# HG changeset patch
# User Balazs Dezso <deba@inf.elte.hu>
# Date 1223898960 -7200
# Node ID 64ad48007fb28697c78f3f4c644894cd9572f14d
# Parent 6dbd5184c6a99e936a7de899e64c114e30c0f94f
Port maximum matching algorithms from svn 3498 (ticket #48)
diff -r 6dbd5184c6a9 -r 64ad48007fb2 lemon/Makefile.am
--- a/lemon/Makefile.am Sun Oct 12 19:35:48 2008 +0100
+++ b/lemon/Makefile.am Mon Oct 13 13:56:00 2008 +0200
@@ -35,6 +35,7 @@
lemon/list_graph.h \
lemon/maps.h \
lemon/math.h \
+ lemon/max_matching.h \
lemon/path.h \
lemon/random.h \
lemon/smart_graph.h \
diff -r 6dbd5184c6a9 -r 64ad48007fb2 lemon/max_matching.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/max_matching.h Mon Oct 13 13:56:00 2008 +0200
@@ -0,0 +1,3112 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_MAX_MATCHING_H
+#define LEMON_MAX_MATCHING_H
+
+#include <vector>
+#include <queue>
+#include <set>
+#include <limits>
+
+#include <lemon/core.h>
+#include <lemon/unionfind.h>
+#include <lemon/bin_heap.h>
+#include <lemon/maps.h>
+
+///\ingroup matching
+///\file
+///\brief Maximum matching algorithms in graph.
+
+namespace lemon {
+
+ ///\ingroup matching
+ ///
+ ///\brief Edmonds' alternating forest maximum matching algorithm.
+ ///
+ ///This class provides Edmonds' alternating forest matching
+ ///algorithm. The starting matching (if any) can be passed to the
+ ///algorithm using some of init functions.
+ ///
+ ///The dual side of a matching is a map of the nodes to
+ ///MaxMatching::DecompType, having values \c D, \c A and \c C
+ ///showing the Gallai-Edmonds decomposition of the digraph. The nodes
+ ///in \c D induce a digraph with factor-critical components, the nodes
+ ///in \c A form the barrier, and the nodes in \c C induce a digraph
+ ///having a perfect matching. This decomposition can be attained by
+ ///calling \c decomposition() after running the algorithm.
+ ///
+ ///\param Digraph The graph type the algorithm runs on.
+ template <typename Graph>
+ class MaxMatching {
+
+ protected:
+
+ TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+ typedef typename Graph::template NodeMap<int> UFECrossRef;
+ typedef UnionFindEnum<UFECrossRef> UFE;
+ typedef std::vector<Node> NV;
+
+ typedef typename Graph::template NodeMap<int> EFECrossRef;
+ typedef ExtendFindEnum<EFECrossRef> EFE;
+
+ public:
+
+ ///\brief Indicates the Gallai-Edmonds decomposition of the digraph.
+ ///
+ ///Indicates the Gallai-Edmonds decomposition of the digraph, which
+ ///shows an upper bound on the size of a maximum matching. The
+ ///nodes with DecompType \c D induce a digraph with factor-critical
+ ///components, the nodes in \c A form the canonical barrier, and the
+ ///nodes in \c C induce a digraph having a perfect matching.
+ enum DecompType {
+ D=0,
+ A=1,
+ C=2
+ };
+
+ protected:
+
+ static const int HEUR_density=2;
+ const Graph& g;
+ typename Graph::template NodeMap<Node> _mate;
+ typename Graph::template NodeMap<DecompType> position;
+
+ public:
+
+ MaxMatching(const Graph& _g)
+ : g(_g), _mate(_g), position(_g) {}
+
+ ///\brief Sets the actual matching to the empty matching.
+ ///
+ ///Sets the actual matching to the empty matching.
+ ///
+ void init() {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ _mate.set(v,INVALID);
+ position.set(v,C);
+ }
+ }
+
+ ///\brief Finds a greedy matching for initial matching.
+ ///
+ ///For initial matchig it finds a maximal greedy matching.
+ void greedyInit() {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ _mate.set(v,INVALID);
+ position.set(v,C);
+ }
+ for(NodeIt v(g); v!=INVALID; ++v)
+ if ( _mate[v]==INVALID ) {
+ for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
+ Node y=g.runningNode(e);
+ if ( _mate[y]==INVALID && y!=v ) {
+ _mate.set(v,y);
+ _mate.set(y,v);
+ break;
+ }
+ }
+ }
+ }
+
+ ///\brief Initialize the matching from each nodes' mate.
+ ///
+ ///Initialize the matching from a \c Node valued \c Node map. 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 arc of the initial
+ ///matching.
+ template <typename MateMap>
+ void mateMapInit(MateMap& map) {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ _mate.set(v,map[v]);
+ position.set(v,C);
+ }
+ }
+
+ ///\brief Initialize the matching from a node map with the
+ ///incident matching arcs.
+ ///
+ ///Initialize the matching from an \c Edge valued \c Node map. \c
+ ///map[v] must be an \c Edge incident to \c v. This map must have
+ ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c
+ ///g.oppositeNode(v,map[v])==u holds, and now some arc joining \c
+ ///u to \c v will be an arc of the matching.
+ template<typename MatchingMap>
+ void matchingMapInit(MatchingMap& map) {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ position.set(v,C);
+ Edge e=map[v];
+ if ( e!=INVALID )
+ _mate.set(v,g.oppositeNode(v,e));
+ else
+ _mate.set(v,INVALID);
+ }
+ }
+
+ ///\brief Initialize the matching from the map containing the
+ ///undirected matching arcs.
+ ///
+ ///Initialize the matching from a \c bool valued \c Edge map. This
+ ///map must have the property that there are no two incident arcs
+ ///\c e, \c f with \c map[e]==map[f]==true. The arcs \c e with \c
+ ///map[e]==true form the matching.
+ template <typename MatchingMap>
+ void matchingInit(MatchingMap& map) {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ _mate.set(v,INVALID);
+ position.set(v,C);
+ }
+ for(EdgeIt e(g); e!=INVALID; ++e) {
+ if ( map[e] ) {
+ Node u=g.u(e);
+ Node v=g.v(e);
+ _mate.set(u,v);
+ _mate.set(v,u);
+ }
+ }
+ }
+
+
+ ///\brief Runs Edmonds' algorithm.
+ ///
+ ///Runs Edmonds' algorithm for sparse digraphs (number of arcs <
+ ///2*number of nodes), and a heuristical Edmonds' algorithm with a
+ ///heuristic of postponing shrinks for dense digraphs.
+ void run() {
+ if (countEdges(g) < HEUR_density * countNodes(g)) {
+ greedyInit();
+ startSparse();
+ } else {
+ init();
+ startDense();
+ }
+ }
+
+
+ ///\brief Starts Edmonds' algorithm.
+ ///
+ ///If runs the original Edmonds' algorithm.
+ void startSparse() {
+
+ 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
+
+ UFECrossRef blossom_base(g);
+ UFE blossom(blossom_base);
+ NV rep(countNodes(g));
+
+ EFECrossRef tree_base(g);
+ EFE tree(tree_base);
+
+ //If these UFE's would be members of the class then also
+ //blossom_base and tree_base should be a member.
+
+ //We build only one tree and the other vertices uncovered by the
+ //matching belong to C. (They can be considered as singleton
+ //trees.) If this tree can be augmented or no more
+ //grow/augmentation/shrink is possible then we return to this
+ //"for" cycle.
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if (position[v]==C && _mate[v]==INVALID) {
+ rep[blossom.insert(v)] = v;
+ tree.insert(v);
+ position.set(v,D);
+ normShrink(v, ear, blossom, rep, tree);
+ }
+ }
+ }
+
+ ///\brief Starts Edmonds' algorithm.
+ ///
+ ///It runs Edmonds' algorithm with a heuristic of postponing
+ ///shrinks, giving a faster algorithm for dense digraphs.
+ void startDense() {
+
+ 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
+
+ UFECrossRef blossom_base(g);
+ UFE blossom(blossom_base);
+ NV rep(countNodes(g));
+
+ EFECrossRef tree_base(g);
+ EFE tree(tree_base);
+
+ //If these UFE's would be members of the class then also
+ //blossom_base and tree_base should be a member.
+
+ //We build only one tree and the other vertices uncovered by the
+ //matching belong to C. (They can be considered as singleton
+ //trees.) If this tree can be augmented or no more
+ //grow/augmentation/shrink is possible then we return to this
+ //"for" cycle.
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( position[v]==C && _mate[v]==INVALID ) {
+ rep[blossom.insert(v)] = v;
+ tree.insert(v);
+ position.set(v,D);
+ lateShrink(v, ear, blossom, rep, tree);
+ }
+ }
+ }
+
+
+
+ ///\brief 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 digraph.
+ int size() const {
+ int s=0;
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( _mate[v]!=INVALID ) {
+ ++s;
+ }
+ }
+ return s/2;
+ }
+
+
+ ///\brief Returns the mate of a node in the actual matching.
+ ///
+ ///Returns the mate of a \c node in the actual matching.
+ ///Returns INVALID if the \c node is not covered by the actual matching.
+ Node mate(const Node& node) const {
+ return _mate[node];
+ }
+
+ ///\brief Returns the matching arc incident to the given node.
+ ///
+ ///Returns the matching arc of a \c node in the actual matching.
+ ///Returns INVALID if the \c node is not covered by the actual matching.
+ Edge matchingArc(const Node& node) const {
+ if (_mate[node] == INVALID) return INVALID;
+ Node n = node < _mate[node] ? node : _mate[node];
+ for (IncEdgeIt e(g, n); e != INVALID; ++e) {
+ if (g.oppositeNode(n, e) == _mate[n]) {
+ return e;
+ }
+ }
+ return INVALID;
+ }
+
+ /// \brief Returns the class of the node in the Edmonds-Gallai
+ /// decomposition.
+ ///
+ /// Returns the class of the node in the Edmonds-Gallai
+ /// decomposition.
+ DecompType decomposition(const Node& n) {
+ return position[n] == A;
+ }
+
+ /// \brief Returns true when the node is in the barrier.
+ ///
+ /// Returns true when the node is in the barrier.
+ bool barrier(const Node& n) {
+ return position[n] == A;
+ }
+
+ ///\brief Gives back the matching in a \c Node of mates.
+ ///
+ ///Writes the stored matching to a \c Node valued \c Node map. 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 arc of the matching.
+ template <typename MateMap>
+ void mateMap(MateMap& map) const {
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ map.set(v,_mate[v]);
+ }
+ }
+
+ ///\brief Gives back the matching in an \c Edge valued \c Node
+ ///map.
+ ///
+ ///Writes the stored matching to an \c Edge valued \c Node
+ ///map. \c map[v] will be an \c Edge incident to \c v. This
+ ///map will have the property that if \c g.oppositeNode(u,map[u])
+ ///== v then \c map[u]==map[v] holds, and now this arc is an arc
+ ///of the matching.
+ template <typename MatchingMap>
+ void matchingMap(MatchingMap& map) const {
+ typename Graph::template NodeMap<bool> todo(g,true);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if (_mate[v]!=INVALID && v < _mate[v]) {
+ Node u=_mate[v];
+ for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
+ if ( g.runningNode(e) == u ) {
+ map.set(u,e);
+ map.set(v,e);
+ todo.set(u,false);
+ todo.set(v,false);
+ break;
+ }
+ }
+ }
+ }
+ }
+
+
+ ///\brief Gives back the matching in a \c bool valued \c Edge
+ ///map.
+ ///
+ ///Writes the matching stored to a \c bool valued \c Arc
+ ///map. This map will have the property that there are no two
+ ///incident arcs \c e, \c f with \c map[e]==map[f]==true. The
+ ///arcs \c e with \c map[e]==true form the matching.
+ template<typename MatchingMap>
+ void matching(MatchingMap& map) const {
+ for(EdgeIt 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.runningNode(e) == u ) {
+ map.set(e,true);
+ todo.set(u,false);
+ todo.set(v,false);
+ break;
+ }
+ }
+ }
+ }
+ }
+
+
+ ///\brief Returns the canonical decomposition of the digraph after running
+ ///the algorithm.
+ ///
+ ///After calling any run methods of the class, it writes the
+ ///Gallai-Edmonds canonical decomposition of the digraph. \c map
+ ///must be a node map of \ref DecompType 's.
+ template <typename DecompositionMap>
+ void decomposition(DecompositionMap& map) const {
+ for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
+ }
+
+ ///\brief Returns a barrier on the nodes.
+ ///
+ ///After calling any run methods of the class, it writes a
+ ///canonical barrier on the nodes. The odd component number of the
+ ///remaining digraph minus the barrier size is a lower bound for the
+ ///uncovered nodes in the digraph. The \c map must be a node map of
+ ///bools.
+ template <typename BarrierMap>
+ void barrier(BarrierMap& barrier) {
+ for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A);
+ }
+
+ private:
+
+
+ void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, NV& rep, EFE& tree) {
+ //We have one tree which we grow, and also shrink but only if it
+ //cannot be postponed. If we augment then we return to the "for"
+ //cycle of runEdmonds().
+
+ 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();
+ for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
+ Node y=g.runningNode(e);
+ //growOrAugment grows if y is covered by the matching and
+ //augments if not. In this latter case it returns 1.
+ if (position[y]==C &&
+ growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
+ }
+ R.push(x);
+ }
+
+ while ( !R.empty() ) {
+ Node x=R.front();
+ R.pop();
+
+ for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
+ Node y=g.runningNode(e);
+
+ if ( position[y] == D && blossom.find(x) != blossom.find(y) )
+ //Recall that we have only one tree.
+ shrink( x, y, ear, blossom, rep, tree, Q);
+
+ while ( !Q.empty() ) {
+ Node z=Q.front();
+ Q.pop();
+ for( IncEdgeIt f(g,z); f!= INVALID; ++f ) {
+ Node w=g.runningNode(f);
+ //growOrAugment grows if y is covered by the matching and
+ //augments if not. In this latter case it returns 1.
+ if (position[w]==C &&
+ growOrAugment(w, z, ear, blossom, rep, tree, Q)) return;
+ }
+ R.push(z);
+ }
+ } //for e
+ } // while ( !R.empty() )
+ }
+
+ void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, NV& rep, EFE& tree) {
+ //We have one tree, which we grow and shrink. If we augment then we
+ //return to the "for" cycle of runEdmonds().
+
+ std::queue<Node> Q; //queue of the unscanned nodes
+ Q.push(v);
+ while ( !Q.empty() ) {
+
+ Node x=Q.front();
+ Q.pop();
+
+ for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
+ Node y=g.runningNode(e);
+
+ switch ( position[y] ) {
+ case D: //x and y must be in the same tree
+ if ( blossom.find(x) != blossom.find(y))
+ //x and y are in the same tree
+ shrink(x, y, ear, blossom, rep, tree, Q);
+ break;
+ case C:
+ //growOrAugment grows if y is covered by the matching and
+ //augments if not. In this latter case it returns 1.
+ if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
+ break;
+ default: break;
+ }
+ }
+ }
+ }
+
+ void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) {
+ //x and y are the two adjacent vertices in two blossoms.
+
+ typename Graph::template NodeMap<bool> path(g,false);
+
+ Node b=rep[blossom.find(x)];
+ path.set(b,true);
+ b=_mate[b];
+ while ( b!=INVALID ) {
+ b=rep[blossom.find(ear[b])];
+ path.set(b,true);
+ b=_mate[b];
+ } //we go until the root through bases of blossoms and odd vertices
+
+ Node top=y;
+ Node middle=rep[blossom.find(top)];
+ Node bottom=x;
+ while ( !path[middle] )
+ shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
+ //Until we arrive to a node on the path, we update blossom, tree
+ //and the positions of the odd nodes.
+
+ Node base=middle;
+ top=x;
+ middle=rep[blossom.find(top)];
+ bottom=y;
+ Node blossom_base=rep[blossom.find(base)];
+ while ( middle!=blossom_base )
+ shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
+ //Until we arrive to a node on the path, we update blossom, tree
+ //and the positions of the odd nodes.
+
+ rep[blossom.find(base)] = base;
+ }
+
+ void shrinkStep(Node& top, Node& middle, Node& bottom,
+ typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) {
+ //We traverse a blossom and update everything.
+
+ 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=rep[blossom.find(top)];
+ tree.erase(bottom);
+ tree.erase(oldmiddle);
+ blossom.insert(bottom);
+ blossom.join(bottom, oldmiddle);
+ blossom.join(top, oldmiddle);
+ }
+
+
+
+ bool growOrAugment(Node& y, Node& x, typename Graph::template
+ NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree,
+ std::queue<Node>& Q) {
+ //x is in a blossom in the tree, y is outside. If y is covered by
+ //the matching we grow, otherwise we augment. In this case we
+ //return 1.
+
+ if ( _mate[y]!=INVALID ) { //grow
+ ear.set(y,x);
+ Node w=_mate[y];
+ rep[blossom.insert(w)] = w;
+ position.set(y,A);
+ position.set(w,D);
+ int t = tree.find(rep[blossom.find(x)]);
+ tree.insert(y,t);
+ tree.insert(w,t);
+ Q.push(w);
+ } else { //augment
+ augment(x, ear, blossom, rep, tree);
+ _mate.set(x,y);
+ _mate.set(y,x);
+ return true;
+ }
+ return false;
+ }
+
+ void augment(Node x, typename Graph::template NodeMap<Node>& ear,
+ UFE& blossom, NV& rep, EFE& 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);
+ }
+ int y = tree.find(rep[blossom.find(x)]);
+ for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) {
+ if ( position[tit] == D ) {
+ int b = blossom.find(tit);
+ for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) {
+ position.set(bit, C);
+ }
+ blossom.eraseClass(b);
+ } else position.set(tit, C);
+ }
+ tree.eraseClass(y);
+
+ }
+
+ };
+
+ /// \ingroup matching
+ ///
+ /// \brief Weighted matching in general graphs
+ ///
+ /// This class provides an efficient implementation of Edmond's
+ /// maximum weighted matching algorithm. The implementation is based
+ /// on extensive use of priority queues and provides
+ /// \f$O(nm\log(n))\f$ time complexity.
+ ///
+ /// The maximum weighted matching problem is to find undirected
+ /// arcs in the digraph with maximum overall weight and no two of
+ /// them shares their endpoints. The problem can be formulated with
+ /// the next linear program:
+ /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
+ ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f]
+ /// \f[x_e \ge 0\quad \forall e\in E\f]
+ /// \f[\max \sum_{e\in E}x_ew_e\f]
+ /// where \f$\delta(X)\f$ is the set of arcs incident to a node in
+ /// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints in
+ /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
+ /// the nodes.
+ ///
+ /// The algorithm calculates an optimal matching and a proof of the
+ /// optimality. The solution of the dual problem can be used to check
+ /// the result of the algorithm. The dual linear problem is the next:
+ /// \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]
+ /// \f[y_u \ge 0 \quad \forall u \in V\f]
+ /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
+ /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
+ ///
+ /// The algorithm can be executed with \c run() or the \c init() and
+ /// then the \c start() member functions. After it the matching can
+ /// be asked with \c matching() or mate() functions. The dual
+ /// solution can be get with \c nodeValue(), \c blossomNum() and \c
+ /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
+ /// "BlossomIt" nested class which is able to iterate on the nodes
+ /// of a blossom. If the value type is integral then the dual
+ /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
+ template <typename _Graph,
+ typename _WeightMap = typename _Graph::template EdgeMap<int> >
+ class MaxWeightedMatching {
+ public:
+
+ typedef _Graph Graph;
+ typedef _WeightMap WeightMap;
+ typedef typename WeightMap::Value Value;
+
+ /// \brief Scaling factor for dual solution
+ ///
+ /// Scaling factor for dual solution, it is equal to 4 or 1
+ /// according to the value type.
+ static const int dualScale =
+ std::numeric_limits<Value>::is_integer ? 4 : 1;
+
+ typedef typename Graph::template NodeMap<typename Graph::Arc>
+ MatchingMap;
+
+ private:
+
+ TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+ typedef typename Graph::template NodeMap<Value> NodePotential;
+ typedef std::vector<Node> BlossomNodeList;
+
+ struct BlossomVariable {
+ int begin, end;
+ Value value;
+
+ BlossomVariable(int _begin, int _end, Value _value)
+ : begin(_begin), end(_end), value(_value) {}
+
+ };
+
+ typedef std::vector<BlossomVariable> BlossomPotential;
+
+ const Graph& _graph;
+ const WeightMap& _weight;
+
+ MatchingMap* _matching;
+
+ NodePotential* _node_potential;
+
+ BlossomPotential _blossom_potential;
+ BlossomNodeList _blossom_node_list;
+
+ int _node_num;
+ int _blossom_num;
+
+ typedef typename Graph::template NodeMap<int> NodeIntMap;
+ typedef typename Graph::template ArcMap<int> ArcIntMap;
+ typedef typename Graph::template EdgeMap<int> EdgeIntMap;
+ typedef RangeMap<int> IntIntMap;
+
+ enum Status {
+ EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
+ };
+
+ typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
+ struct BlossomData {
+ int tree;
+ Status status;
+ Arc pred, next;
+ Value pot, offset;
+ Node base;
+ };
+
+ NodeIntMap *_blossom_index;
+ BlossomSet *_blossom_set;
+ RangeMap<BlossomData>* _blossom_data;
+
+ NodeIntMap *_node_index;
+ ArcIntMap *_node_heap_index;
+
+ struct NodeData {
+
+ NodeData(ArcIntMap& node_heap_index)
+ : heap(node_heap_index) {}
+
+ int blossom;
+ Value pot;
+ BinHeap<Value, ArcIntMap> heap;
+ std::map<int, Arc> heap_index;
+
+ int tree;
+ };
+
+ RangeMap<NodeData>* _node_data;
+
+ typedef ExtendFindEnum<IntIntMap> TreeSet;
+
+ IntIntMap *_tree_set_index;
+ TreeSet *_tree_set;
+
+ NodeIntMap *_delta1_index;
+ BinHeap<Value, NodeIntMap> *_delta1;
+
+ IntIntMap *_delta2_index;
+ BinHeap<Value, IntIntMap> *_delta2;
+
+ EdgeIntMap *_delta3_index;
+ BinHeap<Value, EdgeIntMap> *_delta3;
+
+ IntIntMap *_delta4_index;
+ BinHeap<Value, IntIntMap> *_delta4;
+
+ Value _delta_sum;
+
+ void createStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (!_matching) {
+ _matching = new MatchingMap(_graph);
+ }
+ if (!_node_potential) {
+ _node_potential = new NodePotential(_graph);
+ }
+ if (!_blossom_set) {
+ _blossom_index = new NodeIntMap(_graph);
+ _blossom_set = new BlossomSet(*_blossom_index);
+ _blossom_data = new RangeMap<BlossomData>(_blossom_num);
+ }
+
+ if (!_node_index) {
+ _node_index = new NodeIntMap(_graph);
+ _node_heap_index = new ArcIntMap(_graph);
+ _node_data = new RangeMap<NodeData>(_node_num,
+ NodeData(*_node_heap_index));
+ }
+
+ if (!_tree_set) {
+ _tree_set_index = new IntIntMap(_blossom_num);
+ _tree_set = new TreeSet(*_tree_set_index);
+ }
+ if (!_delta1) {
+ _delta1_index = new NodeIntMap(_graph);
+ _delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index);
+ }
+ if (!_delta2) {
+ _delta2_index = new IntIntMap(_blossom_num);
+ _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
+ }
+ if (!_delta3) {
+ _delta3_index = new EdgeIntMap(_graph);
+ _delta3 = new BinHeap<Value, EdgeIntMap>(*_delta3_index);
+ }
+ if (!_delta4) {
+ _delta4_index = new IntIntMap(_blossom_num);
+ _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
+ }
+ }
+
+ void destroyStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (_matching) {
+ delete _matching;
+ }
+ if (_node_potential) {
+ delete _node_potential;
+ }
+ if (_blossom_set) {
+ delete _blossom_index;
+ delete _blossom_set;
+ delete _blossom_data;
+ }
+
+ if (_node_index) {
+ delete _node_index;
+ delete _node_heap_index;
+ delete _node_data;
+ }
+
+ if (_tree_set) {
+ delete _tree_set_index;
+ delete _tree_set;
+ }
+ if (_delta1) {
+ delete _delta1_index;
+ delete _delta1;
+ }
+ if (_delta2) {
+ delete _delta2_index;
+ delete _delta2;
+ }
+ if (_delta3) {
+ delete _delta3_index;
+ delete _delta3;
+ }
+ if (_delta4) {
+ delete _delta4_index;
+ delete _delta4;
+ }
+ }
+
+ void matchedToEven(int blossom, int tree) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot -=
+ 2 * (_delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+ int ni = (*_node_index)[n];
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+
+ (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
+
+ _delta1->push(n, (*_node_data)[ni].pot);
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) != _delta3->IN_HEAP) {
+ _delta3->push(e, rw);
+ }
+ } else {
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset){
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+ void matchedToOdd(int blossom) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+ (*_blossom_data)[blossom].offset += _delta_sum;
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+
+ void evenToMatched(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot += 2 * _delta_sum;
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+ (*_node_data)[ni].pot -= _delta_sum;
+
+ _delta1->erase(n);
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if (vb == blossom) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else if ((*_blossom_data)[vb].status == EVEN) {
+
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+
+ int vt = _tree_set->find(vb);
+
+ if (vt != tree) {
+
+ Arc r = _graph.oppositeArc(e);
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[ni].heap_index.find(vt);
+
+ if (it != (*_node_data)[ni].heap_index.end()) {
+ if ((*_node_data)[ni].heap[it->second] > rw) {
+ (*_node_data)[ni].heap.replace(it->second, r);
+ (*_node_data)[ni].heap.decrease(r, rw);
+ it->second = r;
+ }
+ } else {
+ (*_node_data)[ni].heap.push(r, rw);
+ (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+ }
+
+ if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+ _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+
+ if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ } else if ((*_delta2)[blossom] >
+ _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset){
+ _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+ }
+
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ (*_node_data)[vi].heap.erase(it->second);
+ (*_node_data)[vi].heap_index.erase(it);
+ if ((*_node_data)[vi].heap.empty()) {
+ _blossom_set->increase(v, std::numeric_limits<Value>::max());
+ } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
+ _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
+ }
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_blossom_set->classPrio(vb) ==
+ std::numeric_limits<Value>::max()) {
+ _delta2->erase(vb);
+ } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->increase(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ void oddToMatched(int blossom) {
+ (*_blossom_data)[blossom].offset -= _delta_sum;
+
+ if (_blossom_set->classPrio(blossom) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ }
+ }
+
+ void oddToEven(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ (*_blossom_data)[blossom].pot -=
+ 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+ (*_node_data)[ni].pot +=
+ 2 * _delta_sum - (*_blossom_data)[blossom].offset;
+
+ _delta1->push(n, (*_node_data)[ni].pot);
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) != _delta3->IN_HEAP) {
+ _delta3->push(e, rw);
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+
+ void matchedToUnmatched(int blossom) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+
+ for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.target(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP) {
+ _delta3->push(e, rw);
+ }
+ }
+ }
+ }
+ }
+
+ void unmatchedToMatched(int blossom) {
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if (vb == blossom) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else if ((*_blossom_data)[vb].status == EVEN) {
+
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+
+ int vt = _tree_set->find(vb);
+
+ Arc r = _graph.oppositeArc(e);
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[ni].heap_index.find(vt);
+
+ if (it != (*_node_data)[ni].heap_index.end()) {
+ if ((*_node_data)[ni].heap[it->second] > rw) {
+ (*_node_data)[ni].heap.replace(it->second, r);
+ (*_node_data)[ni].heap.decrease(r, rw);
+ it->second = r;
+ }
+ } else {
+ (*_node_data)[ni].heap.push(r, rw);
+ (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+ }
+
+ if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+ _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+
+ if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
+ (*_blossom_data)[blossom].offset){
+ _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ }
+ }
+ }
+ }
+
+ void alternatePath(int even, int tree) {
+ int odd;
+
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].status = MATCHED;
+
+ while ((*_blossom_data)[even].pred != INVALID) {
+ odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
+ (*_blossom_data)[odd].status = MATCHED;
+ oddToMatched(odd);
+ (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
+
+ even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
+ (*_blossom_data)[even].status = MATCHED;
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].next =
+ _graph.oppositeArc((*_blossom_data)[odd].pred);
+ }
+
+ }
+
+ void destroyTree(int tree) {
+ for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
+ if ((*_blossom_data)[b].status == EVEN) {
+ (*_blossom_data)[b].status = MATCHED;
+ evenToMatched(b, tree);
+ } else if ((*_blossom_data)[b].status == ODD) {
+ (*_blossom_data)[b].status = MATCHED;
+ oddToMatched(b);
+ }
+ }
+ _tree_set->eraseClass(tree);
+ }
+
+
+ void unmatchNode(const Node& node) {
+ int blossom = _blossom_set->find(node);
+ int tree = _tree_set->find(blossom);
+
+ alternatePath(blossom, tree);
+ destroyTree(tree);
+
+ (*_blossom_data)[blossom].status = UNMATCHED;
+ (*_blossom_data)[blossom].base = node;
+ matchedToUnmatched(blossom);
+ }
+
+
+ void augmentOnArc(const Edge& arc) {
+
+ int left = _blossom_set->find(_graph.u(arc));
+ int right = _blossom_set->find(_graph.v(arc));
+
+ if ((*_blossom_data)[left].status == EVEN) {
+ int left_tree = _tree_set->find(left);
+ alternatePath(left, left_tree);
+ destroyTree(left_tree);
+ } else {
+ (*_blossom_data)[left].status = MATCHED;
+ unmatchedToMatched(left);
+ }
+
+ if ((*_blossom_data)[right].status == EVEN) {
+ int right_tree = _tree_set->find(right);
+ alternatePath(right, right_tree);
+ destroyTree(right_tree);
+ } else {
+ (*_blossom_data)[right].status = MATCHED;
+ unmatchedToMatched(right);
+ }
+
+ (*_blossom_data)[left].next = _graph.direct(arc, true);
+ (*_blossom_data)[right].next = _graph.direct(arc, false);
+ }
+
+ void extendOnArc(const Arc& arc) {
+ int base = _blossom_set->find(_graph.target(arc));
+ int tree = _tree_set->find(base);
+
+ int odd = _blossom_set->find(_graph.source(arc));
+ _tree_set->insert(odd, tree);
+ (*_blossom_data)[odd].status = ODD;
+ matchedToOdd(odd);
+ (*_blossom_data)[odd].pred = arc;
+
+ int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
+ (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
+ _tree_set->insert(even, tree);
+ (*_blossom_data)[even].status = EVEN;
+ matchedToEven(even, tree);
+ }
+
+ void shrinkOnArc(const Edge& edge, int tree) {
+ int nca = -1;
+ std::vector<int> left_path, right_path;
+
+ {
+ std::set<int> left_set, right_set;
+ int left = _blossom_set->find(_graph.u(edge));
+ left_path.push_back(left);
+ left_set.insert(left);
+
+ int right = _blossom_set->find(_graph.v(edge));
+ right_path.push_back(right);
+ right_set.insert(right);
+
+ while (true) {
+
+ if ((*_blossom_data)[left].pred == INVALID) break;
+
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+
+ left_set.insert(left);
+
+ if (right_set.find(left) != right_set.end()) {
+ nca = left;
+ break;
+ }
+
+ if ((*_blossom_data)[right].pred == INVALID) break;
+
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+
+ right_set.insert(right);
+
+ if (left_set.find(right) != left_set.end()) {
+ nca = right;
+ break;
+ }
+
+ }
+
+ if (nca == -1) {
+ if ((*_blossom_data)[left].pred == INVALID) {
+ nca = right;
+ while (left_set.find(nca) == left_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ }
+ } else {
+ nca = left;
+ while (right_set.find(nca) == right_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ }
+ }
+ }
+ }
+
+ std::vector<int> subblossoms;
+ Arc prev;
+
+ prev = _graph.direct(edge, true);
+ for (int i = 0; left_path[i] != nca; i += 2) {
+ subblossoms.push_back(left_path[i]);
+ (*_blossom_data)[left_path[i]].next = prev;
+ _tree_set->erase(left_path[i]);
+
+ subblossoms.push_back(left_path[i + 1]);
+ (*_blossom_data)[left_path[i + 1]].status = EVEN;
+ oddToEven(left_path[i + 1], tree);
+ _tree_set->erase(left_path[i + 1]);
+ prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
+ }
+
+ int k = 0;
+ while (right_path[k] != nca) ++k;
+
+ subblossoms.push_back(nca);
+ (*_blossom_data)[nca].next = prev;
+
+ for (int i = k - 2; i >= 0; i -= 2) {
+ subblossoms.push_back(right_path[i + 1]);
+ (*_blossom_data)[right_path[i + 1]].status = EVEN;
+ oddToEven(right_path[i + 1], tree);
+ _tree_set->erase(right_path[i + 1]);
+
+ (*_blossom_data)[right_path[i + 1]].next =
+ (*_blossom_data)[right_path[i + 1]].pred;
+
+ subblossoms.push_back(right_path[i]);
+ _tree_set->erase(right_path[i]);
+ }
+
+ int surface =
+ _blossom_set->join(subblossoms.begin(), subblossoms.end());
+
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
+ }
+ (*_blossom_data)[subblossoms[i]].status = MATCHED;
+ }
+
+ (*_blossom_data)[surface].pot = -2 * _delta_sum;
+ (*_blossom_data)[surface].offset = 0;
+ (*_blossom_data)[surface].status = EVEN;
+ (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
+ (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
+
+ _tree_set->insert(surface, tree);
+ _tree_set->erase(nca);
+ }
+
+ void splitBlossom(int blossom) {
+ Arc next = (*_blossom_data)[blossom].next;
+ Arc pred = (*_blossom_data)[blossom].pred;
+
+ int tree = _tree_set->find(blossom);
+
+ (*_blossom_data)[blossom].status = MATCHED;
+ oddToMatched(blossom);
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+
+ Value offset = (*_blossom_data)[blossom].offset;
+ int b = _blossom_set->find(_graph.source(pred));
+ int d = _blossom_set->find(_graph.source(next));
+
+ int ib = -1, id = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) ib = i;
+ if (subblossoms[i] == d) id = i;
+
+ (*_blossom_data)[subblossoms[i]].offset = offset;
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
+ }
+ if (_blossom_set->classPrio(subblossoms[i]) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(subblossoms[i],
+ _blossom_set->classPrio(subblossoms[i]) -
+ (*_blossom_data)[subblossoms[i]].offset);
+ }
+ }
+
+ if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
+ for (int i = (id + 1) % subblossoms.size();
+ i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].pred = pred;
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ pred = (*_blossom_data)[ub].next;
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
+ }
+
+ (*_blossom_data)[subblossoms[id]].status = ODD;
+ matchedToOdd(subblossoms[id]);
+ _tree_set->insert(subblossoms[id], tree);
+ (*_blossom_data)[subblossoms[id]].next = next;
+ (*_blossom_data)[subblossoms[id]].pred = pred;
+
+ } else {
+
+ for (int i = (ib + 1) % subblossoms.size();
+ i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].next = next;
+ (*_blossom_data)[sb].pred =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred =
+ (*_blossom_data)[tb].next =
+ _graph.oppositeArc((*_blossom_data)[ub].next);
+ next = (*_blossom_data)[ub].next;
+ }
+
+ (*_blossom_data)[subblossoms[ib]].status = ODD;
+ matchedToOdd(subblossoms[ib]);
+ _tree_set->insert(subblossoms[ib], tree);
+ (*_blossom_data)[subblossoms[ib]].next = next;
+ (*_blossom_data)[subblossoms[ib]].pred = pred;
+ }
+ _tree_set->erase(blossom);
+ }
+
+ void extractBlossom(int blossom, const Node& base, const Arc& matching) {
+ if (_blossom_set->trivial(blossom)) {
+ int bi = (*_node_index)[base];
+ Value pot = (*_node_data)[bi].pot;
+
+ _matching->set(base, matching);
+ _blossom_node_list.push_back(base);
+ _node_potential->set(base, pot);
+ } else {
+
+ Value pot = (*_blossom_data)[blossom].pot;
+ int bn = _blossom_node_list.size();
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+ int b = _blossom_set->find(base);
+ int ib = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) { ib = i; break; }
+ }
+
+ for (int i = 1; i < int(subblossoms.size()); i += 2) {
+ int sb = subblossoms[(ib + i) % subblossoms.size()];
+ int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
+
+ Arc m = (*_blossom_data)[tb].next;
+ extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
+ extractBlossom(tb, _graph.source(m), m);
+ }
+ extractBlossom(subblossoms[ib], base, matching);
+
+ int en = _blossom_node_list.size();
+
+ _blossom_potential.push_back(BlossomVariable(bn, en, pot));
+ }
+ }
+
+ void extractMatching() {
+ std::vector<int> blossoms;
+ for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
+ blossoms.push_back(c);
+ }
+
+ for (int i = 0; i < int(blossoms.size()); ++i) {
+ if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
+
+ Value offset = (*_blossom_data)[blossoms[i]].offset;
+ (*_blossom_data)[blossoms[i]].pot += 2 * offset;
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
+ n != INVALID; ++n) {
+ (*_node_data)[(*_node_index)[n]].pot -= offset;
+ }
+
+ Arc matching = (*_blossom_data)[blossoms[i]].next;
+ Node base = _graph.source(matching);
+ extractBlossom(blossoms[i], base, matching);
+ } else {
+ Node base = (*_blossom_data)[blossoms[i]].base;
+ extractBlossom(blossoms[i], base, INVALID);
+ }
+ }
+ }
+
+ public:
+
+ /// \brief Constructor
+ ///
+ /// Constructor.
+ MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
+ : _graph(graph), _weight(weight), _matching(0),
+ _node_potential(0), _blossom_potential(), _blossom_node_list(),
+ _node_num(0), _blossom_num(0),
+
+ _blossom_index(0), _blossom_set(0), _blossom_data(0),
+ _node_index(0), _node_heap_index(0), _node_data(0),
+ _tree_set_index(0), _tree_set(0),
+
+ _delta1_index(0), _delta1(0),
+ _delta2_index(0), _delta2(0),
+ _delta3_index(0), _delta3(0),
+ _delta4_index(0), _delta4(0),
+
+ _delta_sum() {}
+
+ ~MaxWeightedMatching() {
+ destroyStructures();
+ }
+
+ /// \name Execution control
+ /// The simplest way to execute the algorithm is to use the member
+ /// \c run() member function.
+
+ ///@{
+
+ /// \brief Initialize the algorithm
+ ///
+ /// Initialize the algorithm
+ void init() {
+ createStructures();
+
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ _node_heap_index->set(e, BinHeap<Value, ArcIntMap>::PRE_HEAP);
+ }
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ _delta1_index->set(n, _delta1->PRE_HEAP);
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ _delta3_index->set(e, _delta3->PRE_HEAP);
+ }
+ for (int i = 0; i < _blossom_num; ++i) {
+ _delta2_index->set(i, _delta2->PRE_HEAP);
+ _delta4_index->set(i, _delta4->PRE_HEAP);
+ }
+
+ int index = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ Value max = 0;
+ for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+ if (_graph.target(e) == n) continue;
+ if ((dualScale * _weight[e]) / 2 > max) {
+ max = (dualScale * _weight[e]) / 2;
+ }
+ }
+ _node_index->set(n, index);
+ (*_node_data)[index].pot = max;
+ _delta1->push(n, max);
+ int blossom =
+ _blossom_set->insert(n, std::numeric_limits<Value>::max());
+
+ _tree_set->insert(blossom);
+
+ (*_blossom_data)[blossom].status = EVEN;
+ (*_blossom_data)[blossom].pred = INVALID;
+ (*_blossom_data)[blossom].next = INVALID;
+ (*_blossom_data)[blossom].pot = 0;
+ (*_blossom_data)[blossom].offset = 0;
+ ++index;
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ int si = (*_node_index)[_graph.u(e)];
+ int ti = (*_node_index)[_graph.v(e)];
+ if (_graph.u(e) != _graph.v(e)) {
+ _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
+ dualScale * _weight[e]) / 2);
+ }
+ }
+ }
+
+ /// \brief Starts the algorithm
+ ///
+ /// Starts the algorithm
+ void start() {
+ enum OpType {
+ D1, D2, D3, D4
+ };
+
+ int unmatched = _node_num;
+ while (unmatched > 0) {
+ Value d1 = !_delta1->empty() ?
+ _delta1->prio() : std::numeric_limits<Value>::max();
+
+ Value d2 = !_delta2->empty() ?
+ _delta2->prio() : std::numeric_limits<Value>::max();
+
+ Value d3 = !_delta3->empty() ?
+ _delta3->prio() : std::numeric_limits<Value>::max();
+
+ Value d4 = !_delta4->empty() ?
+ _delta4->prio() : std::numeric_limits<Value>::max();
+
+ _delta_sum = d1; OpType ot = D1;
+ if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
+ if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
+ if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
+
+
+ switch (ot) {
+ case D1:
+ {
+ Node n = _delta1->top();
+ unmatchNode(n);
+ --unmatched;
+ }
+ break;
+ case D2:
+ {
+ int blossom = _delta2->top();
+ Node n = _blossom_set->classTop(blossom);
+ Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
+ extendOnArc(e);
+ }
+ break;
+ case D3:
+ {
+ Edge e = _delta3->top();
+
+ int left_blossom = _blossom_set->find(_graph.u(e));
+ int right_blossom = _blossom_set->find(_graph.v(e));
+
+ if (left_blossom == right_blossom) {
+ _delta3->pop();
+ } else {
+ int left_tree;
+ if ((*_blossom_data)[left_blossom].status == EVEN) {
+ left_tree = _tree_set->find(left_blossom);
+ } else {
+ left_tree = -1;
+ ++unmatched;
+ }
+ int right_tree;
+ if ((*_blossom_data)[right_blossom].status == EVEN) {
+ right_tree = _tree_set->find(right_blossom);
+ } else {
+ right_tree = -1;
+ ++unmatched;
+ }
+
+ if (left_tree == right_tree) {
+ shrinkOnArc(e, left_tree);
+ } else {
+ augmentOnArc(e);
+ unmatched -= 2;
+ }
+ }
+ } break;
+ case D4:
+ splitBlossom(_delta4->top());
+ break;
+ }
+ }
+ extractMatching();
+ }
+
+ /// \brief Runs %MaxWeightedMatching algorithm.
+ ///
+ /// This method runs the %MaxWeightedMatching algorithm.
+ ///
+ /// \note mwm.run() is just a shortcut of the following code.
+ /// \code
+ /// mwm.init();
+ /// mwm.start();
+ /// \endcode
+ void run() {
+ init();
+ start();
+ }
+
+ /// @}
+
+ /// \name Primal solution
+ /// Functions for get the primal solution, ie. the matching.
+
+ /// @{
+
+ /// \brief Returns the matching value.
+ ///
+ /// Returns the matching value.
+ Value matchingValue() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] != INVALID) {
+ sum += _weight[(*_matching)[n]];
+ }
+ }
+ return sum /= 2;
+ }
+
+ /// \brief Returns true when the arc is in the matching.
+ ///
+ /// Returns true when the arc is in the matching.
+ bool matching(const Edge& arc) const {
+ return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
+ }
+
+ /// \brief Returns the incident matching arc.
+ ///
+ /// Returns the incident matching arc from given node. If the
+ /// node is not matched then it gives back \c INVALID.
+ Arc matching(const Node& node) const {
+ return (*_matching)[node];
+ }
+
+ /// \brief Returns the mate of the node.
+ ///
+ /// Returns the adjancent node in a mathcing arc. If the node is
+ /// not matched then it gives back \c INVALID.
+ Node mate(const Node& node) const {
+ return (*_matching)[node] != INVALID ?
+ _graph.target((*_matching)[node]) : INVALID;
+ }
+
+ /// @}
+
+ /// \name Dual solution
+ /// Functions for get the dual solution.
+
+ /// @{
+
+ /// \brief Returns the value of the dual solution.
+ ///
+ /// Returns the value of the dual solution. It should be equal to
+ /// the primal value scaled by \ref dualScale "dual scale".
+ Value dualValue() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ sum += nodeValue(n);
+ }
+ for (int i = 0; i < blossomNum(); ++i) {
+ sum += blossomValue(i) * (blossomSize(i) / 2);
+ }
+ return sum;
+ }
+
+ /// \brief Returns the value of the node.
+ ///
+ /// Returns the the value of the node.
+ Value nodeValue(const Node& n) const {
+ return (*_node_potential)[n];
+ }
+
+ /// \brief Returns the number of the blossoms in the basis.
+ ///
+ /// Returns the number of the blossoms in the basis.
+ /// \see BlossomIt
+ int blossomNum() const {
+ return _blossom_potential.size();
+ }
+
+
+ /// \brief Returns the number of the nodes in the blossom.
+ ///
+ /// Returns the number of the nodes in the blossom.
+ int blossomSize(int k) const {
+ return _blossom_potential[k].end - _blossom_potential[k].begin;
+ }
+
+ /// \brief Returns the value of the blossom.
+ ///
+ /// Returns the the value of the blossom.
+ /// \see BlossomIt
+ Value blossomValue(int k) const {
+ return _blossom_potential[k].value;
+ }
+
+ /// \brief Lemon iterator for get the items of the blossom.
+ ///
+ /// Lemon iterator for get the nodes of the blossom. This class
+ /// provides a common style lemon iterator which gives back a
+ /// subset of the nodes.
+ class BlossomIt {
+ public:
+
+ /// \brief Constructor.
+ ///
+ /// Constructor for get the nodes of the variable.
+ BlossomIt(const MaxWeightedMatching& algorithm, int variable)
+ : _algorithm(&algorithm)
+ {
+ _index = _algorithm->_blossom_potential[variable].begin;
+ _last = _algorithm->_blossom_potential[variable].end;
+ }
+
+ /// \brief Invalid constructor.
+ ///
+ /// Invalid constructor.
+ BlossomIt(Invalid) : _index(-1) {}
+
+ /// \brief Conversion to node.
+ ///
+ /// Conversion to node.
+ operator Node() const {
+ return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
+ }
+
+ /// \brief Increment operator.
+ ///
+ /// Increment operator.
+ BlossomIt& operator++() {
+ ++_index;
+ if (_index == _last) {
+ _index = -1;
+ }
+ return *this;
+ }
+
+ bool operator==(const BlossomIt& it) const {
+ return _index == it._index;
+ }
+ bool operator!=(const BlossomIt& it) const {
+ return _index != it._index;
+ }
+
+ private:
+ const MaxWeightedMatching* _algorithm;
+ int _last;
+ int _index;
+ };
+
+ /// @}
+
+ };
+
+ /// \ingroup matching
+ ///
+ /// \brief Weighted perfect matching in general graphs
+ ///
+ /// This class provides an efficient implementation of Edmond's
+ /// maximum weighted perfecr matching algorithm. The implementation
+ /// is based on extensive use of priority queues and provides
+ /// \f$O(nm\log(n))\f$ time complexity.
+ ///
+ /// The maximum weighted matching problem is to find undirected
+ /// arcs in the digraph with maximum overall weight and no two of
+ /// them shares their endpoints and covers all nodes. The problem
+ /// can be formulated with the next linear program:
+ /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
+ ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f]
+ /// \f[x_e \ge 0\quad \forall e\in E\f]
+ /// \f[\max \sum_{e\in E}x_ew_e\f]
+ /// where \f$\delta(X)\f$ is the set of arcs incident to a node in
+ /// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints in
+ /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
+ /// the nodes.
+ ///
+ /// The algorithm calculates an optimal matching and a proof of the
+ /// optimality. The solution of the dual problem can be used to check
+ /// the result of the algorithm. The dual linear problem is the next:
+ /// \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]
+ /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
+ /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
+ ///
+ /// The algorithm can be executed with \c run() or the \c init() and
+ /// then the \c start() member functions. After it the matching can
+ /// be asked with \c matching() or mate() functions. The dual
+ /// solution can be get with \c nodeValue(), \c blossomNum() and \c
+ /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
+ /// "BlossomIt" nested class which is able to iterate on the nodes
+ /// of a blossom. If the value type is integral then the dual
+ /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
+ template <typename _Graph,
+ typename _WeightMap = typename _Graph::template EdgeMap<int> >
+ class MaxWeightedPerfectMatching {
+ public:
+
+ typedef _Graph Graph;
+ typedef _WeightMap WeightMap;
+ typedef typename WeightMap::Value Value;
+
+ /// \brief Scaling factor for dual solution
+ ///
+ /// Scaling factor for dual solution, it is equal to 4 or 1
+ /// according to the value type.
+ static const int dualScale =
+ std::numeric_limits<Value>::is_integer ? 4 : 1;
+
+ typedef typename Graph::template NodeMap<typename Graph::Arc>
+ MatchingMap;
+
+ private:
+
+ TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+ typedef typename Graph::template NodeMap<Value> NodePotential;
+ typedef std::vector<Node> BlossomNodeList;
+
+ struct BlossomVariable {
+ int begin, end;
+ Value value;
+
+ BlossomVariable(int _begin, int _end, Value _value)
+ : begin(_begin), end(_end), value(_value) {}
+
+ };
+
+ typedef std::vector<BlossomVariable> BlossomPotential;
+
+ const Graph& _graph;
+ const WeightMap& _weight;
+
+ MatchingMap* _matching;
+
+ NodePotential* _node_potential;
+
+ BlossomPotential _blossom_potential;
+ BlossomNodeList _blossom_node_list;
+
+ int _node_num;
+ int _blossom_num;
+
+ typedef typename Graph::template NodeMap<int> NodeIntMap;
+ typedef typename Graph::template ArcMap<int> ArcIntMap;
+ typedef typename Graph::template EdgeMap<int> EdgeIntMap;
+ typedef RangeMap<int> IntIntMap;
+
+ enum Status {
+ EVEN = -1, MATCHED = 0, ODD = 1
+ };
+
+ typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
+ struct BlossomData {
+ int tree;
+ Status status;
+ Arc pred, next;
+ Value pot, offset;
+ };
+
+ NodeIntMap *_blossom_index;
+ BlossomSet *_blossom_set;
+ RangeMap<BlossomData>* _blossom_data;
+
+ NodeIntMap *_node_index;
+ ArcIntMap *_node_heap_index;
+
+ struct NodeData {
+
+ NodeData(ArcIntMap& node_heap_index)
+ : heap(node_heap_index) {}
+
+ int blossom;
+ Value pot;
+ BinHeap<Value, ArcIntMap> heap;
+ std::map<int, Arc> heap_index;
+
+ int tree;
+ };
+
+ RangeMap<NodeData>* _node_data;
+
+ typedef ExtendFindEnum<IntIntMap> TreeSet;
+
+ IntIntMap *_tree_set_index;
+ TreeSet *_tree_set;
+
+ IntIntMap *_delta2_index;
+ BinHeap<Value, IntIntMap> *_delta2;
+
+ EdgeIntMap *_delta3_index;
+ BinHeap<Value, EdgeIntMap> *_delta3;
+
+ IntIntMap *_delta4_index;
+ BinHeap<Value, IntIntMap> *_delta4;
+
+ Value _delta_sum;
+
+ void createStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (!_matching) {
+ _matching = new MatchingMap(_graph);
+ }
+ if (!_node_potential) {
+ _node_potential = new NodePotential(_graph);
+ }
+ if (!_blossom_set) {
+ _blossom_index = new NodeIntMap(_graph);
+ _blossom_set = new BlossomSet(*_blossom_index);
+ _blossom_data = new RangeMap<BlossomData>(_blossom_num);
+ }
+
+ if (!_node_index) {
+ _node_index = new NodeIntMap(_graph);
+ _node_heap_index = new ArcIntMap(_graph);
+ _node_data = new RangeMap<NodeData>(_node_num,
+ NodeData(*_node_heap_index));
+ }
+
+ if (!_tree_set) {
+ _tree_set_index = new IntIntMap(_blossom_num);
+ _tree_set = new TreeSet(*_tree_set_index);
+ }
+ if (!_delta2) {
+ _delta2_index = new IntIntMap(_blossom_num);
+ _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
+ }
+ if (!_delta3) {
+ _delta3_index = new EdgeIntMap(_graph);
+ _delta3 = new BinHeap<Value, EdgeIntMap>(*_delta3_index);
+ }
+ if (!_delta4) {
+ _delta4_index = new IntIntMap(_blossom_num);
+ _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
+ }
+ }
+
+ void destroyStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (_matching) {
+ delete _matching;
+ }
+ if (_node_potential) {
+ delete _node_potential;
+ }
+ if (_blossom_set) {
+ delete _blossom_index;
+ delete _blossom_set;
+ delete _blossom_data;
+ }
+
+ if (_node_index) {
+ delete _node_index;
+ delete _node_heap_index;
+ delete _node_data;
+ }
+
+ if (_tree_set) {
+ delete _tree_set_index;
+ delete _tree_set;
+ }
+ if (_delta2) {
+ delete _delta2_index;
+ delete _delta2;
+ }
+ if (_delta3) {
+ delete _delta3_index;
+ delete _delta3;
+ }
+ if (_delta4) {
+ delete _delta4_index;
+ delete _delta4;
+ }
+ }
+
+ void matchedToEven(int blossom, int tree) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot -=
+ 2 * (_delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+ int ni = (*_node_index)[n];
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+
+ (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else {
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset){
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+ void matchedToOdd(int blossom) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+ (*_blossom_data)[blossom].offset += _delta_sum;
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+
+ void evenToMatched(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot += 2 * _delta_sum;
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+ (*_node_data)[ni].pot -= _delta_sum;
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if (vb == blossom) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else if ((*_blossom_data)[vb].status == EVEN) {
+
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+
+ int vt = _tree_set->find(vb);
+
+ if (vt != tree) {
+
+ Arc r = _graph.oppositeArc(e);
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[ni].heap_index.find(vt);
+
+ if (it != (*_node_data)[ni].heap_index.end()) {
+ if ((*_node_data)[ni].heap[it->second] > rw) {
+ (*_node_data)[ni].heap.replace(it->second, r);
+ (*_node_data)[ni].heap.decrease(r, rw);
+ it->second = r;
+ }
+ } else {
+ (*_node_data)[ni].heap.push(r, rw);
+ (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+ }
+
+ if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+ _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+
+ if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ } else if ((*_delta2)[blossom] >
+ _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset){
+ _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ (*_node_data)[vi].heap.erase(it->second);
+ (*_node_data)[vi].heap_index.erase(it);
+ if ((*_node_data)[vi].heap.empty()) {
+ _blossom_set->increase(v, std::numeric_limits<Value>::max());
+ } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
+ _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
+ }
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_blossom_set->classPrio(vb) ==
+ std::numeric_limits<Value>::max()) {
+ _delta2->erase(vb);
+ } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->increase(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ void oddToMatched(int blossom) {
+ (*_blossom_data)[blossom].offset -= _delta_sum;
+
+ if (_blossom_set->classPrio(blossom) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ }
+ }
+
+ void oddToEven(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ (*_blossom_data)[blossom].pot -=
+ 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+ (*_node_data)[ni].pot +=
+ 2 * _delta_sum - (*_blossom_data)[blossom].offset;
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+ void alternatePath(int even, int tree) {
+ int odd;
+
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].status = MATCHED;
+
+ while ((*_blossom_data)[even].pred != INVALID) {
+ odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
+ (*_blossom_data)[odd].status = MATCHED;
+ oddToMatched(odd);
+ (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
+
+ even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
+ (*_blossom_data)[even].status = MATCHED;
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].next =
+ _graph.oppositeArc((*_blossom_data)[odd].pred);
+ }
+
+ }
+
+ void destroyTree(int tree) {
+ for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
+ if ((*_blossom_data)[b].status == EVEN) {
+ (*_blossom_data)[b].status = MATCHED;
+ evenToMatched(b, tree);
+ } else if ((*_blossom_data)[b].status == ODD) {
+ (*_blossom_data)[b].status = MATCHED;
+ oddToMatched(b);
+ }
+ }
+ _tree_set->eraseClass(tree);
+ }
+
+ void augmentOnArc(const Edge& arc) {
+
+ int left = _blossom_set->find(_graph.u(arc));
+ int right = _blossom_set->find(_graph.v(arc));
+
+ int left_tree = _tree_set->find(left);
+ alternatePath(left, left_tree);
+ destroyTree(left_tree);
+
+ int right_tree = _tree_set->find(right);
+ alternatePath(right, right_tree);
+ destroyTree(right_tree);
+
+ (*_blossom_data)[left].next = _graph.direct(arc, true);
+ (*_blossom_data)[right].next = _graph.direct(arc, false);
+ }
+
+ void extendOnArc(const Arc& arc) {
+ int base = _blossom_set->find(_graph.target(arc));
+ int tree = _tree_set->find(base);
+
+ int odd = _blossom_set->find(_graph.source(arc));
+ _tree_set->insert(odd, tree);
+ (*_blossom_data)[odd].status = ODD;
+ matchedToOdd(odd);
+ (*_blossom_data)[odd].pred = arc;
+
+ int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
+ (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
+ _tree_set->insert(even, tree);
+ (*_blossom_data)[even].status = EVEN;
+ matchedToEven(even, tree);
+ }
+
+ void shrinkOnArc(const Edge& edge, int tree) {
+ int nca = -1;
+ std::vector<int> left_path, right_path;
+
+ {
+ std::set<int> left_set, right_set;
+ int left = _blossom_set->find(_graph.u(edge));
+ left_path.push_back(left);
+ left_set.insert(left);
+
+ int right = _blossom_set->find(_graph.v(edge));
+ right_path.push_back(right);
+ right_set.insert(right);
+
+ while (true) {
+
+ if ((*_blossom_data)[left].pred == INVALID) break;
+
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+
+ left_set.insert(left);
+
+ if (right_set.find(left) != right_set.end()) {
+ nca = left;
+ break;
+ }
+
+ if ((*_blossom_data)[right].pred == INVALID) break;
+
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+
+ right_set.insert(right);
+
+ if (left_set.find(right) != left_set.end()) {
+ nca = right;
+ break;
+ }
+
+ }
+
+ if (nca == -1) {
+ if ((*_blossom_data)[left].pred == INVALID) {
+ nca = right;
+ while (left_set.find(nca) == left_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ }
+ } else {
+ nca = left;
+ while (right_set.find(nca) == right_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ }
+ }
+ }
+ }
+
+ std::vector<int> subblossoms;
+ Arc prev;
+
+ prev = _graph.direct(edge, true);
+ for (int i = 0; left_path[i] != nca; i += 2) {
+ subblossoms.push_back(left_path[i]);
+ (*_blossom_data)[left_path[i]].next = prev;
+ _tree_set->erase(left_path[i]);
+
+ subblossoms.push_back(left_path[i + 1]);
+ (*_blossom_data)[left_path[i + 1]].status = EVEN;
+ oddToEven(left_path[i + 1], tree);
+ _tree_set->erase(left_path[i + 1]);
+ prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
+ }
+
+ int k = 0;
+ while (right_path[k] != nca) ++k;
+
+ subblossoms.push_back(nca);
+ (*_blossom_data)[nca].next = prev;
+
+ for (int i = k - 2; i >= 0; i -= 2) {
+ subblossoms.push_back(right_path[i + 1]);
+ (*_blossom_data)[right_path[i + 1]].status = EVEN;
+ oddToEven(right_path[i + 1], tree);
+ _tree_set->erase(right_path[i + 1]);
+
+ (*_blossom_data)[right_path[i + 1]].next =
+ (*_blossom_data)[right_path[i + 1]].pred;
+
+ subblossoms.push_back(right_path[i]);
+ _tree_set->erase(right_path[i]);
+ }
+
+ int surface =
+ _blossom_set->join(subblossoms.begin(), subblossoms.end());
+
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
+ }
+ (*_blossom_data)[subblossoms[i]].status = MATCHED;
+ }
+
+ (*_blossom_data)[surface].pot = -2 * _delta_sum;
+ (*_blossom_data)[surface].offset = 0;
+ (*_blossom_data)[surface].status = EVEN;
+ (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
+ (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
+
+ _tree_set->insert(surface, tree);
+ _tree_set->erase(nca);
+ }
+
+ void splitBlossom(int blossom) {
+ Arc next = (*_blossom_data)[blossom].next;
+ Arc pred = (*_blossom_data)[blossom].pred;
+
+ int tree = _tree_set->find(blossom);
+
+ (*_blossom_data)[blossom].status = MATCHED;
+ oddToMatched(blossom);
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+
+ Value offset = (*_blossom_data)[blossom].offset;
+ int b = _blossom_set->find(_graph.source(pred));
+ int d = _blossom_set->find(_graph.source(next));
+
+ int ib = -1, id = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) ib = i;
+ if (subblossoms[i] == d) id = i;
+
+ (*_blossom_data)[subblossoms[i]].offset = offset;
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
+ }
+ if (_blossom_set->classPrio(subblossoms[i]) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(subblossoms[i],
+ _blossom_set->classPrio(subblossoms[i]) -
+ (*_blossom_data)[subblossoms[i]].offset);
+ }
+ }
+
+ if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
+ for (int i = (id + 1) % subblossoms.size();
+ i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].pred = pred;
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ pred = (*_blossom_data)[ub].next;
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
+ }
+
+ (*_blossom_data)[subblossoms[id]].status = ODD;
+ matchedToOdd(subblossoms[id]);
+ _tree_set->insert(subblossoms[id], tree);
+ (*_blossom_data)[subblossoms[id]].next = next;
+ (*_blossom_data)[subblossoms[id]].pred = pred;
+
+ } else {
+
+ for (int i = (ib + 1) % subblossoms.size();
+ i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].next = next;
+ (*_blossom_data)[sb].pred =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred =
+ (*_blossom_data)[tb].next =
+ _graph.oppositeArc((*_blossom_data)[ub].next);
+ next = (*_blossom_data)[ub].next;
+ }
+
+ (*_blossom_data)[subblossoms[ib]].status = ODD;
+ matchedToOdd(subblossoms[ib]);
+ _tree_set->insert(subblossoms[ib], tree);
+ (*_blossom_data)[subblossoms[ib]].next = next;
+ (*_blossom_data)[subblossoms[ib]].pred = pred;
+ }
+ _tree_set->erase(blossom);
+ }
+
+ void extractBlossom(int blossom, const Node& base, const Arc& matching) {
+ if (_blossom_set->trivial(blossom)) {
+ int bi = (*_node_index)[base];
+ Value pot = (*_node_data)[bi].pot;
+
+ _matching->set(base, matching);
+ _blossom_node_list.push_back(base);
+ _node_potential->set(base, pot);
+ } else {
+
+ Value pot = (*_blossom_data)[blossom].pot;
+ int bn = _blossom_node_list.size();
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+ int b = _blossom_set->find(base);
+ int ib = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) { ib = i; break; }
+ }
+
+ for (int i = 1; i < int(subblossoms.size()); i += 2) {
+ int sb = subblossoms[(ib + i) % subblossoms.size()];
+ int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
+
+ Arc m = (*_blossom_data)[tb].next;
+ extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
+ extractBlossom(tb, _graph.source(m), m);
+ }
+ extractBlossom(subblossoms[ib], base, matching);
+
+ int en = _blossom_node_list.size();
+
+ _blossom_potential.push_back(BlossomVariable(bn, en, pot));
+ }
+ }
+
+ void extractMatching() {
+ std::vector<int> blossoms;
+ for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
+ blossoms.push_back(c);
+ }
+
+ for (int i = 0; i < int(blossoms.size()); ++i) {
+
+ Value offset = (*_blossom_data)[blossoms[i]].offset;
+ (*_blossom_data)[blossoms[i]].pot += 2 * offset;
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
+ n != INVALID; ++n) {
+ (*_node_data)[(*_node_index)[n]].pot -= offset;
+ }
+
+ Arc matching = (*_blossom_data)[blossoms[i]].next;
+ Node base = _graph.source(matching);
+ extractBlossom(blossoms[i], base, matching);
+ }
+ }
+
+ public:
+
+ /// \brief Constructor
+ ///
+ /// Constructor.
+ MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
+ : _graph(graph), _weight(weight), _matching(0),
+ _node_potential(0), _blossom_potential(), _blossom_node_list(),
+ _node_num(0), _blossom_num(0),
+
+ _blossom_index(0), _blossom_set(0), _blossom_data(0),
+ _node_index(0), _node_heap_index(0), _node_data(0),
+ _tree_set_index(0), _tree_set(0),
+
+ _delta2_index(0), _delta2(0),
+ _delta3_index(0), _delta3(0),
+ _delta4_index(0), _delta4(0),
+
+ _delta_sum() {}
+
+ ~MaxWeightedPerfectMatching() {
+ destroyStructures();
+ }
+
+ /// \name Execution control
+ /// The simplest way to execute the algorithm is to use the member
+ /// \c run() member function.
+
+ ///@{
+
+ /// \brief Initialize the algorithm
+ ///
+ /// Initialize the algorithm
+ void init() {
+ createStructures();
+
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ _node_heap_index->set(e, BinHeap<Value, ArcIntMap>::PRE_HEAP);
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ _delta3_index->set(e, _delta3->PRE_HEAP);
+ }
+ for (int i = 0; i < _blossom_num; ++i) {
+ _delta2_index->set(i, _delta2->PRE_HEAP);
+ _delta4_index->set(i, _delta4->PRE_HEAP);
+ }
+
+ int index = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ Value max = - std::numeric_limits<Value>::max();
+ for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+ if (_graph.target(e) == n) continue;
+ if ((dualScale * _weight[e]) / 2 > max) {
+ max = (dualScale * _weight[e]) / 2;
+ }
+ }
+ _node_index->set(n, index);
+ (*_node_data)[index].pot = max;
+ int blossom =
+ _blossom_set->insert(n, std::numeric_limits<Value>::max());
+
+ _tree_set->insert(blossom);
+
+ (*_blossom_data)[blossom].status = EVEN;
+ (*_blossom_data)[blossom].pred = INVALID;
+ (*_blossom_data)[blossom].next = INVALID;
+ (*_blossom_data)[blossom].pot = 0;
+ (*_blossom_data)[blossom].offset = 0;
+ ++index;
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ int si = (*_node_index)[_graph.u(e)];
+ int ti = (*_node_index)[_graph.v(e)];
+ if (_graph.u(e) != _graph.v(e)) {
+ _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
+ dualScale * _weight[e]) / 2);
+ }
+ }
+ }
+
+ /// \brief Starts the algorithm
+ ///
+ /// Starts the algorithm
+ bool start() {
+ enum OpType {
+ D2, D3, D4
+ };
+
+ int unmatched = _node_num;
+ while (unmatched > 0) {
+ Value d2 = !_delta2->empty() ?
+ _delta2->prio() : std::numeric_limits<Value>::max();
+
+ Value d3 = !_delta3->empty() ?
+ _delta3->prio() : std::numeric_limits<Value>::max();
+
+ Value d4 = !_delta4->empty() ?
+ _delta4->prio() : std::numeric_limits<Value>::max();
+
+ _delta_sum = d2; OpType ot = D2;
+ if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
+ if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
+
+ if (_delta_sum == std::numeric_limits<Value>::max()) {
+ return false;
+ }
+
+ switch (ot) {
+ case D2:
+ {
+ int blossom = _delta2->top();
+ Node n = _blossom_set->classTop(blossom);
+ Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
+ extendOnArc(e);
+ }
+ break;
+ case D3:
+ {
+ Edge e = _delta3->top();
+
+ int left_blossom = _blossom_set->find(_graph.u(e));
+ int right_blossom = _blossom_set->find(_graph.v(e));
+
+ if (left_blossom == right_blossom) {
+ _delta3->pop();
+ } else {
+ int left_tree = _tree_set->find(left_blossom);
+ int right_tree = _tree_set->find(right_blossom);
+
+ if (left_tree == right_tree) {
+ shrinkOnArc(e, left_tree);
+ } else {
+ augmentOnArc(e);
+ unmatched -= 2;
+ }
+ }
+ } break;
+ case D4:
+ splitBlossom(_delta4->top());
+ break;
+ }
+ }
+ extractMatching();
+ return true;
+ }
+
+ /// \brief Runs %MaxWeightedPerfectMatching algorithm.
+ ///
+ /// This method runs the %MaxWeightedPerfectMatching algorithm.
+ ///
+ /// \note mwm.run() is just a shortcut of the following code.
+ /// \code
+ /// mwm.init();
+ /// mwm.start();
+ /// \endcode
+ bool run() {
+ init();
+ return start();
+ }
+
+ /// @}
+
+ /// \name Primal solution
+ /// Functions for get the primal solution, ie. the matching.
+
+ /// @{
+
+ /// \brief Returns the matching value.
+ ///
+ /// Returns the matching value.
+ Value matchingValue() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] != INVALID) {
+ sum += _weight[(*_matching)[n]];
+ }
+ }
+ return sum /= 2;
+ }
+
+ /// \brief Returns true when the arc is in the matching.
+ ///
+ /// Returns true when the arc is in the matching.
+ bool matching(const Edge& arc) const {
+ return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
+ }
+
+ /// \brief Returns the incident matching arc.
+ ///
+ /// Returns the incident matching arc from given node.
+ Arc matching(const Node& node) const {
+ return (*_matching)[node];
+ }
+
+ /// \brief Returns the mate of the node.
+ ///
+ /// Returns the adjancent node in a mathcing arc.
+ Node mate(const Node& node) const {
+ return _graph.target((*_matching)[node]);
+ }
+
+ /// @}
+
+ /// \name Dual solution
+ /// Functions for get the dual solution.
+
+ /// @{
+
+ /// \brief Returns the value of the dual solution.
+ ///
+ /// Returns the value of the dual solution. It should be equal to
+ /// the primal value scaled by \ref dualScale "dual scale".
+ Value dualValue() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ sum += nodeValue(n);
+ }
+ for (int i = 0; i < blossomNum(); ++i) {
+ sum += blossomValue(i) * (blossomSize(i) / 2);
+ }
+ return sum;
+ }
+
+ /// \brief Returns the value of the node.
+ ///
+ /// Returns the the value of the node.
+ Value nodeValue(const Node& n) const {
+ return (*_node_potential)[n];
+ }
+
+ /// \brief Returns the number of the blossoms in the basis.
+ ///
+ /// Returns the number of the blossoms in the basis.
+ /// \see BlossomIt
+ int blossomNum() const {
+ return _blossom_potential.size();
+ }
+
+
+ /// \brief Returns the number of the nodes in the blossom.
+ ///
+ /// Returns the number of the nodes in the blossom.
+ int blossomSize(int k) const {
+ return _blossom_potential[k].end - _blossom_potential[k].begin;
+ }
+
+ /// \brief Returns the value of the blossom.
+ ///
+ /// Returns the the value of the blossom.
+ /// \see BlossomIt
+ Value blossomValue(int k) const {
+ return _blossom_potential[k].value;
+ }
+
+ /// \brief Lemon iterator for get the items of the blossom.
+ ///
+ /// Lemon iterator for get the nodes of the blossom. This class
+ /// provides a common style lemon iterator which gives back a
+ /// subset of the nodes.
+ class BlossomIt {
+ public:
+
+ /// \brief Constructor.
+ ///
+ /// Constructor for get the nodes of the variable.
+ BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
+ : _algorithm(&algorithm)
+ {
+ _index = _algorithm->_blossom_potential[variable].begin;
+ _last = _algorithm->_blossom_potential[variable].end;
+ }
+
+ /// \brief Invalid constructor.
+ ///
+ /// Invalid constructor.
+ BlossomIt(Invalid) : _index(-1) {}
+
+ /// \brief Conversion to node.
+ ///
+ /// Conversion to node.
+ operator Node() const {
+ return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
+ }
+
+ /// \brief Increment operator.
+ ///
+ /// Increment operator.
+ BlossomIt& operator++() {
+ ++_index;
+ if (_index == _last) {
+ _index = -1;
+ }
+ return *this;
+ }
+
+ bool operator==(const BlossomIt& it) const {
+ return _index == it._index;
+ }
+ bool operator!=(const BlossomIt& it) const {
+ return _index != it._index;
+ }
+
+ private:
+ const MaxWeightedPerfectMatching* _algorithm;
+ int _last;
+ int _index;
+ };
+
+ /// @}
+
+ };
+
+
+} //END OF NAMESPACE LEMON
+
+#endif //LEMON_MAX_MATCHING_H
diff -r 6dbd5184c6a9 -r 64ad48007fb2 test/CMakeLists.txt
--- a/test/CMakeLists.txt Sun Oct 12 19:35:48 2008 +0100
+++ b/test/CMakeLists.txt Mon Oct 13 13:56:00 2008 +0200
@@ -16,6 +16,8 @@
heap_test
kruskal_test
maps_test
+ max_matching_test
+ max_weighted_matching_test
random_test
path_test
time_measure_test
diff -r 6dbd5184c6a9 -r 64ad48007fb2 test/Makefile.am
--- a/test/Makefile.am Sun Oct 12 19:35:48 2008 +0100
+++ b/test/Makefile.am Mon Oct 13 13:56:00 2008 +0200
@@ -19,6 +19,8 @@
test/heap_test \
test/kruskal_test \
test/maps_test \
+ test/max_matching_test \
+ test/max_weighted_matching_test \
test/random_test \
test/path_test \
test/test_tools_fail \
@@ -42,6 +44,8 @@
test_heap_test_SOURCES = test/heap_test.cc
test_kruskal_test_SOURCES = test/kruskal_test.cc
test_maps_test_SOURCES = test/maps_test.cc
+test_max_matching_test_SOURCES = test/max_matching_test.cc
+test_max_weighted_matching_test_SOURCES = test/max_weighted_matching_test.cc
test_path_test_SOURCES = test/path_test.cc
test_random_test_SOURCES = test/random_test.cc
test_test_tools_fail_SOURCES = test/test_tools_fail.cc
diff -r 6dbd5184c6a9 -r 64ad48007fb2 test/max_matching_test.cc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/test/max_matching_test.cc Mon Oct 13 13:56:00 2008 +0200
@@ -0,0 +1,181 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <lemon/math.h>
+#include <cstdlib>
+
+#include "test_tools.h"
+#include <lemon/list_graph.h>
+#include <lemon/max_matching.h>
+
+using namespace std;
+using namespace lemon;
+
+int main() {
+
+ typedef ListGraph Graph;
+
+ GRAPH_TYPEDEFS(Graph);
+
+ Graph g;
+ g.clear();
+
+ std::vector<Graph::Node> nodes;
+ for (int i=0; i<13; ++i)
+ nodes.push_back(g.addNode());
+
+ g.addEdge(nodes[0], nodes[0]);
+ g.addEdge(nodes[6], nodes[10]);
+ g.addEdge(nodes[5], nodes[10]);
+ g.addEdge(nodes[4], nodes[10]);
+ g.addEdge(nodes[3], nodes[11]);
+ g.addEdge(nodes[1], nodes[6]);
+ g.addEdge(nodes[4], nodes[7]);
+ g.addEdge(nodes[1], nodes[8]);
+ g.addEdge(nodes[0], nodes[8]);
+ g.addEdge(nodes[3], nodes[12]);
+ g.addEdge(nodes[6], nodes[9]);
+ g.addEdge(nodes[9], nodes[11]);
+ g.addEdge(nodes[2], nodes[10]);
+ g.addEdge(nodes[10], nodes[8]);
+ g.addEdge(nodes[5], nodes[8]);
+ g.addEdge(nodes[6], nodes[3]);
+ g.addEdge(nodes[0], nodes[5]);
+ g.addEdge(nodes[6], nodes[12]);
+
+ MaxMatching<Graph> max_matching(g);
+ max_matching.init();
+ max_matching.startDense();
+
+ int s=0;
+ Graph::NodeMap<Node> mate(g,INVALID);
+ max_matching.mateMap(mate);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( mate[v]!=INVALID ) ++s;
+ }
+ int size=int(s/2); //size will be used as the size of a maxmatching
+
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ max_matching.mate(v);
+ }
+
+ check ( size == max_matching.size(), "mate() returns a different size matching than max_matching.size()" );
+
+ Graph::NodeMap<MaxMatching<Graph>::DecompType> pos0(g);
+ max_matching.decomposition(pos0);
+
+ max_matching.init();
+ max_matching.startSparse();
+ s=0;
+ max_matching.mateMap(mate);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( mate[v]!=INVALID ) ++s;
+ }
+ check ( int(s/2) == size, "The size does not equal!" );
+
+ Graph::NodeMap<MaxMatching<Graph>::DecompType> pos1(g);
+ max_matching.decomposition(pos1);
+
+ max_matching.run();
+ s=0;
+ max_matching.mateMap(mate);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( mate[v]!=INVALID ) ++s;
+ }
+ check ( int(s/2) == size, "The size does not equal!" );
+
+ Graph::NodeMap<MaxMatching<Graph>::DecompType> pos2(g);
+ max_matching.decomposition(pos2);
+
+ max_matching.run();
+ s=0;
+ max_matching.mateMap(mate);
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( mate[v]!=INVALID ) ++s;
+ }
+ check ( int(s/2) == size, "The size does not equal!" );
+
+ Graph::NodeMap<MaxMatching<Graph>::DecompType> pos(g);
+ max_matching.decomposition(pos);
+
+ bool ismatching=true;
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( mate[v]!=INVALID ) {
+ Node u=mate[v];
+ if (mate[u]!=v) ismatching=false;
+ }
+ }
+ check ( ismatching, "It is not a matching!" );
+
+ bool coincide=true;
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( pos0[v] != pos1[v] || pos1[v]!=pos2[v] || pos2[v]!=pos[v] ) {
+ coincide=false;
+ }
+ }
+ check ( coincide, "The decompositions do not coincide! " );
+
+ bool noarc=true;
+ for(EdgeIt e(g); e!=INVALID; ++e) {
+ if ( (pos[g.v(e)]==max_matching.C &&
+ pos[g.u(e)]==max_matching.D) ||
+ (pos[g.v(e)]==max_matching.D &&
+ pos[g.u(e)]==max_matching.C) )
+ noarc=false;
+ }
+ check ( noarc, "There are arcs between D and C!" );
+
+ bool oddcomp=true;
+ Graph::NodeMap<bool> todo(g,true);
+ int num_comp=0;
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( pos[v]==max_matching.D && todo[v] ) {
+ int comp_size=1;
+ ++num_comp;
+ std::queue<Node> Q;
+ Q.push(v);
+ todo.set(v,false);
+ while (!Q.empty()) {
+ Node w=Q.front();
+ Q.pop();
+ for(IncEdgeIt e(g,w); e!=INVALID; ++e) {
+ Node u=g.runningNode(e);
+ if ( pos[u]==max_matching.D && todo[u] ) {
+ ++comp_size;
+ Q.push(u);
+ todo.set(u,false);
+ }
+ }
+ }
+ if ( !(comp_size % 2) ) oddcomp=false;
+ }
+ }
+ check ( oddcomp, "A component of g[D] is not odd." );
+
+ int barrier=0;
+ for(NodeIt v(g); v!=INVALID; ++v) {
+ if ( pos[v]==max_matching.A ) ++barrier;
+ }
+ int expected_size=int( countNodes(g)-num_comp+barrier)/2;
+ check ( size==expected_size, "The size of the matching is wrong." );
+
+ return 0;
+}
diff -r 6dbd5184c6a9 -r 64ad48007fb2 test/max_weighted_matching_test.cc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/test/max_weighted_matching_test.cc Mon Oct 13 13:56:00 2008 +0200
@@ -0,0 +1,250 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <queue>
+#include <lemon/math.h>
+#include <cstdlib>
+
+#include "test_tools.h"
+#include <lemon/smart_graph.h>
+#include <lemon/max_matching.h>
+#include <lemon/lgf_reader.h>
+
+using namespace std;
+using namespace lemon;
+
+GRAPH_TYPEDEFS(SmartGraph);
+
+const int lgfn = 3;
+const std::string lgf[lgfn] = {
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ "label weight\n"
+ "7 4 0 984\n"
+ "0 7 1 73\n"
+ "7 1 2 204\n"
+ "2 3 3 583\n"
+ "2 7 4 565\n"
+ "2 1 5 582\n"
+ "0 4 6 551\n"
+ "2 5 7 385\n"
+ "1 5 8 561\n"
+ "5 3 9 484\n"
+ "7 5 10 904\n"
+ "3 6 11 47\n"
+ "7 6 12 888\n"
+ "3 0 13 747\n"
+ "6 1 14 310\n",
+
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ "label weight\n"
+ "2 5 0 710\n"
+ "0 5 1 241\n"
+ "2 4 2 856\n"
+ "2 6 3 762\n"
+ "4 1 4 747\n"
+ "6 1 5 962\n"
+ "4 7 6 723\n"
+ "1 7 7 661\n"
+ "2 3 8 376\n"
+ "1 0 9 416\n"
+ "6 7 10 391\n",
+
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ "label weight\n"
+ "6 2 0 553\n"
+ "0 7 1 653\n"
+ "6 3 2 22\n"
+ "4 7 3 846\n"
+ "7 2 4 981\n"
+ "7 6 5 250\n"
+ "5 2 6 539\n"
+};
+
+void checkMatching(const SmartGraph& graph,
+ const SmartGraph::EdgeMap<int>& weight,
+ const MaxWeightedMatching<SmartGraph>& mwm) {
+ for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
+ if (graph.u(e) == graph.v(e)) continue;
+ int rw =
+ mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
+
+ for (int i = 0; i < mwm.blossomNum(); ++i) {
+ bool s = false, t = false;
+ for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
+ n != INVALID; ++n) {
+ if (graph.u(e) == n) s = true;
+ if (graph.v(e) == n) t = true;
+ }
+ if (s == true && t == true) {
+ rw += mwm.blossomValue(i);
+ }
+ }
+ rw -= weight[e] * mwm.dualScale;
+
+ check(rw >= 0, "Negative reduced weight");
+ check(rw == 0 || !mwm.matching(e),
+ "Non-zero reduced weight on matching arc");
+ }
+
+ int pv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ if (mwm.matching(n) != INVALID) {
+ check(mwm.nodeValue(n) >= 0, "Invalid node value");
+ pv += weight[mwm.matching(n)];
+ SmartGraph::Node o = graph.target(mwm.matching(n));
+ check(mwm.mate(n) == o, "Invalid matching");
+ check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
+ "Invalid matching");
+ } else {
+ check(mwm.mate(n) == INVALID, "Invalid matching");
+ check(mwm.nodeValue(n) == 0, "Invalid matching");
+ }
+ }
+
+ int dv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ dv += mwm.nodeValue(n);
+ }
+
+ for (int i = 0; i < mwm.blossomNum(); ++i) {
+ check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
+ check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
+ dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
+ }
+
+ check(pv * mwm.dualScale == dv * 2, "Wrong duality");
+
+ return;
+}
+
+void checkPerfectMatching(const SmartGraph& graph,
+ const SmartGraph::EdgeMap<int>& weight,
+ const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
+ for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
+ if (graph.u(e) == graph.v(e)) continue;
+ int rw =
+ mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
+
+ for (int i = 0; i < mwpm.blossomNum(); ++i) {
+ bool s = false, t = false;
+ for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
+ n != INVALID; ++n) {
+ if (graph.u(e) == n) s = true;
+ if (graph.v(e) == n) t = true;
+ }
+ if (s == true && t == true) {
+ rw += mwpm.blossomValue(i);
+ }
+ }
+ rw -= weight[e] * mwpm.dualScale;
+
+ check(rw >= 0, "Negative reduced weight");
+ check(rw == 0 || !mwpm.matching(e),
+ "Non-zero reduced weight on matching arc");
+ }
+
+ int pv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ check(mwpm.matching(n) != INVALID, "Non perfect");
+ pv += weight[mwpm.matching(n)];
+ SmartGraph::Node o = graph.target(mwpm.matching(n));
+ check(mwpm.mate(n) == o, "Invalid matching");
+ check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
+ "Invalid matching");
+ }
+
+ int dv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ dv += mwpm.nodeValue(n);
+ }
+
+ for (int i = 0; i < mwpm.blossomNum(); ++i) {
+ check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
+ check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
+ dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
+ }
+
+ check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
+
+ return;
+}
+
+
+int main() {
+
+ for (int i = 0; i < lgfn; ++i) {
+ SmartGraph graph;
+ SmartGraph::EdgeMap<int> weight(graph);
+
+ istringstream lgfs(lgf[i]);
+ graphReader(graph, lgfs).
+ edgeMap("weight", weight).run();
+
+ MaxWeightedMatching<SmartGraph> mwm(graph, weight);
+ mwm.run();
+ checkMatching(graph, weight, mwm);
+
+ MaxMatching<SmartGraph> mm(graph);
+ mm.run();
+
+ MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
+ bool perfect = mwpm.run();
+
+ check(perfect == (mm.size() * 2 == countNodes(graph)),
+ "Perfect matching found");
+
+ if (perfect) {
+ checkPerfectMatching(graph, weight, mwpm);
+ }
+ }
+
+ return 0;
+}