diff --git a/lemon/fib_heap.h b/lemon/fib_heap.h
new file mode 100644
--- /dev/null
+++ b/lemon/fib_heap.h
@@ -0,0 +1,467 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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_FIB_HEAP_H
+#define LEMON_FIB_HEAP_H
+
+///\file
+///\ingroup auxdat
+///\brief Fibonacci Heap implementation.
+
+#include <vector>
+#include <functional>
+#include <lemon/math.h>
+
+namespace lemon {
+
+  /// \ingroup auxdat
+  ///
+  ///\brief Fibonacci Heap.
+  ///
+  ///This class implements the \e Fibonacci \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 Fibonacci
+  ///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
+#ifdef DOXYGEN
+  template <typename _Prio,
+            typename _ItemIntMap,
+            typename _Compare>
+#else
+  template <typename _Prio,
+            typename _ItemIntMap,
+            typename _Compare = std::less<_Prio> >
+#endif
+  class FibHeap {
+  public:
+    ///\e
+    typedef _ItemIntMap ItemIntMap;
+    ///\e
+    typedef _Prio Prio;
+    ///\e
+    typedef typename ItemIntMap::Key Item;
+    ///\e
+    typedef std::pair<Item,Prio> Pair;
+    ///\e
+    typedef _Compare Compare;
+
+  private:
+    class store;
+
+    std::vector<store> container;
+    int minimum;
+    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 FibHeap(ItemIntMap &_iimap)
+      : minimum(0), 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.
+    FibHeap(ItemIntMap &_iimap, const Compare &_comp)
+      : minimum(0), 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;
+    }
+
+    /// \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].child=-1;
+        container[i].degree=0;
+        container[i].in=true;
+        container[i].marked=false;
+      }
+
+      if ( num_items ) {
+        container[container[minimum].right_neighbor].left_neighbor=i;
+        container[i].right_neighbor=container[minimum].right_neighbor;
+        container[minimum].right_neighbor=i;
+        container[i].left_neighbor=minimum;
+        if ( comp( value, container[minimum].prio) ) minimum=i;
+      } else {
+        container[i].right_neighbor=container[i].left_neighbor=i;
+        minimum=i;
+      }
+      container[i].prio=value;
+      ++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() {
+      /*The first case is that there are only one root.*/
+      if ( container[minimum].left_neighbor==minimum ) {
+        container[minimum].in=false;
+        if ( container[minimum].degree!=0 ) {
+          makeroot(container[minimum].child);
+          minimum=container[minimum].child;
+          balance();
+        }
+      } else {
+        int right=container[minimum].right_neighbor;
+        unlace(minimum);
+        container[minimum].in=false;
+        if ( container[minimum].degree > 0 ) {
+          int left=container[minimum].left_neighbor;
+          int child=container[minimum].child;
+          int last_child=container[child].left_neighbor;
+
+          makeroot(child);
+
+          container[left].right_neighbor=child;
+          container[child].left_neighbor=left;
+          container[right].left_neighbor=last_child;
+          container[last_child].right_neighbor=right;
+        }
+        minimum=right;
+        balance();
+      } // the case where there are more roots
+      --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 Fibonacci heaps.
+    void erase (const Item& item) {
+      int i=iimap[item];
+
+      if ( i >= 0 && container[i].in ) {
+        if ( container[i].parent!=-1 ) {
+          int p=container[i].parent;
+          cut(i,p);
+          cascade(p);
+        }
+        minimum=i;     //As if its prio would be -infinity
+        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];
+      container[i].prio=value;
+      int p=container[i].parent;
+
+      if ( p!=-1 && comp(value, container[p].prio) ) {
+        cut(i,p);
+        cascade(p);
+      }
+      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:
+
+    void balance() {
+
+      int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
+
+      std::vector<int> A(maxdeg,-1);
+
+      /*
+       *Recall that now minimum does not point to the minimum prio element.
+       *We set minimum to this during balance().
+       */
+      int anchor=container[minimum].left_neighbor;
+      int next=minimum;
+      bool end=false;
+
+      do {
+        int active=next;
+        if ( anchor==active ) end=true;
+        int d=container[active].degree;
+        next=container[active].right_neighbor;
+
+        while (A[d]!=-1) {
+          if( comp(container[active].prio, container[A[d]].prio) ) {
+            fuse(active,A[d]);
+          } else {
+            fuse(A[d],active);
+            active=A[d];
+          }
+          A[d]=-1;
+          ++d;
+        }
+        A[d]=active;
+      } while ( !end );
+
+
+      while ( container[minimum].parent >=0 )
+        minimum=container[minimum].parent;
+      int s=minimum;
+      int m=minimum;
+      do {
+        if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
+        s=container[s].right_neighbor;
+      } while ( s != m );
+    }
+
+    void makeroot(int c) {
+      int s=c;
+      do {
+        container[s].parent=-1;
+        s=container[s].right_neighbor;
+      } while ( s != c );
+    }
+
+    void cut(int a, int b) {
+      /*
+       *Replacing a from the children of b.
+       */
+      --container[b].degree;
+
+      if ( container[b].degree !=0 ) {
+        int child=container[b].child;
+        if ( child==a )
+          container[b].child=container[child].right_neighbor;
+        unlace(a);
+      }
+
+
+      /*Lacing a to the roots.*/
+      int right=container[minimum].right_neighbor;
+      container[minimum].right_neighbor=a;
+      container[a].left_neighbor=minimum;
+      container[a].right_neighbor=right;
+      container[right].left_neighbor=a;
+
+      container[a].parent=-1;
+      container[a].marked=false;
+    }
+
+    void cascade(int a) {
+      if ( container[a].parent!=-1 ) {
+        int p=container[a].parent;
+
+        if ( container[a].marked==false ) container[a].marked=true;
+        else {
+          cut(a,p);
+          cascade(p);
+        }
+      }
+    }
+
+    void fuse(int a, int b) {
+      unlace(b);
+
+      /*Lacing b under a.*/
+      container[b].parent=a;
+
+      if (container[a].degree==0) {
+        container[b].left_neighbor=b;
+        container[b].right_neighbor=b;
+        container[a].child=b;
+      } else {
+        int child=container[a].child;
+        int last_child=container[child].left_neighbor;
+        container[child].left_neighbor=b;
+        container[b].right_neighbor=child;
+        container[last_child].right_neighbor=b;
+        container[b].left_neighbor=last_child;
+      }
+
+      ++container[a].degree;
+
+      container[b].marked=false;
+    }
+
+    /*
+     *It is invoked only if a has siblings.
+     */
+    void unlace(int a) {
+      int leftn=container[a].left_neighbor;
+      int rightn=container[a].right_neighbor;
+      container[leftn].right_neighbor=rightn;
+      container[rightn].left_neighbor=leftn;
+    }
+
+
+    class store {
+      friend class FibHeap;
+
+      Item name;
+      int parent;
+      int left_neighbor;
+      int right_neighbor;
+      int child;
+      int degree;
+      bool marked;
+      bool in;
+      Prio prio;
+
+      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
+    };
+  };
+
+} //namespace lemon
+
+#endif //LEMON_FIB_HEAP_H
+