diff --git a/BGL/examples/BGL_surface_mesh/shortest_path.cpp b/BGL/examples/BGL_surface_mesh/shortest_path.cpp
index 988e7c618f6..24a62a8ab5b 100644
--- a/BGL/examples/BGL_surface_mesh/shortest_path.cpp
+++ b/BGL/examples/BGL_surface_mesh/shortest_path.cpp
@@ -56,7 +56,7 @@ int main(int argc, char** argv)
     }
   }
 
-  std::vector<halfedge_descriptor> halfedge_sequence;
+  std::list<halfedge_descriptor> halfedge_sequence;
   CGAL::dijkstra_shortest_path(vs, vt, sm,
     std::back_inserter(halfedge_sequence));
 
@@ -68,12 +68,13 @@ int main(int argc, char** argv)
   auto vpmap = get(CGAL::vertex_point, sm);
 
   std::ofstream out("shortest_path.polylines.txt");
+  out << halfedge_sequence.size() << " " << get(vpmap, source(halfedge_sequence.front(),sm));
   for (const halfedge_descriptor he : halfedge_sequence)
   {
-    const vertex_descriptor v0 = source(he, sm);
-    const vertex_descriptor v1 = target(he, sm);
-    out << "2 " << get(vpmap, v0) << " " << get(vpmap, v1) << std::endl;
+    const vertex_descriptor v = target(he, sm);
+    out << " " << get(vpmap, v);
   }
+  out << std::endl;
   out.close();
 
   return EXIT_SUCCESS;
diff --git a/BGL/include/CGAL/boost/graph/dijkstra_shortest_path.h b/BGL/include/CGAL/boost/graph/dijkstra_shortest_path.h
index f6f16921914..f417ce510aa 100644
--- a/BGL/include/CGAL/boost/graph/dijkstra_shortest_path.h
+++ b/BGL/include/CGAL/boost/graph/dijkstra_shortest_path.h
@@ -146,42 +146,14 @@ OutputIterator dijkstra_shortest_path(
   }
   catch (const internal::Dijkstra_end_exception& ){}
 
-  // Walk back from target to source and collect vertices along the way
-  struct vertex_on_path
-  {
-    vertex_descriptor vertex;
-    bool is_constrained;
-  };
-
-  std::vector<vertex_descriptor> constrained_vertices = { vs };
+  std::list<halfedge_descriptor> path;
   vertex_descriptor t = vt;
-  std::vector<vertex_on_path> path;
-  do
-  {
-    const bool is_new_vertex = (constrained_vertices.end()
-      == std::find(constrained_vertices.begin(), constrained_vertices.end(), t));
-
-    vertex_on_path vop;
-    vop.vertex = t;
-    vop.is_constrained = !is_new_vertex;
-    path.push_back(vop);
-
+  do {
+    path.push_front(halfedge(relaxed_edges_map[t],g));
     t = get(pred_pmap, t);
-  }
-  while (t != vs);
-
-  // Add the last vertex
-  vertex_on_path vop;
-  vop.vertex = constrained_vertices.back();
-  vop.is_constrained = true;
-  path.push_back(vop);
-
-  // Display path
-  for (auto path_it = path.begin(); path_it != path.end() - 1; ++path_it)
-  {
-    const auto map_it = vis.relaxed_edges.find(path_it->vertex);
-    if (map_it != vis.relaxed_edges.end())
-      *halfedge_sequence_oit++ = halfedge(map_it->second, g);
+  }while (t != vs);
+  for(auto he : path){
+    *halfedge_sequence_oit++ = he;
   }
   return halfedge_sequence_oit;
 }