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git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/bottleneckDistance@1092 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 77b2a427cb3ff80b9a0c5d1c71f9f1de11547530

4 files changed, 702 insertions, 0 deletions

diff --git a/src/Bipartite_graphs_matching/include/gudhi/Graph_matching.h b/src/Bipartite_graphs_matching/include/gudhi/Graph_matching.h
new file mode 100644
index 00000000..a2754333
--- /dev/null
+++ b/src/Bipartite_graphs_matching/include/gudhi/Graph_matching.h
@@ -0,0 +1,213 @@
+/*    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(s):       Francois Godi
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Antipolis (France)
+ *
+ *    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 SRC_BOTTLENECK_INCLUDE_GUDHI_GRAPH_MATCHING_H_
+#define SRC_BOTTLENECK_INCLUDE_GUDHI_GRAPH_MATCHING_H_
+
+#include <deque>
+
+#include "Neighbors_finder.h"
+
+namespace Gudhi {
+
+namespace bipartite_graph_matching {
+
+/** \brief Function to use in order to compute the Bottleneck distance between two persistence diagrams.
+ *
+ *
+ *
+ * \ingroup bottleneck_distance
+ */
+template<typename Persistence_diagram1, typename Persistence_diagram2>
+double bottleneck_distance(const Persistence_diagram1& diag1, const Persistence_diagram2& diag2, double e = 0.);
+
+/** \internal \brief Structure representing a graph matching. The graph is a Persistence_diagrams_graph.
+ *
+ * \ingroup bottleneck_distance
+ */
+class Graph_matching {
+public:
+    /** \internal \brief Constructor constructing an empty matching. */
+    explicit Graph_matching();
+    /** \internal \brief Copy operator. */
+    Graph_matching& operator=(const Graph_matching& m);
+    /** \internal \brief Is the matching perfect ? */
+    bool perfect() const;
+    /** \internal \brief Augments the matching with a maximal set of edge-disjoint shortest augmenting paths. */
+    bool multi_augment();
+    /** \internal \brief Sets the maximum length of the edges allowed to be added in the matching, 0 initially. */
+    void set_r(double r);
+
+private:
+    double r;
+    /** \internal \brief Given a point from V, provides its matched point in U, null_point_index() if there isn't. */
+    std::vector<int> v_to_u;
+    /** \internal \brief All the unmatched points in U. */
+    std::list<int> unmatched_in_u;
+
+    /** \internal \brief Provides a Layered_neighbors_finder dividing the graph in layers. Basically a BFS. */
+    std::unique_ptr<Layered_neighbors_finder> layering() const;
+    /** \internal \brief Augments the matching with a simple path no longer than max_depth. Basically a DFS. */
+    bool augment(Layered_neighbors_finder & layered_nf, int u_start_index, int max_depth);
+    /** \internal \brief Update the matching with the simple augmenting path given as parameter. */
+    void update(std::deque<int> & path);
+};
+
+inline Graph_matching::Graph_matching()
+    : r(0.), v_to_u(G::size(), null_point_index()), unmatched_in_u() {
+    for (int u_point_index = 0; u_point_index < G::size(); ++u_point_index)
+        unmatched_in_u.emplace_back(u_point_index);
+}
+
+inline Graph_matching& Graph_matching::operator=(const Graph_matching& m) {
+    r = m.r;
+    v_to_u = m.v_to_u;
+    unmatched_in_u = m.unmatched_in_u;
+    return *this;
+}
+
+inline bool Graph_matching::perfect() const {
+    return unmatched_in_u.empty();
+}
+
+inline bool Graph_matching::multi_augment() {
+    if (perfect())
+        return false;
+    Layered_neighbors_finder layered_nf = *layering();
+    int max_depth = layered_nf.vlayers_number()*2 - 1;
+    double rn = sqrt(G::size());
+    // verification of a necessary criterion in order to shortcut if possible
+    if (max_depth <0 || (unmatched_in_u.size() > rn && max_depth >= rn))
+        return false;
+    bool successful = false;
+    std::list<int> tries(unmatched_in_u);
+    for (auto it = tries.cbegin(); it != tries.cend(); it++)
+        // 'augment' has side-effects which have to be always executed, don't change order
+        successful =  augment(layered_nf, *it, max_depth) || successful;
+    return successful;
+}
+
+inline void Graph_matching::set_r(double r) {
+    this->r = r;
+}
+
+inline bool Graph_matching::augment(Layered_neighbors_finder & layered_nf, int u_start_index, int max_depth) {
+    //V vertices have at most one successor, thus when we backtrack from U we can directly pop_back 2 vertices.
+    std::deque<int> path;
+    path.emplace_back(u_start_index);
+    do {
+        if (static_cast<int>(path.size()) > max_depth) {
+            path.pop_back();
+            path.pop_back();
+        }
+        if (path.empty())
+            return false;
+        path.emplace_back(layered_nf.pull_near(path.back(), static_cast<int>(path.size())/2));
+        while (path.back() == null_point_index()) {
+            path.pop_back();
+            path.pop_back();
+            if (path.empty())
+                return false;
+            path.pop_back();
+            path.emplace_back(layered_nf.pull_near(path.back(), path.size() / 2));
+        }
+        path.emplace_back(v_to_u.at(path.back()));
+    } while (path.back() != null_point_index());
+    //if v_to_u.at(path.back()) has no successor, path.back() is an exposed vertex
+    path.pop_back();
+    update(path);
+    return true;
+}
+
+inline std::unique_ptr<Layered_neighbors_finder> Graph_matching::layering() const {
+    std::list<int> u_vertices(unmatched_in_u);
+    std::list<int> v_vertices;
+    Neighbors_finder nf(r);
+    for (int v_point_index = 0; v_point_index < G::size(); ++v_point_index)
+        nf.add(v_point_index);
+    std::unique_ptr<Layered_neighbors_finder> layered_nf(new Layered_neighbors_finder(r));
+    for(int layer = 0; !u_vertices.empty(); layer++) {
+        // one layer is one step in the BFS
+        for (auto it = u_vertices.cbegin(); it != u_vertices.cend(); ++it) {
+            std::unique_ptr< std::list<int> > u_succ = std::move(nf.pull_all_near(*it));
+            for (auto it = u_succ->cbegin(); it != u_succ->cend(); ++it) {
+                layered_nf->add(*it, layer);
+                v_vertices.emplace_back(*it);
+            }
+        }
+        // When the above for finishes, we have progress of one half-step (from U to V) in the BFS
+        u_vertices.clear();
+        bool end = false;
+        for (auto it = v_vertices.cbegin(); it != v_vertices.cend(); it++)
+            if (v_to_u.at(*it) == null_point_index())
+                // we stop when a nearest exposed V vertex (from U exposed vertices) has been found
+                end = true;
+            else
+                u_vertices.emplace_back(v_to_u.at(*it));
+        // When the above for finishes, we have progress of one half-step (from V to U) in the BFS
+        if (end)
+            return layered_nf;
+        v_vertices.clear();
+    }
+    return layered_nf;
+}
+
+inline void Graph_matching::update(std::deque<int>& path) {
+    unmatched_in_u.remove(path.front());
+    for (auto it = path.cbegin(); it != path.cend(); ++it) {
+        // Be careful, the iterator is incremented twice each time
+        int tmp = *it;
+        v_to_u[*(++it)] = tmp;
+    }
+}
+
+template<typename Persistence_diagram1, typename Persistence_diagram2>
+double bottleneck_distance(const Persistence_diagram1 &diag1, const Persistence_diagram2 &diag2, double e) {
+    G::initialize(diag1, diag2, e);
+    std::unique_ptr< std::vector<double> > sd = std::move(G::sorted_distances());
+    int idmin = 0;
+    int idmax = sd->size() - 1;
+    // alpha can be modified, this will change the complexity
+    double alpha = pow(sd->size(), 0.25);
+    Graph_matching m;
+    Graph_matching biggest_unperfect;
+    while (idmin != idmax) {
+        int step = static_cast<int>((idmax - idmin) / alpha);
+        m.set_r(sd->at(idmin + step));
+        while (m.multi_augment());
+        // The above while compute a maximum matching (according to the r setted before)
+        if (m.perfect()) {
+            idmax = idmin + step;
+            m = biggest_unperfect;
+        } else {
+            biggest_unperfect = m;
+            idmin = idmin + step + 1;
+        }
+    }
+    return sd->at(idmin);
+}
+
+}  // namespace bipartite_graph_matching
+
+}  // namespace Gudhi
+
+#endif  // SRC_BOTTLENECK_INCLUDE_GUDHI_GRAPH_MATCHING_H_
diff --git a/src/Bipartite_graphs_matching/include/gudhi/Neighbors_finder.h b/src/Bipartite_graphs_matching/include/gudhi/Neighbors_finder.h
new file mode 100644
index 00000000..78b9debc
--- /dev/null
+++ b/src/Bipartite_graphs_matching/include/gudhi/Neighbors_finder.h
@@ -0,0 +1,155 @@
+/*    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(s):       Francois Godi
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Antipolis (France)
+ *
+ *    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 SRC_BOTTLENECK_INCLUDE_GUDHI_NEIGHBORS_FINDER_H_
+#define SRC_BOTTLENECK_INCLUDE_GUDHI_NEIGHBORS_FINDER_H_
+
+#include <unordered_set>
+
+#include "Planar_neighbors_finder.h"
+
+namespace Gudhi {
+
+namespace bipartite_graph_matching {
+
+/** \internal \brief data structure used to find any point (including projections) in V near to a query point from U
+ * (which can be a projection).
+ *
+ * V points have to be added manually using their index and before the first pull. A neighbor pulled is automatically removed.
+ *
+ * \ingroup bottleneck_distance
+ */
+class Neighbors_finder {
+public:
+    /** \internal \brief Constructor taking the near distance definition as parameter. */
+    Neighbors_finder(double r);
+    /** \internal \brief A point added will be possibly pulled. */
+    void add(int v_point_index);
+    /** \internal \brief Returns and remove a V point near to the U point given as parameter, null_point_index() if there isn't such a point. */
+    int pull_near(int u_point_index);
+    /** \internal \brief Returns and remove all the V points near to the U point given as parameter. */
+    std::unique_ptr< std::list<int> > pull_all_near(int u_point_index);
+
+private:
+    const double r;
+    Planar_neighbors_finder planar_neighbors_f;
+    std::unordered_set<int> projections_f;
+    void remove(int v_point_index);
+    bool contains(int v_point_index);
+};
+
+/** \internal \brief data structure used to find any point (including projections) in V near to a query point from U
+ * (which can be a projection) in a layered graph layer given as parmeter.
+ *
+ * V points have to be added manually using their index and before the first pull. A neighbor pulled is automatically removed.
+ *
+ * \ingroup bottleneck_distance
+ */
+class Layered_neighbors_finder {
+public:
+    /** \internal \brief Constructor taking the near distance definition as parameter. */
+    Layered_neighbors_finder(double r);
+    /** \internal \brief A point added will be possibly pulled. */
+    void add(int v_point_index, int vlayer);
+    /** \internal \brief Returns and remove a V point near to the U point given as parameter, null_point_index() if there isn't such a point. */
+    int pull_near(int u_point_index, int vlayer);
+    /** \internal \brief Returns the number of layers. */
+    int vlayers_number() const;
+
+private:
+    const double r;
+    std::vector<Neighbors_finder> neighbors_finder;
+};
+
+inline Neighbors_finder::Neighbors_finder(double r) :
+    r(r), planar_neighbors_f(r), projections_f() { }
+
+inline void Neighbors_finder::add(int v_point_index) {
+    if (G::on_the_v_diagonal(v_point_index))
+        projections_f.emplace(v_point_index);
+    else
+        planar_neighbors_f.add(v_point_index);
+}
+
+inline void Neighbors_finder::remove(int v_point_index) {
+    if(v_point_index == null_point_index())
+        return;
+    if (G::on_the_v_diagonal(v_point_index))
+        projections_f.erase(v_point_index);
+    else
+        planar_neighbors_f.remove(v_point_index);
+}
+
+inline bool Neighbors_finder::contains(int v_point_index) {
+    return planar_neighbors_f.contains(v_point_index) || (projections_f.count(v_point_index)>0);
+}
+
+inline int Neighbors_finder::pull_near(int u_point_index) {
+    int tmp;
+    int c = G::corresponding_point_in_v(u_point_index);
+    if (G::on_the_u_diagonal(u_point_index) && !projections_f.empty())
+        //All projections are at distance 0
+        tmp = *projections_f.cbegin();
+    else if (contains(c) && (G::distance(u_point_index, c) <= r))
+        //Is the query point near to its projection ?
+        tmp = c;
+    else
+        //Is the query point near to a V point in the plane ?
+        tmp = planar_neighbors_f.pull_near(u_point_index);
+    remove(tmp);
+    return tmp;
+}
+
+inline std::unique_ptr< std::list<int> > Neighbors_finder::pull_all_near(int u_point_index) {
+    std::unique_ptr< std::list<int> > all_pull = std::move(planar_neighbors_f.pull_all_near(u_point_index));
+    int last_pull = pull_near(u_point_index);
+    while (last_pull != null_point_index()) {
+        all_pull->emplace_back(last_pull);
+        last_pull = pull_near(u_point_index);
+    }
+    return all_pull;
+}
+
+inline Layered_neighbors_finder::Layered_neighbors_finder(double r) :
+    r(r), neighbors_finder() { }
+
+inline void Layered_neighbors_finder::add(int v_point_index, int vlayer) {
+    for (int l = neighbors_finder.size(); l <= vlayer; l++)
+        neighbors_finder.emplace_back(Neighbors_finder(r));
+    neighbors_finder.at(vlayer).add(v_point_index);
+}
+
+inline int Layered_neighbors_finder::pull_near(int u_point_index, int vlayer) {
+    if (static_cast<int> (neighbors_finder.size()) <= vlayer)
+        return null_point_index();
+    return neighbors_finder.at(vlayer).pull_near(u_point_index);
+}
+
+inline int Layered_neighbors_finder::vlayers_number() const {
+    return static_cast<int>(neighbors_finder.size());
+}
+
+}  // namespace bipartite_graph_matching
+
+}  // namespace Gudhi
+
+#endif  // SRC_BOTTLENECK_INCLUDE_GUDHI_NEIGHBORS_FINDER_H_
diff --git a/src/Bipartite_graphs_matching/include/gudhi/Persistence_diagrams_graph.h b/src/Bipartite_graphs_matching/include/gudhi/Persistence_diagrams_graph.h
new file mode 100644
index 00000000..6420b772
--- /dev/null
+++ b/src/Bipartite_graphs_matching/include/gudhi/Persistence_diagrams_graph.h
@@ -0,0 +1,164 @@
+/*    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(s):       Francois Godi
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Antipolis (France)
+ *
+ *    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 SRC_BOTTLENECK_INCLUDE_GUDHI_PERSISTENCE_DIAGRAMS_GRAPH_H_
+#define SRC_BOTTLENECK_INCLUDE_GUDHI_PERSISTENCE_DIAGRAMS_GRAPH_H_
+
+#include <vector>
+#include <set>
+#include <cmath>
+#include <utility>
+#include <algorithm>
+#include <math.h>
+#include <memory>
+
+namespace Gudhi {
+
+namespace bipartite_graph_matching {
+
+/** \internal \brief Returns the used index for encoding none of the points */
+int null_point_index();
+
+/** \internal \brief Structure representing an euclidean bipartite graph containing
+ *  the points from the two persistence diagrams (including the projections).
+ *
+ * \ingroup bottleneck_distance
+ */
+class Persistence_diagrams_graph {
+public:
+    /** \internal \brief Initializer taking 2 Point (concept) ranges as parameters. */
+    template<typename Persistence_diagram1, typename Persistence_diagram2>
+    static void initialize(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 ? */
+    static bool on_the_u_diagonal(int u_point_index);
+    /** \internal \brief Is the given point from V the projection of a point in U ? */
+    static bool on_the_v_diagonal(int v_point_index);
+    /** \internal \brief Given a point from V, returns the corresponding (projection or projector) point in U. */
+    static int corresponding_point_in_u(int v_point_index);
+    /** \internal \brief Given a point from U, returns the corresponding (projection or projector) point in V. */
+    static int corresponding_point_in_v(int u_point_index);
+    /** \internal \brief Given a point from U and a point from V, returns the distance between those points. */
+    static double distance(int u_point_index, int v_point_index);
+    /** \internal \brief Returns size = |U| = |V|. */
+    static int size();
+    /** \internal \brief Returns the O(n^2) sorted distances between the points. */
+    static std::unique_ptr< std::vector<double> > sorted_distances();
+
+private:
+    /** \internal \typedef \brief Internal_point is the internal points representation, indexes used outside. */
+    typedef std::pair<double, double> Internal_point;
+    static std::vector<Internal_point> u;
+    static std::vector<Internal_point> v;
+    static Internal_point get_u_point(int u_point_index);
+    static Internal_point get_v_point(int v_point_index);
+
+    friend class Naive_pnf;
+    friend class Upper_envelope_tree;
+};
+
+/** \internal \typedef \brief Shorter alias */
+typedef Persistence_diagrams_graph G;
+
+// static initialization, seems to work but strange
+std::vector<G::Internal_point> G::u = [] {return std::vector<G::Internal_point>();}();
+std::vector<G::Internal_point> G::v = [] {return std::vector<G::Internal_point>();}();
+
+inline int null_point_index() {
+    return -1;
+}
+
+template<typename Persistence_diagram1, typename Persistence_diagram2>
+inline void G::initialize(const Persistence_diagram1 &diag1,
+                          const Persistence_diagram2 &diag2, double e){
+    u.clear();
+    v.clear();
+    for (auto it = diag1.cbegin(); it != diag1.cend(); ++it)
+        if (it->second - it->first > e)
+            u.emplace_back(*it);
+    for (auto it = diag2.cbegin(); it != diag2.cend(); ++it)
+        if (it->second - it->first > e)
+            v.emplace_back(*it);
+    if (u.size() < v.size())
+        swap(u, v);
+}
+
+inline bool G::on_the_u_diagonal(int u_point_index) {
+    return u_point_index >= static_cast<int> (u.size());
+}
+
+inline bool G::on_the_v_diagonal(int v_point_index) {
+    return v_point_index >= static_cast<int> (v.size());
+}
+
+inline int G::corresponding_point_in_u(int v_point_index) {
+    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 G::corresponding_point_in_v(int u_point_index) {
+    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 G::distance(int u_point_index, int v_point_index) {
+    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.first - p_v.first), std::fabs(p_u.second - p_v.second));
+}
+
+inline int G::size() {
+    return static_cast<int> (u.size() + v.size());
+}
+
+inline std::unique_ptr< std::vector<double> > G::sorted_distances() {
+    // could be optimized
+    std::set<double> sorted_distances;
+    for (int u_point_index = 0; u_point_index < size(); ++u_point_index)
+        for (int v_point_index = 0; v_point_index < size(); ++v_point_index)
+            sorted_distances.emplace(distance(u_point_index, v_point_index));
+    std::unique_ptr< std::vector<double> > sd_up(new std::vector<double>(sorted_distances.cbegin(), sorted_distances.cend()));
+    return sd_up;
+}
+
+inline G::Internal_point G::get_u_point(int u_point_index) {
+    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 x = (projector.first + projector.second) / 2;
+    return Internal_point(x, x);
+}
+
+inline G::Internal_point G::get_v_point(int v_point_index) {
+    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 x = (projector.first + projector.second) / 2;
+    return Internal_point(x, x);
+}
+
+}  // namespace bipartite_graph_matching
+
+}  // namespace Gudhi
+
+#endif  // SRC_BOTTLENECK_INCLUDE_GUDHI_PERSISTENCE_DIAGRAMS_GRAPH_H_
diff --git a/src/Bipartite_graphs_matching/include/gudhi/Planar_neighbors_finder.h b/src/Bipartite_graphs_matching/include/gudhi/Planar_neighbors_finder.h
new file mode 100644
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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(s):       Francois Godi
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Antipolis (France)
+ *
+ *    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 SRC_BOTTLENECK_INCLUDE_GUDHI_PLANAR_NEIGHBORS_FINDER_H_
+#define SRC_BOTTLENECK_INCLUDE_GUDHI_PLANAR_NEIGHBORS_FINDER_H_
+
+#include <list>
+#include <map>
+
+#include "Persistence_diagrams_graph.h"
+
+namespace Gudhi {
+
+namespace bipartite_graph_matching {
+
+/** \internal \brief Structure used to find any point in V near (according to the planar distance) to a query point from U.
+ *
+ * V points have to be added manually using their index and before the first remove/pull. A neighbor pulled is automatically removed. but we can also
+ * remove points manually using their index.
+ *
+ * \ingroup bottleneck_distance
+ */
+class Abstract_planar_neighbors_finder {
+public:
+    /** \internal \brief Constructor TODO. */
+    Abstract_planar_neighbors_finder(double r);
+    virtual ~Abstract_planar_neighbors_finder() = 0;
+    /** \internal \brief A point added will be possibly pulled. */
+    virtual void add(int v_point_index) = 0;
+    /** \internal \brief A point manually removed will no longer be possibly pulled. */
+    virtual void remove(int v_point_index) = 0;
+    /** \internal \brief Can the point given as parameter be returned ? */
+    virtual bool contains(int v_point_index) const = 0;
+    /** \internal \brief Provide and remove a V point near to the U point given as parameter, null_point_index() if there isn't such a point. */
+    virtual int pull_near(int u_point_index) = 0;
+    /** \internal \brief Provide and remove all the V points near to the U point given as parameter. */
+    virtual std::unique_ptr< std::list<int> > pull_all_near(int u_point_index);
+
+protected:
+    const double r;
+};
+
+/** \internal \brief Naive_pnf is an naïve Abstract_planar_neighbors_finder implementation
+ *
+ * \ingroup bottleneck_distance
+ */
+class Naive_pnf : public Abstract_planar_neighbors_finder {
+public:
+    /** \internal \brief Constructor taking the near distance definition as parameter. */
+    Naive_pnf(double r);
+    /** \internal \brief A point added will be possibly pulled. */
+    void add(int v_point_index);
+    /** \internal \brief A point manually removed will no longer be possibly pulled. */
+    void remove(int v_point_index);
+    /** \internal \brief Can the point given as parameter be returned ? */
+    bool contains(int v_point_index) const;
+    /** \internal \brief Provide and remove a V point near to the U point given as parameter, null_point_index() if there isn't such a point. */
+    int pull_near(int u_point_index);
+    /** \internal \brief Provide and remove all the V points near to the U point given as parameter. */
+    virtual std::unique_ptr< std::list<int> > pull_all_near(int u_point_index);
+
+private:
+    std::pair<int,int> get_v_key(int v_point_index) const;
+    std::multimap<std::pair<int,int>,int> grid;
+};
+
+/** \internal \typedef \brief Planar_neighbors_finder is the used Abstract_planar_neighbors_finder's implementation. */
+typedef Naive_pnf Planar_neighbors_finder;
+
+
+inline Abstract_planar_neighbors_finder::Abstract_planar_neighbors_finder(double r) :
+    r(r) { }
+
+inline Abstract_planar_neighbors_finder::~Abstract_planar_neighbors_finder() {}
+
+inline std::unique_ptr< std::list<int> > Abstract_planar_neighbors_finder::pull_all_near(int u_point_index) {
+    std::unique_ptr< std::list<int> > all_pull(new std::list<int>);
+    int last_pull = pull_near(u_point_index);
+    while (last_pull != null_point_index()) {
+        all_pull->emplace_back(last_pull);
+        last_pull = pull_near(u_point_index);
+    }
+    return all_pull;
+}
+
+inline Naive_pnf::Naive_pnf(double r) :
+    Abstract_planar_neighbors_finder(r), grid() { }
+
+
+inline std::pair<int,int> Naive_pnf::get_v_key(int v_point_index) const{
+    G::Internal_point v_point = G::get_v_point(v_point_index);
+    return std::make_pair(static_cast<int>(v_point.first/r), static_cast<int>(v_point.second/r));
+}
+
+inline void Naive_pnf::add(int v_point_index) {
+    grid.emplace(get_v_key(v_point_index),v_point_index);
+}
+
+inline void Naive_pnf::remove(int v_point_index) {
+    for(auto it = grid.find(get_v_key(v_point_index)); it!=grid.end(); it++)
+        if(it->second==v_point_index){
+            grid.erase(it);
+            return;
+        }
+}
+
+inline bool Naive_pnf::contains(int v_point_index) const {
+    if(v_point_index == null_point_index())
+        return false;
+    for(auto it = grid.find(get_v_key(v_point_index)); it!=grid.end(); it++)
+        if(it->second==v_point_index)
+            return true;
+    return false;
+}
+
+inline int Naive_pnf::pull_near(int u_point_index) {
+    G::Internal_point u_point = G::get_u_point(u_point_index);
+    int i0 = static_cast<int>(u_point.first/r);
+    int j0 = static_cast<int>(u_point.second/r);
+    for(int i = 1; i<= 3; i++)
+        for(int j = 1; j<= 3; j++)
+            for(auto it = grid.find(std::make_pair(i0 +(i%3)-1, j0+(j%3)-1)); it!=grid.end(); it++)
+                if (G::distance(u_point_index, it->second) <= r) {
+                    int tmp = it->second;
+                    grid.erase(it);
+                    return tmp;
+                }
+    return null_point_index();
+}
+
+inline std::unique_ptr< std::list<int> > Naive_pnf::pull_all_near(int u_point_index) {
+    std::unique_ptr< std::list<int> > all_pull(new std::list<int>);
+    G::Internal_point u_point = G::get_u_point(u_point_index);
+    int i0 = static_cast<int>(u_point.first/r);
+    int j0 = static_cast<int>(u_point.second/r);
+    for(int i = 1; i<= 3; i++)
+        for(int j = 1; j<= 3; j++)
+            for(auto it = grid.find(std::make_pair(i0 +(i%3)-1, j0+(j%3)-1)); it!=grid.end(); it++)
+                if (G::distance(u_point_index, it->second) <= r) {
+                    int tmp = it->second;
+                    grid.erase(it);
+                    all_pull->emplace_back(tmp);
+                }
+    return all_pull;
+}
+
+}  // namespace bipartite_graph_matching
+
+}  // namespace Gudhi
+
+#endif  // SRC_BOTTLENECK_INCLUDE_GUDHI_PLANAR_NEIGHBORS_FINDER_H_