[blossom.insert(w)] = w;
deba@2505: 	position.set(y,A);
deba@2505: 	position.set(w,D);
deba@2505: 	int t = tree.find(rep[blossom.find(x)]);
deba@2505: 	tree.insert(y,t);  
deba@2505: 	tree.insert(w,t);  
deba@2505: 	Q.push(w);
deba@2505:       } else {                      //augment 
deba@2505: 	augment(x, ear, blossom, rep, tree);
deba@2505: 	_mate.set(x,y);
deba@2505: 	_mate.set(y,x);
deba@2505: 	return true;
deba@2505:       }
deba@2505:       return false;
deba@2505:     }
jacint@2023: 
alpar@1234:     void augment(Node x, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		 UFE& blossom, NV& rep, EFE& tree) {
deba@2505:       Node v=_mate[x];
deba@2505:       while ( v!=INVALID ) {
deba@2505: 	
deba@2505: 	Node u=ear[v];
deba@2505: 	_mate.set(v,u);
deba@2505: 	Node tmp=v;
deba@2505: 	v=_mate[u];
deba@2505: 	_mate.set(u,tmp);
deba@2505:       }
deba@2505:       int y = tree.find(rep[blossom.find(x)]);
deba@2505:       for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) {   
deba@2505: 	if ( position[tit] == D ) {
deba@2505: 	  int b = blossom.find(tit);
deba@2505: 	  for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) { 
deba@2505: 	    position.set(bit, C);
deba@2505: 	  }
deba@2505: 	  blossom.eraseClass(b);
deba@2505: 	} else position.set(tit, C);
deba@2505:       }
deba@2505:       tree.eraseClass(y);
deba@2505: 
deba@2505:     }
jacint@1077: 
jacint@1077:   };
deba@2548: 
deba@2548:   /// \ingroup matching
deba@2548:   ///
deba@2548:   /// \brief Weighted matching in general undirected graphs
deba@2548:   ///
deba@2548:   /// This class provides an efficient implementation of Edmond's
deba@2548:   /// maximum weighted matching algorithm. The implementation is based
deba@2548:   /// on extensive use of priority queues and provides
deba@2548:   /// \f$O(nm\log(n))\f$ time complexity.
deba@2548:   ///
deba@2548:   /// The maximum weighted matching problem is to find undirected
deba@2548:   /// edges in the graph with maximum overall weight and no two of
deba@2548:   /// them shares their endpoints. The problem can be formulated with
deba@2548:   /// the next linear program: 
deba@2548:   /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
deba@2548:   ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f] 
deba@2548:   /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@2548:   /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@2548:   /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@2548:   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both endpoints in
deba@2548:   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
deba@2548:   /// the nodes.
deba@2548:   ///
deba@2548:   /// The algorithm calculates an optimal matching and a proof of the
deba@2548:   /// optimality. The solution of the dual problem can be used to check
deba@2548:   /// the result of the algorithm. The dual linear problem is the next:
deba@2548:   /// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f]
deba@2548:   /// \f[y_u \ge 0 \quad \forall u \in V\f]
deba@2548:   /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@2548:   /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
deba@2548:   ///
deba@2548:   /// The algorithm can be executed with \c run() or the \c init() and
deba@2548:   /// then the \c start() member functions. After it the matching can
deba@2548:   /// be asked with \c matching() or mate() functions. The dual
deba@2548:   /// solution can be get with \c nodeValue(), \c blossomNum() and \c
deba@2548:   /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
deba@2548:   /// "BlossomIt" nested class which is able to iterate on the nodes
deba@2548:   /// of a blossom. If the value type is integral then the dual
deba@2548:   /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
deba@2548:   ///
deba@2548:   /// \author Balazs Dezso
deba@2548:   template <typename _UGraph, 
deba@2548: 	    typename _WeightMap = typename _UGraph::template UEdgeMap<int> >
deba@2548:   class MaxWeightedMatching {
deba@2548:   public:
deba@2548: 
deba@2548:     typedef _UGraph UGraph;
deba@2548:     typedef _WeightMap WeightMap;
deba@2548:     typedef typename WeightMap::Value Value;
deba@2548: 
deba@2548:     /// \brief Scaling factor for dual solution
deba@2548:     ///
deba@2548:     /// Scaling factor for dual solution, it is equal to 4 or 1
deba@2548:     /// according to the value type.
deba@2548:     static const int dualScale = 
deba@2548:       std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@2548: 
deba@2548:     typedef typename UGraph::template NodeMap<typename UGraph::Edge> 
deba@2548:     MatchingMap;
deba@2548:     
deba@2548:   private:
deba@2548: 
deba@2548:     UGRAPH_TYPEDEFS(typename UGraph);
deba@2548: 
deba@2548:     typedef typename UGraph::template NodeMap<Value> NodePotential;
deba@2548:     typedef std::vector<Node> BlossomNodeList;
deba@2548: 
deba@2548:     struct BlossomVariable {
deba@2548:       int begin, end;
deba@2548:       Value value;
deba@2548:       
deba@2548:       BlossomVariable(int _begin, int _end, Value _value)
deba@2548:         : begin(_begin), end(_end), value(_value) {}
deba@2548: 
deba@2548:     };
deba@2548: 
deba@2548:     typedef std::vector<BlossomVariable> BlossomPotential;
deba@2548: 
deba@2548:     const UGraph& _ugraph;
deba@2548:     const WeightMap& _weight;
deba@2548: 
deba@2548:     MatchingMap* _matching;
deba@2548: 
deba@2548:     NodePotential* _node_potential;
deba@2548: 
deba@2548:     BlossomPotential _blossom_potential;
deba@2548:     BlossomNodeList _blossom_node_list;
deba@2548: 
deba@2548:     int _node_num;
deba@2548:     int _blossom_num;
deba@2548: 
deba@2548:     typedef typename UGraph::template NodeMap<int> NodeIntMap;
deba@2548:     typedef typename UGraph::template EdgeMap<int> EdgeIntMap;
deba@2548:     typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap;
deba@2548:     typedef IntegerMap<int> IntIntMap;
deba@2548: 
deba@2548:     enum Status {
deba@2548:       EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
deba@2548:     };
deba@2548: 
deba@2548:     typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
deba@2548:     struct BlossomData {
deba@2548:       int tree;
deba@2548:       Status status;
deba@2548:       Edge pred, next;
deba@2548:       Value pot, offset;
deba@2548:       Node base;
deba@2548:     };
deba@2548: 
deba@2548:     NodeIntMap *_blossom_index;
deba@2548:     BlossomSet *_blossom_set;
deba@2548:     IntegerMap<BlossomData>* _blossom_data;
deba@2548: 
deba@2548:     NodeIntMap *_node_index;
deba@2548:     EdgeIntMap *_node_heap_index;
deba@2548: 
deba@2548:     struct NodeData {
deba@2548:       
deba@2548:       NodeData(EdgeIntMap& node_heap_index) 
deba@2548: 	: heap(node_heap_index) {}
deba@2548:       
deba@2548:       int blossom;
deba@2548:       Value pot;
deba@2548:       BinHeap<Value, EdgeIntMap> heap;
deba@2548:       std::map<int, Edge> heap_index;
deba@2548:       
deba@2548:       int tree;
deba@2548:     };
deba@2548: 
deba@2548:     IntegerMap<NodeData>* _node_data;
deba@2548: 
deba@2548:     typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@2548: 
deba@2548:     IntIntMap *_tree_set_index;
deba@2548:     TreeSet *_tree_set;
deba@2548: 
deba@2548:     NodeIntMap *_delta1_index;
deba@2548:     BinHeap<Value, NodeIntMap> *_delta1;
deba@2548: 
deba@2548:     IntIntMap *_delta2_index;
deba@2548:     BinHeap<Value, IntIntMap> *_delta2;
deba@2548:     
deba@2548:     UEdgeIntMap *_delta3_index;
deba@2548:     BinHeap<Value, UEdgeIntMap> *_delta3;
deba@2548: 
deba@2548:     IntIntMap *_delta4_index;
deba@2548:     BinHeap<Value, IntIntMap> *_delta4;
deba@2548: 
deba@2548:     Value _delta_sum;
deba@2548: 
deba@2548:     void createStructures() {
deba@2548:       _node_num = countNodes(_ugraph); 
deba@2548:       _blossom_num = _node_num * 3 / 2;
deba@2548: 
deba@2548:       if (!_matching) {
deba@2548: 	_matching = new MatchingMap(_ugraph);
deba@2548:       }
deba@2548:       if (!_node_potential) {
deba@2548: 	_node_potential = new NodePotential(_ugraph);
deba@2548:       }
deba@2548:       if (!_blossom_set) {
deba@2548: 	_blossom_index = new NodeIntMap(_ugraph);
deba@2548: 	_blossom_set = new BlossomSet(*_blossom_index);
deba@2548: 	_blossom_data = new IntegerMap<BlossomData>(_blossom_num);
deba@2548:       }
deba@2548: 
deba@2548:       if (!_node_index) {
deba@2548: 	_node_index = new NodeIntMap(_ugraph);
deba@2548: 	_node_heap_index = new EdgeIntMap(_ugraph);
deba@2548: 	_node_data = new IntegerMap<NodeData>(_node_num, 
deba@2548: 					      NodeData(*_node_heap_index));
deba@2548:       }
deba@2548: 
deba@2548:       if (!_tree_set) {
deba@2548: 	_tree_set_index = new IntIntMap(_blossom_num);
deba@2548: 	_tree_set = new TreeSet(*_tree_set_index);
deba@2548:       }
deba@2548:       if (!_delta1) {
deba@2548: 	_delta1_index = new NodeIntMap(_ugraph);
deba@2548: 	_delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index);
deba@2548:       }
deba@2548:       if (!_delta2) {
deba@2548: 	_delta2_index = new IntIntMap(_blossom_num);
deba@2548: 	_delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@2548:       }
deba@2548:       if (!_delta3) {
deba@2548: 	_delta3_index = new UEdgeIntMap(_ugraph);
deba@2548: 	_delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index);
deba@2548:       }
deba@2548:       if (!_delta4) {
deba@2548: 	_delta4_index = new IntIntMap(_blossom_num);
deba@2548: 	_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void destroyStructures() {
deba@2548:       _node_num = countNodes(_ugraph); 
deba@2548:       _blossom_num = _node_num * 3 / 2;
deba@2548: 
deba@2548:       if (_matching) {
deba@2548: 	delete _matching;
deba@2548:       }
deba@2548:       if (_node_potential) {
deba@2548: 	delete _node_potential;
deba@2548:       }
deba@2548:       if (_blossom_set) {
deba@2548: 	delete _blossom_index;
deba@2548: 	delete _blossom_set;
deba@2548: 	delete _blossom_data;
deba@2548:       }
deba@2548: 
deba@2548:       if (_node_index) {
deba@2548: 	delete _node_index;
deba@2548: 	delete _node_heap_index;
deba@2548: 	delete _node_data;			      
deba@2548:       }
deba@2548: 
deba@2548:       if (_tree_set) {
deba@2548: 	delete _tree_set_index;
deba@2548: 	delete _tree_set;
deba@2548:       }
deba@2548:       if (_delta1) {
deba@2548: 	delete _delta1_index;
deba@2548: 	delete _delta1;
deba@2548:       }
deba@2548:       if (_delta2) {
deba@2548: 	delete _delta2_index;
deba@2548: 	delete _delta2;
deba@2548:       }
deba@2548:       if (_delta3) {
deba@2548: 	delete _delta3_index;
deba@2548: 	delete _delta3;
deba@2548:       }
deba@2548:       if (_delta4) {
deba@2548: 	delete _delta4_index;
deba@2548: 	delete _delta4;
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void matchedToEven(int blossom, int tree) {
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548: 
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	(*_blossom_data)[blossom].pot -= 
deba@2548: 	  2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); 
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 
deba@2548: 	_blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 
deba@2548: 	(*_node_data)[ni].heap.clear();
deba@2548: 	(*_node_data)[ni].heap_index.clear();
deba@2548: 
deba@2548: 	(*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@2548: 
deba@2548: 	_delta1->push(n, (*_node_data)[ni].pot);
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@2548: 	      _delta3->push(e, rw / 2);
deba@2548: 	    }
deba@2548: 	  } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@2548: 	      _delta3->push(e, rw);
deba@2548: 	    }	    
deba@2548: 	  } else {
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[vi].heap_index.find(tree);	  
deba@2548: 
deba@2548: 	    if (it != (*_node_data)[vi].heap_index.end()) {
deba@2548: 	      if ((*_node_data)[vi].heap[it->second] > rw) {
deba@2548: 		(*_node_data)[vi].heap.replace(it->second, e);
deba@2548: 		(*_node_data)[vi].heap.decrease(e, rw);
deba@2548: 		it->second = e;
deba@2548: 	      }
deba@2548: 	    } else {
deba@2548: 	      (*_node_data)[vi].heap.push(e, rw);
deba@2548: 	      (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@2548: 	    }
deba@2548: 
deba@2548: 	    if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@2548: 	      _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@2548: 
deba@2548: 	      if ((*_blossom_data)[vb].status == MATCHED) {
deba@2548: 		if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@2548: 		  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@2548: 			       (*_blossom_data)[vb].offset);
deba@2548: 		} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@2548: 			   (*_blossom_data)[vb].offset){
deba@2548: 		  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@2548: 				   (*_blossom_data)[vb].offset);
deba@2548: 		}
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:       (*_blossom_data)[blossom].offset = 0;
deba@2548:     }
deba@2548: 
deba@2548:     void matchedToOdd(int blossom) {
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548:       (*_blossom_data)[blossom].offset += _delta_sum;
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	_delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + 
deba@2548: 		     (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void evenToMatched(int blossom, int tree) {
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	(*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 	(*_node_data)[ni].pot -= _delta_sum;
deba@2548: 
deba@2548: 	_delta1->erase(n);
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if (vb == blossom) {
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 	  } else if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 
deba@2548: 	    int vt = _tree_set->find(vb);
deba@2548: 	    
deba@2548: 	    if (vt != tree) {
deba@2548: 
deba@2548: 	      Edge r = _ugraph.oppositeEdge(e);
deba@2548: 
deba@2548: 	      typename std::map<int, Edge>::iterator it = 
deba@2548: 		(*_node_data)[ni].heap_index.find(vt);	  
deba@2548: 
deba@2548: 	      if (it != (*_node_data)[ni].heap_index.end()) {
deba@2548: 		if ((*_node_data)[ni].heap[it->second] > rw) {
deba@2548: 		  (*_node_data)[ni].heap.replace(it->second, r);
deba@2548: 		  (*_node_data)[ni].heap.decrease(r, rw);
deba@2548: 		  it->second = r;
deba@2548: 		}
deba@2548: 	      } else {
deba@2548: 		(*_node_data)[ni].heap.push(r, rw);
deba@2548: 		(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@2548: 	      }
deba@2548: 	      
deba@2548: 	      if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@2548: 		_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@2548: 		
deba@2548: 		if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@2548: 		  _delta2->push(blossom, _blossom_set->classPrio(blossom) - 
deba@2548: 			       (*_blossom_data)[blossom].offset);
deba@2548: 		} else if ((*_delta2)[blossom] > 
deba@2548: 			   _blossom_set->classPrio(blossom) - 
deba@2548: 			   (*_blossom_data)[blossom].offset){
deba@2548: 		  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@2548: 				   (*_blossom_data)[blossom].offset);
deba@2548: 		}
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	    
deba@2548: 	  } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	  
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[vi].heap_index.find(tree);
deba@2548: 
deba@2548: 	    if (it != (*_node_data)[vi].heap_index.end()) {
deba@2548: 	      (*_node_data)[vi].heap.erase(it->second);
deba@2548: 	      (*_node_data)[vi].heap_index.erase(it);
deba@2548: 	      if ((*_node_data)[vi].heap.empty()) {
deba@2548: 		_blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@2548: 	      } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@2548: 		_blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@2548: 	      }
deba@2548: 	      
deba@2548: 	      if ((*_blossom_data)[vb].status == MATCHED) {
deba@2548: 		if (_blossom_set->classPrio(vb) == 
deba@2548: 		    std::numeric_limits<Value>::max()) {
deba@2548: 		  _delta2->erase(vb);
deba@2548: 		} else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@2548: 			   (*_blossom_data)[vb].offset) {
deba@2548: 		  _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@2548: 				   (*_blossom_data)[vb].offset);
deba@2548: 		}
deba@2548: 	      }	
deba@2548: 	    }	
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void oddToMatched(int blossom) {
deba@2548:       (*_blossom_data)[blossom].offset -= _delta_sum;
deba@2548: 
deba@2548:       if (_blossom_set->classPrio(blossom) != 
deba@2548: 	  std::numeric_limits<Value>::max()) {
deba@2548: 	_delta2->push(blossom, _blossom_set->classPrio(blossom) - 
deba@2548: 		       (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548: 
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	_delta4->erase(blossom);
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void oddToEven(int blossom, int tree) {
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	_delta4->erase(blossom);
deba@2548: 	(*_blossom_data)[blossom].pot -= 
deba@2548: 	  2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); 
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 
deba@2548: 	_blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@2548: 
deba@2548: 	(*_node_data)[ni].heap.clear();
deba@2548: 	(*_node_data)[ni].heap_index.clear();
deba@2548: 	(*_node_data)[ni].pot += 
deba@2548: 	  2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@2548: 
deba@2548: 	_delta1->push(n, (*_node_data)[ni].pot);
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@2548: 	      _delta3->push(e, rw / 2);
deba@2548: 	    }
deba@2548: 	  } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@2548: 	      _delta3->push(e, rw);
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	  
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[vi].heap_index.find(tree);	  
deba@2548: 
deba@2548: 	    if (it != (*_node_data)[vi].heap_index.end()) {
deba@2548: 	      if ((*_node_data)[vi].heap[it->second] > rw) {
deba@2548: 		(*_node_data)[vi].heap.replace(it->second, e);
deba@2548: 		(*_node_data)[vi].heap.decrease(e, rw);
deba@2548: 		it->second = e;
deba@2548: 	      }
deba@2548: 	    } else {
deba@2548: 	      (*_node_data)[vi].heap.push(e, rw);
deba@2548: 	      (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@2548: 	    }
deba@2548: 
deba@2548: 	    if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@2548: 	      _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@2548: 
deba@2548: 	      if ((*_blossom_data)[vb].status == MATCHED) {
deba@2548: 		if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@2548: 		  _delta2->push(vb, _blossom_set->classPrio(vb) - 
deba@2548: 			       (*_blossom_data)[vb].offset);
deba@2548: 		} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - 
deba@2548: 			   (*_blossom_data)[vb].offset) {
deba@2548: 		  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@2548: 				   (*_blossom_data)[vb].offset);
deba@2548: 		}
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:       (*_blossom_data)[blossom].offset = 0;
deba@2548:     }
deba@2548: 
deba@2548: 
deba@2548:     void matchedToUnmatched(int blossom) {
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); 
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 
deba@2548: 	_blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@2548: 
deba@2548: 	(*_node_data)[ni].heap.clear();
deba@2548: 	(*_node_data)[ni].heap_index.clear();
deba@2548: 
deba@2548: 	for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.target(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@2548: 	      _delta3->push(e, rw);
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void unmatchedToMatched(int blossom) {
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if (vb == blossom) {
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 	  } else if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 
deba@2548: 	    int vt = _tree_set->find(vb);
deba@2548: 	    
deba@2548: 	    Edge r = _ugraph.oppositeEdge(e);
deba@2548: 	    
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[ni].heap_index.find(vt);	  
deba@2548: 	    
deba@2548: 	    if (it != (*_node_data)[ni].heap_index.end()) {
deba@2548: 	      if ((*_node_data)[ni].heap[it->second] > rw) {
deba@2548: 		(*_node_data)[ni].heap.replace(it->second, r);
deba@2548: 		(*_node_data)[ni].heap.decrease(r, rw);
deba@2548: 		it->second = r;
deba@2548: 	      }
deba@2548: 	    } else {
deba@2548: 	      (*_node_data)[ni].heap.push(r, rw);
deba@2548: 	      (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@2548: 	    }
deba@2548: 	      
deba@2548: 	    if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@2548: 	      _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@2548: 	      
deba@2548: 	      if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@2548: 		_delta2->push(blossom, _blossom_set->classPrio(blossom) - 
deba@2548: 			     (*_blossom_data)[blossom].offset);
deba@2548: 	      } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
deba@2548: 			 (*_blossom_data)[blossom].offset){
deba@2548: 		_delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@2548: 				 (*_blossom_data)[blossom].offset);
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	    
deba@2548: 	  } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void alternatePath(int even, int tree) {
deba@2548:       int odd;
deba@2548: 
deba@2548:       evenToMatched(even, tree);
deba@2548:       (*_blossom_data)[even].status = MATCHED;
deba@2548: 
deba@2548:       while ((*_blossom_data)[even].pred != INVALID) {
deba@2548: 	odd = _blossom_set->find(_ugraph.target((*_blossom_data)[even].pred));
deba@2548: 	(*_blossom_data)[odd].status = MATCHED;
deba@2548: 	oddToMatched(odd);
deba@2548: 	(*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@2548:       
deba@2548: 	even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred));
deba@2548: 	(*_blossom_data)[even].status = MATCHED;
deba@2548: 	evenToMatched(even, tree);
deba@2548: 	(*_blossom_data)[even].next = 
deba@2548: 	  _ugraph.oppositeEdge((*_blossom_data)[odd].pred);
deba@2548:       }
deba@2548:       
deba@2548:     }
deba@2548: 
deba@2548:     void destroyTree(int tree) {
deba@2548:       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@2548: 	if ((*_blossom_data)[b].status == EVEN) {
deba@2548: 	  (*_blossom_data)[b].status = MATCHED;
deba@2548: 	  evenToMatched(b, tree);
deba@2548: 	} else if ((*_blossom_data)[b].status == ODD) {
deba@2548: 	  (*_blossom_data)[b].status = MATCHED;
deba@2548: 	  oddToMatched(b);
deba@2548: 	}
deba@2548:       }
deba@2548:       _tree_set->eraseClass(tree);
deba@2548:     }
deba@2548:     
deba@2548: 
deba@2548:     void unmatchNode(const Node& node) {
deba@2548:       int blossom = _blossom_set->find(node);
deba@2548:       int tree = _tree_set->find(blossom);
deba@2548: 
deba@2548:       alternatePath(blossom, tree);
deba@2548:       destroyTree(tree);
deba@2548: 
deba@2548:       (*_blossom_data)[blossom].status = UNMATCHED;
deba@2548:       (*_blossom_data)[blossom].base = node;
deba@2548:       matchedToUnmatched(blossom);
deba@2548:     }
deba@2548: 
deba@2548: 
deba@2548:     void augmentOnEdge(const UEdge& edge) {
deba@2548:       
deba@2548:       int left = _blossom_set->find(_ugraph.source(edge));
deba@2548:       int right = _blossom_set->find(_ugraph.target(edge));
deba@2548: 
deba@2548:       if ((*_blossom_data)[left].status == EVEN) {
deba@2548: 	int left_tree = _tree_set->find(left);
deba@2548: 	alternatePath(left, left_tree);
deba@2548: 	destroyTree(left_tree);
deba@2548:       } else {
deba@2548: 	(*_blossom_data)[left].status = MATCHED;
deba@2548: 	unmatchedToMatched(left);
deba@2548:       }
deba@2548: 
deba@2548:       if ((*_blossom_data)[right].status == EVEN) {
deba@2548: 	int right_tree = _tree_set->find(right);
deba@2548: 	alternatePath(right, right_tree);
deba@2548: 	destroyTree(right_tree);
deba@2548:       } else {
deba@2548: 	(*_blossom_data)[right].status = MATCHED;
deba@2548: 	unmatchedToMatched(right);
deba@2548:       }
deba@2548: 
deba@2548:       (*_blossom_data)[left].next = _ugraph.direct(edge, true);
deba@2548:       (*_blossom_data)[right].next = _ugraph.direct(edge, false);
deba@2548:     }
deba@2548: 
deba@2548:     void extendOnEdge(const Edge& edge) {
deba@2548:       int base = _blossom_set->find(_ugraph.target(edge));
deba@2548:       int tree = _tree_set->find(base);
deba@2548:       
deba@2548:       int odd = _blossom_set->find(_ugraph.source(edge));
deba@2548:       _tree_set->insert(odd, tree);
deba@2548:       (*_blossom_data)[odd].status = ODD;
deba@2548:       matchedToOdd(odd);
deba@2548:       (*_blossom_data)[odd].pred = edge;
deba@2548: 
deba@2548:       int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next));
deba@2548:       (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@2548:       _tree_set->insert(even, tree);
deba@2548:       (*_blossom_data)[even].status = EVEN;
deba@2548:       matchedToEven(even, tree);
deba@2548:     }
deba@2548:     
deba@2548:     void shrinkOnEdge(const UEdge& uedge, int tree) {
deba@2548:       int nca = -1;
deba@2548:       std::vector<int> left_path, right_path;
deba@2548: 
deba@2548:       {
deba@2548: 	std::set<int> left_set, right_set;
deba@2548: 	int left = _blossom_set->find(_ugraph.source(uedge));
deba@2548: 	left_path.push_back(left);
deba@2548: 	left_set.insert(left);
deba@2548: 
deba@2548: 	int right = _blossom_set->find(_ugraph.target(uedge));
deba@2548: 	right_path.push_back(right);
deba@2548: 	right_set.insert(right);
deba@2548: 
deba@2548: 	while (true) {
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[left].pred == INVALID) break;
deba@2548: 
deba@2548: 	  left = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred));
deba@2548: 	  left_path.push_back(left);
deba@2548: 	  left = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred));
deba@2548: 	  left_path.push_back(left);
deba@2548: 
deba@2548: 	  left_set.insert(left);
deba@2548: 
deba@2548: 	  if (right_set.find(left) != right_set.end()) {
deba@2548: 	    nca = left;
deba@2548: 	    break;
deba@2548: 	  }
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[right].pred == INVALID) break;
deba@2548: 
deba@2548: 	  right = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred));
deba@2548: 	  right_path.push_back(right);
deba@2548: 	  right = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred));
deba@2548: 	  right_path.push_back(right);
deba@2548: 
deba@2548: 	  right_set.insert(right);
deba@2548:  
deba@2548: 	  if (left_set.find(right) != left_set.end()) {
deba@2548: 	    nca = right;
deba@2548: 	    break;
deba@2548: 	  }
deba@2548: 
deba@2548: 	}
deba@2548: 
deba@2548: 	if (nca == -1) {
deba@2548: 	  if ((*_blossom_data)[left].pred == INVALID) {
deba@2548: 	    nca = right;
deba@2548: 	    while (left_set.find(nca) == left_set.end()) {
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      right_path.push_back(nca);
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      right_path.push_back(nca);
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	    nca = left;
deba@2548: 	    while (right_set.find(nca) == right_set.end()) {
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      left_path.push_back(nca);
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      left_path.push_back(nca);
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548: 
deba@2548:       std::vector<int> subblossoms;
deba@2548:       Edge prev;
deba@2548: 
deba@2548:       prev = _ugraph.direct(uedge, true);
deba@2548:       for (int i = 0; left_path[i] != nca; i += 2) {
deba@2548: 	subblossoms.push_back(left_path[i]);
deba@2548: 	(*_blossom_data)[left_path[i]].next = prev;
deba@2548: 	_tree_set->erase(left_path[i]);
deba@2548: 
deba@2548: 	subblossoms.push_back(left_path[i + 1]);
deba@2548: 	(*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@2548: 	oddToEven(left_path[i + 1], tree);
deba@2548: 	_tree_set->erase(left_path[i + 1]);
deba@2548: 	prev = _ugraph.oppositeEdge((*_blossom_data)[left_path[i + 1]].pred);
deba@2548:       }
deba@2548: 
deba@2548:       int k = 0;
deba@2548:       while (right_path[k] != nca) ++k;
deba@2548: 
deba@2548:       subblossoms.push_back(nca);
deba@2548:       (*_blossom_data)[nca].next = prev;
deba@2548:       
deba@2548:       for (int i = k - 2; i >= 0; i -= 2) {
deba@2548: 	subblossoms.push_back(right_path[i + 1]);
deba@2548: 	(*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@2548: 	oddToEven(right_path[i + 1], tree);
deba@2548: 	_tree_set->erase(right_path[i + 1]);
deba@2548: 
deba@2548: 	(*_blossom_data)[right_path[i + 1]].next = 
deba@2548: 	  (*_blossom_data)[right_path[i + 1]].pred;
deba@2548: 
deba@2548: 	subblossoms.push_back(right_path[i]);
deba@2548: 	_tree_set->erase(right_path[i]);
deba@2548:       }
deba@2548: 
deba@2548:       int surface = 
deba@2548: 	_blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@2548: 
deba@2548:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@2548: 	if (!_blossom_set->trivial(subblossoms[i])) {
deba@2548: 	  (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@2548: 	}
deba@2548: 	(*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@2548:       }
deba@2548: 
deba@2548:       (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@2548:       (*_blossom_data)[surface].offset = 0;
deba@2548:       (*_blossom_data)[surface].status = EVEN;
deba@2548:       (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@2548:       (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@2548: 
deba@2548:       _tree_set->insert(surface, tree);
deba@2548:       _tree_set->erase(nca);
deba@2548:     }
deba@2548: 
deba@2548:     void splitBlossom(int blossom) {
deba@2548:       Edge next = (*_blossom_data)[blossom].next; 
deba@2548:       Edge pred = (*_blossom_data)[blossom].pred;
deba@2548: 
deba@2548:       int tree = _tree_set->find(blossom);
deba@2548: 
deba@2548:       (*_blossom_data)[blossom].status = MATCHED;
deba@2548:       oddToMatched(blossom);
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548: 
deba@2548:       std::vector<int> subblossoms;
deba@2548:       _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@2548: 
deba@2548:       Value offset = (*_blossom_data)[blossom].offset;
deba@2548:       int b = _blossom_set->find(_ugraph.source(pred));
deba@2548:       int d = _blossom_set->find(_ugraph.source(next));
deba@2548:       
deba@2549:       int ib = -1, id = -1;
deba@2548:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@2548: 	if (subblossoms[i] == b) ib = i;
deba@2548: 	if (subblossoms[i] == d) id = i;
deba@2548: 
deba@2548: 	(*_blossom_data)[subblossoms[i]].offset = offset;
deba@2548: 	if (!_blossom_set->trivial(subblossoms[i])) {
deba@2548: 	  (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@2548: 	}
deba@2548: 	if (_blossom_set->classPrio(subblossoms[i]) != 
deba@2548: 	    std::numeric_limits<Value>::max()) {
deba@2548: 	  _delta2->push(subblossoms[i], 
deba@2548: 			_blossom_set->classPrio(subblossoms[i]) - 
deba@2548: 			(*_blossom_data)[subblossoms[i]].offset);
deba@2548: 	}
deba@2548:       }
deba@2548:       
deba@2548:       if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@2548: 	for (int i = (id + 1) % subblossoms.size(); 
deba@2548: 	     i != ib; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  (*_blossom_data)[sb].next = 
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 	}
deba@2548: 
deba@2548: 	for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@2548: 
deba@2548: 	  (*_blossom_data)[sb].status = ODD;
deba@2548: 	  matchedToOdd(sb);
deba@2548: 	  _tree_set->insert(sb, tree);
deba@2548: 	  (*_blossom_data)[sb].pred = pred;
deba@2548: 	  (*_blossom_data)[sb].next = 
deba@2548: 			   _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 	  
deba@2548: 	  pred = (*_blossom_data)[ub].next;
deba@2548:       
deba@2548: 	  (*_blossom_data)[tb].status = EVEN;
deba@2548: 	  matchedToEven(tb, tree);
deba@2548: 	  _tree_set->insert(tb, tree);
deba@2548: 	  (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@2548: 	}
deba@2548:       
deba@2548: 	(*_blossom_data)[subblossoms[id]].status = ODD;
deba@2548: 	matchedToOdd(subblossoms[id]);
deba@2548: 	_tree_set->insert(subblossoms[id], tree);
deba@2548: 	(*_blossom_data)[subblossoms[id]].next = next;
deba@2548: 	(*_blossom_data)[subblossoms[id]].pred = pred;
deba@2548:       
deba@2548:       } else {
deba@2548: 
deba@2548: 	for (int i = (ib + 1) % subblossoms.size(); 
deba@2548: 	     i != id; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  (*_blossom_data)[sb].next = 
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 	}	
deba@2548: 
deba@2548: 	for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@2548: 
deba@2548: 	  (*_blossom_data)[sb].status = ODD;
deba@2548: 	  matchedToOdd(sb);
deba@2548: 	  _tree_set->insert(sb, tree);
deba@2548: 	  (*_blossom_data)[sb].next = next; 
deba@2548: 	  (*_blossom_data)[sb].pred =
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 
deba@2548: 	  (*_blossom_data)[tb].status = EVEN;
deba@2548: 	  matchedToEven(tb, tree);
deba@2548: 	  _tree_set->insert(tb, tree);
deba@2548: 	  (*_blossom_data)[tb].pred =
deba@2548: 	    (*_blossom_data)[tb].next = 
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[ub].next);
deba@2548: 	  next = (*_blossom_data)[ub].next;
deba@2548: 	}
deba@2548: 
deba@2548: 	(*_blossom_data)[subblossoms[ib]].status = ODD;
deba@2548: 	matchedToOdd(subblossoms[ib]);
deba@2548: 	_tree_set->insert(subblossoms[ib], tree);
deba@2548: 	(*_blossom_data)[subblossoms[ib]].next = next;
deba@2548: 	(*_blossom_data)[subblossoms[ib]].pred = pred;
deba@2548:       }
deba@2548:       _tree_set->erase(blossom);
deba@2548:     }
deba@2548: 
deba@2548:     void extractBlossom(int blossom, const Node& base, const Edge& matching) {
deba@2548:       if (_blossom_set->trivial(blossom)) {
deba@2548: 	int bi = (*_node_index)[base];
deba@2548: 	Value pot = (*_node_data)[bi].pot;
deba@2548: 
deba@2548: 	_matching->set(base, matching);
deba@2548: 	_blossom_node_list.push_back(base);
deba@2548: 	_node_potential->set(base, pot);
deba@2548:       } else {
deba@2548: 
deba@2548: 	Value pot = (*_blossom_data)[blossom].pot;
deba@2548: 	int bn = _blossom_node_list.size();
deba@2548: 	
deba@2548: 	std::vector<int> subblossoms;
deba@2548: 	_blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@2548: 	int b = _blossom_set->find(base);
deba@2548: 	int ib = -1;
deba@2548: 	for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@2548: 	  if (subblossoms[i] == b) { ib = i; break; }
deba@2548: 	}
deba@2548: 	
deba@2548: 	for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@2548: 	  int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@2548: 	  int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@2548: 	  
deba@2548: 	  Edge m = (*_blossom_data)[tb].next;
deba@2548: 	  extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m));
deba@2548: 	  extractBlossom(tb, _ugraph.source(m), m);
deba@2548: 	}
deba@2548: 	extractBlossom(subblossoms[ib], base, matching);      
deba@2548: 	
deba@2548: 	int en = _blossom_node_list.size();
deba@2548: 	
deba@2548: 	_blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void extractMatching() {
deba@2548:       std::vector<int> blossoms;
deba@2548:       for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@2548: 	blossoms.push_back(c);
deba@2548:       }
deba@2548: 
deba@2548:       for (int i = 0; i < int(blossoms.size()); ++i) {
deba@2548: 	if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
deba@2548: 
deba@2548: 	  Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@2548: 	  (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@2548: 	  for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); 
deba@2548: 	       n != INVALID; ++n) {
deba@2548: 	    (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@2548: 	  }
deba@2548: 
deba@2548: 	  Edge matching = (*_blossom_data)[blossoms[i]].next;
deba@2548: 	  Node base = _ugraph.source(matching);
deba@2548: 	  extractBlossom(blossoms[i], base, matching);
deba@2548: 	} else {
deba@2548: 	  Node base = (*_blossom_data)[blossoms[i]].base;	  
deba@2548: 	  extractBlossom(blossoms[i], base, INVALID);
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548:     
deba@2548:   public:
deba@2548: 
deba@2548:     /// \brief Constructor
deba@2548:     ///
deba@2548:     /// Constructor.
deba@2548:     MaxWeightedMatching(const UGraph& ugraph, const WeightMap& weight)
deba@2548:       : _ugraph(ugraph), _weight(weight), _matching(0),
deba@2548: 	_node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@2548: 	_node_num(0), _blossom_num(0),
deba@2548: 
deba@2548: 	_blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@2548: 	_node_index(0), _node_heap_index(0), _node_data(0),
deba@2548: 	_tree_set_index(0), _tree_set(0),
deba@2548: 
deba@2548: 	_delta1_index(0), _delta1(0),
deba@2548: 	_delta2_index(0), _delta2(0),
deba@2548: 	_delta3_index(0), _delta3(0), 
deba@2548: 	_delta4_index(0), _delta4(0),
deba@2548: 
deba@2548: 	_delta_sum() {}
deba@2548: 
deba@2548:     ~MaxWeightedMatching() {
deba@2548:       destroyStructures();
deba@2548:     }
deba@2548: 
deba@2548:     /// \name Execution control 
deba@2548:     /// The simplest way to execute the algorithm is to use the member
deba@2548:     /// \c run() member function.
deba@2548: 
deba@2548:     ///@{
deba@2548: 
deba@2548:     /// \brief Initialize the algorithm
deba@2548:     ///
deba@2548:     /// Initialize the algorithm
deba@2548:     void init() {
deba@2548:       createStructures();
deba@2548: 
deba@2548:       for (EdgeIt e(_ugraph); e != INVALID; ++e) {
deba@2548: 	_node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP);
deba@2548:       }
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2548: 	_delta1_index->set(n, _delta1->PRE_HEAP);
deba@2548:       }
deba@2548:       for (UEdgeIt e(_ugraph); e != INVALID; ++e) {
deba@2548: 	_delta3_index->set(e, _delta3->PRE_HEAP);
deba@2548:       }
deba@2548:       for (int i = 0; i < _blossom_num; ++i) {
deba@2548: 	_delta2_index->set(i, _delta2->PRE_HEAP);
deba@2548: 	_delta4_index->set(i, _delta4->PRE_HEAP);
deba@2548:       }
deba@2548: 
deba@2548:       int index = 0;
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2548: 	Value max = 0;
deba@2548: 	for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  if (_ugraph.target(e) == n) continue;
deba@2548: 	  if ((dualScale * _weight[e]) / 2 > max) {
deba@2548: 	    max = (dualScale * _weight[e]) / 2;
deba@2548: 	  }
deba@2548: 	}
deba@2548: 	_node_index->set(n, index);
deba@2548: 	(*_node_data)[index].pot = max;
deba@2548: 	_delta1->push(n, max);
deba@2548: 	int blossom = 
deba@2548: 	  _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@2548: 
deba@2548: 	_tree_set->insert(blossom);
deba@2548: 
deba@2548: 	(*_blossom_data)[blossom].status = EVEN;
deba@2548: 	(*_blossom_data)[blossom].pred = INVALID;
deba@2548: 	(*_blossom_data)[blossom].next = INVALID;
deba@2548: 	(*_blossom_data)[blossom].pot = 0;
deba@2548: 	(*_blossom_data)[blossom].offset = 0;
deba@2548: 	++index;
deba@2548:       }
deba@2548:       for (UEdgeIt e(_ugraph); e != INVALID; ++e) {
deba@2548: 	int si = (*_node_index)[_ugraph.source(e)];
deba@2548: 	int ti = (*_node_index)[_ugraph.target(e)];
deba@2548: 	if (_ugraph.source(e) != _ugraph.target(e)) {
deba@2548: 	  _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - 
deba@2548: 			    dualScale * _weight[e]) / 2);
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Starts the algorithm
deba@2548:     ///
deba@2548:     /// Starts the algorithm
deba@2548:     void start() {
deba@2548:       enum OpType {
deba@2548: 	D1, D2, D3, D4
deba@2548:       };
deba@2548: 
deba@2548:       int unmatched = _node_num;
deba@2548:       while (unmatched > 0) {
deba@2548: 	Value d1 = !_delta1->empty() ? 
deba@2548: 	  _delta1->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	Value d2 = !_delta2->empty() ? 
deba@2548: 	  _delta2->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	Value d3 = !_delta3->empty() ? 
deba@2548: 	  _delta3->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	Value d4 = !_delta4->empty() ? 
deba@2548: 	  _delta4->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	_delta_sum = d1; OpType ot = D1;
deba@2548: 	if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
deba@2548: 	if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@2548: 	if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@2548: 
deba@2548: 	
deba@2548: 	switch (ot) {
deba@2548: 	case D1:
deba@2548: 	  {
deba@2548: 	    Node n = _delta1->top();
deba@2548: 	    unmatchNode(n);
deba@2548: 	    --unmatched;
deba@2548: 	  }
deba@2548: 	  break;
deba@2548: 	case D2:
deba@2548: 	  {
deba@2548: 	    int blossom = _delta2->top();
deba@2548: 	    Node n = _blossom_set->classTop(blossom);
deba@2548: 	    Edge e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@2548: 	    extendOnEdge(e);
deba@2548: 	  }
deba@2548: 	  break;
deba@2548: 	case D3:
deba@2548: 	  {
deba@2548: 	    UEdge e = _delta3->top();
deba@2548: 	    
deba@2548: 	    int left_blossom = _blossom_set->find(_ugraph.source(e));
deba@2548: 	    int right_blossom = _blossom_set->find(_ugraph.target(e));
deba@2548: 	  
deba@2548: 	    if (left_blossom == right_blossom) {
deba@2548: 	      _delta3->pop();
deba@2548: 	    } else {
deba@2548: 	      int left_tree;
deba@2548: 	      if ((*_blossom_data)[left_blossom].status == EVEN) {
deba@2548: 		left_tree = _tree_set->find(left_blossom);
deba@2548: 	      } else {
deba@2548: 		left_tree = -1;
deba@2548: 		++unmatched;
deba@2548: 	      }
deba@2548: 	      int right_tree;
deba@2548: 	      if ((*_blossom_data)[right_blossom].status == EVEN) {
deba@2548: 		right_tree = _tree_set->find(right_blossom);
deba@2548: 	      } else {
deba@2548: 		right_tree = -1;
deba@2548: 		++unmatched;
deba@2548: 	      }
deba@2548: 	    
deba@2548: 	      if (left_tree == right_tree) {
deba@2548: 		shrinkOnEdge(e, left_tree);
deba@2548: 	      } else {
deba@2548: 		augmentOnEdge(e);
deba@2548: 		unmatched -= 2;
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  } break;
deba@2548: 	case D4:
deba@2548: 	  splitBlossom(_delta4->top());
deba@2548: 	  break;
deba@2548: 	}
deba@2548:       }
deba@2548:       extractMatching();
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Runs %MaxWeightedMatching algorithm.
deba@2548:     ///
deba@2548:     /// This method runs the %MaxWeightedMatching algorithm.
deba@2548:     ///
deba@2548:     /// \note mwm.run() is just a shortcut of the following code.
deba@2548:     /// \code
deba@2548:     ///   mwm.init();
deba@2548:     ///   mwm.start();
deba@2548:     /// \endcode
deba@2548:     void run() {
deba@2548:       init();
deba@2548:       start();
deba@2548:     }
deba@2548: 
deba@2548:     /// @}
deba@2548: 
deba@2548:     /// \name Primal solution
deba@2548:     /// Functions for get the primal solution, ie. the matching.
deba@2548:     
deba@2548:     /// @{
deba@2548: 
deba@2548:     /// \brief Returns the matching value.
deba@2548:     ///
deba@2548:     /// Returns the matching value.
deba@2548:     Value matchingValue() const {
deba@2548:       Value sum = 0;
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2548: 	if ((*_matching)[n] != INVALID) {
deba@2548: 	  sum += _weight[(*_matching)[n]];
deba@2548: 	}
deba@2548:       }
deba@2548:       return sum /= 2;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns true when the edge is in the matching.
deba@2548:     ///
deba@2548:     /// Returns true when the edge is in the matching.
deba@2548:     bool matching(const UEdge& edge) const {
deba@2548:       return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true);
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the incident matching edge.
deba@2548:     ///
deba@2548:     /// Returns the incident matching edge from given node. If the
deba@2548:     /// node is not matched then it gives back \c INVALID.
deba@2548:     Edge matching(const Node& node) const {
deba@2548:       return (*_matching)[node];
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the mate of the node.
deba@2548:     ///
deba@2548:     /// Returns the adjancent node in a mathcing edge. If the node is
deba@2548:     /// not matched then it gives back \c INVALID.
deba@2548:     Node mate(const Node& node) const {
deba@2548:       return (*_matching)[node] != INVALID ?
deba@2548: 	_ugraph.target((*_matching)[node]) : INVALID;
deba@2548:     }
deba@2548: 
deba@2548:     /// @}
deba@2548: 
deba@2548:     /// \name Dual solution
deba@2548:     /// Functions for get the dual solution.
deba@2548:     
deba@2548:     /// @{
deba@2548: 
deba@2548:     /// \brief Returns the value of the dual solution.
deba@2548:     ///
deba@2548:     /// Returns the value of the dual solution. It should be equal to
deba@2548:     /// the primal value scaled by \ref dualScale "dual scale".
deba@2548:     Value dualValue() const {
deba@2548:       Value sum = 0;
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2548: 	sum += nodeValue(n);
deba@2548:       }
deba@2548:       for (int i = 0; i < blossomNum(); ++i) {
deba@2548:         sum += blossomValue(i) * (blossomSize(i) / 2);
deba@2548:       }
deba@2548:       return sum;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the value of the node.
deba@2548:     ///
deba@2548:     /// Returns the the value of the node.
deba@2548:     Value nodeValue(const Node& n) const {
deba@2548:       return (*_node_potential)[n];
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the number of the blossoms in the basis.
deba@2548:     ///
deba@2548:     /// Returns the number of the blossoms in the basis.
deba@2548:     /// \see BlossomIt
deba@2548:     int blossomNum() const {
deba@2548:       return _blossom_potential.size();
deba@2548:     }
deba@2548: 
deba@2548: 
deba@2548:     /// \brief Returns the number of the nodes in the blossom.
deba@2548:     ///
deba@2548:     /// Returns the number of the nodes in the blossom.
deba@2548:     int blossomSize(int k) const {
deba@2548:       return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the value of the blossom.
deba@2548:     ///
deba@2548:     /// Returns the the value of the blossom.
deba@2548:     /// \see BlossomIt
deba@2548:     Value blossomValue(int k) const {
deba@2548:       return _blossom_potential[k].value;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Lemon iterator for get the items of the blossom.
deba@2548:     ///
deba@2548:     /// Lemon iterator for get the nodes of the blossom. This class
deba@2548:     /// provides a common style lemon iterator which gives back a
deba@2548:     /// subset of the nodes.
deba@2548:     class BlossomIt {
deba@2548:     public:
deba@2548: 
deba@2548:       /// \brief Constructor.
deba@2548:       ///
deba@2548:       /// Constructor for get the nodes of the variable. 
deba@2548:       BlossomIt(const MaxWeightedMatching& algorithm, int variable) 
deba@2548:         : _algorithm(&algorithm)
deba@2548:       {
deba@2548:         _index = _algorithm->_blossom_potential[variable].begin;
deba@2548:         _last = _algorithm->_blossom_potential[variable].end;
deba@2548:       }
deba@2548: 
deba@2548:       /// \brief Invalid constructor.
deba@2548:       ///
deba@2548:       /// Invalid constructor.
deba@2548:       BlossomIt(Invalid) : _index(-1) {}
deba@2548: 
deba@2548:       /// \brief Conversion to node.
deba@2548:       ///
deba@2548:       /// Conversion to node.
deba@2548:       operator Node() const { 
deba@2548:         return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
deba@2548:       }
deba@2548: 
deba@2548:       /// \brief Increment operator.
deba@2548:       ///
deba@2548:       /// Increment operator.
deba@2548:       BlossomIt& operator++() {
deba@2548:         ++_index;
deba@2548:         if (_index == _last) {
deba@2548:           _index = -1;
deba@2548:         }
deba@2548:         return *this; 
deba@2548:       }
deba@2548: 
deba@2548:       bool operator==(const BlossomIt& it) const { 
deba@2548:         return _index == it._index; 
deba@2548:       }
deba@2548:       bool operator!=(const BlossomIt& it) const { 
deba@2548:         return _index != it._index;
deba@2548:       }
deba@2548: 
deba@2548:     private:
deba@2548:       const MaxWeightedMatching* _algorithm;
deba@2548:       int _last;
deba@2548:       int _index;
deba@2548:     };
deba@2548: 
deba@2548:     /// @}
deba@2548:     
deba@2548:   };
deba@2548: 
deba@2548:   /// \ingroup matching
deba@2548:   ///
deba@2548:   /// \brief Weighted perfect matching in general undirected graphs
deba@2548:   ///
deba@2548:   /// This class provides an efficient implementation of Edmond's
deba@2548:   /// maximum weighted perfecr matching algorithm. The implementation
deba@2548:   /// is based on extensive use of priority queues and provides
deba@2548:   /// \f$O(nm\log(n))\f$ time complexity.
deba@2548:   ///
deba@2548:   /// The maximum weighted matching problem is to find undirected
deba@2548:   /// edges in the graph with maximum overall weight and no two of
deba@2548:   /// them shares their endpoints and covers all nodes. The problem
deba@2548:   /// can be formulated with the next linear program:
deba@2548:   /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
deba@2548:   ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f] 
deba@2548:   /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@2548:   /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@2548:   /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@2548:   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both endpoints in
deba@2548:   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
deba@2548:   /// the nodes.
deba@2548:   ///
deba@2548:   /// The algorithm calculates an optimal matching and a proof of the
deba@2548:   /// optimality. The solution of the dual problem can be used to check
deba@2548:   /// the result of the algorithm. The dual linear problem is the next:
deba@2548:   /// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f]
deba@2548:   /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@2548:   /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
deba@2548:   ///
deba@2548:   /// The algorithm can be executed with \c run() or the \c init() and
deba@2548:   /// then the \c start() member functions. After it the matching can
deba@2548:   /// be asked with \c matching() or mate() functions. The dual
deba@2548:   /// solution can be get with \c nodeValue(), \c blossomNum() and \c
deba@2548:   /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
deba@2548:   /// "BlossomIt" nested class which is able to iterate on the nodes
deba@2548:   /// of a blossom. If the value type is integral then the dual
deba@2548:   /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
deba@2548:   ///
deba@2548:   /// \author Balazs Dezso
deba@2548:   template <typename _UGraph, 
deba@2548: 	    typename _WeightMap = typename _UGraph::template UEdgeMap<int> >
deba@2548:   class MaxWeightedPerfectMatching {
deba@2548:   public:
deba@2548: 
deba@2548:     typedef _UGraph UGraph;
deba@2548:     typedef _WeightMap WeightMap;
deba@2548:     typedef typename WeightMap::Value Value;
deba@2548: 
deba@2548:     /// \brief Scaling factor for dual solution
deba@2548:     ///
deba@2548:     /// Scaling factor for dual solution, it is equal to 4 or 1
deba@2548:     /// according to the value type.
deba@2548:     static const int dualScale = 
deba@2548:       std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@2548: 
deba@2548:     typedef typename UGraph::template NodeMap<typename UGraph::Edge> 
deba@2548:     MatchingMap;
deba@2548:     
deba@2548:   private:
deba@2548: 
deba@2548:     UGRAPH_TYPEDEFS(typename UGraph);
deba@2548: 
deba@2548:     typedef typename UGraph::template NodeMap<Value> NodePotential;
deba@2548:     typedef std::vector<Node> BlossomNodeList;
deba@2548: 
deba@2548:     struct BlossomVariable {
deba@2548:       int begin, end;
deba@2548:       Value value;
deba@2548:       
deba@2548:       BlossomVariable(int _begin, int _end, Value _value)
deba@2548:         : begin(_begin), end(_end), value(_value) {}
deba@2548: 
deba@2548:     };
deba@2548: 
deba@2548:     typedef std::vector<BlossomVariable> BlossomPotential;
deba@2548: 
deba@2548:     const UGraph& _ugraph;
deba@2548:     const WeightMap& _weight;
deba@2548: 
deba@2548:     MatchingMap* _matching;
deba@2548: 
deba@2548:     NodePotential* _node_potential;
deba@2548: 
deba@2548:     BlossomPotential _blossom_potential;
deba@2548:     BlossomNodeList _blossom_node_list;
deba@2548: 
deba@2548:     int _node_num;
deba@2548:     int _blossom_num;
deba@2548: 
deba@2548:     typedef typename UGraph::template NodeMap<int> NodeIntMap;
deba@2548:     typedef typename UGraph::template EdgeMap<int> EdgeIntMap;
deba@2548:     typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap;
deba@2548:     typedef IntegerMap<int> IntIntMap;
deba@2548: 
deba@2548:     enum Status {
deba@2548:       EVEN = -1, MATCHED = 0, ODD = 1
deba@2548:     };
deba@2548: 
deba@2548:     typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
deba@2548:     struct BlossomData {
deba@2548:       int tree;
deba@2548:       Status status;
deba@2548:       Edge pred, next;
deba@2548:       Value pot, offset;
deba@2548:     };
deba@2548: 
deba@2548:     NodeIntMap *_blossom_index;
deba@2548:     BlossomSet *_blossom_set;
deba@2548:     IntegerMap<BlossomData>* _blossom_data;
deba@2548: 
deba@2548:     NodeIntMap *_node_index;
deba@2548:     EdgeIntMap *_node_heap_index;
deba@2548: 
deba@2548:     struct NodeData {
deba@2548:       
deba@2548:       NodeData(EdgeIntMap& node_heap_index) 
deba@2548: 	: heap(node_heap_index) {}
deba@2548:       
deba@2548:       int blossom;
deba@2548:       Value pot;
deba@2548:       BinHeap<Value, EdgeIntMap> heap;
deba@2548:       std::map<int, Edge> heap_index;
deba@2548:       
deba@2548:       int tree;
deba@2548:     };
deba@2548: 
deba@2548:     IntegerMap<NodeData>* _node_data;
deba@2548: 
deba@2548:     typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@2548: 
deba@2548:     IntIntMap *_tree_set_index;
deba@2548:     TreeSet *_tree_set;
deba@2548: 
deba@2548:     IntIntMap *_delta2_index;
deba@2548:     BinHeap<Value, IntIntMap> *_delta2;
deba@2548:     
deba@2548:     UEdgeIntMap *_delta3_index;
deba@2548:     BinHeap<Value, UEdgeIntMap> *_delta3;
deba@2548: 
deba@2548:     IntIntMap *_delta4_index;
deba@2548:     BinHeap<Value, IntIntMap> *_delta4;
deba@2548: 
deba@2548:     Value _delta_sum;
deba@2548: 
deba@2548:     void createStructures() {
deba@2548:       _node_num = countNodes(_ugraph); 
deba@2548:       _blossom_num = _node_num * 3 / 2;
deba@2548: 
deba@2548:       if (!_matching) {
deba@2548: 	_matching = new MatchingMap(_ugraph);
deba@2548:       }
deba@2548:       if (!_node_potential) {
deba@2548: 	_node_potential = new NodePotential(_ugraph);
deba@2548:       }
deba@2548:       if (!_blossom_set) {
deba@2548: 	_blossom_index = new NodeIntMap(_ugraph);
deba@2548: 	_blossom_set = new BlossomSet(*_blossom_index);
deba@2548: 	_blossom_data = new IntegerMap<BlossomData>(_blossom_num);
deba@2548:       }
deba@2548: 
deba@2548:       if (!_node_index) {
deba@2548: 	_node_index = new NodeIntMap(_ugraph);
deba@2548: 	_node_heap_index = new EdgeIntMap(_ugraph);
deba@2548: 	_node_data = new IntegerMap<NodeData>(_node_num, 
deba@2548: 					      NodeData(*_node_heap_index));
deba@2548:       }
deba@2548: 
deba@2548:       if (!_tree_set) {
deba@2548: 	_tree_set_index = new IntIntMap(_blossom_num);
deba@2548: 	_tree_set = new TreeSet(*_tree_set_index);
deba@2548:       }
deba@2548:       if (!_delta2) {
deba@2548: 	_delta2_index = new IntIntMap(_blossom_num);
deba@2548: 	_delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@2548:       }
deba@2548:       if (!_delta3) {
deba@2548: 	_delta3_index = new UEdgeIntMap(_ugraph);
deba@2548: 	_delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index);
deba@2548:       }
deba@2548:       if (!_delta4) {
deba@2548: 	_delta4_index = new IntIntMap(_blossom_num);
deba@2548: 	_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void destroyStructures() {
deba@2548:       _node_num = countNodes(_ugraph); 
deba@2548:       _blossom_num = _node_num * 3 / 2;
deba@2548: 
deba@2548:       if (_matching) {
deba@2548: 	delete _matching;
deba@2548:       }
deba@2548:       if (_node_potential) {
deba@2548: 	delete _node_potential;
deba@2548:       }
deba@2548:       if (_blossom_set) {
deba@2548: 	delete _blossom_index;
deba@2548: 	delete _blossom_set;
deba@2548: 	delete _blossom_data;
deba@2548:       }
deba@2548: 
deba@2548:       if (_node_index) {
deba@2548: 	delete _node_index;
deba@2548: 	delete _node_heap_index;
deba@2548: 	delete _node_data;			      
deba@2548:       }
deba@2548: 
deba@2548:       if (_tree_set) {
deba@2548: 	delete _tree_set_index;
deba@2548: 	delete _tree_set;
deba@2548:       }
deba@2548:       if (_delta2) {
deba@2548: 	delete _delta2_index;
deba@2548: 	delete _delta2;
deba@2548:       }
deba@2548:       if (_delta3) {
deba@2548: 	delete _delta3_index;
deba@2548: 	delete _delta3;
deba@2548:       }
deba@2548:       if (_delta4) {
deba@2548: 	delete _delta4_index;
deba@2548: 	delete _delta4;
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void matchedToEven(int blossom, int tree) {
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548: 
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	(*_blossom_data)[blossom].pot -= 
deba@2548: 	  2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); 
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 
deba@2548: 	_blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 
deba@2548: 	(*_node_data)[ni].heap.clear();
deba@2548: 	(*_node_data)[ni].heap_index.clear();
deba@2548: 
deba@2548: 	(*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@2548: 	      _delta3->push(e, rw / 2);
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[vi].heap_index.find(tree);	  
deba@2548: 
deba@2548: 	    if (it != (*_node_data)[vi].heap_index.end()) {
deba@2548: 	      if ((*_node_data)[vi].heap[it->second] > rw) {
deba@2548: 		(*_node_data)[vi].heap.replace(it->second, e);
deba@2548: 		(*_node_data)[vi].heap.decrease(e, rw);
deba@2548: 		it->second = e;
deba@2548: 	      }
deba@2548: 	    } else {
deba@2548: 	      (*_node_data)[vi].heap.push(e, rw);
deba@2548: 	      (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@2548: 	    }
deba@2548: 
deba@2548: 	    if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@2548: 	      _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@2548: 
deba@2548: 	      if ((*_blossom_data)[vb].status == MATCHED) {
deba@2548: 		if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@2548: 		  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@2548: 			       (*_blossom_data)[vb].offset);
deba@2548: 		} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@2548: 			   (*_blossom_data)[vb].offset){
deba@2548: 		  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@2548: 				   (*_blossom_data)[vb].offset);
deba@2548: 		}
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:       (*_blossom_data)[blossom].offset = 0;
deba@2548:     }
deba@2548: 
deba@2548:     void matchedToOdd(int blossom) {
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548:       (*_blossom_data)[blossom].offset += _delta_sum;
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	_delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + 
deba@2548: 		     (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void evenToMatched(int blossom, int tree) {
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	(*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 	(*_node_data)[ni].pot -= _delta_sum;
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if (vb == blossom) {
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 	  } else if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 
deba@2548: 	    if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@2548: 	      _delta3->erase(e);
deba@2548: 	    }
deba@2548: 
deba@2548: 	    int vt = _tree_set->find(vb);
deba@2548: 	    
deba@2548: 	    if (vt != tree) {
deba@2548: 
deba@2548: 	      Edge r = _ugraph.oppositeEdge(e);
deba@2548: 
deba@2548: 	      typename std::map<int, Edge>::iterator it = 
deba@2548: 		(*_node_data)[ni].heap_index.find(vt);	  
deba@2548: 
deba@2548: 	      if (it != (*_node_data)[ni].heap_index.end()) {
deba@2548: 		if ((*_node_data)[ni].heap[it->second] > rw) {
deba@2548: 		  (*_node_data)[ni].heap.replace(it->second, r);
deba@2548: 		  (*_node_data)[ni].heap.decrease(r, rw);
deba@2548: 		  it->second = r;
deba@2548: 		}
deba@2548: 	      } else {
deba@2548: 		(*_node_data)[ni].heap.push(r, rw);
deba@2548: 		(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@2548: 	      }
deba@2548: 	      
deba@2548: 	      if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@2548: 		_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@2548: 		
deba@2548: 		if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@2548: 		  _delta2->push(blossom, _blossom_set->classPrio(blossom) - 
deba@2548: 			       (*_blossom_data)[blossom].offset);
deba@2548: 		} else if ((*_delta2)[blossom] > 
deba@2548: 			   _blossom_set->classPrio(blossom) - 
deba@2548: 			   (*_blossom_data)[blossom].offset){
deba@2548: 		  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@2548: 				   (*_blossom_data)[blossom].offset);
deba@2548: 		}
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	  
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[vi].heap_index.find(tree);
deba@2548: 
deba@2548: 	    if (it != (*_node_data)[vi].heap_index.end()) {
deba@2548: 	      (*_node_data)[vi].heap.erase(it->second);
deba@2548: 	      (*_node_data)[vi].heap_index.erase(it);
deba@2548: 	      if ((*_node_data)[vi].heap.empty()) {
deba@2548: 		_blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@2548: 	      } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@2548: 		_blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@2548: 	      }
deba@2548: 	      
deba@2548: 	      if ((*_blossom_data)[vb].status == MATCHED) {
deba@2548: 		if (_blossom_set->classPrio(vb) == 
deba@2548: 		    std::numeric_limits<Value>::max()) {
deba@2548: 		  _delta2->erase(vb);
deba@2548: 		} else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@2548: 			   (*_blossom_data)[vb].offset) {
deba@2548: 		  _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@2548: 				   (*_blossom_data)[vb].offset);
deba@2548: 		}
deba@2548: 	      }	
deba@2548: 	    }	
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void oddToMatched(int blossom) {
deba@2548:       (*_blossom_data)[blossom].offset -= _delta_sum;
deba@2548: 
deba@2548:       if (_blossom_set->classPrio(blossom) != 
deba@2548: 	  std::numeric_limits<Value>::max()) {
deba@2548: 	_delta2->push(blossom, _blossom_set->classPrio(blossom) - 
deba@2548: 		       (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548: 
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	_delta4->erase(blossom);
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void oddToEven(int blossom, int tree) {
deba@2548:       if (!_blossom_set->trivial(blossom)) {
deba@2548: 	_delta4->erase(blossom);
deba@2548: 	(*_blossom_data)[blossom].pot -= 
deba@2548: 	  2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@2548:       }
deba@2548: 
deba@2548:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); 
deba@2548: 	   n != INVALID; ++n) {
deba@2548: 	int ni = (*_node_index)[n];
deba@2548: 
deba@2548: 	_blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@2548: 
deba@2548: 	(*_node_data)[ni].heap.clear();
deba@2548: 	(*_node_data)[ni].heap_index.clear();
deba@2548: 	(*_node_data)[ni].pot += 
deba@2548: 	  2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@2548: 
deba@2548: 	for (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  Node v = _ugraph.source(e);
deba@2548: 	  int vb = _blossom_set->find(v);
deba@2548: 	  int vi = (*_node_index)[v];
deba@2548: 
deba@2548: 	  Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - 
deba@2548: 	    dualScale * _weight[e];
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[vb].status == EVEN) {
deba@2548: 	    if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@2548: 	      _delta3->push(e, rw / 2);
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	  
deba@2548: 	    typename std::map<int, Edge>::iterator it = 
deba@2548: 	      (*_node_data)[vi].heap_index.find(tree);	  
deba@2548: 
deba@2548: 	    if (it != (*_node_data)[vi].heap_index.end()) {
deba@2548: 	      if ((*_node_data)[vi].heap[it->second] > rw) {
deba@2548: 		(*_node_data)[vi].heap.replace(it->second, e);
deba@2548: 		(*_node_data)[vi].heap.decrease(e, rw);
deba@2548: 		it->second = e;
deba@2548: 	      }
deba@2548: 	    } else {
deba@2548: 	      (*_node_data)[vi].heap.push(e, rw);
deba@2548: 	      (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@2548: 	    }
deba@2548: 
deba@2548: 	    if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@2548: 	      _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@2548: 
deba@2548: 	      if ((*_blossom_data)[vb].status == MATCHED) {
deba@2548: 		if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@2548: 		  _delta2->push(vb, _blossom_set->classPrio(vb) - 
deba@2548: 			       (*_blossom_data)[vb].offset);
deba@2548: 		} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - 
deba@2548: 			   (*_blossom_data)[vb].offset) {
deba@2548: 		  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@2548: 				   (*_blossom_data)[vb].offset);
deba@2548: 		}
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548:       (*_blossom_data)[blossom].offset = 0;
deba@2548:     }
deba@2548:     
deba@2548:     void alternatePath(int even, int tree) {
deba@2548:       int odd;
deba@2548: 
deba@2548:       evenToMatched(even, tree);
deba@2548:       (*_blossom_data)[even].status = MATCHED;
deba@2548: 
deba@2548:       while ((*_blossom_data)[even].pred != INVALID) {
deba@2548: 	odd = _blossom_set->find(_ugraph.target((*_blossom_data)[even].pred));
deba@2548: 	(*_blossom_data)[odd].status = MATCHED;
deba@2548: 	oddToMatched(odd);
deba@2548: 	(*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@2548:       
deba@2548: 	even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred));
deba@2548: 	(*_blossom_data)[even].status = MATCHED;
deba@2548: 	evenToMatched(even, tree);
deba@2548: 	(*_blossom_data)[even].next = 
deba@2548: 	  _ugraph.oppositeEdge((*_blossom_data)[odd].pred);
deba@2548:       }
deba@2548:       
deba@2548:     }
deba@2548: 
deba@2548:     void destroyTree(int tree) {
deba@2548:       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@2548: 	if ((*_blossom_data)[b].status == EVEN) {
deba@2548: 	  (*_blossom_data)[b].status = MATCHED;
deba@2548: 	  evenToMatched(b, tree);
deba@2548: 	} else if ((*_blossom_data)[b].status == ODD) {
deba@2548: 	  (*_blossom_data)[b].status = MATCHED;
deba@2548: 	  oddToMatched(b);
deba@2548: 	}
deba@2548:       }
deba@2548:       _tree_set->eraseClass(tree);
deba@2548:     }
deba@2548: 
deba@2548:     void augmentOnEdge(const UEdge& edge) {
deba@2548:       
deba@2548:       int left = _blossom_set->find(_ugraph.source(edge));
deba@2548:       int right = _blossom_set->find(_ugraph.target(edge));
deba@2548: 
deba@2548:       int left_tree = _tree_set->find(left);
deba@2548:       alternatePath(left, left_tree);
deba@2548:       destroyTree(left_tree);
deba@2548: 
deba@2548:       int right_tree = _tree_set->find(right);
deba@2548:       alternatePath(right, right_tree);
deba@2548:       destroyTree(right_tree);
deba@2548: 
deba@2548:       (*_blossom_data)[left].next = _ugraph.direct(edge, true);
deba@2548:       (*_blossom_data)[right].next = _ugraph.direct(edge, false);
deba@2548:     }
deba@2548: 
deba@2548:     void extendOnEdge(const Edge& edge) {
deba@2548:       int base = _blossom_set->find(_ugraph.target(edge));
deba@2548:       int tree = _tree_set->find(base);
deba@2548:       
deba@2548:       int odd = _blossom_set->find(_ugraph.source(edge));
deba@2548:       _tree_set->insert(odd, tree);
deba@2548:       (*_blossom_data)[odd].status = ODD;
deba@2548:       matchedToOdd(odd);
deba@2548:       (*_blossom_data)[odd].pred = edge;
deba@2548: 
deba@2548:       int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next));
deba@2548:       (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@2548:       _tree_set->insert(even, tree);
deba@2548:       (*_blossom_data)[even].status = EVEN;
deba@2548:       matchedToEven(even, tree);
deba@2548:     }
deba@2548:     
deba@2548:     void shrinkOnEdge(const UEdge& uedge, int tree) {
deba@2548:       int nca = -1;
deba@2548:       std::vector<int> left_path, right_path;
deba@2548: 
deba@2548:       {
deba@2548: 	std::set<int> left_set, right_set;
deba@2548: 	int left = _blossom_set->find(_ugraph.source(uedge));
deba@2548: 	left_path.push_back(left);
deba@2548: 	left_set.insert(left);
deba@2548: 
deba@2548: 	int right = _blossom_set->find(_ugraph.target(uedge));
deba@2548: 	right_path.push_back(right);
deba@2548: 	right_set.insert(right);
deba@2548: 
deba@2548: 	while (true) {
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[left].pred == INVALID) break;
deba@2548: 
deba@2548: 	  left = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred));
deba@2548: 	  left_path.push_back(left);
deba@2548: 	  left = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred));
deba@2548: 	  left_path.push_back(left);
deba@2548: 
deba@2548: 	  left_set.insert(left);
deba@2548: 
deba@2548: 	  if (right_set.find(left) != right_set.end()) {
deba@2548: 	    nca = left;
deba@2548: 	    break;
deba@2548: 	  }
deba@2548: 
deba@2548: 	  if ((*_blossom_data)[right].pred == INVALID) break;
deba@2548: 
deba@2548: 	  right = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred));
deba@2548: 	  right_path.push_back(right);
deba@2548: 	  right = 
deba@2548: 	    _blossom_set->find(_ugraph.target((*_blossom_data)[right].pred));
deba@2548: 	  right_path.push_back(right);
deba@2548: 
deba@2548: 	  right_set.insert(right);
deba@2548:  
deba@2548: 	  if (left_set.find(right) != left_set.end()) {
deba@2548: 	    nca = right;
deba@2548: 	    break;
deba@2548: 	  }
deba@2548: 
deba@2548: 	}
deba@2548: 
deba@2548: 	if (nca == -1) {
deba@2548: 	  if ((*_blossom_data)[left].pred == INVALID) {
deba@2548: 	    nca = right;
deba@2548: 	    while (left_set.find(nca) == left_set.end()) {
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      right_path.push_back(nca);
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      right_path.push_back(nca);
deba@2548: 	    }
deba@2548: 	  } else {
deba@2548: 	    nca = left;
deba@2548: 	    while (right_set.find(nca) == right_set.end()) {
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      left_path.push_back(nca);
deba@2548: 	      nca = 
deba@2548: 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));
deba@2548: 	      left_path.push_back(nca);
deba@2548: 	    }
deba@2548: 	  }
deba@2548: 	}
deba@2548:       }
deba@2548: 
deba@2548:       std::vector<int> subblossoms;
deba@2548:       Edge prev;
deba@2548: 
deba@2548:       prev = _ugraph.direct(uedge, true);
deba@2548:       for (int i = 0; left_path[i] != nca; i += 2) {
deba@2548: 	subblossoms.push_back(left_path[i]);
deba@2548: 	(*_blossom_data)[left_path[i]].next = prev;
deba@2548: 	_tree_set->erase(left_path[i]);
deba@2548: 
deba@2548: 	subblossoms.push_back(left_path[i + 1]);
deba@2548: 	(*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@2548: 	oddToEven(left_path[i + 1], tree);
deba@2548: 	_tree_set->erase(left_path[i + 1]);
deba@2548: 	prev = _ugraph.oppositeEdge((*_blossom_data)[left_path[i + 1]].pred);
deba@2548:       }
deba@2548: 
deba@2548:       int k = 0;
deba@2548:       while (right_path[k] != nca) ++k;
deba@2548: 
deba@2548:       subblossoms.push_back(nca);
deba@2548:       (*_blossom_data)[nca].next = prev;
deba@2548:       
deba@2548:       for (int i = k - 2; i >= 0; i -= 2) {
deba@2548: 	subblossoms.push_back(right_path[i + 1]);
deba@2548: 	(*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@2548: 	oddToEven(right_path[i + 1], tree);
deba@2548: 	_tree_set->erase(right_path[i + 1]);
deba@2548: 
deba@2548: 	(*_blossom_data)[right_path[i + 1]].next = 
deba@2548: 	  (*_blossom_data)[right_path[i + 1]].pred;
deba@2548: 
deba@2548: 	subblossoms.push_back(right_path[i]);
deba@2548: 	_tree_set->erase(right_path[i]);
deba@2548:       }
deba@2548: 
deba@2548:       int surface = 
deba@2548: 	_blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@2548: 
deba@2548:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@2548: 	if (!_blossom_set->trivial(subblossoms[i])) {
deba@2548: 	  (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@2548: 	}
deba@2548: 	(*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@2548:       }
deba@2548: 
deba@2548:       (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@2548:       (*_blossom_data)[surface].offset = 0;
deba@2548:       (*_blossom_data)[surface].status = EVEN;
deba@2548:       (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@2548:       (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@2548: 
deba@2548:       _tree_set->insert(surface, tree);
deba@2548:       _tree_set->erase(nca);
deba@2548:     }
deba@2548: 
deba@2548:     void splitBlossom(int blossom) {
deba@2548:       Edge next = (*_blossom_data)[blossom].next; 
deba@2548:       Edge pred = (*_blossom_data)[blossom].pred;
deba@2548: 
deba@2548:       int tree = _tree_set->find(blossom);
deba@2548: 
deba@2548:       (*_blossom_data)[blossom].status = MATCHED;
deba@2548:       oddToMatched(blossom);
deba@2548:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@2548: 	_delta2->erase(blossom);
deba@2548:       }
deba@2548: 
deba@2548:       std::vector<int> subblossoms;
deba@2548:       _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@2548: 
deba@2548:       Value offset = (*_blossom_data)[blossom].offset;
deba@2548:       int b = _blossom_set->find(_ugraph.source(pred));
deba@2548:       int d = _blossom_set->find(_ugraph.source(next));
deba@2548:       
deba@2549:       int ib = -1, id = -1;
deba@2548:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@2548: 	if (subblossoms[i] == b) ib = i;
deba@2548: 	if (subblossoms[i] == d) id = i;
deba@2548: 
deba@2548: 	(*_blossom_data)[subblossoms[i]].offset = offset;
deba@2548: 	if (!_blossom_set->trivial(subblossoms[i])) {
deba@2548: 	  (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@2548: 	}
deba@2548: 	if (_blossom_set->classPrio(subblossoms[i]) != 
deba@2548: 	    std::numeric_limits<Value>::max()) {
deba@2548: 	  _delta2->push(subblossoms[i], 
deba@2548: 			_blossom_set->classPrio(subblossoms[i]) - 
deba@2548: 			(*_blossom_data)[subblossoms[i]].offset);
deba@2548: 	}
deba@2548:       }
deba@2548:       
deba@2548:       if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@2548: 	for (int i = (id + 1) % subblossoms.size(); 
deba@2548: 	     i != ib; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  (*_blossom_data)[sb].next = 
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 	}
deba@2548: 
deba@2548: 	for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@2548: 
deba@2548: 	  (*_blossom_data)[sb].status = ODD;
deba@2548: 	  matchedToOdd(sb);
deba@2548: 	  _tree_set->insert(sb, tree);
deba@2548: 	  (*_blossom_data)[sb].pred = pred;
deba@2548: 	  (*_blossom_data)[sb].next = 
deba@2548: 			   _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 	  
deba@2548: 	  pred = (*_blossom_data)[ub].next;
deba@2548:       
deba@2548: 	  (*_blossom_data)[tb].status = EVEN;
deba@2548: 	  matchedToEven(tb, tree);
deba@2548: 	  _tree_set->insert(tb, tree);
deba@2548: 	  (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@2548: 	}
deba@2548:       
deba@2548: 	(*_blossom_data)[subblossoms[id]].status = ODD;
deba@2548: 	matchedToOdd(subblossoms[id]);
deba@2548: 	_tree_set->insert(subblossoms[id], tree);
deba@2548: 	(*_blossom_data)[subblossoms[id]].next = next;
deba@2548: 	(*_blossom_data)[subblossoms[id]].pred = pred;
deba@2548:       
deba@2548:       } else {
deba@2548: 
deba@2548: 	for (int i = (ib + 1) % subblossoms.size(); 
deba@2548: 	     i != id; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  (*_blossom_data)[sb].next = 
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 	}	
deba@2548: 
deba@2548: 	for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@2548: 	  int sb = subblossoms[i];
deba@2548: 	  int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@2548: 	  int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@2548: 
deba@2548: 	  (*_blossom_data)[sb].status = ODD;
deba@2548: 	  matchedToOdd(sb);
deba@2548: 	  _tree_set->insert(sb, tree);
deba@2548: 	  (*_blossom_data)[sb].next = next; 
deba@2548: 	  (*_blossom_data)[sb].pred =
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[tb].next);
deba@2548: 
deba@2548: 	  (*_blossom_data)[tb].status = EVEN;
deba@2548: 	  matchedToEven(tb, tree);
deba@2548: 	  _tree_set->insert(tb, tree);
deba@2548: 	  (*_blossom_data)[tb].pred =
deba@2548: 	    (*_blossom_data)[tb].next = 
deba@2548: 	    _ugraph.oppositeEdge((*_blossom_data)[ub].next);
deba@2548: 	  next = (*_blossom_data)[ub].next;
deba@2548: 	}
deba@2548: 
deba@2548: 	(*_blossom_data)[subblossoms[ib]].status = ODD;
deba@2548: 	matchedToOdd(subblossoms[ib]);
deba@2548: 	_tree_set->insert(subblossoms[ib], tree);
deba@2548: 	(*_blossom_data)[subblossoms[ib]].next = next;
deba@2548: 	(*_blossom_data)[subblossoms[ib]].pred = pred;
deba@2548:       }
deba@2548:       _tree_set->erase(blossom);
deba@2548:     }
deba@2548: 
deba@2548:     void extractBlossom(int blossom, const Node& base, const Edge& matching) {
deba@2548:       if (_blossom_set->trivial(blossom)) {
deba@2548: 	int bi = (*_node_index)[base];
deba@2548: 	Value pot = (*_node_data)[bi].pot;
deba@2548: 
deba@2548: 	_matching->set(base, matching);
deba@2548: 	_blossom_node_list.push_back(base);
deba@2548: 	_node_potential->set(base, pot);
deba@2548:       } else {
deba@2548: 
deba@2548: 	Value pot = (*_blossom_data)[blossom].pot;
deba@2548: 	int bn = _blossom_node_list.size();
deba@2548: 	
deba@2548: 	std::vector<int> subblossoms;
deba@2548: 	_blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@2548: 	int b = _blossom_set->find(base);
deba@2548: 	int ib = -1;
deba@2548: 	for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@2548: 	  if (subblossoms[i] == b) { ib = i; break; }
deba@2548: 	}
deba@2548: 	
deba@2548: 	for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@2548: 	  int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@2548: 	  int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@2548: 	  
deba@2548: 	  Edge m = (*_blossom_data)[tb].next;
deba@2548: 	  extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m));
deba@2548: 	  extractBlossom(tb, _ugraph.source(m), m);
deba@2548: 	}
deba@2548: 	extractBlossom(subblossoms[ib], base, matching);      
deba@2548: 	
deba@2548: 	int en = _blossom_node_list.size();
deba@2548: 	
deba@2548: 	_blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     void extractMatching() {
deba@2548:       std::vector<int> blossoms;
deba@2548:       for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@2548: 	blossoms.push_back(c);
deba@2548:       }
deba@2548: 
deba@2548:       for (int i = 0; i < int(blossoms.size()); ++i) {
deba@2548: 
deba@2548: 	Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@2548: 	(*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@2548: 	for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); 
deba@2548: 	     n != INVALID; ++n) {
deba@2548: 	  (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@2548: 	}
deba@2548: 	
deba@2548: 	Edge matching = (*_blossom_data)[blossoms[i]].next;
deba@2548: 	Node base = _ugraph.source(matching);
deba@2548: 	extractBlossom(blossoms[i], base, matching);
deba@2548:       }
deba@2548:     }
deba@2548:     
deba@2548:   public:
deba@2548: 
deba@2548:     /// \brief Constructor
deba@2548:     ///
deba@2548:     /// Constructor.
deba@2548:     MaxWeightedPerfectMatching(const UGraph& ugraph, const WeightMap& weight)
deba@2548:       : _ugraph(ugraph), _weight(weight), _matching(0),
deba@2548: 	_node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@2548: 	_node_num(0), _blossom_num(0),
deba@2548: 
deba@2548: 	_blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@2548: 	_node_index(0), _node_heap_index(0), _node_data(0),
deba@2548: 	_tree_set_index(0), _tree_set(0),
deba@2548: 
deba@2548: 	_delta2_index(0), _delta2(0),
deba@2548: 	_delta3_index(0), _delta3(0), 
deba@2548: 	_delta4_index(0), _delta4(0),
deba@2548: 
deba@2548: 	_delta_sum() {}
deba@2548: 
deba@2548:     ~MaxWeightedPerfectMatching() {
deba@2548:       destroyStructures();
deba@2548:     }
deba@2548: 
deba@2548:     /// \name Execution control 
deba@2548:     /// The simplest way to execute the algorithm is to use the member
deba@2548:     /// \c run() member function.
deba@2548: 
deba@2548:     ///@{
deba@2548: 
deba@2548:     /// \brief Initialize the algorithm
deba@2548:     ///
deba@2548:     /// Initialize the algorithm
deba@2548:     void init() {
deba@2548:       createStructures();
deba@2548: 
deba@2548:       for (EdgeIt e(_ugraph); e != INVALID; ++e) {
deba@2548: 	_node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP);
deba@2548:       }
deba@2548:       for (UEdgeIt e(_ugraph); e != INVALID; ++e) {
deba@2548: 	_delta3_index->set(e, _delta3->PRE_HEAP);
deba@2548:       }
deba@2548:       for (int i = 0; i < _blossom_num; ++i) {
deba@2548: 	_delta2_index->set(i, _delta2->PRE_HEAP);
deba@2548: 	_delta4_index->set(i, _delta4->PRE_HEAP);
deba@2548:       }
deba@2548: 
deba@2548:       int index = 0;
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2612: 	Value max = - std::numeric_limits<Value>::max();
deba@2548: 	for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {
deba@2548: 	  if (_ugraph.target(e) == n) continue;
deba@2548: 	  if ((dualScale * _weight[e]) / 2 > max) {
deba@2548: 	    max = (dualScale * _weight[e]) / 2;
deba@2548: 	  }
deba@2548: 	}
deba@2548: 	_node_index->set(n, index);
deba@2548: 	(*_node_data)[index].pot = max;
deba@2548: 	int blossom = 
deba@2548: 	  _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@2548: 
deba@2548: 	_tree_set->insert(blossom);
deba@2548: 
deba@2548: 	(*_blossom_data)[blossom].status = EVEN;
deba@2548: 	(*_blossom_data)[blossom].pred = INVALID;
deba@2548: 	(*_blossom_data)[blossom].next = INVALID;
deba@2548: 	(*_blossom_data)[blossom].pot = 0;
deba@2548: 	(*_blossom_data)[blossom].offset = 0;
deba@2548: 	++index;
deba@2548:       }
deba@2548:       for (UEdgeIt e(_ugraph); e != INVALID; ++e) {
deba@2548: 	int si = (*_node_index)[_ugraph.source(e)];
deba@2548: 	int ti = (*_node_index)[_ugraph.target(e)];
deba@2548: 	if (_ugraph.source(e) != _ugraph.target(e)) {
deba@2548: 	  _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - 
deba@2548: 			    dualScale * _weight[e]) / 2);
deba@2548: 	}
deba@2548:       }
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Starts the algorithm
deba@2548:     ///
deba@2548:     /// Starts the algorithm
deba@2548:     bool start() {
deba@2548:       enum OpType {
deba@2548: 	D2, D3, D4
deba@2548:       };
deba@2548: 
deba@2548:       int unmatched = _node_num;
deba@2548:       while (unmatched > 0) {
deba@2548: 	Value d2 = !_delta2->empty() ? 
deba@2548: 	  _delta2->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	Value d3 = !_delta3->empty() ? 
deba@2548: 	  _delta3->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	Value d4 = !_delta4->empty() ? 
deba@2548: 	  _delta4->prio() : std::numeric_limits<Value>::max();
deba@2548: 
deba@2548: 	_delta_sum = d2; OpType ot = D2;
deba@2548: 	if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@2548: 	if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@2548: 
deba@2548: 	if (_delta_sum == std::numeric_limits<Value>::max()) {
deba@2548: 	  return false;
deba@2548: 	}
deba@2548: 	
deba@2548: 	switch (ot) {
deba@2548: 	case D2:
deba@2548: 	  {
deba@2548: 	    int blossom = _delta2->top();
deba@2548: 	    Node n = _blossom_set->classTop(blossom);
deba@2548: 	    Edge e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@2548: 	    extendOnEdge(e);
deba@2548: 	  }
deba@2548: 	  break;
deba@2548: 	case D3:
deba@2548: 	  {
deba@2548: 	    UEdge e = _delta3->top();
deba@2548: 	    
deba@2548: 	    int left_blossom = _blossom_set->find(_ugraph.source(e));
deba@2548: 	    int right_blossom = _blossom_set->find(_ugraph.target(e));
deba@2548: 	  
deba@2548: 	    if (left_blossom == right_blossom) {
deba@2548: 	      _delta3->pop();
deba@2548: 	    } else {
deba@2548: 	      int left_tree = _tree_set->find(left_blossom);
deba@2548: 	      int right_tree = _tree_set->find(right_blossom);
deba@2548: 	    
deba@2548: 	      if (left_tree == right_tree) {
deba@2548: 		shrinkOnEdge(e, left_tree);
deba@2548: 	      } else {
deba@2548: 		augmentOnEdge(e);
deba@2548: 		unmatched -= 2;
deba@2548: 	      }
deba@2548: 	    }
deba@2548: 	  } break;
deba@2548: 	case D4:
deba@2548: 	  splitBlossom(_delta4->top());
deba@2548: 	  break;
deba@2548: 	}
deba@2548:       }
deba@2548:       extractMatching();
deba@2548:       return true;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Runs %MaxWeightedPerfectMatching algorithm.
deba@2548:     ///
deba@2548:     /// This method runs the %MaxWeightedPerfectMatching algorithm.
deba@2548:     ///
deba@2548:     /// \note mwm.run() is just a shortcut of the following code.
deba@2548:     /// \code
deba@2548:     ///   mwm.init();
deba@2548:     ///   mwm.start();
deba@2548:     /// \endcode
deba@2548:     bool run() {
deba@2548:       init();
deba@2548:       return start();
deba@2548:     }
deba@2548: 
deba@2548:     /// @}
deba@2548: 
deba@2548:     /// \name Primal solution
deba@2548:     /// Functions for get the primal solution, ie. the matching.
deba@2548:     
deba@2548:     /// @{
deba@2548: 
deba@2548:     /// \brief Returns the matching value.
deba@2548:     ///
deba@2548:     /// Returns the matching value.
deba@2548:     Value matchingValue() const {
deba@2548:       Value sum = 0;
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2548: 	if ((*_matching)[n] != INVALID) {
deba@2548: 	  sum += _weight[(*_matching)[n]];
deba@2548: 	}
deba@2548:       }
deba@2548:       return sum /= 2;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns true when the edge is in the matching.
deba@2548:     ///
deba@2548:     /// Returns true when the edge is in the matching.
deba@2548:     bool matching(const UEdge& edge) const {
deba@2548:       return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true);
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the incident matching edge.
deba@2548:     ///
deba@2548:     /// Returns the incident matching edge from given node.
deba@2548:     Edge matching(const Node& node) const {
deba@2548:       return (*_matching)[node];
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the mate of the node.
deba@2548:     ///
deba@2548:     /// Returns the adjancent node in a mathcing edge.
deba@2548:     Node mate(const Node& node) const {
deba@2548:       return _ugraph.target((*_matching)[node]);
deba@2548:     }
deba@2548: 
deba@2548:     /// @}
deba@2548: 
deba@2548:     /// \name Dual solution
deba@2548:     /// Functions for get the dual solution.
deba@2548:     
deba@2548:     /// @{
deba@2548: 
deba@2548:     /// \brief Returns the value of the dual solution.
deba@2548:     ///
deba@2548:     /// Returns the value of the dual solution. It should be equal to
deba@2548:     /// the primal value scaled by \ref dualScale "dual scale".
deba@2548:     Value dualValue() const {
deba@2548:       Value sum = 0;
deba@2548:       for (NodeIt n(_ugraph); n != INVALID; ++n) {
deba@2548: 	sum += nodeValue(n);
deba@2548:       }
deba@2548:       for (int i = 0; i < blossomNum(); ++i) {
deba@2548:         sum += blossomValue(i) * (blossomSize(i) / 2);
deba@2548:       }
deba@2548:       return sum;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the value of the node.
deba@2548:     ///
deba@2548:     /// Returns the the value of the node.
deba@2548:     Value nodeValue(const Node& n) const {
deba@2548:       return (*_node_potential)[n];
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the number of the blossoms in the basis.
deba@2548:     ///
deba@2548:     /// Returns the number of the blossoms in the basis.
deba@2548:     /// \see BlossomIt
deba@2548:     int blossomNum() const {
deba@2548:       return _blossom_potential.size();
deba@2548:     }
deba@2548: 
deba@2548: 
deba@2548:     /// \brief Returns the number of the nodes in the blossom.
deba@2548:     ///
deba@2548:     /// Returns the number of the nodes in the blossom.
deba@2548:     int blossomSize(int k) const {
deba@2548:       return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Returns the value of the blossom.
deba@2548:     ///
deba@2548:     /// Returns the the value of the blossom.
deba@2548:     /// \see BlossomIt
deba@2548:     Value blossomValue(int k) const {
deba@2548:       return _blossom_potential[k].value;
deba@2548:     }
deba@2548: 
deba@2548:     /// \brief Lemon iterator for get the items of the blossom.
deba@2548:     ///
deba@2548:     /// Lemon iterator for get the nodes of the blossom. This class
deba@2548:     /// provides a common style lemon iterator which gives back a
deba@2548:     /// subset of the nodes.
deba@2548:     class BlossomIt {
deba@2548:     public:
deba@2548: 
deba@2548:       /// \brief Constructor.
deba@2548:       ///
deba@2548:       /// Constructor for get the nodes of the variable. 
deba@2548:       BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) 
deba@2548:         : _algorithm(&algorithm)
deba@2548:       {
deba@2548:         _index = _algorithm->_blossom_potential[variable].begin;
deba@2548:         _last = _algorithm->_blossom_potential[variable].end;
deba@2548:       }
deba@2548: 
deba@2548:       /// \brief Invalid constructor.
deba@2548:       ///
deba@2548:       /// Invalid constructor.
deba@2548:       BlossomIt(Invalid) : _index(-1) {}
deba@2548: 
deba@2548:       /// \brief Conversion to node.
deba@2548:       ///
deba@2548:       /// Conversion to node.
deba@2548:       operator Node() const { 
deba@2548:         return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
deba@2548:       }
deba@2548: 
deba@2548:       /// \brief Increment operator.
deba@2548:       ///
deba@2548:       /// Increment operator.
deba@2548:       BlossomIt& operator++() {
deba@2548:         ++_index;
deba@2548:         if (_index == _last) {
deba@2548:           _index = -1;
deba@2548:         }
deba@2548:         return *this; 
deba@2548:       }
deba@2548: 
deba@2548:       bool operator==(const BlossomIt& it) const { 
deba@2548:         return _index == it._index; 
deba@2548:       }
deba@2548:       bool operator!=(const BlossomIt& it) const { 
deba@2548:         return _index != it._index;
deba@2548:       }
deba@2548: 
deba@2548:     private:
deba@2548:       const MaxWeightedPerfectMatching* _algorithm;
deba@2548:       int _last;
deba@2548:       int _index;
deba@2548:     };
deba@2548: 
deba@2548:     /// @}
deba@2548:     
deba@2548:   };
deba@2548: 
jacint@1077:   
jacint@1077: } //END OF NAMESPACE LEMON
jacint@1077: 
jacint@1165: #endif //LEMON_MAX_MATCHING_H