diff --git a/STL_Extension/include/CGAL/Modifiable_priority_queue.h b/STL_Extension/include/CGAL/Modifiable_priority_queue.h
index 765605a5777..cdad2f2aef6 100644
--- a/STL_Extension/include/CGAL/Modifiable_priority_queue.h
+++ b/STL_Extension/include/CGAL/Modifiable_priority_queue.h
@@ -17,11 +17,13 @@
 #include <CGAL/STL_Extension/internal/boost/relaxed_heap.hpp>
 #include <CGAL/STL_Extension/internal/boost/mutable_queue.hpp>
 
+#include <boost/heap/fibonacci_heap.hpp>
+
 #include <type_traits>
 
 namespace CGAL {
 
-enum Heap_type { CGAL_BOOST_PENDING_MUTABLE_QUEUE, CGAL_BOOST_PENDING_RELAXED_HEAP };
+enum Heap_type { CGAL_BOOST_FIBONACCI_HEAP, CGAL_BOOST_PENDING_MUTABLE_QUEUE, CGAL_BOOST_PENDING_RELAXED_HEAP };
 
 template <class IndexedType_
          ,class Compare_ = std::less<IndexedType_>
@@ -89,6 +91,88 @@ private:
 
 } ;
 
+template <class IndexedType_
+         ,class Compare_ 
+         ,class ID_>
+class Modifiable_priority_queue<IndexedType_, Compare_, ID_, CGAL_BOOST_FIBONACCI_HEAP>
+{
+public:
+
+  typedef Modifiable_priority_queue Self;
+
+  typedef IndexedType_ IndexedType ;
+  typedef Compare_     Compare;
+  typedef ID_          ID ;
+
+  struct Reverse_compare{
+    const Compare c;
+    Reverse_compare(){}
+    Reverse_compare(Compare const& c):c(c){}
+    template<typename T>
+     bool operator() (T const& a, T const& b) const
+     {
+       return !c(a,b);
+     }
+  };
+
+  typedef boost::heap::fibonacci_heap<IndexedType,boost::heap::compare<Reverse_compare> > Heap;
+
+  typedef typename Heap::value_type value_type;
+  typedef typename Heap::size_type  size_type;
+
+public:
+
+  Modifiable_priority_queue( size_type largest_ID, Compare const& c = Compare(), ID const& id = ID() )
+    : mHeap(Reverse_compare(c))
+    , mID(id)
+    , mHandles(largest_ID)
+  {}
+
+  void push ( value_type const& v ) { mHandles[get(mID, v)]=mHeap.push(v) ; }
+
+  void update ( value_type const& v ) { mHeap.update(mHandles[get(mID, v)]); }
+
+  void erase ( value_type const& v  ) { 
+    auto vid = get(mID, v);
+    mHeap.erase(mHandles[vid]);
+    mHandles[vid]=typename Heap::handle_type();
+  }
+
+  value_type top() const { return mHeap.top(); }
+
+  void pop() { mHeap.pop(); }
+
+  bool empty() const { return mHeap.empty() ; }
+
+  bool contains ( value_type const& v ) { return mHandles[get(mID, v)] != typename Heap::handle_type(); }
+
+  boost::optional<value_type> extract_top()
+  {
+    boost::optional<value_type> r ;
+    if ( !empty() )
+    {
+      value_type v = top();
+      pop();
+      r = boost::optional<value_type>(v) ;
+    }
+    return r ;
+  }
+
+  value_type top_and_pop()
+  {
+    CGAL_precondition(!empty());
+    value_type v = top();
+    pop();
+    return v;
+  }
+
+private:
+
+  Heap mHeap ;
+  ID mID;
+  std::vector<typename Heap::handle_type> mHandles;
+} ;
+
 } //namespace CGAL
 
 #endif