[Lemon-commits] [lemon_svn] jacint: r1453 - hugo/trunk/src/work/jacint
Lemon SVN
svn at lemon.cs.elte.hu
Mon Nov 6 20:45:34 CET 2006
Author: jacint
Date: Fri Jan 7 09:39:53 2005
New Revision: 1453
Added:
hugo/trunk/src/work/jacint/matching.h
Log:
undirgrafbug
Added: hugo/trunk/src/work/jacint/matching.h
==============================================================================
--- (empty file)
+++ hugo/trunk/src/work/jacint/matching.h Fri Jan 7 09:39:53 2005
@@ -0,0 +1,608 @@
+// -*- C++ -*-
+#ifndef LEMON_MAX_MATCHING_H
+#define LEMON_MAX_MATCHING_H
+
+///\ingroup galgs
+///\file
+///\brief Maximum matching algorithm.
+
+#include <queue>
+
+
+#include <iostream>
+
+
+
+#include <invalid.h>
+#include <unionfind.h>
+#include <lemon/graph_utils.h>
+
+namespace lemon {
+
+ /// \addtogroup galgs
+ /// @{
+
+ ///Maximum matching algorithms class.
+
+ ///This class provides Edmonds' alternating forest matching
+ ///algorithm. The starting matching (if any) can be passed to the
+ ///algorithm using read-in functions \ref readNMapNode, \ref
+ ///readNMapEdge or \ref readEMapBool depending on the container. The
+ ///resulting maximum matching can be attained by write-out functions
+ ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
+ ///depending on the preferred container.
+ ///
+ ///The dual side of a mathcing is a map of the nodes to
+ ///MaxMatching::pos_enum, having values D, A and C showing the
+ ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
+ ///a graph with factor-critical components, the nodes in A form the
+ ///barrier, and the nodes in C induce a graph having a perfect
+ ///matching. This decomposition can be attained by calling \ref
+ ///writePos after running the algorithm. Before subsequent runs,
+ ///the function \ref resetPos() must be called.
+ ///
+ ///\param Graph The undirected graph type the algorithm runs on.
+ ///
+ ///\author Jacint Szabo
+ template <typename Graph>
+ class MaxMatching {
+ typedef typename Graph::Node Node;
+ typedef typename Graph::Edge Edge;
+ typedef typename Graph::UndirEdgeIt UndirEdgeIt;
+ typedef typename Graph::NodeIt NodeIt;
+ typedef typename Graph::IncEdgeIt IncEdgeIt;
+
+ typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;
+
+ public:
+
+ ///Indicates the Gallai-Edmonds decomposition of the graph.
+
+ ///Indicates the Gallai-Edmonds decomposition of the graph, which
+ ///shows an upper bound on the size of a maximum matching. The
+ ///nodes with pos_enum \c D induce a graph with factor-critical
+ ///components, the nodes in \c A form the canonical barrier, and the
+ ///nodes in \c C induce a graph having a perfect matching.
+ enum pos_enum {
+ D=0,
+ A=1,
+ C=2
+ };
+
+ private:
+
+ static const int HEUR_density=2;
+ const Graph& g;
+ typename Graph::template NodeMap<Node> mate;
+ typename Graph::template NodeMap<pos_enum> position;
+
+ public:
+
+ MaxMatching(const Graph& _g) : g(_g), mate(_g,INVALID), position(_g,C) {}
+
+ ///Runs Edmonds' algorithm.
+
+ ///Runs Edmonds' algorithm for sparse graphs (countEdges <=
+ ///2*countNodes), and a heuristical Edmonds' algorithm with a
+ ///heuristic of postponing shrinks for dense graphs. \pre Before
+ ///the subsequent calls \ref resetPos must be called.
+ inline void run();
+
+ ///Runs Edmonds' algorithm.
+
+ ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
+ ///Edmonds' algorithm with a heuristic of postponing shrinks,
+ ///giving a faster algorithm for dense graphs. \pre Before the
+ ///subsequent calls \ref resetPos must be called.
+ void runEdmonds( int heur );
+
+ ///Finds a greedy matching starting from the actual matching.
+
+ ///Starting form the actual matching stored, it finds a maximal
+ ///greedy matching.
+ void greedyMatching();
+
+ ///Returns the size of the actual matching stored.
+
+ ///Returns the size of the actual matching stored. After \ref
+ ///run() it returns the size of a maximum matching in the graph.
+ int size () const;
+
+ ///Resets the map storing the Gallai-Edmonds decomposition.
+
+ ///Resets the map storing the Gallai-Edmonds decomposition of the
+ ///graph, making it possible to run the algorithm. Must be called
+ ///before all runs of the Edmonds algorithm, except for the first
+ ///run.
+ void resetPos();
+
+ ///Resets the actual matching to the empty matching.
+
+ ///Resets the actual matching to the empty matching.
+ ///
+ void resetMatching();
+
+ ///Reads a matching from a \c Node map of \c Nodes.
+
+ ///Reads a matching from a \c Node map of \c Nodes. This map must be \e
+ ///symmetric, i.e. if \c map[u]=v then \c map[v]=u must hold, and
+ ///\c uv will be an edge of the matching.
+ template<typename NMapN>
+ void readNMapNode(NMapN& map) {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ mate.set(v,map[v]);
+ }
+ }
+
+ ///Writes the stored matching to a \c Node map of \c Nodes.
+
+ ///Writes the stored matching to a \c Node map of \c Nodes. The
+ ///resulting map will be \e symmetric, i.e. if \c map[u]=v then \c
+ ///map[v]=u will hold, and now \c uv is an edge of the matching.
+ template<typename NMapN>
+ void writeNMapNode (NMapN& map) const {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ map.set(v,mate[v]);
+ }
+ }
+
+ ///Reads a matching from a \c Node map of \c Edges.
+
+ ///Reads a matching from a \c Node map of incident \c Edges. This
+ ///map must have the property that if \c G.target(map[u])=v then \c
+ ///G.target(map[v])=u must hold, and now this edge is an edge of
+ ///the matching.
+ template<typename NMapE>
+ void readNMapEdge(NMapE& map) {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ Edge e=map[v];
+ if ( g.valid(e) )
+ g.source(e) == v ? mate.set(v,g.target(e)) : mate.set(v,g.source(e));
+ }
+ }
+
+ ///Writes the matching stored to a \c Node map of \c Edges.
+
+ ///Writes the stored matching to a \c Node map of incident \c
+ ///Edges. This map will have the property that if \c
+ ///g.target(map[u])=v then \c g.target(map[v])=u holds, and now this
+ ///edge is an edge of the matching.
+ template<typename NMapE>
+ void writeNMapEdge (NMapE& map) const {
+ typename Graph::template NodeMap<bool> todo(g,true);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( todo[v] && mate[v]!=INVALID ) {
+ Node u=mate[v];
+ for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
+ if ( g.target(e) == u ) {
+ map.set(u,e);
+ map.set(v,e);
+ todo.set(u,false);
+ todo.set(v,false);
+ break;
+ }
+ }
+ }
+ }
+ }
+
+
+ ///Reads a matching from an \c Edge map of \c bools.
+
+ ///Reads a matching from an \c Edge map of \c bools. This map must
+ ///have the property that there are no two adjacent edges \c e, \c
+ ///f with \c map[e]=map[f]=true. The edges \c e with \c
+ ///map[e]=true form the matching.
+ template<typename EMapB>
+ void readEMapBool(EMapB& map) {
+ for(UndirEdgeIt e(g); e!=INVALID; ++e) {
+ if ( map[e] ) {
+ Node u=g.source(e);
+ Node v=g.target(e);
+ mate.set(u,v);
+ mate.set(v,u);
+ }
+ }
+ }
+ //iterable boolmap?
+
+
+ ///Writes the matching stored to an \c Edge map of \c bools.
+
+ ///Writes the matching stored to an \c Edge map of \c bools. This
+ ///map will have the property that there are no two adjacent edges
+ ///\c e, \c f with \c map[e]=map[f]=true. The edges \c e with \c
+ ///map[e]=true form the matching.
+ template<typename EMapB>
+ void writeEMapBool (EMapB& map) const {
+ for(UndirEdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
+
+ typename Graph::template NodeMap<bool> todo(g,true);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( todo[v] && mate[v]!=INVALID ) {
+ Node u=mate[v];
+ for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
+ if ( g.target(e) == u ) {
+ map.set(e,true);
+ todo.set(u,false);
+ todo.set(v,false);
+ break;
+ }
+ }
+ }
+ }
+ }
+
+
+ ///Writes the canonical decomposition of the graph after running
+ ///the algorithm.
+
+ ///After calling any run methods of the class, and before calling
+ ///\ref resetPos(), it writes the Gallai-Edmonds canonical
+ ///decomposition of the graph. \c map must be a node map
+ ///of \ref pos_enum 's.
+ template<typename NMapEnum>
+ void writePos (NMapEnum& map) const {
+ for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
+ }
+
+ private:
+
+ void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree);
+
+ void normShrink(Node v, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree);
+
+ bool noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree, std::queue<Node>& Q);
+
+ void shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree, std::queue<Node>& Q);
+
+ void augment(Node x, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree);
+ };
+
+
+ // **********************************************************************
+ // IMPLEMENTATIONS
+ // **********************************************************************
+
+
+ template <typename Graph>
+ void MaxMatching<Graph>::run() {
+ if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) {
+ greedyMatching();
+ runEdmonds(1);
+ } else runEdmonds(0);
+ }
+
+
+ template <typename Graph>
+ void MaxMatching<Graph>::runEdmonds( int heur=1 ) {
+
+ std::cout<<"Entering runEdmonds"<<std::endl;
+
+ typename Graph::template NodeMap<Node> ear(g,INVALID);
+ //undefined for the base nodes of the blossoms (i.e. for the
+ //representative elements of UFE blossom) and for the nodes in C
+
+ typename UFE::MapType blossom_base(g);
+ UFE blossom(blossom_base);
+ typename UFE::MapType tree_base(g);
+ UFE tree(tree_base);
+
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( position[v]==C && mate[v]==INVALID ) {
+ blossom.insert(v);
+ tree.insert(v);
+ position.set(v,D);
+ if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
+ else normShrink( v, ear, blossom, tree );
+ }
+ }
+
+
+ std::cout<<" runEdmonds end"<<std::endl;
+
+
+ }
+
+ template <typename Graph>
+ void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree) {
+
+
+ std::cout<<"Entering lateShrink"<<std::endl;
+
+
+ std::queue<Node> Q; //queue of the totally unscanned nodes
+ Q.push(v);
+ std::queue<Node> R;
+ //queue of the nodes which must be scanned for a possible shrink
+
+ while ( !Q.empty() ) {
+ Node x=Q.front();
+ Q.pop();
+ if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
+ else R.push(x);
+ }
+
+ while ( !R.empty() ) {
+ Node x=R.front();
+ R.pop();
+
+ for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
+ Node y=g.target(e);
+
+ if ( position[y] == D && blossom.find(x) != blossom.find(y) ) {
+ //x and y must be in the same tree//biztos? az oddbol d-belive lettek is?
+
+ typename Graph::template NodeMap<bool> path(g,false);
+
+ Node b=blossom.find(x);
+ path.set(b,true);
+ b=mate[b];
+ while ( b!=INVALID ) {
+ b=blossom.find(ear[b]);
+ path.set(b,true);
+ b=mate[b];
+ } //going till the root
+
+ Node top=y;
+ Node middle=blossom.find(top);
+ Node bottom=x;
+ while ( !path[middle] )
+ shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
+
+ Node base=middle;
+ top=x;
+ middle=blossom.find(top);
+ bottom=y;
+ Node blossom_base=blossom.find(base);
+ while ( middle!=blossom_base )
+ shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
+
+ blossom.makeRep(base);
+ } // if shrink is needed
+
+ //most nehany odd node is d-beli lett, es rajuk az is megnezendo hogy mely d-beliekkel szonszedosak mas faban
+
+ while ( !Q.empty() ) {
+ Node x=Q.front();
+ Q.pop();
+ if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
+ else R.push(x);
+ }
+ } //for e
+ } // while ( !R.empty() )
+ }
+
+
+ template <typename Graph>
+ void MaxMatching<Graph>::normShrink(Node v, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree) {
+
+
+ std::cout<<"Entering normShrink with node "<<g.id(v)<<std::endl;
+
+
+ std::queue<Node> Q; //queue of the unscanned nodes
+ Q.push(v);
+ while ( !Q.empty() ) {
+
+ std::cout<<"beginning of norm while"<<std::endl;
+
+ Node x=Q.front();
+ Q.pop();
+
+ for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
+
+
+ for( IncEdgeIt f(g,x); f!=INVALID; ++f ) {
+ std::cout<<"Starting for." <<std::endl;
+ std::cout<<"edges " << g.id(f)<< " : " << g.id(g.target(f))<<std::endl;
+ std::cout<<"Ending for." <<std::endl;
+ }
+
+ std::cout<<"Ending the whole for." <<std::endl;
+ std::cout<<"for (In normShrink) with edge " << g.id(e)<< " : " << g.id(x);
+
+ Node y=g.target(e);
+
+ std::cout<<" "<<g.id(y)<<std::endl;
+
+ switch ( position[y] ) {
+ case D: //x and y must be in the same tree //asszem nem!!!
+
+ std::cout<<" pos[y] " << position[y]<<std::endl;
+ std::cout<<" blossom.find(x) ="<< g.id(blossom.find(x))<<std::endl;
+ std::cout<<" blossom.find(y) ="<< g.id(blossom.find(y))<<std::endl;
+
+
+ if ( blossom.find(x) != blossom.find(y) ) { //shrink
+ typename Graph::template NodeMap<bool> path(g,false);
+
+ Node b=blossom.find(x);
+ path.set(b,true);
+ b=mate[b];
+ while ( b!=INVALID ) {
+ b=blossom.find(ear[b]);
+ path.set(b,true);
+ b=mate[b];
+ } //going till the root
+
+ Node top=y;
+ Node middle=blossom.find(top);
+ Node bottom=x;
+ while ( !path[middle] )
+ shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
+
+ Node base=middle;
+ top=x;
+ middle=blossom.find(top);
+ bottom=y;
+ Node blossom_base=blossom.find(base);
+ while ( middle!=blossom_base )
+ shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
+
+ blossom.makeRep(base);
+ }
+ break;
+ case C:
+ if ( mate[y]!=INVALID ) { //grow
+
+ std::cout<<"grow"<<std::endl;
+
+ ear.set(y,x);
+ Node w=mate[y];
+ blossom.insert(w);
+ position.set(y,A);
+ position.set(w,D);
+ tree.insert(y);
+ tree.insert(w);
+ tree.join(y,blossom.find(x));
+ tree.join(w,y);
+ Q.push(w);
+
+ } else { //augment
+
+ std::cout<<"augment"<<std::endl;
+
+ augment(x, ear, blossom, tree);
+ mate.set(x,y);
+ mate.set(y,x);
+ return;
+ } //if
+
+ std::cout<<"end c eset"<<std::endl;
+ break;
+ default: break;
+ }
+ std::cout<<"end switch"<<std::endl;
+ }
+ }
+ }
+
+ template <typename Graph>
+ void MaxMatching<Graph>::greedyMatching() {
+ for(NodeIt v(g); v!=INVALID; ++v)
+ if ( mate[v]==INVALID ) {
+ for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
+ Node y=g.target(e);
+ if ( mate[y]==INVALID && y!=v ) {
+ mate.set(v,y);
+ mate.set(y,v);
+ break;
+ }
+ }
+ }
+ }
+
+ template <typename Graph>
+ int MaxMatching<Graph>::size() const {
+ int s=0;
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( mate[v]!=INVALID ) {
+ ++s;
+ }
+ }
+ return (int)s/2;
+ }
+
+ template <typename Graph>
+ void MaxMatching<Graph>::resetPos() {
+ for(NodeIt v(g); v!=INVALID; ++v)
+ position.set(v,C);
+ }
+
+ template <typename Graph>
+ void MaxMatching<Graph>::resetMatching() {
+ for(NodeIt v(g); v!=INVALID; ++v)
+ mate.set(v,INVALID);
+ }
+
+ template <typename Graph>
+ bool MaxMatching<Graph>::noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree, std::queue<Node>& Q) {
+ for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
+ Node y=g.target(e);
+
+ if ( position[y]==C ) {
+ if ( mate[y]!=INVALID ) { //grow
+ ear.set(y,x);
+ Node w=mate[y];
+ blossom.insert(w);
+ position.set(y,A);
+ position.set(w,D);
+ tree.insert(y);
+ tree.insert(w);
+ tree.join(y,blossom.find(x));
+ tree.join(w,y);
+ Q.push(w);
+ } else { //augment
+ augment(x, ear, blossom, tree);
+ mate.set(x,y);
+ mate.set(y,x);
+ return true;
+ }
+ }
+ }
+ return false;
+ }
+
+ template <typename Graph>
+ void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree, std::queue<Node>& Q) {
+ ear.set(top,bottom);
+ Node t=top;
+ while ( t!=middle ) {
+ Node u=mate[t];
+ t=ear[u];
+ ear.set(t,u);
+ }
+ bottom=mate[middle];
+ position.set(bottom,D);
+ Q.push(bottom);
+ top=ear[bottom];
+ Node oldmiddle=middle;
+ middle=blossom.find(top);
+ tree.erase(bottom);
+ tree.erase(oldmiddle);
+ blossom.insert(bottom);
+ blossom.join(bottom, oldmiddle);
+ blossom.join(top, oldmiddle);
+ }
+
+ template <typename Graph>
+ void MaxMatching<Graph>::augment(Node x, typename Graph::NodeMap<Node>& ear,
+ UFE& blossom, UFE& tree) {
+ Node v=mate[x];
+ while ( v!=INVALID ) {
+
+ Node u=ear[v];
+ mate.set(v,u);
+ Node tmp=v;
+ v=mate[u];
+ mate.set(u,tmp);
+ }
+ typename UFE::ItemIt it;
+ for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {
+ if ( position[it] == D ) {
+ typename UFE::ItemIt b_it;
+ for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {
+ position.set( b_it ,C);
+ }
+ blossom.eraseClass(it);
+ } else position.set( it ,C);
+ }
+ tree.eraseClass(x);
+
+ }
+
+ /// @}
+
+} //END OF NAMESPACE LEMON
+
+#endif //EDMONDS_H
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