jacint@1077: /* -*- C++ -*-
ladanyi@1435: * lemon/max_matching.h - Part of LEMON, a generic C++ optimization library
jacint@1077: *
alpar@1164: * Copyright (C) 2005 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:
jacint@1077: #include <queue>
jacint@1093: #include <lemon/invalid.h>
jacint@1093: #include <lemon/unionfind.h>
jacint@1077: #include <lemon/graph_utils.h>
jacint@1077:
jacint@1077: ///\ingroup galgs
jacint@1077: ///\file
jacint@1077: ///\brief Maximum matching algorithm.
jacint@1077:
jacint@1077: namespace lemon {
jacint@1077:
jacint@1077: /// \addtogroup galgs
jacint@1077: /// @{
jacint@1077:
jacint@1077: ///Edmonds' alternating forest maximum matching algorithm.
jacint@1077:
jacint@1077: ///This class provides Edmonds' alternating forest matching
jacint@1077: ///algorithm. The starting matching (if any) can be passed to the
jacint@1077: ///algorithm using read-in functions \ref readNMapNode, \ref
jacint@1077: ///readNMapEdge or \ref readEMapBool depending on the container. The
jacint@1077: ///resulting maximum matching can be attained by write-out functions
jacint@1077: ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
jacint@1077: ///depending on the preferred container.
jacint@1077: ///
jacint@1077: ///The dual side of a matching is a map of the nodes to
jacint@1077: ///MaxMatching::pos_enum, having values D, A and C showing the
jacint@1077: ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
jacint@1077: ///a graph with factor-critical components, the nodes in A form the
jacint@1077: ///barrier, and the nodes in C induce a graph having a perfect
jacint@1077: ///matching. This decomposition can be attained by calling \ref
jacint@1090: ///writePos 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;
alpar@1177: typedef typename Graph::UndirEdge UndirEdge;
jacint@1077: typedef typename Graph::UndirEdgeIt UndirEdgeIt;
jacint@1077: typedef typename Graph::NodeIt NodeIt;
jacint@1077: typedef typename Graph::IncEdgeIt IncEdgeIt;
jacint@1077:
jacint@1077: typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;
jacint@1077:
jacint@1077: public:
jacint@1077:
jacint@1077: ///Indicates the Gallai-Edmonds decomposition of the graph.
jacint@1077:
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
jacint@1077: ///nodes with pos_enum \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.
jacint@1077: enum pos_enum {
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;
jacint@1077: typename Graph::template NodeMap<pos_enum> position;
jacint@1077:
jacint@1077: public:
jacint@1077:
jacint@1093: MaxMatching(const Graph& _g) : g(_g), _mate(_g,INVALID), position(_g) {}
jacint@1077:
jacint@1077: ///Runs Edmonds' algorithm.
jacint@1077:
jacint@1077: ///Runs Edmonds' algorithm for sparse graphs (number of edges <
jacint@1077: ///2*number of nodes), and a heuristical Edmonds' algorithm with a
jacint@1090: ///heuristic of postponing shrinks for dense graphs.
alpar@1587: void run() {
alpar@1587: if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) {
alpar@1587: greedyMatching();
alpar@1587: runEdmonds(0);
alpar@1587: } else runEdmonds(1);
alpar@1587: }
alpar@1587:
jacint@1077:
jacint@1077: ///Runs Edmonds' algorithm.
jacint@1077:
jacint@1077: ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
jacint@1077: ///Edmonds' algorithm with a heuristic of postponing shrinks,
jacint@1090: ///giving a faster algorithm for dense graphs.
alpar@1587: void runEdmonds( int heur = 1 ) {
alpar@1587:
alpar@1587: for(NodeIt v(g); v!=INVALID; ++v)
alpar@1587: position.set(v,C);
alpar@1587:
alpar@1587: typename Graph::template NodeMap<Node> ear(g,INVALID);
alpar@1587: //undefined for the base nodes of the blossoms (i.e. for the
alpar@1587: //representative elements of UFE blossom) and for the nodes in C
alpar@1587:
alpar@1587: typename UFE::MapType blossom_base(g);
alpar@1587: UFE blossom(blossom_base);
alpar@1587: typename UFE::MapType tree_base(g);
alpar@1587: UFE tree(tree_base);
alpar@1587: //If these UFE's would be members of the class then also
alpar@1587: //blossom_base and tree_base should be a member.
alpar@1587:
alpar@1587: for(NodeIt v(g); v!=INVALID; ++v) {
alpar@1587: if ( position[v]==C && _mate[v]==INVALID ) {
alpar@1587: blossom.insert(v);
alpar@1587: tree.insert(v);
alpar@1587: position.set(v,D);
alpar@1587: if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
alpar@1587: else normShrink( v, ear, blossom, tree );
alpar@1587: }
alpar@1587: }
alpar@1587: }
alpar@1587:
jacint@1077:
jacint@1077: ///Finds a greedy matching starting from the actual matching.
jacint@1077:
jacint@1077: ///Starting form the actual matching stored, it finds a maximal
jacint@1077: ///greedy matching.
alpar@1587: void greedyMatching() {
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:
jacint@1077: ///Returns the size of the actual matching stored.
jacint@1077:
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:
jacint@1077: ///Resets the actual matching to the empty matching.
jacint@1077:
jacint@1077: ///Resets the actual matching to the empty matching.
jacint@1077: ///
alpar@1587: void resetMatching() {
alpar@1587: for(NodeIt v(g); v!=INVALID; ++v)
alpar@1587: _mate.set(v,INVALID);
alpar@1587: }
jacint@1077:
jacint@1093: ///Returns the mate of a node in the actual matching.
jacint@1093:
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.
jacint@1093: Node mate(Node& node) const {
jacint@1093: return _mate[node];
jacint@1093: }
jacint@1093:
jacint@1165: ///Reads a matching from a \c Node valued \c Node map.
jacint@1077:
jacint@1165: ///Reads a matching from a \c Node valued \c Node map. This map
jacint@1165: ///must be \e symmetric, i.e. if \c map[u]==v then \c map[v]==u
jacint@1165: ///must hold, and \c uv will be an edge of the matching.
jacint@1077: template<typename NMapN>
jacint@1077: void readNMapNode(NMapN& map) {
jacint@1077: for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: _mate.set(v,map[v]);
jacint@1077: }
jacint@1077: }
jacint@1077:
jacint@1165: ///Writes the stored matching to a \c Node valued \c Node map.
jacint@1077:
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.
jacint@1077: template<typename NMapN>
jacint@1077: void writeNMapNode (NMapN& map) const {
jacint@1077: for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: map.set(v,_mate[v]);
jacint@1077: }
jacint@1077: }
jacint@1077:
jacint@1165: ///Reads a matching from an \c UndirEdge valued \c Node map.
jacint@1077:
jacint@1165: ///Reads a matching from an \c UndirEdge valued \c Node map. \c
jacint@1165: ///map[v] must be an \c UndirEdge incident to \c v. This map must
jacint@1165: ///have the property that if \c g.oppositeNode(u,map[u])==v then
jacint@1165: ///\c \c g.oppositeNode(v,map[v])==u holds, and now some edge
marci@1172: ///joining \c u to \c v will be an edge of the matching.
jacint@1077: template<typename NMapE>
jacint@1077: void readNMapEdge(NMapE& map) {
jacint@1077: for(NodeIt v(g); v!=INVALID; ++v) {
alpar@1177: UndirEdge e=map[v];
jacint@1165: if ( e!=INVALID )
jacint@1166: _mate.set(v,g.oppositeNode(v,e));
jacint@1077: }
jacint@1077: }
jacint@1077:
jacint@1165: ///Writes the matching stored to an \c UndirEdge valued \c Node map.
jacint@1077:
jacint@1165: ///Writes the stored matching to an \c UndirEdge valued \c Node
jacint@1165: ///map. \c map[v] will be an \c UndirEdge 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.
jacint@1077: template<typename NMapE>
jacint@1077: void writeNMapEdge (NMapE& map) const {
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(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:
jacint@1165: ///Reads a matching from a \c bool valued \c Edge map.
jacint@1077:
jacint@1165: ///Reads a matching from a \c bool valued \c Edge map. This map
jacint@1165: ///must have the property that there are no two incident edges \c
jacint@1165: ///e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
jacint@1077: ///map[e]==true form the matching.
jacint@1077: template<typename EMapB>
jacint@1077: void readEMapBool(EMapB& map) {
jacint@1077: for(UndirEdgeIt e(g); e!=INVALID; ++e) {
jacint@1077: if ( map[e] ) {
jacint@1077: Node u=g.source(e);
jacint@1077: Node v=g.target(e);
jacint@1093: _mate.set(u,v);
jacint@1093: _mate.set(v,u);
jacint@1077: }
jacint@1077: }
jacint@1077: }
jacint@1077:
jacint@1077:
jacint@1165: ///Writes the matching stored to a \c bool valued \c Edge map.
jacint@1077:
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.
jacint@1077: template<typename EMapB>
jacint@1077: void writeEMapBool (EMapB& map) const {
jacint@1077: for(UndirEdgeIt 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:
jacint@1077: ///Writes the canonical decomposition of the graph after running
jacint@1077: ///the algorithm.
jacint@1077:
jacint@1090: ///After calling any run methods of the class, it writes the
jacint@1090: ///Gallai-Edmonds canonical decomposition of the graph. \c map
jacint@1090: ///must be a node map of \ref pos_enum 's.
jacint@1077: template<typename NMapEnum>
jacint@1077: void writePos (NMapEnum& map) const {
jacint@1077: for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
jacint@1077: }
jacint@1077:
jacint@1077: private:
jacint@1077:
jacint@1165:
jacint@1077: void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree);
jacint@1077:
alpar@1234: void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree);
jacint@1077:
alpar@1234: bool noShrinkStep(Node x, typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree, std::queue<Node>& Q);
jacint@1077:
alpar@1234: void shrinkStep(Node& top, Node& middle, Node& bottom,
alpar@1234: typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree, std::queue<Node>& Q);
jacint@1077:
alpar@1234: void augment(Node x, typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree);
jacint@1077:
jacint@1077: };
jacint@1077:
jacint@1077:
jacint@1077: // **********************************************************************
jacint@1077: // IMPLEMENTATIONS
jacint@1077: // **********************************************************************
jacint@1077:
jacint@1077:
jacint@1077: template <typename Graph>
jacint@1077: void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree) {
jacint@1077:
jacint@1077: std::queue<Node> Q; //queue of the totally unscanned nodes
jacint@1077: Q.push(v);
jacint@1077: std::queue<Node> R;
jacint@1077: //queue of the nodes which must be scanned for a possible shrink
jacint@1077:
jacint@1077: while ( !Q.empty() ) {
jacint@1077: Node x=Q.front();
jacint@1077: Q.pop();
jacint@1077: if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
jacint@1077: else R.push(x);
jacint@1077: }
jacint@1077:
jacint@1077: while ( !R.empty() ) {
jacint@1077: Node x=R.front();
jacint@1077: R.pop();
jacint@1077:
jacint@1077: for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
klao@1158: Node y=g.runningNode(e);
jacint@1077:
jacint@1077: if ( position[y] == D && blossom.find(x) != blossom.find(y) ) {
jacint@1077: //x and y must be in the same tree
jacint@1077:
jacint@1077: typename Graph::template NodeMap<bool> path(g,false);
jacint@1077:
jacint@1077: Node b=blossom.find(x);
jacint@1077: path.set(b,true);
jacint@1093: b=_mate[b];
jacint@1077: while ( b!=INVALID ) {
jacint@1077: b=blossom.find(ear[b]);
jacint@1077: path.set(b,true);
jacint@1093: b=_mate[b];
jacint@1077: } //going till the root
jacint@1077:
jacint@1077: Node top=y;
jacint@1077: Node middle=blossom.find(top);
jacint@1077: Node bottom=x;
jacint@1077: while ( !path[middle] )
jacint@1077: shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077:
jacint@1077: Node base=middle;
jacint@1077: top=x;
jacint@1077: middle=blossom.find(top);
jacint@1077: bottom=y;
jacint@1077: Node blossom_base=blossom.find(base);
jacint@1077: while ( middle!=blossom_base )
jacint@1077: shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077:
jacint@1077: blossom.makeRep(base);
jacint@1077: } // if shrink is needed
jacint@1077:
jacint@1077: while ( !Q.empty() ) {
jacint@1077: Node x=Q.front();
jacint@1077: Q.pop();
jacint@1077: if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
jacint@1077: else R.push(x);
jacint@1077: }
jacint@1077: } //for e
jacint@1077: } // while ( !R.empty() )
jacint@1077: }
jacint@1077:
jacint@1077:
jacint@1077: template <typename Graph>
alpar@1234: void MaxMatching<Graph>::normShrink(Node v,
alpar@1234: typename Graph::template
alpar@1234: NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree) {
jacint@1077: std::queue<Node> Q; //queue of the unscanned nodes
jacint@1077: Q.push(v);
jacint@1077: while ( !Q.empty() ) {
jacint@1077:
jacint@1077: Node x=Q.front();
jacint@1077: Q.pop();
jacint@1077:
jacint@1077: for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
klao@1158: Node y=g.runningNode(e);
jacint@1077:
jacint@1077: switch ( position[y] ) {
jacint@1077: case D: //x and y must be in the same tree
jacint@1077:
jacint@1077: if ( blossom.find(x) != blossom.find(y) ) { //shrink
jacint@1077: typename Graph::template NodeMap<bool> path(g,false);
jacint@1077:
jacint@1077: Node b=blossom.find(x);
jacint@1077: path.set(b,true);
jacint@1093: b=_mate[b];
jacint@1077: while ( b!=INVALID ) {
jacint@1077: b=blossom.find(ear[b]);
jacint@1077: path.set(b,true);
jacint@1093: b=_mate[b];
jacint@1077: } //going till the root
jacint@1077:
jacint@1077: Node top=y;
jacint@1077: Node middle=blossom.find(top);
jacint@1077: Node bottom=x;
jacint@1077: while ( !path[middle] )
jacint@1077: shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077:
jacint@1077: Node base=middle;
jacint@1077: top=x;
jacint@1077: middle=blossom.find(top);
jacint@1077: bottom=y;
jacint@1077: Node blossom_base=blossom.find(base);
jacint@1077: while ( middle!=blossom_base )
jacint@1077: shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077:
jacint@1077: blossom.makeRep(base);
jacint@1077: }
jacint@1077: break;
jacint@1077: case C:
jacint@1093: if ( _mate[y]!=INVALID ) { //grow
jacint@1077:
jacint@1077: ear.set(y,x);
jacint@1093: Node w=_mate[y];
jacint@1077: blossom.insert(w);
jacint@1077: position.set(y,A);
jacint@1077: position.set(w,D);
jacint@1077: tree.insert(y);
jacint@1077: tree.insert(w);
jacint@1077: tree.join(y,blossom.find(x));
jacint@1077: tree.join(w,y);
jacint@1077: Q.push(w);
jacint@1077: } else { //augment
jacint@1077: augment(x, ear, blossom, tree);
jacint@1093: _mate.set(x,y);
jacint@1093: _mate.set(y,x);
jacint@1077: return;
jacint@1077: } //if
jacint@1077: break;
jacint@1077: default: break;
jacint@1077: }
jacint@1077: }
jacint@1077: }
jacint@1077: }
jacint@1077:
jacint@1077: template <typename Graph>
alpar@1234: bool MaxMatching<Graph>::noShrinkStep(Node x,
alpar@1234: typename Graph::template
alpar@1234: NodeMap<Node>& ear,
alpar@1234: UFE& blossom, UFE& tree,
alpar@1234: std::queue<Node>& Q) {
jacint@1077: for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
klao@1158: Node y=g.runningNode(e);
jacint@1077:
jacint@1077: if ( position[y]==C ) {
jacint@1093: if ( _mate[y]!=INVALID ) { //grow
jacint@1077: ear.set(y,x);
jacint@1093: Node w=_mate[y];
jacint@1077: blossom.insert(w);
jacint@1077: position.set(y,A);
jacint@1077: position.set(w,D);
jacint@1077: tree.insert(y);
jacint@1077: tree.insert(w);
jacint@1077: tree.join(y,blossom.find(x));
jacint@1077: tree.join(w,y);
jacint@1077: Q.push(w);
jacint@1077: } else { //augment
jacint@1077: augment(x, ear, blossom, tree);
jacint@1093: _mate.set(x,y);
jacint@1093: _mate.set(y,x);
jacint@1077: return true;
jacint@1077: }
jacint@1077: }
jacint@1077: }
jacint@1077: return false;
jacint@1077: }
jacint@1077:
jacint@1077: template <typename Graph>
alpar@1234: void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom,
alpar@1234: typename Graph::template
alpar@1234: NodeMap<Node>& ear,
alpar@1234: UFE& blossom, UFE& tree,
alpar@1234: std::queue<Node>& Q) {
jacint@1077: ear.set(top,bottom);
jacint@1077: Node t=top;
jacint@1077: while ( t!=middle ) {
jacint@1093: Node u=_mate[t];
jacint@1077: t=ear[u];
jacint@1077: ear.set(t,u);
jacint@1077: }
jacint@1093: bottom=_mate[middle];
jacint@1077: position.set(bottom,D);
jacint@1077: Q.push(bottom);
jacint@1077: top=ear[bottom];
jacint@1077: Node oldmiddle=middle;
jacint@1077: middle=blossom.find(top);
jacint@1077: tree.erase(bottom);
jacint@1077: tree.erase(oldmiddle);
jacint@1077: blossom.insert(bottom);
jacint@1077: blossom.join(bottom, oldmiddle);
jacint@1077: blossom.join(top, oldmiddle);
jacint@1077: }
jacint@1077:
jacint@1077: template <typename Graph>
alpar@1234: void MaxMatching<Graph>::augment(Node x,
alpar@1234: typename Graph::template NodeMap<Node>& ear,
jacint@1077: UFE& blossom, UFE& tree) {
jacint@1093: Node v=_mate[x];
jacint@1077: while ( v!=INVALID ) {
jacint@1077:
jacint@1077: Node u=ear[v];
jacint@1093: _mate.set(v,u);
jacint@1077: Node tmp=v;
jacint@1093: v=_mate[u];
jacint@1093: _mate.set(u,tmp);
jacint@1077: }
jacint@1077: typename UFE::ItemIt it;
jacint@1077: for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {
jacint@1077: if ( position[it] == D ) {
jacint@1077: typename UFE::ItemIt b_it;
jacint@1077: for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {
jacint@1077: position.set( b_it ,C);
jacint@1077: }
jacint@1077: blossom.eraseClass(it);
jacint@1077: } else position.set( it ,C);
jacint@1077: }
jacint@1077: tree.eraseClass(x);
jacint@1077:
jacint@1077: }
jacint@1077:
jacint@1077: /// @}
jacint@1077:
jacint@1077: } //END OF NAMESPACE LEMON
jacint@1077:
jacint@1165: #endif //LEMON_MAX_MATCHING_H