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diff --git a/include/gudhi/Persistence_graph.h b/include/gudhi/Persistence_graph.h
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+/*    This file is part of the Gudhi Library. The Gudhi library
+ *    (Geometric Understanding in Higher Dimensions) is a generic C++
+ *    library for computational topology.
+ *
+ *    Author:       Francois Godi
+ *
+ *    Copyright (C) 2015  INRIA
+ *
+ *    This program is free software: you can redistribute it and/or modify
+ *    it under the terms of the GNU General Public License as published by
+ *    the Free Software Foundation, either version 3 of the License, or
+ *    (at your option) any later version.
+ *
+ *    This program is distributed in the hope that it will be useful,
+ *    but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *    GNU General Public License for more details.
+ *
+ *    You should have received a copy of the GNU General Public License
+ *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef PERSISTENCE_GRAPH_H_
+#define PERSISTENCE_GRAPH_H_
+
+#include <gudhi/Internal_point.h>
+
+#ifdef GUDHI_USE_TBB
+#include <tbb/parallel_sort.h>
+#endif
+
+#include <vector>
+#include <algorithm>
+#include <limits>  // for numeric_limits
+
+namespace Gudhi {
+
+namespace persistence_diagram {
+
+/** \internal \brief Structure representing an euclidean bipartite graph containing
+ *  the points from the two persistence diagrams (including the projections).
+ *
+ * \ingroup bottleneck_distance
+ */
+class Persistence_graph {
+ public:
+  /** \internal \brief Constructor taking 2 PersistenceDiagrams (concept) as parameters. */
+  template<typename Persistence_diagram1, typename Persistence_diagram2>
+  Persistence_graph(const Persistence_diagram1& diag1, const Persistence_diagram2& diag2, double e);
+  /** \internal \brief Is the given point from U the projection of a point in V ? */
+  bool on_the_u_diagonal(int u_point_index) const;
+  /** \internal \brief Is the given point from V the projection of a point in U ? */
+  bool on_the_v_diagonal(int v_point_index) const;
+  /** \internal \brief Given a point from V, returns the corresponding (projection or projector) point in U. */
+  int corresponding_point_in_u(int v_point_index) const;
+  /** \internal \brief Given a point from U, returns the corresponding (projection or projector) point in V. */
+  int corresponding_point_in_v(int u_point_index) const;
+  /** \internal \brief Given a point from U and a point from V, returns the distance between those points. */
+  double distance(int u_point_index, int v_point_index) const;
+  /** \internal \brief Returns size = |U| = |V|. */
+  int size() const;
+  /** \internal \brief Is there as many infinite points (alive components) in both diagrams ? */
+  double bottleneck_alive() const;
+  /** \internal \brief Returns the O(n^2) sorted distances between the points. */
+  std::vector<double> sorted_distances() const;
+  /** \internal \brief Returns an upper bound for the diameter of the convex hull of all non infinite points */
+  double diameter_bound() const;
+  /** \internal \brief Returns the corresponding internal point */
+  Internal_point get_u_point(int u_point_index) const;
+  /** \internal \brief Returns the corresponding internal point */
+  Internal_point get_v_point(int v_point_index) const;
+
+ private:
+  std::vector<Internal_point> u;
+  std::vector<Internal_point> v;
+  double b_alive;
+};
+
+template<typename Persistence_diagram1, typename Persistence_diagram2>
+Persistence_graph::Persistence_graph(const Persistence_diagram1 &diag1,
+                                     const Persistence_diagram2 &diag2, double e)
+    : u(), v(), b_alive(0.) {
+  std::vector<double> u_alive;
+  std::vector<double> v_alive;
+  for (auto it = std::begin(diag1); it != std::end(diag1); ++it) {
+    if (std::get<1>(*it) == std::numeric_limits<double>::infinity())
+      u_alive.push_back(std::get<0>(*it));
+    else if (std::get<1>(*it) - std::get<0>(*it) > e)
+      u.push_back(Internal_point(std::get<0>(*it), std::get<1>(*it), u.size()));
+  }
+  for (auto it = std::begin(diag2); it != std::end(diag2); ++it) {
+    if (std::get<1>(*it) == std::numeric_limits<double>::infinity())
+      v_alive.push_back(std::get<0>(*it));
+    else if (std::get<1>(*it) - std::get<0>(*it) > e)
+      v.push_back(Internal_point(std::get<0>(*it), std::get<1>(*it), v.size()));
+  }
+  if (u.size() < v.size())
+    swap(u, v);
+  std::sort(u_alive.begin(), u_alive.end());
+  std::sort(v_alive.begin(), v_alive.end());
+  if (u_alive.size() != v_alive.size()) {
+    b_alive = std::numeric_limits<double>::infinity();
+  } else {
+    for (auto it_u = u_alive.cbegin(), it_v = v_alive.cbegin(); it_u != u_alive.cend(); ++it_u, ++it_v)
+      b_alive = std::max(b_alive, std::fabs(*it_u - *it_v));
+  }
+}
+
+inline bool Persistence_graph::on_the_u_diagonal(int u_point_index) const {
+  return u_point_index >= static_cast<int> (u.size());
+}
+
+inline bool Persistence_graph::on_the_v_diagonal(int v_point_index) const {
+  return v_point_index >= static_cast<int> (v.size());
+}
+
+inline int Persistence_graph::corresponding_point_in_u(int v_point_index) const {
+  return on_the_v_diagonal(v_point_index) ?
+      v_point_index - static_cast<int> (v.size()) : v_point_index + static_cast<int> (u.size());
+}
+
+inline int Persistence_graph::corresponding_point_in_v(int u_point_index) const {
+  return on_the_u_diagonal(u_point_index) ?
+      u_point_index - static_cast<int> (u.size()) : u_point_index + static_cast<int> (v.size());
+}
+
+inline double Persistence_graph::distance(int u_point_index, int v_point_index) const {
+  if (on_the_u_diagonal(u_point_index) && on_the_v_diagonal(v_point_index))
+    return 0.;
+  Internal_point p_u = get_u_point(u_point_index);
+  Internal_point p_v = get_v_point(v_point_index);
+  return std::max(std::fabs(p_u.x() - p_v.x()), std::fabs(p_u.y() - p_v.y()));
+}
+
+inline int Persistence_graph::size() const {
+  return static_cast<int> (u.size() + v.size());
+}
+
+inline double Persistence_graph::bottleneck_alive() const {
+  return b_alive;
+}
+
+inline std::vector<double> Persistence_graph::sorted_distances() const {
+  std::vector<double> distances;
+  distances.push_back(0.);  // for empty diagrams
+  for (int u_point_index = 0; u_point_index < size(); ++u_point_index) {
+    distances.push_back(distance(u_point_index, corresponding_point_in_v(u_point_index)));
+    for (int v_point_index = 0; v_point_index < size(); ++v_point_index)
+      distances.push_back(distance(u_point_index, v_point_index));
+  }
+#ifdef GUDHI_USE_TBB
+  tbb::parallel_sort(distances.begin(), distances.end());
+#else
+  std::sort(distances.begin(), distances.end());
+#endif
+  return distances;
+}
+
+inline Internal_point Persistence_graph::get_u_point(int u_point_index) const {
+  if (!on_the_u_diagonal(u_point_index))
+    return u.at(u_point_index);
+  Internal_point projector = v.at(corresponding_point_in_v(u_point_index));
+  double m = (projector.x() + projector.y()) / 2.;
+  return Internal_point(m, m, u_point_index);
+}
+
+inline Internal_point Persistence_graph::get_v_point(int v_point_index) const {
+  if (!on_the_v_diagonal(v_point_index))
+    return v.at(v_point_index);
+  Internal_point projector = u.at(corresponding_point_in_u(v_point_index));
+  double m = (projector.x() + projector.y()) / 2.;
+  return Internal_point(m, m, v_point_index);
+}
+
+inline double Persistence_graph::diameter_bound() const {
+  double max = 0.;
+  for (auto it = u.cbegin(); it != u.cend(); it++)
+    max = std::max(max, it->y());
+  for (auto it = v.cbegin(); it != v.cend(); it++)
+    max = std::max(max, it->y());
+  return max;
+}
+
+}  // namespace persistence_diagram
+
+}  // namespace Gudhi
+
+#endif  // PERSISTENCE_GRAPH_H_