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diff --git a/include/gudhi/Contraction/CGAL_queue/Modifiable_priority_queue.h b/include/gudhi/Contraction/CGAL_queue/Modifiable_priority_queue.h
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+// Copyright (c) 2006-2011  GeometryFactory (France). All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+//
+// Author(s)     : Fernando Cacciola <fernando.cacciola@geometryfactory.com>
+//
+#ifndef CONTRACTION_CGAL_QUEUE_MODIFIABLE_PRIORITY_QUEUE_H_
+#define CONTRACTION_CGAL_QUEUE_MODIFIABLE_PRIORITY_QUEUE_H_
+
+#define CGAL_SURFACE_MESH_SIMPLIFICATION_USE_RELAXED_HEAP
+
+#include <boost/optional.hpp>
+#include <boost/pending/relaxed_heap.hpp>
+
+#include <climits>  // Neeeded by the following Boost header for CHAR_BIT.
+#include <functional>  // for less
+
+namespace CGAL {
+
+template <class IndexedType_, class Compare_ = std::less<IndexedType_>, class ID_ = boost::identity_property_map>
+class Modifiable_priority_queue {
+ public:
+  typedef Modifiable_priority_queue Self;
+
+  typedef IndexedType_ IndexedType;
+  typedef Compare_ Compare;
+  typedef ID_ ID;
+
+  typedef boost::relaxed_heap<IndexedType, Compare, ID> Heap;
+  typedef typename Heap::value_type value_type;
+  typedef typename Heap::size_type size_type;
+
+  typedef bool handle;
+
+ public:
+  Modifiable_priority_queue(size_type largest_ID, Compare const& c, ID const& id) : mHeap(largest_ID, c, id) { }
+
+  handle push(value_type const& v) {
+    mHeap.push(v);
+    return handle(true);
+  }
+
+  handle update(value_type const& v, handle h) {
+    mHeap.update(v);
+    return h;
+  }
+
+  handle erase(value_type const& v, handle) {
+    mHeap.remove(v);
+    return null_handle();
+  }
+
+  value_type top() const {
+    return mHeap.top();
+  }
+
+  void pop() {
+    mHeap.pop();
+  }
+
+  bool empty() const {
+    return mHeap.empty();
+  }
+
+  bool contains(value_type const& v) {
+    return mHeap.contains(v);
+  }
+
+  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;
+  }
+
+  static handle null_handle() {
+    return handle(false);
+  }
+
+ private:
+  Heap mHeap;
+};
+
+}  // namespace CGAL
+
+#endif  // CONTRACTION_CGAL_QUEUE_MODIFIABLE_PRIORITY_QUEUE_H_