Ticket #48: 64ad48007fb2.patch

lemon/Makefile.am

@@ -35 +35 @@
         lemon/list_graph.h \
         lemon/maps.h \
         lemon/math.h \
+        lemon/max_matching.h \
         lemon/path.h \
         lemon/random.h \
         lemon/smart_graph.h \

new file lemon/max_matching.h

@@ +1 @@
+/* -*- 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

test/CMakeLists.txt

@@ -16 +16 @@
   heap_test
   kruskal_test
   maps_test
+  max_matching_test
+  max_weighted_matching_test
   random_test
   path_test
   time_measure_test

test/Makefile.am

@@ -19 +19 @@
         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 +44 @@
 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

new file test/max_matching_test.cc

@@ +1 @@
+/* -*- 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;
+}

new file test/max_weighted_matching_test.cc

@@ +1 @@
+/* -*- 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;
+}