diff --git a/lemon/binom_heap.h b/lemon/binom_heap.h
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+/* -*- C++ -*-
+ *
+ * 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_BINOM_HEAP_H
+#define LEMON_BINOM_HEAP_H
+
+///\file
+///\ingroup auxdat
+///\brief Binomial Heap implementation.
+
+#include <vector>
+#include <functional>
+#include <lemon/math.h>
+#include <lemon/counter.h>
+
+namespace lemon {
+
+  /// \ingroup auxdat
+  ///
+  ///\brief Binomial Heap.
+  ///
+  ///This class implements the \e Binomial \e heap data structure. A \e heap
+  ///is a data structure for storing items with specified values called \e
+  ///priorities in such a way that finding the item with minimum priority is
+  ///efficient. \c Compare specifies the ordering of the priorities. In a heap
+  ///one can change the priority of an item, add or erase an item, etc.
+  ///
+  ///The methods \ref increase and \ref erase are not efficient in a Binomial
+  ///heap. In case of many calls to these operations, it is better to use a
+  ///\ref BinHeap "binary heap".
+  ///
+  ///\param _Prio Type of the priority of the items.
+  ///\param _ItemIntMap A read and writable Item int map, used internally
+  ///to handle the cross references.
+  ///\param _Compare A class for the ordering of the priorities. The
+  ///default is \c std::less<_Prio>.
+  ///
+  ///\sa BinHeap
+  ///\sa Dijkstra
+  ///\author Dorian Batha
+
+#ifdef DOXYGEN
+  template <typename _Prio,
+            typename _ItemIntMap,
+            typename _Compare>
+#else
+  template <typename _Prio,
+            typename _ItemIntMap,
+            typename _Compare = std::less<_Prio> >
+#endif
+  class BinomHeap {
+  public:
+    typedef _ItemIntMap ItemIntMap;
+    typedef _Prio Prio;
+    typedef typename ItemIntMap::Key Item;
+    typedef std::pair<Item,Prio> Pair;
+    typedef _Compare Compare;
+
+  private:
+    class store;
+
+    std::vector<store> container;
+    int minimum, head;
+    ItemIntMap &iimap;
+    Compare comp;
+    int num_items;
+
+  public:
+    ///Status of the nodes
+    enum State {
+      ///The node is in the heap
+      IN_HEAP = 0,
+      ///The node has never been in the heap
+      PRE_HEAP = -1,
+      ///The node was in the heap but it got out of it
+      POST_HEAP = -2
+    };
+
+    /// \brief The constructor
+    ///
+    /// \c _iimap should be given to the constructor, since it is
+    ///   used internally to handle the cross references.
+    explicit BinomHeap(ItemIntMap &_iimap)
+      : minimum(0), head(-1), iimap(_iimap), num_items() {}
+
+    /// \brief The constructor
+    ///
+    /// \c _iimap should be given to the constructor, since it is used
+    /// internally to handle the cross references. \c _comp is an
+    /// object for ordering of the priorities.
+    BinomHeap(ItemIntMap &_iimap, const Compare &_comp)
+      : minimum(0), head(-1), iimap(_iimap), comp(_comp), num_items() {}
+
+    /// \brief The number of items stored in the heap.
+    ///
+    /// Returns the number of items stored in the heap.
+    int size() const { return num_items; }
+
+    /// \brief Checks if the heap stores no items.
+    ///
+    ///   Returns \c true if and only if the heap stores no items.
+    bool empty() const { return num_items==0; }
+
+    /// \brief Make empty this heap.
+    ///
+    /// Make empty this heap. It does not change the cross reference
+    /// map.  If you want to reuse a heap what is not surely empty you
+    /// should first clear the heap and after that you should set the
+    /// cross reference map for each item to \c PRE_HEAP.
+    void clear() {
+      container.clear(); minimum=0; num_items=0; head=-1;
+    }
+
+    /// \brief \c item gets to the heap with priority \c value independently
+    /// if \c item was already there.
+    ///
+    /// This method calls \ref push(\c item, \c value) if \c item is not
+    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
+    /// \ref increase(\c item, \c value) otherwise.
+    void set (const Item& item, const Prio& value) {
+      int i=iimap[item];
+      if ( i >= 0 && container[i].in ) {
+        if ( comp(value, container[i].prio) ) decrease(item, value);
+        if ( comp(container[i].prio, value) ) increase(item, value);
+      } else push(item, value);
+    }
+
+    /// \brief Adds \c item to the heap with priority \c value.
+    ///
+    /// Adds \c item to the heap with priority \c value.
+    /// \pre \c item must not be stored in the heap.
+    void push (const Item& item, const Prio& value) {
+      int i=iimap[item];
+      if ( i<0 ) {
+        int s=container.size();
+        iimap.set( item,s );
+        store st;
+        st.name=item;
+        container.push_back(st);
+        i=s;
+      }
+      else {
+        container[i].parent=container[i].right_neighbor=container[i].child=-1;
+        container[i].degree=0;
+        container[i].in=true;
+      }
+      container[i].prio=value;
+
+      if( 0==num_items ) { head=i; minimum=i; }
+      else { merge(i); }
+
+      minimum = find_min();
+
+      ++num_items;
+    }
+
+    /// \brief Returns the item with minimum priority relative to \c Compare.
+    ///
+    /// This method returns the item with minimum priority relative to \c
+    /// Compare.
+    /// \pre The heap must be nonempty.
+    Item top() const { return container[minimum].name; }
+
+    /// \brief Returns the minimum priority relative to \c Compare.
+    ///
+    /// It returns the minimum priority relative to \c Compare.
+    /// \pre The heap must be nonempty.
+    const Prio& prio() const { return container[minimum].prio; }
+
+    /// \brief Returns the priority of \c item.
+    ///
+    /// It returns the priority of \c item.
+    /// \pre \c item must be in the heap.
+    const Prio& operator[](const Item& item) const {
+      return container[iimap[item]].prio;
+    }
+
+    /// \brief Deletes the item with minimum priority relative to \c Compare.
+    ///
+    /// This method deletes the item with minimum priority relative to \c
+    /// Compare from the heap.
+    /// \pre The heap must be non-empty.
+    void pop() {
+      container[minimum].in=false;
+
+      int head_child=-1;
+      if ( container[minimum].child!=-1 ) {
+        int child=container[minimum].child;
+        int neighb;
+        int prev=-1;
+        while( child!=-1 ) {
+          neighb=container[child].right_neighbor;
+          container[child].parent=-1;
+          container[child].right_neighbor=prev;
+          head_child=child;
+          prev=child;
+          child=neighb;
+        }
+      }
+
+      // The first case is that there are only one root.
+      if ( -1==container[head].right_neighbor ) {
+        head=head_child;
+      }
+      // The case where there are more roots.
+      else {
+        if( head!=minimum )  { unlace(minimum); }
+        else { head=container[head].right_neighbor; }
+
+        merge(head_child);
+      }
+      minimum=find_min();
+      --num_items;
+    }
+
+    /// \brief Deletes \c item from the heap.
+    ///
+    /// This method deletes \c item from the heap, if \c item was already
+    /// stored in the heap. It is quite inefficient in Binomial heaps.
+    void erase (const Item& item) {
+      int i=iimap[item];
+      if ( i >= 0 && container[i].in ) {
+        decrease( item, container[minimum].prio-1 );
+        pop();
+      }
+    }
+
+    /// \brief Decreases the priority of \c item to \c value.
+    ///
+    /// This method decreases the priority of \c item to \c value.
+    /// \pre \c item must be stored in the heap with priority at least \c
+    ///   value relative to \c Compare.
+    void decrease (Item item, const Prio& value) {
+      int i=iimap[item];
+
+      if( comp( value,container[i].prio ) ) {
+        container[i].prio=value;
+
+        int p_loc=container[i].parent, loc=i;
+        int parent, child, neighb;
+
+        while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) {
+
+          // parent set for other loc_child
+          child=container[loc].child;
+          while( -1!=child ) {
+            container[child].parent=p_loc;
+            child=container[child].right_neighbor;
+          }
+
+          // parent set for other p_loc_child
+          child=container[p_loc].child;
+          while( -1!=child ) {
+            container[child].parent=loc;
+            child=container[child].right_neighbor;
+          }
+
+          child=container[p_loc].child;
+          container[p_loc].child=container[loc].child;
+          if( child==loc )
+            child=p_loc;
+          container[loc].child=child;
+
+          // left_neighb set for p_loc
+          if( container[loc].child!=p_loc ) {
+            while( container[child].right_neighbor!=loc )
+              child=container[child].right_neighbor;
+            container[child].right_neighbor=p_loc;
+          }
+
+          // left_neighb set for loc
+          parent=container[p_loc].parent;
+          if( -1!=parent ) child=container[parent].child;
+          else child=head;
+
+          if( child!=p_loc ) {
+            while( container[child].right_neighbor!=p_loc )
+              child=container[child].right_neighbor;
+            container[child].right_neighbor=loc;
+          }
+
+          neighb=container[p_loc].right_neighbor;
+          container[p_loc].right_neighbor=container[loc].right_neighbor;
+          container[loc].right_neighbor=neighb;
+
+          container[p_loc].parent=loc;
+          container[loc].parent=parent;
+
+          if( -1!=parent && container[parent].child==p_loc )
+            container[parent].child=loc;
+
+          /*if new parent will be the first root*/
+          if( head==p_loc )
+            head=loc;
+
+          p_loc=container[loc].parent;
+        }
+      }
+      if( comp(value,container[minimum].prio) ) {
+        minimum=i;
+      }
+    }
+
+    /// \brief Increases the priority of \c item to \c value.
+    ///
+    /// This method sets the priority of \c item to \c value. Though
+    /// there is no precondition on the priority of \c item, this
+    /// method should be used only if it is indeed necessary to increase
+    /// (relative to \c Compare) the priority of \c item, because this
+    /// method is inefficient.
+    void increase (Item item, const Prio& value) {
+      erase(item);
+      push(item, value);
+    }
+
+
+    /// \brief Returns if \c item is in, has already been in, or has never
+    /// been in the heap.
+    ///
+    /// This method returns PRE_HEAP if \c item has never been in the
+    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
+    /// otherwise. In the latter case it is possible that \c item will
+    /// get back to the heap again.
+    State state(const Item &item) const {
+      int i=iimap[item];
+      if( i>=0 ) {
+        if ( container[i].in ) i=0;
+        else i=-2;
+      }
+      return State(i);
+    }
+
+    /// \brief Sets the state of the \c item in the heap.
+    ///
+    /// Sets the state of the \c item in the heap. It can be used to
+    /// manually clear the heap when it is important to achive the
+    /// better time complexity.
+    /// \param i The item.
+    /// \param st The state. It should not be \c IN_HEAP.
+    void state(const Item& i, State st) {
+      switch (st) {
+      case POST_HEAP:
+      case PRE_HEAP:
+        if (state(i) == IN_HEAP) {
+          erase(i);
+        }
+        iimap[i] = st;
+        break;
+      case IN_HEAP:
+        break;
+      }
+    }
+
+  private:
+    int find_min() {
+      int min_loc=-1, min_val;
+      int x=head;
+      if( x!=-1 ) {
+        min_val=container[x].prio;
+        min_loc=x;
+        x=container[x].right_neighbor;
+
+        while( x!=-1 ) {
+          if( comp( container[x].prio,min_val ) ) {
+            min_val=container[x].prio;
+            min_loc=x;
+          }
+          x=container[x].right_neighbor;
+        }
+      }
+      return min_loc;
+    }
+
+    void merge(int a) {
+      interleave(a);
+
+      int x=head;
+      if( -1!=x ) {
+        int x_prev=-1, x_next=container[x].right_neighbor;
+        while( -1!=x_next ) {
+          if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) {
+            x_prev=x;
+            x=x_next;
+          }
+          else {
+            if( comp(container[x].prio,container[x_next].prio) ) {
+              container[x].right_neighbor=container[x_next].right_neighbor;
+              fuse(x_next,x);
+            }
+            else {
+              if( -1==x_prev ) { head=x_next; }
+              else {
+                container[x_prev].right_neighbor=x_next;
+              }
+              fuse(x,x_next);
+              x=x_next;
+            }
+          }
+          x_next=container[x].right_neighbor;
+        }
+      }
+    }
+
+    void interleave(int a) {
+      int other=-1, head_other=-1;
+
+      while( -1!=a || -1!=head ) {
+        if( -1==a ) {
+          if( -1==head_other ) {
+            head_other=head;
+          }
+          else {
+            container[other].right_neighbor=head;
+          }
+          head=-1;
+        }
+        else if( -1==head ) {
+          if( -1==head_other ) {
+            head_other=a;
+          }
+          else {
+            container[other].right_neighbor=a;
+          }
+          a=-1;
+        }
+        else {
+          if( container[a].degree<container[head].degree ) {
+            if( -1==head_other ) {
+              head_other=a;
+            }
+            else {
+              container[other].right_neighbor=a;
+            }
+            other=a;
+            a=container[a].right_neighbor;
+          }
+          else {
+            if( -1==head_other ) {
+              head_other=head;
+            }
+            else {
+              container[other].right_neighbor=head;
+            }
+            other=head;
+            head=container[head].right_neighbor;
+          }
+        }
+      }
+      head=head_other;
+    }
+
+    // Lacing a under b
+    void fuse(int a, int b) {
+      container[a].parent=b;
+      container[a].right_neighbor=container[b].child;
+      container[b].child=a;
+
+      ++container[b].degree;
+    }
+
+    // It is invoked only if a has siblings.
+    void unlace(int a) {
+      int neighb=container[a].right_neighbor;
+      int other=head;
+
+      while( container[other].right_neighbor!=a )
+        other=container[other].right_neighbor;
+      container[other].right_neighbor=neighb;
+    }
+
+  private:
+
+    class store {
+      friend class BinomHeap;
+
+      Item name;
+      int parent;
+      int right_neighbor;
+      int child;
+      int degree;
+      bool in;
+      Prio prio;
+
+      store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {}
+    };
+  };
+
+} //namespace lemon
+
+#endif //LEMON_BINOM_HEAP_H
+