diff --git a/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h b/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h
index de1fc17a10d..232c5796e0d 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h
@@ -38,13 +38,13 @@ public:
   typedef typename Kernel::Line_2 Line_2;
   typedef typename Kernel::Segment_2 Segment_2;
 
-  typedef Support_line<Kernel> Support_line;
+  typedef Support_line<Kernel> Support_line_DS;
   typedef Segment Segment;
   typedef Vertex<FT> Vertex;
 
   typedef Meta_vertex<Point_2> Meta_vertex;
 
-  typedef std::vector<Support_line> Support_lines;
+  typedef std::vector<Support_line_DS> Support_lines;
   typedef std::vector<Segment> Segments;
   typedef std::vector<Vertex> Vertices;
 
@@ -96,8 +96,8 @@ public:
   Segment& segment(std::size_t idx) { return m_segments[idx]; }
 
   std::size_t number_of_support_lines() const { return m_support_lines.size(); }
-  const Support_line& support_line(std::size_t idx) const { return m_support_lines[idx]; }
-  Support_line& support_line(std::size_t idx) { return m_support_lines[idx]; }
+  const Support_line_DS& support_line(std::size_t idx) const { return m_support_lines[idx]; }
+  Support_line_DS& support_line(std::size_t idx) { return m_support_lines[idx]; }
 
   std::size_t number_of_meta_vertices() const { return m_meta_vertices.size(); }
   const Meta_vertex& meta_vertex(std::size_t idx) const { return m_meta_vertices[idx]; }
@@ -216,37 +216,37 @@ public:
 
 
   // Segment/idx -> Support_line
-  inline const Support_line& support_line_of_segment(const Segment& segment) const
+  inline const Support_line_DS& support_line_of_segment(const Segment& segment) const
   {
     return m_support_lines[segment.support_line_idx()];
   }
-  inline Support_line& support_line_of_segment(const Segment& segment)
+  inline Support_line_DS& support_line_of_segment(const Segment& segment)
   {
     return m_support_lines[segment.support_line_idx()];
   }
-  inline const Support_line& support_line_of_segment(std::size_t segment_idx) const
+  inline const Support_line_DS& support_line_of_segment(std::size_t segment_idx) const
   {
     return support_line_of_segment(m_segments[segment_idx]);
   }
-  inline Support_line& support_line_of_segment(std::size_t segment_idx)
+  inline Support_line_DS& support_line_of_segment(std::size_t segment_idx)
   {
     return support_line_of_segment(m_segments[segment_idx]);
   }
 
   // Vertex/idx -> Support_line
-  inline const Support_line& support_line_of_vertex(const Vertex& vertex) const
+  inline const Support_line_DS& support_line_of_vertex(const Vertex& vertex) const
   {
     return support_line_of_segment(vertex.segment_idx());
   }
-  inline Support_line& support_line_of_vertex(const Vertex& vertex)
+  inline Support_line_DS& support_line_of_vertex(const Vertex& vertex)
   {
     return support_line_of_segment(vertex.segment_idx());
   }
-  inline const Support_line& support_line_of_vertex(std::size_t vertex_idx) const
+  inline const Support_line_DS& support_line_of_vertex(std::size_t vertex_idx) const
   {
     return support_line_of_vertex(m_vertices[vertex_idx]);
   }
-  inline Support_line& support_line_of_vertex(std::size_t vertex_idx)
+  inline Support_line_DS& support_line_of_vertex(std::size_t vertex_idx)
   {
     return support_line_of_vertex(m_vertices[vertex_idx]);
   }
@@ -294,7 +294,7 @@ public:
     const Meta_vertex& meta_vertex = m_meta_vertices[meta_vertex_idx];
     for (std::size_t support_line_idx : meta_vertex.support_lines_idx())
     {
-      const Support_line& support_line = m_support_lines[support_line_idx];
+      const Support_line_DS& support_line = m_support_lines[support_line_idx];
       for (std::size_t segment_idx : support_line.segments_idx())
       {
         const Segment& segment = m_segments[segment_idx];
@@ -309,7 +309,7 @@ public:
   {
     return point_of_vertex(vertex).bbox();
   }
-  inline CGAL::Bbox_2 bbox(const Support_line& support_line) const
+  inline CGAL::Bbox_2 bbox(const Support_line_DS& support_line) const
   {
     return std::accumulate(support_line.segments_idx().begin(), support_line.segments_idx().end(),
       CGAL::Bbox_2(),
@@ -330,7 +330,7 @@ public:
   Segment_2 segment_2(std::size_t segment_idx) const
   {
     const Segment& segment = m_segments[segment_idx];
-    const Support_line& support_line = m_support_lines[segment.support_line_idx()];
+    const Support_line_DS& support_line = m_support_lines[segment.support_line_idx()];
     const Vertex& source = m_vertices[segment.source_idx()];
     const Vertex& target = m_vertices[segment.target_idx()];
 
@@ -426,14 +426,14 @@ public:
 
   std::size_t add_support_line(const Segment_2& segment)
   {
-    m_support_lines.push_back(Support_line(segment));
+    m_support_lines.push_back(Support_line_DS(segment));
     return std::size_t(m_support_lines.size() - 1);
   }
 
   Segment& add_segment(const Segment_2 segment, std::size_t input_idx = std::size_t(-1))
   {
     // Check if support line exists first
-    Support_line new_support_line(segment);
+    Support_line_DS new_support_line(segment);
     std::size_t support_line_idx = std::size_t(-1);
     for (std::size_t i = 0; i < number_of_support_lines(); ++i)
       if (new_support_line == support_line(i))
@@ -563,7 +563,7 @@ public:
     // std::size_t source_idx = segment.source_idx();
     std::size_t target_idx = segment.target_idx();
 
-    Support_line& support_line = support_line_of_segment(segment_idx);
+    Support_line_DS& support_line = support_line_of_segment(segment_idx);
 
     std::sort(meta_vertices_idx.begin(), meta_vertices_idx.end(),
       [&](const std::size_t& a,
diff --git a/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_2.h b/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_2.h
index 053f9854cf6..0c2d4090d9c 100644
--- a/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_2.h
+++ b/Kinetic_space_partition/include/CGAL/Kinetic_space_partition_2.h
@@ -44,7 +44,7 @@ public:
   typedef typename Kernel::Vector_2 Vector_2;
 
   typedef KSP_2::internal::Data_structure<Kernel> Data;
-  typedef typename Data::Support_line Support_line;
+  typedef typename Data::Support_line_DS Support_line_DS;
   typedef typename Data::Segment Segment;
   typedef typename Data::Vertex Vertex;
 
@@ -107,7 +107,7 @@ public:
     // Prepare output by sorting segments along support lines;
     for (std::size_t i = 0; i < m_data.number_of_support_lines(); ++ i)
     {
-      Support_line& support_line = m_data.support_line(i);
+      Support_line_DS& support_line = m_data.support_line(i);
       std::sort (support_line.segments_idx().begin(), support_line.segments_idx().end(),
                  [&](const std::size_t& a, const std::size_t& b) -> bool
                  {
@@ -121,7 +121,7 @@ public:
   {
     for (std::size_t i = 0; i < m_data.number_of_support_lines(); ++ i)
     {
-      const Support_line& support_line = m_data.support_line(i);
+      const Support_line_DS& support_line = m_data.support_line(i);
       for (std::size_t s : support_line.segments_idx())
       {
         if (s == std::size_t(-1))
@@ -555,7 +555,7 @@ private:
 
   void initialize_vertices_directions (Segment& segment, unsigned int k)
   {
-    const Support_line& support_line = m_data.support_line_of_segment (segment);
+    const Support_line_DS& support_line = m_data.support_line_of_segment (segment);
 
     Vertex& source = m_data.source_of_segment (segment);
     Vertex& target = m_data.target_of_segment (segment);
@@ -701,7 +701,7 @@ private:
         if (m_data.segment_of_vertex(vertex).support_line_idx() == j)
           continue;
 
-        const Support_line& support_line = m_data.support_line(j);
+        const Support_line_DS& support_line = m_data.support_line(j);
 
         if (!CGAL::do_overlap(si_bbox, support_line_bboxes[j]))
          continue;
@@ -715,7 +715,7 @@ private:
           if (!KSP::internal::intersection(si, segments_2[segment_idx], point))
             continue;
 
-          Support_line& sli = m_data.support_line_of_vertex(vertex);
+          Support_line_DS& sli = m_data.support_line_of_vertex(vertex);
           FT dist = CGAL::approximate_sqrt (CGAL::squared_distance (sli.to_2d(vertex.point(0)), point));
           FT time = dist / vertex.speed();
 
@@ -755,7 +755,7 @@ private:
     // intersection between two colinear segments
     for (std::size_t i = 0; i < m_data.number_of_support_lines(); ++ i)
     {
-      Support_line& support_line = m_data.support_line(i);
+      Support_line_DS& support_line = m_data.support_line(i);
       if (support_line.connected_components() < 2)
         continue;
 
@@ -814,7 +814,7 @@ private:
 
     for (std::size_t i = 0; i < m_data.number_of_support_lines(); ++ i)
     {
-      Support_line& support_line = m_data.support_line(i);
+      Support_line_DS& support_line = m_data.support_line(i);
 
       for (std::size_t segment_idx : support_line.segments_idx())
       {
@@ -930,7 +930,7 @@ private:
   {
     for (std::size_t i = 0; i < m_data.number_of_support_lines(); ++ i)
     {
-      const Support_line& support_line = m_data.support_line(i);
+      const Support_line_DS& support_line = m_data.support_line(i);
 
       CGAL_assertion (support_line.meta_vertices_idx().size() > 1);