25 files changed, 120119 insertions, 80 deletions

diff --git a/data/Alvarez_surface_deg9_k2_D8_from_42K_to_34K.txt b/data/Alvarez_surface_deg9_k2_D8_from_42K_to_34K.txt
new file mode 100644
index 00000000..d0a34713
--- /dev/null
+++ b/data/Alvarez_surface_deg9_k2_D8_from_42K_to_34K.txt
@@ -0,0 +1,33904 @@
+33903

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diff --git a/data/Alvarez_variete_k2_D4_300k_to_31k_2x2.txt b/data/Alvarez_variete_k2_D4_300k_to_31k_2x2.txt
new file mode 100644
index 00000000..8c0cf027
--- /dev/null
+++ b/data/Alvarez_variete_k2_D4_300k_to_31k_2x2.txt
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diff --git a/data/Alvarez_variete_k2_D8_900k_to_50k_2x2.txt b/data/Alvarez_variete_k2_D8_900k_to_50k_2x2.txt
new file mode 100644
index 00000000..6e40e268
--- /dev/null
+++ b/data/Alvarez_variete_k2_D8_900k_to_50k_2x2.txt
@@ -0,0 +1,50329 @@
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diff --git a/src/Witness_complex/example/CMakeLists.txt b/src/Witness_complex/example/CMakeLists.txt
index 9b874261..80396392 100644
--- a/src/Witness_complex/example/CMakeLists.txt
+++ b/src/Witness_complex/example/CMakeLists.txt
@@ -38,6 +38,14 @@ if(CGAL_FOUND)
       add_executable ( relaxed_witness_persistence relaxed_witness_persistence.cpp )
       target_link_libraries(relaxed_witness_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
       add_test( relaxed_witness_persistence_10 ${CMAKE_CURRENT_BINARY_DIR}/relaxed_witness_persistence 10)   
+      add_executable ( a0_persistence a0_persistence.cpp )
+      target_link_libraries(a0_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+      add_test( a0_persistence_10 ${CMAKE_CURRENT_BINARY_DIR}/a0_persistence 10)
+      add_executable ( bench_rwit bench_rwit.cpp )
+                  
+      add_executable ( relaxed_delaunay relaxed_delaunay.cpp )
+      target_link_libraries(relaxed_delaunay ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+      add_test( relaxed_delaunay_10 ${CMAKE_CURRENT_BINARY_DIR}/relaxed_delaunay 10)   
     else()
       message(WARNING "Eigen3 not found. Version 3.1.0 is required for witness_complex_sphere example.")      
     endif()
diff --git a/src/Witness_complex/example/Landmark_choice_random_knn.h b/src/Witness_complex/example/Landmark_choice_random_knn.h
new file mode 100644
index 00000000..3797b4c5
--- /dev/null
+++ b/src/Witness_complex/example/Landmark_choice_random_knn.h
@@ -0,0 +1,142 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 LANDMARK_CHOICE_BY_RANDOM_KNN_H_
+#define LANDMARK_CHOICE_BY_RANDOM_KNN_H_
+
+#include <utility>  // for pair<>
+#include <vector>
+#include <cstddef> // for ptrdiff_t type
+
+//#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+//#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_incremental_neighbor_search.h>
+#include <CGAL/Orthogonal_k_neighbor_search.h>
+#include <CGAL/Kd_tree.h>
+#include <CGAL/Euclidean_distance.h>
+//#include <CGAL/Kernel_d/Vector_d.h>
+#include <CGAL/Random.h>
+
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
+typedef K::FT FT;
+typedef K::Point_d Point_d;
+typedef CGAL::Search_traits< FT,
+                             Point_d,
+                             typename K::Cartesian_const_iterator_d,
+                             typename K::Construct_cartesian_const_iterator_d > Traits_base;
+typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
+typedef CGAL::Search_traits_adapter< std::ptrdiff_t,
+                                     Point_d*,
+                                     Traits_base> STraits;
+typedef CGAL::Distance_adapter< std::ptrdiff_t,
+                                Point_d*,
+                                Euclidean_distance > Distance_adapter;
+typedef CGAL::Orthogonal_incremental_neighbor_search< STraits,
+                                                      Distance_adapter > Neighbor_search;
+  typedef CGAL::Orthogonal_k_neighbor_search< STraits > Neighbor_search2;
+typedef Neighbor_search::Tree Tree;
+
+  
+  /** \brief Landmark choice strategy by taking random vertices for landmarks.
+   *  \details It chooses nbL distinct landmarks from a random access range `points`
+   *  and outputs a matrix {witness}*{closest landmarks} in knn.
+   */
+  template <typename KNearestNeighbours,
+            typename Point_random_access_range,
+            typename Distance_matrix>
+  void landmark_choice_by_random_knn(Point_random_access_range const & points,
+                                     int nbL,
+                                     FT alpha,
+                                     unsigned limD,
+                                     KNearestNeighbours & knn,
+                                     Distance_matrix & distances) {
+    int nbP = points.end() - points.begin();
+    assert(nbP >= nbL);
+    std::vector<Point_d> landmarks;
+    std::vector<int> landmarks_ind;
+    Point_d p;
+    int chosen_landmark;
+    CGAL::Random rand;
+    // TODO(SK) Consider using rand_r(...) instead of rand(...) for improved thread safety
+    int current_number_of_landmarks = 0;  // counter for landmarks
+    for (; current_number_of_landmarks != nbL; current_number_of_landmarks++) {
+      do chosen_landmark = rand.get_int(0,nbP);
+      while (std::find(landmarks_ind.begin(), landmarks_ind.end(), chosen_landmark) != landmarks_ind.end());
+      p = points[chosen_landmark];
+      landmarks.push_back(p);
+      landmarks_ind.push_back(chosen_landmark);
+    }
+    // std::cout << "Choice finished!" << std::endl;
+    
+    //int dim = points.begin()->size();
+    knn = KNearestNeighbours(nbP);
+    distances = Distance_matrix(nbP);
+    STraits traits(&(landmarks[0]));
+    CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance> adapter(&(landmarks[0]));
+    Euclidean_distance ed;
+    Tree landmark_tree(boost::counting_iterator<std::ptrdiff_t>(0),
+                       boost::counting_iterator<std::ptrdiff_t>(nbL),
+                       typename Tree::Splitter(),
+                       traits);
+    for (int points_i = 0; points_i < nbP; points_i++) {
+      Point_d const & w = points[points_i];
+      Neighbor_search search(landmark_tree,
+                             w,
+                             FT(0),
+                             true,
+                             adapter);
+      Neighbor_search::iterator search_it = search.begin();
+      // Neighbor_search2 search(landmark_tree,
+      //                         w, limD+1,
+      //                         FT(0),
+      //                         true,
+      //                         adapter);
+      // Neighbor_search2::iterator search_it = search.begin();
+      
+      while (knn[points_i].size() < limD) {
+        distances[points_i].push_back(sqrt(search_it->second));
+        knn[points_i].push_back((search_it++)->first);
+      }
+      FT dtow = distances[points_i][limD-1];
+      
+      if (alpha != 0)
+        while (search_it != search.end() && search_it->second < dtow + alpha) {
+          distances[points_i].push_back(sqrt(search_it->second));
+          knn[points_i].push_back((search_it++)->first);
+        }
+      std::cout << "k = " << knn[points_i].size() << std::endl;
+    }
+  }
+
+}  // namespace witness_complex
+
+}  // namespace Gudhi
+
+#endif  // LANDMARK_CHOICE_BY_RANDOM_POINT_H_
diff --git a/src/Witness_complex/example/Landmark_choice_sparsification.h b/src/Witness_complex/example/Landmark_choice_sparsification.h
new file mode 100644
index 00000000..1052b0c4
--- /dev/null
+++ b/src/Witness_complex/example/Landmark_choice_sparsification.h
@@ -0,0 +1,230 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 LANDMARK_CHOICE_BY_SPARSIFICATION_H_
+#define LANDMARK_CHOICE_BY_SPARSIFICATION_H_
+
+#include <utility>  // for pair<>
+#include <vector>
+#include <cstddef> // for ptrdiff_t type
+#include <algorithm>
+
+//#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+//#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_incremental_neighbor_search.h>
+#include <CGAL/Orthogonal_k_neighbor_search.h>
+#include <CGAL/Kd_tree.h>
+#include <CGAL/Euclidean_distance.h>
+//#include <CGAL/Kernel_d/Vector_d.h>
+#include <CGAL/Random.h>
+#include <CGAL/Fuzzy_sphere.h>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
+  typedef K::FT FT;
+  typedef K::Point_d Point_d;
+  typedef CGAL::Search_traits< FT,
+                               Point_d,
+                               typename K::Cartesian_const_iterator_d,
+                               typename K::Construct_cartesian_const_iterator_d > Traits_base;
+  typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
+  typedef CGAL::Search_traits_adapter< std::ptrdiff_t,
+                                       Point_d*,
+                                       Traits_base> STraits;
+  typedef CGAL::Distance_adapter< std::ptrdiff_t,
+                                  Point_d*,
+                                  Euclidean_distance > Distance_adapter;
+  typedef CGAL::Orthogonal_incremental_neighbor_search< STraits,
+                                                        Distance_adapter > Neighbor_search;
+  typedef CGAL::Orthogonal_k_neighbor_search< STraits > Neighbor_search2;
+  typedef Neighbor_search::Tree Tree;
+  typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
+
+  /** \brief Landmark selection function by as a sub-epsilon-net of the
+   *  given set of points.
+   */
+  template <typename Point_random_access_range>
+  void landmark_choice_by_sparsification(Point_random_access_range & points,
+                                         unsigned nbL,
+                                         FT mu_epsilon,
+                                         Point_random_access_range & landmarks)
+  {
+    int nbP = points.end() - points.begin();
+    assert(nbP >= nbL);
+    CGAL::Random rand;
+    // TODO(SK) Consider using rand_r(...) instead of rand(...) for improved thread safety
+    STraits points_traits(&(points[0]));
+    CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance> points_adapter(&(points[0]));
+    std::vector<bool> dropped_points(nbP, false);
+    
+    Tree witness_tree(boost::counting_iterator<std::ptrdiff_t>(0),
+                      boost::counting_iterator<std::ptrdiff_t>(nbP),
+                      typename Tree::Splitter(),
+                      points_traits);
+    
+    for (int points_i = 0; points_i < nbP; points_i++) {
+      if (dropped_points[points_i])
+        continue;
+      Point_d & w = points[points_i];
+      Fuzzy_sphere fs(w, mu_epsilon, 0, points_traits);
+      std::vector<int> close_neighbors;
+      witness_tree.search(std::insert_iterator<std::vector<int>>(close_neighbors,close_neighbors.begin()),fs);
+      for (int i: close_neighbors)
+        dropped_points[i] = true;
+    }
+
+    for (int points_i = 0; points_i < nbP; points_i++) {
+      if (dropped_points[points_i])
+        landmarks.push_back(points[points_i]);
+    }
+
+    if (nbL < landmarks.size()) {
+      std::random_shuffle(landmarks.begin(), landmarks.end());
+      landmarks.resize(nbL);
+    }
+  }
+    
+
+
+  
+  /** \brief Landmark choice strategy by taking random vertices for landmarks.
+   *  \details It chooses nbL distinct landmarks from a random access range `points`
+   *  and outputs a matrix {witness}*{closest landmarks} in knn.
+   */
+  template <typename KNearestNeighbours,
+            typename Point_random_access_range,
+            typename Distance_matrix>
+  void build_distance_matrix(Point_random_access_range const & points,
+                             Point_random_access_range & landmarks,
+                             FT alpha,
+                             unsigned limD,
+                             KNearestNeighbours & knn,
+                             Distance_matrix & distances)
+  {
+    int nbP = points.end() - points.begin();
+    knn = KNearestNeighbours(nbP);
+    distances = Distance_matrix(nbP);
+    STraits traits(&(landmarks[0]));
+    CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance> adapter(&(landmarks[0]));
+    Euclidean_distance ed;
+    Tree landmark_tree(boost::counting_iterator<std::ptrdiff_t>(0),
+                       boost::counting_iterator<std::ptrdiff_t>(landmarks.size()),
+                       typename Tree::Splitter(),
+                       traits);
+    for (int points_i = 0; points_i < nbP; points_i++) {
+      Point_d const & w = points[points_i];
+      Neighbor_search search(landmark_tree,
+                             w,
+                             FT(0),
+                             true,
+                             adapter);
+      Neighbor_search::iterator search_it = search.begin();
+      // Neighbor_search2 search(landmark_tree,
+      //                         w, limD+1,
+      //                         FT(0),
+      //                         true,
+      //                         adapter);
+      // Neighbor_search2::iterator search_it = search.begin();
+      
+      while (knn[points_i].size() <= limD) {
+        distances[points_i].push_back(search_it->second); //!sq_dist
+        knn[points_i].push_back((search_it++)->first);
+      }
+      FT dtow = distances[points_i][limD];
+      
+      while (search_it != search.end() && search_it->second < dtow + alpha) {
+        distances[points_i].push_back(search_it->second);
+        knn[points_i].push_back((search_it++)->first);
+      }
+      //std::cout << "k = " << knn[points_i].size() << std::endl;
+    }
+  }
+ 
+  /*
+  template <typename Kernel, typename Point_container>
+  std::vector<typename Point_container::value_type>
+  sparsify_point_set(const Kernel &k,
+                     Point_container const& input_pts,
+                     typename Kernel::FT min_squared_dist)
+  {
+    typedef typename CGAL::Tangential_complex_::Point_cloud_data_structure<Kernel, Point_container> Points_ds;
+    typedef typename Points_ds::INS_iterator      INS_iterator;
+    typedef typename Points_ds::INS_range         INS_range;
+
+  typename Kernel::Squared_distance_d sqdist = k.squared_distance_d_object();
+
+  // Create the output container
+  std::vector<typename Point_container::value_type> output;
+
+  Points_ds points_ds(input_pts);
+
+  std::vector<bool> dropped_points(input_pts.size(), false);
+
+  // Parse the input points, and add them if they are not too close to
+  // the other points
+  std::size_t pt_idx = 0;
+  for (typename Point_container::const_iterator it_pt = input_pts.begin() ;
+       it_pt != input_pts.end();
+       ++it_pt, ++pt_idx)
+  {
+    if (dropped_points[pt_idx])
+      continue;
+
+    output.push_back(*it_pt);
+
+    INS_range ins_range = points_ds.query_incremental_ANN(*it_pt);
+
+    // If another point Q is closer that min_squared_dist, mark Q to be dropped
+    for (INS_iterator nn_it = ins_range.begin() ;
+        nn_it != ins_range.end() ;
+        ++nn_it)
+    {
+      std::size_t neighbor_point_idx = nn_it->first;
+      // If the neighbor is too close, we drop the neighbor
+      if (nn_it->second < min_squared_dist)
+      {
+        // N.B.: If neighbor_point_idx < pt_idx, 
+        // dropped_points[neighbor_point_idx] is already true but adding a
+        // test doesn't make things faster, so why bother?
+        dropped_points[neighbor_point_idx] = true;
+      }
+      else
+        break;
+    }
+  }
+
+  return output;
+}
+  */  
+
+
+}  // namespace witness_complex
+
+}  // namespace Gudhi
+
+#endif  // LANDMARK_CHOICE_BY_RANDOM_POINT_H_
diff --git a/src/Witness_complex/example/a0_persistence.cpp b/src/Witness_complex/example/a0_persistence.cpp
new file mode 100644
index 00000000..295c7115
--- /dev/null
+++ b/src/Witness_complex/example/a0_persistence.cpp
@@ -0,0 +1,632 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2016  INRIA Sophia Antipolis-Méditerranée (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/>.
+ */
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/A0_complex.h>
+#include <gudhi/Relaxed_witness_complex.h>
+#include <gudhi/Dim_lists.h>
+#include <gudhi/reader_utils.h>
+#include <gudhi/Persistent_cohomology.h>
+#include "Landmark_choice_random_knn.h"
+#include "Landmark_choice_sparsification.h"
+
+#include <iostream>
+#include <fstream>
+#include <ctime>
+#include <utility>
+#include <algorithm>
+#include <set>
+#include <queue>
+#include <iterator>
+#include <string>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+#include "generators.h"
+#include "output.h"
+#include "output_tikz.h"
+
+using namespace Gudhi;
+using namespace Gudhi::witness_complex;
+using namespace Gudhi::persistent_cohomology;
+
+typedef std::vector<Point_d> Point_Vector;
+typedef A0_complex< Simplex_tree<> > A0Complex;
+typedef Simplex_tree<>::Simplex_handle Simplex_handle;
+
+typedef A0_complex< Simplex_tree<> > SRWit;
+typedef Relaxed_witness_complex< Simplex_tree<> > WRWit;
+
+/**
+ * \brief Customized version of read_points
+ * which takes into account a possible nbP first line
+ *
+ */
+inline void
+read_points_cust(std::string file_name, std::vector< std::vector< double > > & points) {
+  std::ifstream in_file(file_name.c_str(), std::ios::in);
+  if (!in_file.is_open()) {
+    std::cerr << "Unable to open file " << file_name << std::endl;
+    return;
+  }
+  std::string line;
+  double x;
+  while (getline(in_file, line)) {
+    std::vector< double > point;
+    std::istringstream iss(line);
+    while (iss >> x) {
+      point.push_back(x);
+    }
+    if (point.size() != 1)
+      points.push_back(point);
+  }
+  in_file.close();
+}
+
+void output_experiment_information(char * const file_name)
+{
+    std::cout << "Enter a valid experiment number. Usage: "
+              << file_name << " exp_no options\n";
+    std::cout << "Experiment description:\n"
+              << "0 nbP nbL dim alpha limD mu_epsilon: "
+              << "Build persistence diagram on relaxed witness complex "
+              << "built from a point cloud on (dim-1)-dimensional sphere "
+              << "consisting of nbP witnesses and nbL landmarks. "
+              << "The maximal relaxation is alpha and the limit on simplicial complex "
+              << "dimension is limD.\n";
+    std::cout << "1 file_name nbL alpha limD: "
+              << "Build persistence diagram on relaxed witness complex "
+              << "build from a point cloud stored in a file and nbL landmarks. "
+              << "The maximal relaxation is alpha and the limit on simplicial complex dimension is limD\n";
+}
+
+void rw_experiment(Point_Vector & point_vector, int nbL, FT alpha2, int limD, FT mu_epsilon = 0.1)
+{
+  clock_t start, end;
+  Simplex_tree<> simplex_tree;
+
+  // Choose landmarks
+  std::vector<std::vector< int > > knn;
+  std::vector<std::vector< FT > > distances;
+  start = clock();
+  //Gudhi::witness_complex::landmark_choice_by_random_knn(point_vector, nbL, alpha, limD, knn, distances);
+
+  std::vector<Point_d> landmarks;
+  Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+  Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                landmarks,  // aka landmarks
+                                                alpha2,
+                                                limD,
+                                                knn,
+                                                distances);
+  end = clock();
+  double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Choice of " << nbL << " landmarks took "
+            << time << " s. \n";
+  // Compute witness complex
+  start = clock();
+  A0Complex rw(distances,
+                knn,
+                simplex_tree,
+                nbL,
+                alpha2,
+                limD);
+  end = clock();
+  time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Witness complex for " << nbL << " landmarks took "
+            << time << " s. \n";
+  std::cout << "The complex contains " << simplex_tree.num_simplices() << " simplices \n";
+  //std::cout << simplex_tree << "\n";
+  
+  // Compute the persistence diagram of the complex
+  simplex_tree.set_dimension(limD);
+  persistent_cohomology::Persistent_cohomology< Simplex_tree<>, Field_Zp > pcoh(simplex_tree, true);
+  int p = 3;
+  pcoh.init_coefficients( p ); //initilizes the coefficient field for homology
+  start = clock();
+  pcoh.compute_persistent_cohomology( alpha2/10 );
+  end = clock();
+  time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Persistence diagram took "
+            << time << " s. \n";
+  pcoh.output_diagram();
+
+  int chi = 0;
+  for (auto sh: simplex_tree.complex_simplex_range())
+    chi += 1-2*(simplex_tree.dimension(sh)%2);
+  std::cout << "Euler characteristic is " << chi << std::endl;
+
+  // Gudhi::witness_complex::Dim_lists<Simplex_tree<>> simplices(simplex_tree, limD); 
+  
+  // simplices.collapse();
+  // simplices.output_simplices();
+
+  // Simplex_tree<> collapsed_tree;
+  // for (auto sh: simplices) {
+  //   std::vector<int> vertices;
+  //   for (int v: collapsed_tree.simplex_vertex_range(sh))
+  //     vertices.push_back(v);
+  //   collapsed_tree.insert_simplex(vertices);
+  // } 
+  std::vector<int> landmarks_ind(nbL); 
+  for (unsigned i = 0; i != distances.size(); ++i) {
+    if (distances[i][0] == 0)
+      landmarks_ind[knn[i][0]] = i;
+  }
+  //write_witness_mesh(point_vector, landmarks_ind, simplex_tree, simplices, false, true);
+  write_witness_mesh(point_vector, landmarks_ind, simplex_tree, simplex_tree.complex_simplex_range(), false, true, "witness_before_collapse.mesh");
+
+  // collapsed_tree.set_dimension(limD);
+  // persistent_cohomology::Persistent_cohomology< Simplex_tree<>, Field_Zp > pcoh2(collapsed_tree, true);
+  // pcoh2.init_coefficients( p ); //initilizes the coefficient field for homology
+  // pcoh2.compute_persistent_cohomology( alpha2/10 );
+  // pcoh2.output_diagram();
+
+  // chi = 0;
+  // for (auto sh: simplices)
+  //   chi += 1-2*(simplex_tree.dimension(sh)%2);
+  // std::cout << "Euler characteristic is " << chi << std::endl;
+  // write_witness_mesh(point_vector, landmarks_ind, collapsed_tree, collapsed_tree.complex_simplex_range(), false, true, "witness_after_collapse.mesh");
+}
+
+void rips_experiment(Point_Vector & points, double threshold, int dim_max)
+{
+  typedef std::vector<double> Point_t;
+  typedef Simplex_tree<Simplex_tree_options_fast_persistence> ST;
+  clock_t start, end;
+  ST st;
+
+  // Compute the proximity graph of the points
+  start = clock();
+  Graph_t prox_graph = compute_proximity_graph(points, threshold
+                                               , euclidean_distance<Point_t>);
+  // Construct the Rips complex in a Simplex Tree
+  // insert the proximity graph in the simplex tree
+  st.insert_graph(prox_graph);
+  // expand the graph until dimension dim_max
+  st.expansion(dim_max);
+  end = clock();
+  
+  double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Rips complex took "
+            << time << " s. \n";
+  std::cout << "The complex contains " << st.num_simplices() << " simplices \n";
+  //std::cout << "   and has dimension " << st.dimension() << " \n";
+
+  // Sort the simplices in the order of the filtration
+  st.initialize_filtration();
+
+  // Compute the persistence diagram of the complex
+  persistent_cohomology::Persistent_cohomology<ST, Field_Zp > pcoh(st);
+  // initializes the coefficient field for homology
+  int p = 3;
+  double min_persistence = -1; //threshold/5;
+  pcoh.init_coefficients(p);
+  pcoh.compute_persistent_cohomology(min_persistence);
+  pcoh.output_diagram();
+}
+
+
+int experiment0 (int argc, char * const argv[])
+{
+  if (argc != 8) {
+    std::cerr << "Usage: " << argv[0]
+              << " 0 nbP nbL dim alpha limD mu_epsilon\n";
+    return 0;
+  }
+  /*
+    boost::filesystem::path p;
+    for (; argc > 2; --argc, ++argv)
+    p /= argv[1];
+  */
+  
+  int nbP       = atoi(argv[2]);
+  int nbL       = atoi(argv[3]);
+  int dim       = atoi(argv[4]);
+  double alpha  = atof(argv[5]);
+  int limD      = atoi(argv[6]);
+  double mu_epsilon = atof(argv[7]);
+
+  // Read the point file
+  Point_Vector point_vector;
+  generate_points_sphere(point_vector, nbP, dim);
+  std::cout << "Successfully generated " << point_vector.size() << " points.\n";
+  std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+  rw_experiment(point_vector, nbL, alpha, limD);
+  return 0;
+}
+
+// int experiment1 (int argc, char * const argv[])
+// {
+//   if (argc != 3) {
+//     std::cerr << "Usage: " << argv[0]
+//               << " 1 file_name\n";
+//     return 0;
+//   }
+//   /*
+//     boost::filesystem::path p;
+//     for (; argc > 2; --argc, ++argv)
+//     p /= argv[1];
+//   */
+  
+//   std::string file_name = argv[2];
+
+//   // Read the point file
+//   Point_Vector point_vector;
+//   read_points_cust(file_name, point_vector);
+//   std::cout << "The file contains " << point_vector.size() << " points.\n";
+//   std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+//   bool ok = false;
+//   int nbL, limD;
+//   double alpha;
+//   while (!ok) {
+//     std::cout << "Relaxed witness complex: parameters nbL, alpha, limD.\n";
+//     std::cout << "Enter nbL: ";
+//     std::cin >> nbL;
+//     std::cout << "Enter alpha: ";
+//     std::cin >> alpha;
+//     std::cout << "Enter limD: ";
+//     std::cin >> limD;
+//     std::cout << "Start relaxed witness complex...\n";
+//     rw_experiment(point_vector, nbL, alpha, limD);
+//     std::cout << "Is the result correct? [y/n]: ";
+//     char answer;
+//     std::cin >> answer;
+//     switch (answer) {
+//     case 'n':
+//       ok = false; break;
+//     default :
+//       ok = true; break;
+//     }
+//   }
+//   // ok = false;
+//   // while (!ok) {
+//   //   std::cout << "Rips complex: parameters threshold, limD.\n";
+//   //   std::cout << "Enter threshold: ";
+//   //   std::cin >> alpha;
+//   //   std::cout << "Enter limD: ";
+//   //   std::cin >> limD;
+//   //   std::cout << "Start Rips complex...\n";
+//   //   rips_experiment(point_vector, alpha, limD);
+//   //   std::cout << "Is the result correct? [y/n]: ";
+//   //   char answer;
+//   //   std::cin >> answer;
+//   //   switch (answer) {
+//   //   case 'n':
+//   //     ok = false; break;
+//   //   default :
+//   //     ok = true; break;
+//   //   }
+//   // }
+//   return 0;
+// }
+
+int experiment1 (int argc, char * const argv[])
+{
+  if (argc != 8) {
+    std::cerr << "Usage: " << argv[0]
+              << " 1 file_name nbL alpha mu_epsilon limD experiment_name\n";
+    return 0;
+  }
+  /*
+    boost::filesystem::path p;
+    for (; argc > 2; --argc, ++argv)
+    p /= argv[1];
+  */
+  
+  std::string file_name = argv[2];
+  int nbL = atoi(argv[3]), limD = atoi(argv[6]);
+  double alpha2 = atof(argv[4]), mu_epsilon = atof(argv[5]);
+  std::string experiment_name = argv[7];
+
+  // Read the point file
+  Point_Vector point_vector;
+  read_points_cust(file_name, point_vector);
+  std::cout << "The file contains " << point_vector.size() << " points.\n";
+  std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+  Simplex_tree<> simplex_tree;
+  std::vector<std::vector< int > > knn;
+  std::vector<std::vector< FT > > distances;
+  std::vector<Point_d> landmarks;
+  Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+  Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                landmarks,  // aka landmarks
+                                                alpha2,
+                                                limD,
+                                                knn,
+                                                distances);
+
+  rw_experiment(point_vector, nbL, alpha2, limD, mu_epsilon);
+  
+  // ok = false;
+  // while (!ok) {
+  //   std::cout << "Rips complex: parameters threshold, limD.\n";
+  //   std::cout << "Enter threshold: ";
+  //   std::cin >> alpha;
+  //   std::cout << "Enter limD: ";
+  //   std::cin >> limD;
+  //   std::cout << "Start Rips complex...\n";
+  //   rips_experiment(point_vector, alpha, limD);
+  //   std::cout << "Is the result correct? [y/n]: ";
+  //   char answer;
+  //   std::cin >> answer;
+  //   switch (answer) {
+  //   case 'n':
+  //     ok = false; break;
+  //   default :
+  //     ok = true; break;
+  //   }
+  // }
+  return 0;
+}
+
+
+/********************************************************************************************
+ * Length of the good interval experiment
+ *******************************************************************************************/
+
+struct Pers_endpoint {
+  double alpha;
+  bool start;
+  int dim;
+  Pers_endpoint(double alpha_, bool start_, int dim_)
+    : alpha(alpha_), start(start_), dim(dim_)
+  {}
+};
+
+/*
+struct less_than_key {
+  inline bool operator() (const MyStruct& struct1, const MyStruct& struct2) {
+    return (struct1.key < struct2.key);
+  }
+};
+*/
+
+double good_interval_length(const std::vector<int> & desired_homology, Simplex_tree<> & simplex_tree, double alpha2)
+{
+  int nbL = simplex_tree.num_vertices();
+  int p = 3;
+  persistent_cohomology::Persistent_cohomology< Simplex_tree<>, Field_Zp > pcoh(simplex_tree, true);
+  pcoh.init_coefficients( p ); //initilizes the coefficient field for homology
+  pcoh.compute_persistent_cohomology( -1 );
+  std::ofstream out_stream("pers_diag.tmp");
+  pcoh.output_diagram(out_stream);
+  out_stream.close();
+  std::ifstream in_stream("pers_diag.tmp", std::ios::in);
+  std::string line;
+  std::vector<Pers_endpoint> pers_endpoints;
+  while (getline(in_stream, line)) {
+    int p, dim;
+    double alpha_start, alpha_end;
+    std::istringstream iss(line);
+    iss >> p >> dim >> alpha_start >> alpha_end;
+    if (alpha_start != alpha_end) {
+      if (alpha_end < alpha_start)
+        alpha_end = alpha2;
+      pers_endpoints.push_back(Pers_endpoint(alpha_start, true, dim));
+      pers_endpoints.push_back(Pers_endpoint(alpha_end, false, dim));
+    }
+  }
+  std::cout << "Pers_endpoints.size = " << pers_endpoints.size() << std::endl;
+  in_stream.close();
+  std::sort(pers_endpoints.begin(),
+            pers_endpoints.end(),
+            [](const Pers_endpoint & p1, const Pers_endpoint & p2){
+              return p1.alpha < p2.alpha;}
+            );
+  write_barcodes("pers_diag.tmp", alpha2);
+  /*
+  for (auto p: pers_endpoints) {
+    std::cout << p.alpha << " " << p.dim << " " << p.start << "\n";
+  }
+  */
+  std::vector<int> current_homology(nbL-1,0);
+  current_homology[0] = 1; // for the compulsary "0 0 inf" entry
+  double good_start = 0, good_end = 0;
+  double sum_intervals = 0;
+  int num_pieces = 0;
+  bool interval_in_process = (desired_homology == current_homology);
+  for (auto p: pers_endpoints) {
+    /*
+    std::cout << "Treating " << p.alpha << " " << p.dim << " " << p.start
+              << " [";
+    for (int v: current_homology)
+      std::cout << v << " ";
+    std::cout << "]\n";
+    */
+    if (p.start)
+      current_homology[p.dim]++;
+    else
+      current_homology[p.dim]--;
+    if (interval_in_process) {
+      good_end = p.alpha;
+      sum_intervals += good_end - good_start;
+      std::cout << "good_start = " << good_start
+                << ", good_end = " << good_end << "\n";
+                
+      Gudhi::witness_complex::Dim_lists<Simplex_tree<>> simplices(simplex_tree, nbL-1, (good_end - good_start)/2);
+      simplices.collapse();
+      simplices.output_simplices();
+      interval_in_process = false;
+      //break;
+    }
+    else if (desired_homology == current_homology) {
+      interval_in_process = true;
+      good_start = p.alpha;
+      num_pieces++;
+    }
+  }
+  std::cout << "Number of good homology intervals: " << num_pieces << "\n";
+  return sum_intervals;
+}
+
+void run_comparison(std::vector<std::vector< int > > const & knn,
+                    std::vector<std::vector< FT > > const & distances,
+                    unsigned nbL,
+                    double alpha2,
+                    std::vector<int>& desired_homology)
+{
+  clock_t start, end;
+  Simplex_tree<> simplex_tree;
+
+  start = clock();
+  SRWit srwit(distances,
+              knn,
+              simplex_tree,
+              nbL,
+              alpha2,
+              nbL-1);
+  end = clock();
+  std::cout << "SRWit.size = " << simplex_tree.num_simplices() << std::endl;
+  simplex_tree.set_dimension(nbL-1);
+
+  std::cout << "Good homology interval length for SRWit is "
+                << good_interval_length(desired_homology, simplex_tree, alpha2) << "\n";
+  std::cout << "Time: " << static_cast<double>(end - start) / CLOCKS_PER_SEC << " s. \n";
+
+  /*
+  Simplex_tree<> simplex_tree2;
+  start = clock();
+  WRWit wrwit(distances,
+              knn,
+              simplex_tree2,
+              nbL,
+              alpha2,
+              nbL-1);
+  end = clock();
+  std::cout << "WRWit.size = " << simplex_tree2.num_simplices() << std::endl;
+  simplex_tree.set_dimension(nbL-1);
+  
+  std::cout << "Good homology interval length for WRWit is "
+            << good_interval_length(desired_homology, simplex_tree2, alpha2) << "\n";
+  std::cout << "Time: " << static_cast<double>(end - start) / CLOCKS_PER_SEC << " s. \n";
+  */
+}
+
+int experiment2(int argc, char * const argv[])
+{
+  for (unsigned d = 2; d < 2; d++) {
+    // Sphere S^d 
+    Point_Vector point_vector;
+    unsigned N = 1;
+    double alpha2 = 2.4 - 0.4*d; 
+    switch (d) {
+    case 1: alpha2 = 2.2; break;
+    case 2: alpha2 = 1.8; break;
+    case 3: alpha2 = 1.5; break;
+    case 4: alpha2 = 1.4; break;
+    default: alpha2 = 1.4; break;
+    }
+    std::cout << "alpha2 = " << alpha2 << "\n";
+    unsigned nbL = 20;
+    std::vector<int> desired_homology(nbL-1,0);
+    desired_homology[0] = 1; desired_homology[d] = 1;
+    
+    
+    for (unsigned i = 1; i <= N; ++i) {
+      unsigned nbW = 1000*i;//, nbL = 20;
+      double mu_epsilon = 1/sqrt(nbL);
+      std::cout << "Running test S"<< d <<", |W|=" << nbW << ", |L|=" << nbL << std::endl;
+      generate_points_sphere(point_vector, i*1000, d+1);
+      std::vector<Point_d> landmarks;
+      Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+
+      std::vector<std::vector< int > > knn;
+      std::vector<std::vector< FT > > distances;
+    
+      std::cout << "|L| after sparsification: " << landmarks.size() << "\n";
+      Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                    landmarks,  // aka landmarks
+                                                    alpha2,
+                                                    nbL-1,
+                                                    knn,
+                                                    distances);
+      run_comparison(knn, distances, nbL, alpha2, desired_homology);
+    }
+  }
+  {
+    // SO(3)
+    Point_Vector point_vector;
+    double alpha2 = 0.6; 
+    std::cout << "alpha2 = " << alpha2 << "\n";
+    unsigned nbL = 150;
+    std::vector<int> desired_homology(nbL-1,0);
+    desired_homology[0] = 1; desired_homology[1] = 1; desired_homology[2] = 1; //Kl
+    // desired_homology[0] = 1; desired_homology[3] = 1; //SO3
+
+    double mu_epsilon = 1/sqrt(nbL);
+    if (argc < 3) std::cerr << "No file name indicated!\n";
+    read_points_cust(argv[2], point_vector);
+    int nbW = point_vector.size();
+    std::cout << "Running test SO(3), |W|=" << nbW << ", |L|=" << nbL << std::endl;
+    std::vector<Point_d> landmarks;
+    Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+    
+    std::vector<std::vector< int > > knn;
+    std::vector<std::vector< FT > > distances;
+    
+    std::cout << "|L| after sparsification: " << landmarks.size() << "\n";
+    Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                  landmarks,  // aka landmarks
+                                                  alpha2,
+                                                  nbL-1,
+                                                  knn,
+                                                  distances);
+    run_comparison(knn, distances, nbL, alpha2, desired_homology);
+  }
+  return 0;
+}
+
+int experiment3(int argc, char * const argv[])
+{
+  // COLLAPSES EXPERIMENT
+  
+  return 0;
+}
+
+int main (int argc, char * const argv[])
+{
+  if (argc == 1) {
+    output_experiment_information(argv[0]);
+    return 1;
+  }
+  switch (atoi(argv[1])) {
+  case 0 :
+    return experiment0(argc, argv);
+    break;
+  case 1 :
+    return experiment1(argc, argv);
+    break;
+  case 2 :
+    return experiment2(argc, argv);
+    break;
+  default :
+    output_experiment_information(argv[0]);
+    return 1;
+  }
+}
diff --git a/src/Witness_complex/example/bench_rwit.cpp b/src/Witness_complex/example/bench_rwit.cpp
new file mode 100644
index 00000000..f83f9f42
--- /dev/null
+++ b/src/Witness_complex/example/bench_rwit.cpp
@@ -0,0 +1,616 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2016  INRIA Sophia Antipolis-Méditerranée (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/>.
+ */
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/A0_complex.h>
+#include <gudhi/Relaxed_witness_complex.h>
+#include <gudhi/Dim_lists.h>
+#include <gudhi/reader_utils.h>
+#include <gudhi/Persistent_cohomology.h>
+#include "Landmark_choice_random_knn.h"
+#include "Landmark_choice_sparsification.h"
+
+#include <iostream>
+#include <fstream>
+#include <ctime>
+#include <utility>
+#include <algorithm>
+#include <set>
+#include <queue>
+#include <iterator>
+#include <string>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+#include "generators.h"
+#include "output.h"
+#include "output_tikz.h"
+
+using namespace Gudhi;
+using namespace Gudhi::witness_complex;
+using namespace Gudhi::persistent_cohomology;
+
+typedef std::vector<Point_d> Point_Vector;
+typedef Simplex_tree<Simplex_tree_options_fast_persistence> STree;
+//typedef Simplex_tree<> STree;
+typedef A0_complex< STree> A0Complex;
+typedef STree::Simplex_handle Simplex_handle;
+
+typedef A0_complex< STree > SRWit;
+typedef Relaxed_witness_complex< STree > WRWit;
+
+/**
+ * \brief Customized version of read_points
+ * which takes into account a possible nbP first line
+ *
+ */
+inline void
+read_points_cust(std::string file_name, std::vector< std::vector< double > > & points) {
+  std::ifstream in_file(file_name.c_str(), std::ios::in);
+  if (!in_file.is_open()) {
+    std::cerr << "Unable to open file " << file_name << std::endl;
+    return;
+  }
+  std::string line;
+  double x;
+  while (getline(in_file, line)) {
+    std::vector< double > point;
+    std::istringstream iss(line);
+    while (iss >> x) {
+      point.push_back(x);
+    }
+    if (point.size() != 1)
+      points.push_back(point);
+  }
+  in_file.close();
+}
+
+void rips(Point_Vector & points, double alpha2, int dim_max, STree& st)
+{
+  Graph_t prox_graph = compute_proximity_graph(points, sqrt(alpha2)
+                                               , euclidean_distance<std::vector<FT> >);
+  // Construct the Rips complex in a Simplex Tree
+  // insert the proximity graph in the simplex tree
+  st.insert_graph(prox_graph);
+  // expand the graph until dimension dim_max
+  st.expansion(dim_max);
+}
+
+void output_experiment_information(char * const file_name)
+{
+    std::cout << "Enter a valid experiment number. Usage: "
+              << file_name << " exp_no options\n";
+    std::cout << "Experiment description:\n"
+              << "0 nbP nbL dim alpha limD mu_epsilon: "
+              << "Build persistence diagram on relaxed witness complex "
+              << "built from a point cloud on (dim-1)-dimensional sphere "
+              << "consisting of nbP witnesses and nbL landmarks. "
+              << "The maximal relaxation is alpha and the limit on simplicial complex "
+              << "dimension is limD.\n";
+    std::cout << "1 file_name nbL alpha limD: "
+              << "Build persistence diagram on relaxed witness complex "
+              << "build from a point cloud stored in a file and nbL landmarks. "
+              << "The maximal relaxation is alpha and the limit on simplicial complex dimension is limD\n";
+}
+
+void rw_experiment(Point_Vector & point_vector, int nbL, FT alpha2, int limD, FT mu_epsilon = 0.1,
+                   std::string mesh_filename = "witness")
+{
+  clock_t start, end;
+  STree simplex_tree;
+
+  // Choose landmarks
+  std::vector<std::vector< int > > knn;
+  std::vector<std::vector< FT > > distances;
+  start = clock();
+  //Gudhi::witness_complex::landmark_choice_by_random_knn(point_vector, nbL, alpha, limD, knn, distances);
+
+  std::vector<Point_d> landmarks;
+  Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+  Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                landmarks,  // aka landmarks
+                                                alpha2,
+                                                limD,
+                                                knn,
+                                                distances);
+  end = clock();
+  double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Choice of " << nbL << " landmarks took "
+            << time << " s. \n";
+  // Compute witness complex
+  start = clock();
+  A0Complex rw(distances,
+                knn,
+                simplex_tree,
+                nbL,
+                alpha2,
+                limD);
+  end = clock();
+  time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Witness complex for " << nbL << " landmarks took "
+            << time << " s. \n";
+  std::cout << "The complex contains " << simplex_tree.num_simplices() << " simplices \n";
+  //std::cout << simplex_tree << "\n";
+  
+  // Compute the persistence diagram of the complex
+  simplex_tree.set_dimension(limD);
+  persistent_cohomology::Persistent_cohomology< STree, Field_Zp > pcoh(simplex_tree, true);
+  int p = 3;
+  pcoh.init_coefficients( p ); //initilizes the coefficient field for homology
+  start = clock();
+  pcoh.compute_persistent_cohomology( alpha2/10 );
+  end = clock();
+  time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Persistence diagram took "
+            << time << " s. \n";
+  pcoh.output_diagram();
+
+  int chi = 0;
+  for (auto sh: simplex_tree.complex_simplex_range())
+    chi += 1-2*(simplex_tree.dimension(sh)%2);
+  std::cout << "Euler characteristic is " << chi << std::endl;
+
+  Gudhi::witness_complex::Dim_lists<STree> simplices(simplex_tree, limD); 
+  
+  // std::vector<Simplex_handle> simplices;
+  simplices.collapse();
+  simplices.output_simplices();
+
+  STree collapsed_tree;
+  for (auto sh: simplices) {
+    std::vector<int> vertices;
+    for (int v: collapsed_tree.simplex_vertex_range(sh))
+      vertices.push_back(v);
+    collapsed_tree.insert_simplex(vertices);
+  } 
+  std::vector<int> landmarks_ind(nbL); 
+  for (unsigned i = 0; i != distances.size(); ++i) {
+    if (distances[i][0] == 0)
+      landmarks_ind[knn[i][0]] = i;
+  }
+  //write_witness_mesh(point_vector, landmarks_ind, simplex_tree, simplices, false, true);
+  write_witness_mesh(point_vector, landmarks_ind, simplex_tree, simplex_tree.complex_simplex_range(), false, true, mesh_filename+"_before_collapse.mesh");
+
+  collapsed_tree.set_dimension(limD);
+  persistent_cohomology::Persistent_cohomology< STree, Field_Zp > pcoh2(collapsed_tree, true);
+  pcoh2.init_coefficients( p ); //initilizes the coefficient field for homology
+  pcoh2.compute_persistent_cohomology( alpha2/10 );
+  pcoh2.output_diagram();
+
+  chi = 0;
+  for (auto sh: simplices)
+    chi += 1-2*(simplex_tree.dimension(sh)%2);
+  std::cout << "Euler characteristic is " << chi << std::endl;
+  write_witness_mesh(point_vector, landmarks_ind, collapsed_tree, collapsed_tree.complex_simplex_range(), false, true, mesh_filename+"_after_collapse.mesh");
+}
+
+void rips_experiment(Point_Vector & points, double threshold, int dim_max)
+{
+  typedef STree ST;
+  clock_t start, end;
+  ST st;
+
+  // Compute the proximity graph of the points
+  start = clock();
+  rips(points, threshold, dim_max, st);
+  end = clock();
+  
+  double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Rips complex took "
+            << time << " s. \n";
+  std::cout << "The complex contains " << st.num_simplices() << " simplices \n";
+  //std::cout << "   and has dimension " << st.dimension() << " \n";
+
+  // Sort the simplices in the order of the filtration
+  st.initialize_filtration();
+
+  // Compute the persistence diagram of the complex
+  persistent_cohomology::Persistent_cohomology<ST, Field_Zp > pcoh(st);
+  // initializes the coefficient field for homology
+  int p = 3;
+  double min_persistence = -1; //threshold/5;
+  pcoh.init_coefficients(p);
+  pcoh.compute_persistent_cohomology(min_persistence);
+  pcoh.output_diagram();
+}
+
+
+int experiment0 (int argc, char * const argv[])
+{
+  if (argc != 8) {
+    std::cerr << "Usage: " << argv[0]
+              << " 0 nbP nbL dim alpha limD mu_epsilon\n";
+    return 0;
+  }
+  /*
+    boost::filesystem::path p;
+    for (; argc > 2; --argc, ++argv)
+    p /= argv[1];
+  */
+  
+  int nbP       = atoi(argv[2]);
+  int nbL       = atoi(argv[3]);
+  int dim       = atoi(argv[4]);
+  double alpha  = atof(argv[5]);
+  int limD      = atoi(argv[6]);
+  double mu_epsilon = atof(argv[7]);
+
+  // Read the point file
+  Point_Vector point_vector;
+  generate_points_sphere(point_vector, nbP, dim);
+  std::cout << "Successfully generated " << point_vector.size() << " points.\n";
+  std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+  rw_experiment(point_vector, nbL, alpha, limD);
+  return 0;
+}
+
+int experiment1 (int argc, char * const argv[])
+{
+  if (argc != 8) {
+    std::cerr << "Usage: " << argv[0]
+              << " 1 file_name nbL alpha mu_epsilon limD experiment_name\n";
+    return 0;
+  }
+  /*
+    boost::filesystem::path p;
+    for (; argc > 2; --argc, ++argv)
+    p /= argv[1];
+  */
+  
+  std::string file_name = argv[2];
+  int nbL = atoi(argv[3]), limD = atoi(argv[6]);
+  double alpha2 = atof(argv[4]), mu_epsilon = atof(argv[5]);
+  std::string experiment_name = argv[7];
+
+  // Read the point file
+  Point_Vector point_vector;
+  read_points_cust(file_name, point_vector);
+  std::cout << "The file contains " << point_vector.size() << " points.\n";
+  std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+  STree simplex_tree;
+  std::vector<std::vector< int > > knn;
+  std::vector<std::vector< FT > > distances;
+  std::vector<Point_d> landmarks;
+  Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+  Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                landmarks,  // aka landmarks
+                                                alpha2,
+                                                limD,
+                                                knn,
+                                                distances);
+  WRWit      rw(distances,
+                knn,
+                simplex_tree,
+                nbL,
+                0,
+                limD);
+  std::vector<int> landmarks_ind(nbL); 
+  for (unsigned i = 0; i != distances.size(); ++i) {
+    if (distances[i][0] == 0)
+      landmarks_ind[knn[i][0]] = i;
+  }
+
+  write_witness_mesh(point_vector, landmarks_ind, simplex_tree, simplex_tree.complex_simplex_range(), false, true, experiment_name+"_witness_complex.mesh");
+
+  int chi = 0;
+  for (auto sh: simplex_tree.complex_simplex_range())
+    chi += 1-2*(simplex_tree.dimension(sh)%2);
+  std::cout << "Euler characteristic is " << chi << std::endl;
+
+  rw_experiment(point_vector, nbL, alpha2, limD, mu_epsilon, experiment_name);
+  
+  // ok = false;
+  // while (!ok) {
+  //   std::cout << "Rips complex: parameters threshold, limD.\n";
+  //   std::cout << "Enter threshold: ";
+  //   std::cin >> alpha;
+  //   std::cout << "Enter limD: ";
+  //   std::cin >> limD;
+  //   std::cout << "Start Rips complex...\n";
+  //   rips_experiment(point_vector, alpha, limD);
+  //   std::cout << "Is the result correct? [y/n]: ";
+  //   char answer;
+  //   std::cin >> answer;
+  //   switch (answer) {
+  //   case 'n':
+  //     ok = false; break;
+  //   default :
+  //     ok = true; break;
+  //   }
+  // }
+  return 0;
+}
+
+/********************************************************************************************
+ * Length of the good interval experiment
+ *******************************************************************************************/
+
+struct Pers_endpoint {
+  double alpha;
+  bool start;
+  int dim;
+  Pers_endpoint(double alpha_, bool start_, int dim_)
+    : alpha(alpha_), start(start_), dim(dim_)
+  {}
+};
+
+/*
+struct less_than_key {
+  inline bool operator() (const MyStruct& struct1, const MyStruct& struct2) {
+    return (struct1.key < struct2.key);
+  }
+};
+*/
+
+double good_interval_length(const std::vector<int> & desired_homology, STree & simplex_tree, double alpha2)
+{
+  int nbL = simplex_tree.num_vertices();
+  int p = 3;
+  persistent_cohomology::Persistent_cohomology< STree, Field_Zp > pcoh(simplex_tree, true);
+  pcoh.init_coefficients( p ); //initilizes the coefficient field for homology
+  pcoh.compute_persistent_cohomology( -1 );
+  std::ofstream out_stream("pers_diag.tmp");
+  pcoh.output_diagram(out_stream);
+  out_stream.close();
+  std::ifstream in_stream("pers_diag.tmp", std::ios::in);
+  std::string line;
+  std::vector<Pers_endpoint> pers_endpoints;
+  while (getline(in_stream, line)) {
+    int p, dim;
+    double alpha_start, alpha_end;
+    std::istringstream iss(line);
+    iss >> p >> dim >> alpha_start >> alpha_end;
+    if (alpha_start != alpha_end) {
+      if (alpha_end < alpha_start)
+        alpha_end = alpha2;
+      pers_endpoints.push_back(Pers_endpoint(alpha_start, true, dim));
+      pers_endpoints.push_back(Pers_endpoint(alpha_end, false, dim));
+    }
+  }
+  std::cout << "Pers_endpoints.size = " << pers_endpoints.size() << std::endl;
+  in_stream.close();
+  std::sort(pers_endpoints.begin(),
+            pers_endpoints.end(),
+            [](const Pers_endpoint & p1, const Pers_endpoint & p2){
+              return p1.alpha < p2.alpha;}
+            );
+  write_barcodes("pers_diag.tmp", alpha2);
+  /*
+  for (auto p: pers_endpoints) {
+    std::cout << p.alpha << " " << p.dim << " " << p.start << "\n";
+  }
+  */
+  std::vector<int> current_homology(nbL-1,0);
+  current_homology[0] = 1; // for the compulsary "0 0 inf" entry
+  double good_start = 0, good_end = 0;
+  double sum_intervals = 0;
+  int num_pieces = 0;
+  bool interval_in_process = (desired_homology == current_homology);
+  for (auto p: pers_endpoints) {
+    /*
+    std::cout << "Treating " << p.alpha << " " << p.dim << " " << p.start
+              << " [";
+    for (int v: current_homology)
+      std::cout << v << " ";
+    std::cout << "]\n";
+    */
+    if (p.start)
+      current_homology[p.dim]++;
+    else
+      current_homology[p.dim]--;
+    if (interval_in_process) {
+      good_end = p.alpha;
+      sum_intervals += good_end - good_start;
+      std::cout << "good_start = " << good_start
+                << ", good_end = " << good_end << "\n";
+                
+      Gudhi::witness_complex::Dim_lists<STree> simplices(simplex_tree, nbL-1, (good_end - good_start)/2);
+      //simplices.collapse();
+      //simplices.output_simplices();
+      interval_in_process = false;
+      //break;
+    }
+    else if (desired_homology == current_homology) {
+      interval_in_process = true;
+      good_start = p.alpha;
+      num_pieces++;
+    }
+  }
+  std::cout << "Number of good homology intervals: " << num_pieces << "\n";
+  return sum_intervals;
+}
+
+
+
+void run_comparison(std::vector<std::vector< int > > const & knn,
+                    std::vector<std::vector< FT > > const & distances,
+                    Point_Vector & points,
+                    unsigned nbL,
+                    double alpha2,
+                    std::vector<int>& desired_homology)
+{
+  clock_t start, end;
+  STree simplex_tree;
+
+  alpha2 = 0.55;
+  std::cout << "alpha2 = " << alpha2 << "\n";
+  start = clock();
+  SRWit srwit(distances,
+              knn,
+              simplex_tree,
+              nbL,
+              alpha2,
+              nbL-1);
+  end = clock();
+  std::cout << "SRWit.size = " << simplex_tree.num_simplices() << std::endl;
+  simplex_tree.set_dimension(nbL-1);
+
+  std::cout << "Good homology interval length for SRWit is "
+                << good_interval_length(desired_homology, simplex_tree, alpha2) << "\n";
+  std::cout << "Time: " << static_cast<double>(end - start) / CLOCKS_PER_SEC << " s. \n";
+
+  STree simplex_tree2;
+  alpha2 = 0.35;
+  std::cout << "alpha2 = " << alpha2 << "\n";
+  start = clock();
+  WRWit wrwit(distances,
+              knn,
+              simplex_tree2,
+              nbL,
+              alpha2,
+              nbL-1);
+  end = clock();
+  std::cout << "WRWit.size = " << simplex_tree2.num_simplices() << std::endl;
+  simplex_tree.set_dimension(nbL-1);
+  
+  std::cout << "Good homology interval length for WRWit is "
+            << good_interval_length(desired_homology, simplex_tree2, alpha2) << "\n";
+  std::cout << "Time: " << static_cast<double>(end - start) / CLOCKS_PER_SEC << " s. \n";
+
+  STree simplex_tree3;
+  std::cout << "Enter alpha2 for Rips: ";
+  std::cin >> alpha2;
+  std::cout << "\n";
+  std::cout << "points.size() = " << points.size() << "\n";
+  start = clock();
+  rips(points,
+       0.2, 
+       nbL-1,
+       simplex_tree3);
+  end = clock();
+  std::cout << "Rips.size = " << simplex_tree3.num_simplices() << std::endl;
+  simplex_tree.set_dimension(nbL-1);
+  
+  std::cout << "Good homology interval length for WRWit is "
+            << good_interval_length(desired_homology, simplex_tree3, alpha2) << "\n";
+  std::cout << "Time: " << static_cast<double>(end - start) / CLOCKS_PER_SEC << " s. \n";
+}
+
+int experiment2(int argc, char * const argv[])
+{
+  for (unsigned d = 3; d < 4; d++) {
+    // Sphere S^d 
+    Point_Vector point_vector;
+    unsigned N = 1;
+    double alpha2 = 2.4 - 0.4*d; 
+    switch (d) {
+    case 1: alpha2 = 2.2; break;
+    case 2: alpha2 = 1.7; break;
+    case 3: alpha2 = 1.5; break;
+    case 4: alpha2 = 1.4; break;
+    default: alpha2 = 1.4; break;
+    }
+    std::cout << "alpha2 = " << alpha2 << "\n";
+    unsigned nbL = 20;
+    std::vector<int> desired_homology(nbL-1,0);
+    desired_homology[0] = 1; desired_homology[d] = 1;
+    
+    
+    for (unsigned i = 1; i <= N; ++i) {
+      unsigned nbW = 1000*i;//, nbL = 20;
+      double mu_epsilon = 1/sqrt(nbL);
+      std::cout << "Running test S"<< d <<", |W|=" << nbW << ", |L|=" << nbL << std::endl;
+      generate_points_sphere(point_vector, i*1000, d+1);
+      std::vector<Point_d> landmarks;
+      Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+
+      std::vector<std::vector< int > > knn;
+      std::vector<std::vector< FT > > distances;
+    
+      std::cout << "|L| after sparsification: " << landmarks.size() << "\n";
+      Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                    landmarks,  // aka landmarks
+                                                    alpha2,
+                                                    nbL-1,
+                                                    knn,
+                                                    distances);
+      run_comparison(knn, distances, point_vector, nbL, alpha2, desired_homology);
+    }
+  }
+  /*
+  {
+    // SO(3)
+    Point_Vector point_vector;
+    double alpha2 = 0.6; 
+    std::cout << "alpha2 = " << alpha2 << "\n";
+    unsigned nbL = 150;
+    std::vector<int> desired_homology(nbL-1,0);
+    desired_homology[0] = 1; desired_homology[1] = 1; desired_homology[2] = 1; //Kl
+    // desired_homology[0] = 1; desired_homology[3] = 1; //SO3
+
+    double mu_epsilon = 1/sqrt(nbL);
+    if (argc < 3) std::cerr << "No file name indicated!\n";
+    read_points_cust(argv[2], point_vector);
+    int nbW = point_vector.size();
+    std::cout << "Running test SO(3), |W|=" << nbW << ", |L|=" << nbL << std::endl;
+    std::vector<Point_d> landmarks;
+    Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+    
+    std::vector<std::vector< int > > knn;
+    std::vector<std::vector< FT > > distances;
+    
+    std::cout << "|L| after sparsification: " << landmarks.size() << "\n";
+    Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                  landmarks,  // aka landmarks
+                                                  alpha2,
+                                                  nbL-1,
+                                                  knn,
+                                                  distances);
+    run_comparison(knn, distances, point_vector, nbL, alpha2, desired_homology);
+  }
+  */
+  return 0;
+}
+
+int experiment3(int argc, char * const argv[])
+{
+  // COLLAPSES EXPERIMENT
+  
+  return 0;
+}
+
+int main (int argc, char * const argv[])
+{
+  if (argc == 1) {
+    output_experiment_information(argv[0]);
+    return 1;
+  }
+  switch (atoi(argv[1])) {
+  case 0 :
+    return experiment0(argc, argv);
+    break;
+  case 1 :
+    return experiment1(argc, argv);
+    break;
+  case 2 :
+    return experiment2(argc, argv);
+    break;
+  default :
+    output_experiment_information(argv[0]);
+    return 1;
+  }
+}
diff --git a/src/Witness_complex/example/color-picker.cpp b/src/Witness_complex/example/color-picker.cpp
new file mode 100644
index 00000000..fcea033e
--- /dev/null
+++ b/src/Witness_complex/example/color-picker.cpp
@@ -0,0 +1,37 @@
+#include <iostream>
+#include <assert.h>
+
+struct Color {
+  double r, g, b;
+  Color() : r(0), g(0), b(0) { }
+  Color(double r_, double g_, double b_)
+    : r(r_), g(g_), b(b_) { } 
+};
+
+// Convert a double in [0,1] to a color
+template< typename ColorType >
+void double_to_color(double t, ColorType & color) {
+  assert(t >= 0 && t <= 1);
+  double s = 1.0/6;
+  if (t >= 0 && t <= s)
+    color = ColorType(1, 6*t, 0);
+  else if (t > s && t <= 2*s)
+    color = ColorType(1-6*(t-s), 1, 0);
+  else if (t > 2*s && t <= 3*s)
+    color = ColorType(0, 1, 6*(t-2*s));
+  else if (t > 3*s && t <= 4*s)
+    color = ColorType(0, 1-6*(t-3*s), 1);
+  else if (t > 4*s && t <= 5*s)
+    color = ColorType(6*(t-4*s), 0, 1);
+  else
+    color = ColorType(1, 0, 1-6*(t-5*s));
+}
+
+int main (int argc, char * const argv[]) {
+  double number_to_convert = 0;
+  std::cout << "Enter a real number in [0,1]: ";
+  std::cin >> number_to_convert;
+  Color color;
+  double_to_color(number_to_convert, color);
+  std::cout << "The corresponding color in rgb is: (" << color.r << ", " << color.g << ", " << color.b << ")\n";
+}
diff --git a/src/Witness_complex/example/generators.h b/src/Witness_complex/example/generators.h
index ac445261..23915546 100644
--- a/src/Witness_complex/example/generators.h
+++ b/src/Witness_complex/example/generators.h
@@ -144,4 +144,12 @@ void generate_points_sphere(Point_Vector& W, int nbP, int dim) {
     W.push_back(*rp++);
 }
 
+/** \brief Generate nbP points on a d-torus
+ *
+ */
+void generate_points_torus(Point_Vector& W, int nbP, int dim) {
+  CGAL::Random_points_on_sphere_d<Point_d> rp(2, 1);
+  
+}
+
 #endif  // EXAMPLE_WITNESS_COMPLEX_GENERATORS_H_
diff --git a/src/Witness_complex/example/off_writer.h b/src/Witness_complex/example/off_writer.h
new file mode 100644
index 00000000..8cafe9e2
--- /dev/null
+++ b/src/Witness_complex/example/off_writer.h
@@ -0,0 +1,11 @@
+#ifndef OFF_WRITER_H_
+#define OFF_WRITER_H_
+
+
+class Off_Writer {
+
+private:
+
+}
+
+#endif
diff --git a/src/Witness_complex/example/output.h b/src/Witness_complex/example/output.h
new file mode 100644
index 00000000..0e74387a
--- /dev/null
+++ b/src/Witness_complex/example/output.h
@@ -0,0 +1,305 @@
+#ifndef OUTPUT_H
+#define OUTPUT_H
+
+#include <fstream>
+#include <vector>
+#include <string>
+
+#include <gudhi/Simplex_tree.h>
+
+#include <CGAL/Epick_d.h>
+#include <CGAL/Delaunay_triangulation.h>
+
+//typename Gudhi::Witness_complex<> Witness_complex;
+
+typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
+typedef K::Point_d Point_d;
+typedef std::vector<Point_d> Point_Vector;
+typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
+
+/** \brief Write the table of the nearest landmarks to each witness
+ *  to a file.
+ */
+template <class Value>
+void write_wl( std::string file_name, std::vector< std::vector <Value> > & WL)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  for (auto w : WL)
+    {
+      for (auto l: w)
+        ofs << l << " ";
+      ofs << "\n";
+    }
+  ofs.close();
+}
+
+/** \brief Write the coordinates of points in points to a file. 
+ *
+ */
+void write_points( std::string file_name, std::vector< Point_d > & points)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  for (auto w : points)
+    {
+      for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
+        ofs << *it << " ";
+      ofs << "\n";
+    }
+  ofs.close();
+}
+
+/** Write edges of a witness complex in a file.
+ *  The format of an edge is coordinates of u \n coordinates of v \n\n\n
+ *  This format is compatible with gnuplot
+ */
+template< typename STree >
+void write_edges(std::string file_name, STree& witness_complex, Point_Vector& landmarks)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  for (auto u: witness_complex.complex_vertex_range())
+    for (auto v: witness_complex.complex_vertex_range())
+      {
+        std::vector<int> edge = {u,v};
+        if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
+          {
+            for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it)
+              ofs << *it << " ";
+            ofs << "\n";
+            for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it)
+              ofs << *it << " ";
+            ofs << "\n\n\n";
+          }
+      }
+  ofs.close();
+}
+
+/** \brief Write triangles (tetrahedra in 3d) of a witness
+ *  complex in a file, compatible with medit.
+ *  l_is_v = landmark is vertex
+ */
+template <typename SimplexHandleRange,
+          typename STree >
+void write_witness_mesh(Point_Vector& W, std::vector<int>& landmarks_ind, STree& st, SimplexHandleRange const & shr, bool is2d, bool l_is_v, std::string file_name = "witness.mesh")
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  if (is2d)
+    ofs << "MeshVersionFormatted 1\nDimension 2\n";
+  else
+    ofs << "MeshVersionFormatted 1\nDimension 3\n";
+  
+  if (!l_is_v)
+    ofs << "Vertices\n" << W.size() << "\n";
+  else
+    ofs << "Vertices\n" << landmarks_ind.size() << "\n";
+  
+  if (l_is_v)
+    for (auto p_it : landmarks_ind) {
+      for (auto coord = W[p_it].cartesian_begin(); coord != W[p_it].cartesian_end() && coord != W[p_it].cartesian_begin()+3 ; ++coord)
+        ofs << *coord << " ";
+      ofs << "508\n";
+    }
+  else
+    for (auto p_it : W) {
+      for (auto coord = p_it.cartesian_begin(); coord != p_it.cartesian_end() && coord != p_it.cartesian_begin()+3 ; ++coord)
+        ofs << *coord << " ";
+      ofs << "508\n";
+    }
+
+  //  int num_triangles = W.size(), num_tetrahedra = 0;
+  int num_edges = 0, num_triangles = 0, num_tetrahedra = 0;
+  if (!l_is_v) {
+      for (auto sh_it : shr)
+        if (st.dimension(sh_it) == 1)
+          num_edges++;
+        else if (st.dimension(sh_it) == 2)
+          num_triangles++;
+        else if (st.dimension(sh_it) == 3)
+          num_tetrahedra++;
+      ofs << "Edges " << num_edges << "\n";
+      for (auto sh_it : shr) {
+           if (st.dimension(sh_it) == 1) {
+            for (auto v_it : st.simplex_vertex_range(sh_it))
+              ofs << landmarks_ind[v_it]+1 << " ";
+           ofs << "200\n";
+          }
+        }
+      ofs << "Triangles " << num_triangles << "\n";
+      for (unsigned i = 0; i < W.size(); ++i)
+        ofs << i << " " << i << " " << i << " " << "508\n";
+      for (auto sh_it : shr)
+        {
+           if (st.dimension(sh_it) == 2) {
+            for (auto v_it : st.simplex_vertex_range(sh_it))
+              ofs << landmarks_ind[v_it]+1 << " ";
+           ofs << "508\n";
+          }
+        }
+      ofs << "Tetrahedra " << num_tetrahedra << "\n";
+      for (auto sh_it : shr)
+        {
+           if (st.dimension(sh_it) == 3) {
+            for (auto v_it : st.simplex_vertex_range(sh_it))
+              ofs << landmarks_ind[v_it]+1 << " ";
+           ofs << "250\n";
+          }
+        }
+  }
+  else {
+      for (auto sh_it : shr)
+        if (st.dimension(sh_it) == 1)
+          num_edges++;
+        else if (st.dimension(sh_it) == 2)
+          num_triangles++;
+        else if (st.dimension(sh_it) == 3)
+          num_tetrahedra++;
+      ofs << "Edges " << num_edges << "\n";
+      for (auto sh_it : shr) {
+           if (st.dimension(sh_it) == 1) {
+            for (auto v_it : st.simplex_vertex_range(sh_it))
+              ofs << v_it+1 << " ";
+           ofs << "200\n";
+          }
+        }
+      ofs << "Triangles " << num_triangles << "\n";
+      for (auto sh_it : shr)
+        {
+           if (st.dimension(sh_it) == 2) {
+            for (auto v_it : st.simplex_vertex_range(sh_it))
+              ofs << v_it+1 << " ";
+           ofs << "508\n";
+          }
+        }
+      ofs << "Tetrahedra " << num_tetrahedra << "\n";
+      for (auto sh_it : shr)
+        {
+           if (st.dimension(sh_it) == 3) {
+            for (auto v_it : st.simplex_vertex_range(sh_it))
+              ofs << v_it+1 << " ";
+           ofs << "250\n";
+          }
+        }
+  }
+    
+  ofs << "End\n";
+  /*
+  else
+    {
+      ofs << "Tetrahedra " << t.number_of_finite_full_cells()+1 << "\n";
+      for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
+        {
+          if (t.is_infinite(fc_it))
+            continue;
+          for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it)
+            ofs << index_of_vertex[*vh_it] << " ";
+          ofs << "508\n";
+        }
+      ofs << nbV << " " << nbV << " " << nbV << " " << nbV << " " << 208 << "\n";
+      ofs << "End\n";
+    }
+  */
+  ofs.close();
+}
+
+void write_witness_mesh(Point_Vector& W, std::vector<int>& landmarks_ind, Gudhi::Simplex_tree<>& st, bool is2d, bool l_is_v, std::string file_name = "witness.mesh")
+{
+  write_witness_mesh(W, landmarks_ind, st, st.complex_simplex_range(), is2d, l_is_v, file_name);
+}
+
+/** \brief Write triangles (tetrahedra in 3d) of a Delaunay
+ *  triangulation in a file, compatible with medit.
+ */
+void write_delaunay_mesh(Delaunay_triangulation& t, const Point_d& p, bool is2d)
+{
+  std::ofstream ofs ("delaunay.mesh", std::ofstream::out);
+  int nbV = t.number_of_vertices()+1;
+  if (is2d)
+    ofs << "MeshVersionFormatted 1\nDimension 2\n";
+  else
+    ofs << "MeshVersionFormatted 1\nDimension 3\n";
+  ofs << "Vertices\n" << nbV << "\n";
+  int ind = 1; //index of a vertex
+  std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex;
+  for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it)
+    {
+      if (t.is_infinite(v_it))
+        continue;
+      // Add maximum 3 coordinates
+      for (auto coord = v_it->point().cartesian_begin(); coord != v_it->point().cartesian_end() && coord != v_it->point().cartesian_begin()+3; ++coord)
+        ofs << *coord << " ";
+      ofs << "508\n";
+      index_of_vertex[v_it] = ind++;
+    }
+  for (auto coord = p.cartesian_begin(); coord != p.cartesian_end(); ++coord)
+    ofs << *coord << " ";
+  ofs << "208\n";
+  if (is2d)
+    {
+      ofs << "Triangles " << t.number_of_finite_full_cells()+1 << "\n";
+      for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
+        {
+          if (t.is_infinite(fc_it))
+            continue;
+          for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it)
+            ofs << index_of_vertex[*vh_it] << " ";
+          ofs << "508\n";
+        }
+      ofs << nbV << " " << nbV << " " << nbV << " " << 208 << "\n";
+      ofs << "End\n";
+    }
+  else if (p.size() == 3)
+    {
+      ofs << "Tetrahedra " << t.number_of_finite_full_cells()+1 << "\n";
+      for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
+        {
+          if (t.is_infinite(fc_it))
+            continue;
+          for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it)
+            ofs << index_of_vertex[*vh_it] << " ";
+          ofs << "508\n";
+        }
+      ofs << nbV << " " << nbV << " " << nbV << " " << nbV << " " << 208 << "\n";
+      ofs << "End\n";
+    }
+  else if (p.size() == 4)
+    {
+      ofs << "Tetrahedra " << 5*(t.number_of_finite_full_cells())+1 << "\n";
+      for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it)
+        {
+          if (t.is_infinite(fc_it))
+            continue;
+          for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it)
+            {
+              for (auto vh_it2 = fc_it->vertices_begin(); vh_it2 != fc_it->vertices_end(); ++vh_it2)
+                if (vh_it != vh_it2)
+                  ofs << index_of_vertex[*vh_it2] << " ";
+              ofs << "508\n"; 
+            }
+        }
+      ofs << nbV << " " << nbV << " " << nbV << " " << nbV << " " << 208 << "\n";
+      ofs << "End\n";
+    }
+  ofs.close();
+}
+
+///////////////////////////////////////////////////////////////////////
+// PRINT VECTOR
+///////////////////////////////////////////////////////////////////////
+
+template <typename T>
+void print_vector(std::vector<T> v)
+{
+  std::cout << "[";
+  if (!v.empty())
+    {
+      std::cout << *(v.begin());
+      for (auto it = v.begin()+1; it != v.end(); ++it)
+        {
+          std::cout << ",";
+          std::cout << *it;
+        }
+    }
+  std::cout << "]";
+}
+
+
+#endif
diff --git a/src/Witness_complex/example/output_tikz.h b/src/Witness_complex/example/output_tikz.h
new file mode 100644
index 00000000..281c65b7
--- /dev/null
+++ b/src/Witness_complex/example/output_tikz.h
@@ -0,0 +1,178 @@
+#ifndef OUTPUT_TIKZ_H
+#define OUTPUT_TIKZ_H
+
+#include <vector>
+#include <string>
+#include <algorithm>
+#include <fstream>
+#include <cmath>
+
+typedef double FT;
+
+
+//////////////////AUX/////////////////////
+
+void write_preamble(std::ofstream& ofs)
+{
+  ofs << "\\documentclass{standalone}\n"
+      << "\\usepackage{tikz}\n\n"
+      << "\\begin{document}\n"
+      << "\\begin{tikzpicture}\n";
+}
+
+void write_end(std::ofstream& ofs)
+{
+  ofs << "\\end{tikzpicture}\n"
+      << "\\end{document}";
+}
+
+
+/////////////////MAIN//////////////////////
+
+void write_tikz_plot(std::vector<FT> data, std::string filename)
+{
+  int n = data.size();
+  FT vmax = *(std::max_element(data.begin(), data.end()));
+  //std::cout << std::log10(vmax) << " " << std::floor(std::log10(vmax));
+  
+  FT order10 = pow(10,std::floor(std::log10(vmax)));
+  int digit = std::floor( vmax / order10) + 1;
+  if (digit == 4 || digit == 6) digit = 5;
+  if (digit > 6) digit = 10;
+  FT plot_max = digit*order10;
+  std::cout << plot_max << " " << vmax;
+  FT hstep = 10.0/(n-1);
+  FT wstep = 10.0 / plot_max;
+
+  std::cout << "(eps_max-eps_min)/(N-48) = " << (vmax-*data.begin())/(data.size()-48) << "\n";
+  std::ofstream ofs(filename, std::ofstream::out);
+
+  ofs <<
+    "\\documentclass{standalone}\n" <<
+    "\\usepackage[utf8]{inputenc}\n" <<
+    "\\usepackage{amsmath}\n" <<
+    "\\usepackage{tikz}\n\n" <<
+    "\\begin{document}\n" <<
+    "\\begin{tikzpicture}\n";
+  
+  ofs <<  "\\draw[->] (0,0) -- (0,11);" << std::endl <<
+    "\\draw[->] (0,0) -- (11,0);" << std::endl <<
+    "\\foreach \\i in {1,...,10}" << std::endl <<
+    "\\draw (0,\\i) -- (-0.05,\\i);" << std::endl <<
+    "\\foreach \\i in {1,...,10}" << std::endl <<
+    "\\draw (\\i,0) -- (\\i,-0.05);" << std::endl << std::endl <<
+
+    "\\foreach \\i in {1,...,10}" << std::endl <<
+    "\\draw[dashed] (-0.05,\\i) -- (11,\\i);" << std::endl << std::endl <<
+    
+    "\\node at (-0.5,11) {$*$}; " << std::endl <<
+    "\\node at (11,-0.5) {$*$}; " << std::endl <<
+    "\\node at (-0.5,-0.5) {0}; " << std::endl <<
+    "\\node at (-0.5,10) {" << plot_max << "}; " << std::endl <<
+    "%\\node at (10,-0.5) {2}; " << std::endl;
+
+  ofs << "\\draw[red] (0," << wstep*data[0] << ")";
+  for (int i = 1; i < n; ++i)
+    ofs << " -- (" << hstep*i << "," << wstep*data[i] << ")";
+  ofs << ";\n";
+
+  ofs <<
+    "\\end{tikzpicture}\n" <<
+    "\\end{document}";
+  
+  ofs.close();  
+}
+
+
+// A little script to make a tikz histogram of epsilon distribution
+// Returns the average epsilon
+void write_histogram(std::vector<double> histo, std::string file_name = "histogram.tikz", std::string xaxis = "$\\epsilon/\\epsilon_{max}$",  std::string yaxis = "$\\epsilon$", FT max_x = 1)
+{
+  int n = histo.size();
+  
+  std::ofstream ofs (file_name, std::ofstream::out);
+  FT barwidth = 20.0/n;
+  FT max_value = *(std::max_element(histo.begin(), histo.end()));
+  std::cout << max_value << std::endl;
+  FT ten_power = pow(10, ceil(log10(max_value)));
+  FT max_histo = ten_power;
+  if (max_value/ten_power > 1) {
+    if (max_value/ten_power < 2)
+      max_histo = 0.2*ten_power;
+    else if (max_value/ten_power < 5)
+      max_histo = 0.5*ten_power;
+  }
+  std::cout << ceil(log10(max_value)) << std::endl << max_histo << std::endl;
+  FT unitht = max_histo/10.0;
+  write_preamble(ofs);
+  
+  ofs << "\\draw[->] (0,0) -- (0,11);\n" <<
+    "\\draw[->] (0,0) -- (21,0);\n" <<
+    "\\foreach \\i in {1,...,10}\n" <<
+    "\\draw (0,\\i) -- (-0.1,\\i);\n" <<
+    "\\foreach \\i in {1,...,20}\n" <<
+    "\\draw (\\i,0) -- (\\i,-0.1);\n" <<
+ 
+    "\\node at (-1,11) {" << yaxis << "};\n" << 
+    "\\node at (22,-1) {" << xaxis << "};\n" << 
+    "\\node at (-0.5,-0.5) {0};\n" << 
+    "\\node at (-0.5,10) {" << max_histo << "};\n" << 
+    "\\node at (20,-0.5) {" << max_x << "};\n";
+    
+  for (int i = 0; i < n; ++i)
+    ofs << "\\draw (" << barwidth*i << "," << histo[i]/unitht << ") -- ("
+        << barwidth*(i+1) << "," << histo[i]/unitht << ") -- ("
+  << barwidth*(i+1) << ",0) -- (" << barwidth*i << ",0) -- cycle;\n";
+
+  write_end(ofs);  
+  ofs.close();
+}
+
+struct Pers_interval {
+  double alpha_start, alpha_end;
+  int dim;
+  Pers_interval(double alpha_start_, double alpha_end_, int dim_)
+    : alpha_start(alpha_start_), alpha_end(alpha_end_), dim(dim_)
+  {}
+};
+
+void write_barcodes(std::string in_file, double alpha2, std::string out_file = "barcodes.tikz.tex")
+{
+  std::ifstream ifs(in_file, std::ios::in);
+  std::string line;
+  std::vector<Pers_interval> pers_intervals;
+  while (getline(ifs, line)) {
+    int p, dim;
+    double alpha_start, alpha_end;
+    std::istringstream iss(line);
+    iss >> p >> dim >> alpha_start >> alpha_end;
+    if (alpha_start != alpha_end) {
+      if (alpha_end < alpha_start)
+        alpha_end = alpha2;
+      pers_intervals.push_back(Pers_interval(alpha_start, alpha_end, dim));
+    }
+  }
+  ifs.close();
+  std::ofstream ofs (out_file, std::ofstream::out);
+  write_preamble(ofs);
+  double barwidth = 0.01;
+  int i = 0;
+  for (auto interval: pers_intervals) {
+    std::string color = "black";
+    switch (interval.dim) {
+    case 0: color = "orange"; break;
+    case 1: color = "red"; break;
+    case 2: color = "blue"; break;
+    case 3: color = "green"; break;
+    case 4: color = "yellow"; break;
+    default: color = "orange"; break;
+    }
+    ofs << "\\fill[" << color << "] (" << interval.alpha_start << "," << barwidth*i << ") rectangle ("
+        << interval.alpha_end << "," << barwidth*(i+1) <<");\n";
+    i++;
+  }
+  write_end(ofs);
+  ofs.close();
+}
+
+#endif
diff --git a/src/Witness_complex/example/relaxed_delaunay.cpp b/src/Witness_complex/example/relaxed_delaunay.cpp
new file mode 100644
index 00000000..b0190446
--- /dev/null
+++ b/src/Witness_complex/example/relaxed_delaunay.cpp
@@ -0,0 +1,180 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2016  INRIA Sophia Antipolis-Méditerranée (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/>.
+ */
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Relaxed_witness_complex.h>
+#include <gudhi/Dim_lists.h>
+#include <gudhi/reader_utils.h>
+#include <gudhi/Persistent_cohomology.h>
+#include "Landmark_choice_random_knn.h"
+#include "Landmark_choice_sparsification.h"
+
+#include <iostream>
+#include <fstream>
+#include <ctime>
+#include <utility>
+#include <algorithm>
+#include <set>
+#include <queue>
+#include <iterator>
+#include <string>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+#include <CGAL/Epick_d.h>
+#include <CGAL/Delaunay_triangulation.h>
+//#include <CGAL/Sphere_d.h>
+
+#include "generators.h"
+#include "output.h"
+
+using namespace Gudhi;
+using namespace Gudhi::witness_complex;
+using namespace Gudhi::persistent_cohomology;
+
+typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
+typedef K::Point_d Point_d;
+typedef K::Sphere_d Sphere_d;
+typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation;
+
+typedef std::vector<Point_d> Point_Vector;
+typedef Relaxed_witness_complex< Simplex_tree<> > RelaxedWitnessComplex;
+typedef Simplex_tree<>::Simplex_handle Simplex_handle;
+
+
+
+/**
+ * \brief Customized version of read_points
+ * which takes into account a possible nbP first line
+ *
+ */
+inline void
+read_points_cust(std::string file_name, std::vector< std::vector< double > > & points) {
+  std::ifstream in_file(file_name.c_str(), std::ios::in);
+  if (!in_file.is_open()) {
+    std::cerr << "Unable to open file " << file_name << std::endl;
+    return;
+  }
+  std::string line;
+  double x;
+  while (getline(in_file, line)) {
+    std::vector< double > point;
+    std::istringstream iss(line);
+    while (iss >> x) {
+      point.push_back(x);
+    }
+    if (point.size() != 1)
+      points.push_back(point);
+  }
+  in_file.close();
+}
+
+int main (int argc, char * const argv[])
+{
+  if (argc != 4) {
+    std::cerr << "Usage: " << argv[0]
+              << " 1 file_name alpha limD\n";
+    return 0;
+  }
+  std::string file_name = argv[1];
+  double alpha2  = atof(argv[2]);
+  int limD = atoi(argv[3]);
+  
+  // Read points
+  Point_Vector point_vector;
+  read_points_cust(file_name, point_vector);
+  generate_points_random_box(point_vector, 200, 2);
+  write_points(file_name, point_vector);
+  
+  std::cout << "The file contains " << point_vector.size() << " points.\n";
+  std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+  // 1. Compute Delaunay centers
+  Delaunay_triangulation delaunay(point_vector[0].size());
+  delaunay.insert(point_vector.begin(), point_vector.end());
+  Point_Vector del_centers;
+  for (auto f_it = delaunay.full_cells_begin(); f_it != delaunay.full_cells_end(); ++f_it) {
+    if (delaunay.is_infinite(f_it))
+      continue;
+    Point_Vector vertices;
+    for (auto v_it = f_it->vertices_begin(); v_it != f_it->vertices_end(); ++v_it)
+      vertices.push_back((*v_it)->point());
+    Sphere_d sphere(vertices.begin(), vertices.end());
+    del_centers.push_back(sphere.center());
+  }
+  std::cout << "Delaunay center count: " << del_centers.size() << ".\n";
+
+  // 2. Build Relaxed Witness Complex
+  std::vector<std::vector<int>> knn;
+  std::vector<std::vector<double>> distances;
+  Gudhi::witness_complex::build_distance_matrix(del_centers,   // aka witnesses
+                                                point_vector,  // aka landmarks
+                                                alpha2,
+                                                limD,
+                                                knn,
+                                                distances);
+  
+  write_wl("wl_distances.txt", distances);
+  Simplex_tree<> simplex_tree;
+  Gudhi::witness_complex::Relaxed_witness_complex<Simplex_tree<>> rwc(distances,
+                                                                      knn,
+                                                                      simplex_tree,
+                                                                      point_vector.size(),
+                                                                      alpha2,
+                                                                      limD);
+  std::vector<int> dim_simplices(limD+1);
+  for (auto sh: simplex_tree.complex_simplex_range()) {
+    dim_simplices[simplex_tree.dimension(sh)]++;
+  }
+  for (unsigned i =0; i != dim_simplices.size(); ++i)
+    std::cout << "dim[" << i << "]: " << dim_simplices[i] << " simplices.\n";
+
+  std::vector<int> landmarks_ind;
+  for (unsigned i = 0; i < point_vector.size(); ++i)
+    landmarks_ind.push_back(i);
+  write_witness_mesh(point_vector, landmarks_ind, simplex_tree, simplex_tree.complex_simplex_range(), true, true, "relaxed_delaunay.mesh");
+  
+  // 3. Check if the thing is Relaxed Delaunay
+  for (auto sh: simplex_tree.complex_simplex_range()) {
+    Point_Vector vertices;
+    for (auto v: simplex_tree.simplex_vertex_range(sh))
+      vertices.push_back(point_vector[v]);
+    Sphere_d sphere(vertices.begin(), vertices.end());
+    Point_d center = sphere.center();
+    double r2 = sphere.squared_radius();
+    typename K::Squared_distance_d dist2;
+    std::vector<int> v_inds;
+    for (auto v: simplex_tree.simplex_vertex_range(sh))
+      v_inds.push_back(v);
+    auto range_begin = std::begin(v_inds);
+    auto range_end = std::end(v_inds);
+    if (simplex_tree.dimension(sh) == (int)point_vector[0].size())
+    for (auto v: simplex_tree.complex_vertex_range())
+      if (std::find(range_begin, range_end, v) == range_end) {
+        if (dist2(point_vector[v], center) < r2 - alpha2)
+          std::cout << "WARNING! The vertex " << point_vector[v] << " is inside the (r2-alpha2)-ball (" << center << ", " << r2 << ") distance is " << dist2(point_vector[v], center) << "\n";
+      }
+  }
+}
diff --git a/src/Witness_complex/example/relaxed_witness_complex_sphere.cpp b/src/Witness_complex/example/relaxed_witness_complex_sphere.cpp
new file mode 100644
index 00000000..067321ce
--- /dev/null
+++ b/src/Witness_complex/example/relaxed_witness_complex_sphere.cpp
@@ -0,0 +1,461 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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/>.
+ */
+
+#include <iostream>
+#include <fstream>
+#include <ctime>
+#include <utility>
+#include <algorithm>
+#include <set>
+#include <queue>
+#include <iterator>
+
+#include <sys/types.h>
+#include <sys/stat.h>
+//#include <stdlib.h>
+
+//#include "gudhi/graph_simplicial_complex.h"
+#include "gudhi/Relaxed_witness_complex.h"
+#include "gudhi/reader_utils.h"
+#include "gudhi/Collapse/Collapse.h"
+//#include <boost/filesystem.hpp> 
+
+//#include <CGAL/Delaunay_triangulation.h>
+#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_incremental_neighbor_search.h>
+#include <CGAL/Kd_tree.h>
+#include <CGAL/Euclidean_distance.h>
+
+#include <CGAL/Kernel_d/Vector_d.h>
+#include <CGAL/point_generators_d.h>
+#include <CGAL/constructions_d.h>
+#include <CGAL/Fuzzy_sphere.h>
+#include <CGAL/Random.h>
+
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+using namespace Gudhi;
+//using namespace boost::filesystem;
+
+typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
+typedef K::FT FT;
+typedef K::Point_d Point_d;
+typedef CGAL::Search_traits<
+  FT, Point_d,
+  typename K::Cartesian_const_iterator_d,
+  typename K::Construct_cartesian_const_iterator_d> Traits_base;
+typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
+
+typedef std::vector< Vertex_handle > typeVectorVertex;
+
+//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex;
+//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool;
+
+typedef CGAL::Search_traits_adapter<
+  std::ptrdiff_t, Point_d*, Traits_base> STraits;
+//typedef K TreeTraits;
+//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter;
+//typedef CGAL::Kd_tree<STraits> Kd_tree;
+typedef CGAL::Orthogonal_incremental_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> Neighbor_search;
+typedef Neighbor_search::Tree Tree;
+typedef Neighbor_search::Distance Distance;
+typedef Neighbor_search::iterator KNS_iterator;
+typedef Neighbor_search::iterator KNS_range;
+typedef boost::container::flat_map<int, int> Point_etiquette_map;
+typedef CGAL::Kd_tree<STraits> Tree2;
+
+typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
+
+typedef std::vector<Point_d> Point_Vector;
+
+//typedef K::Equal_d Equal_d;
+typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator;
+typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator;
+
+bool toric=false;
+
+/**
+ * \brief Customized version of read_points
+ * which takes into account a possible nbP first line
+ *
+ */
+inline void
+read_points_cust ( std::string file_name , Point_Vector & points)
+{  
+  std::ifstream in_file (file_name.c_str(),std::ios::in);
+  if(!in_file.is_open())
+    {
+      std::cerr << "Unable to open file " << file_name << std::endl;
+      return;
+    }
+  std::string line;
+  double x;
+  while( getline ( in_file , line ) )
+    {
+      std::vector< double > point;
+      std::istringstream iss( line );
+      while(iss >> x) { point.push_back(x); }
+      Point_d p(point.begin(), point.end());
+      if (point.size() != 1)
+        points.push_back(p);
+    }
+  in_file.close();
+}
+
+
+void generate_points_sphere(Point_Vector& W, int nbP, int dim)
+{
+  CGAL::Random_points_on_sphere_d<Point_d> rp(dim,1);
+  for (int i = 0; i < nbP; i++)
+    W.push_back(*rp++);
+}
+
+
+void write_wl( std::string file_name, std::vector< std::vector <int> > & WL)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  for (auto w : WL)
+    {
+      for (auto l: w)
+        ofs << l << " ";
+      ofs << "\n";
+    }
+  ofs.close();
+}
+
+void write_rl( std::string file_name, std::vector< std::vector <std::vector<int>::iterator> > & rl)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  for (auto w : rl)
+    {
+      for (auto l: w)
+        ofs << *l << " ";
+      ofs << "\n";
+    }
+  ofs.close();
+}
+
+std::vector<Point_d> convert_to_torus(std::vector< Point_d>& points)
+{
+  std::vector< Point_d > points_torus;
+  for (auto p: points)
+    {
+      FT theta = M_PI*p[0];
+      FT phi = M_PI*p[1];
+      std::vector<FT> p_torus;
+      p_torus.push_back((1+0.2*cos(theta))*cos(phi));
+      p_torus.push_back((1+0.2*cos(theta))*sin(phi));
+      p_torus.push_back(0.2*sin(theta));
+      points_torus.push_back(Point_d(p_torus));
+    }
+  return points_torus;
+}
+
+
+void write_points_torus( std::string file_name, std::vector< Point_d > & points)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  std::vector<Point_d> points_torus = convert_to_torus(points);
+  for (auto w : points_torus)
+    {
+      for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
+        ofs << *it << " ";
+      ofs << "\n";
+    }
+  ofs.close();
+}
+
+
+void write_points( std::string file_name, std::vector< Point_d > & points)
+{
+  if (toric) write_points_torus(file_name, points);
+  else
+    {
+      std::ofstream ofs (file_name, std::ofstream::out);
+      for (auto w : points)
+        {
+          for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it)
+            ofs << *it << " ";
+          ofs << "\n";
+        }
+      ofs.close();
+    }
+}
+
+
+void write_edges_torus(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  Point_Vector l_torus = convert_to_torus(landmarks);
+  for (auto u: witness_complex.complex_vertex_range())
+    for (auto v: witness_complex.complex_vertex_range())
+      {
+        typeVectorVertex edge = {u,v};
+        if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
+          {
+            for (auto it = l_torus[u].cartesian_begin(); it != l_torus[u].cartesian_end(); ++it)
+              ofs << *it << " ";
+            ofs << "\n";
+            for (auto it = l_torus[v].cartesian_begin(); it != l_torus[v].cartesian_end(); ++it)
+              ofs << *it << " ";
+            ofs << "\n\n\n";
+          }
+    }
+  ofs.close();
+}
+
+void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks)
+{
+  std::ofstream ofs (file_name, std::ofstream::out);
+  if (toric) write_edges_torus(file_name, witness_complex, landmarks);
+  else
+    {
+      for (auto u: witness_complex.complex_vertex_range())
+        for (auto v: witness_complex.complex_vertex_range())
+          {
+            typeVectorVertex edge = {u,v};
+            if (u < v && witness_complex.find(edge) != witness_complex.null_simplex())   
+              {
+                for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it)
+                  ofs << *it << " ";
+                ofs << "\n";
+                for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it)
+                  ofs << *it << " ";
+                ofs << "\n\n\n";
+              }
+          }
+      ofs.close();
+    }
+}
+
+
+/** Function that chooses landmarks from W and place it in the kd-tree L.
+ *  Note: nbL hould be removed if the code moves to Witness_complex
+ */
+void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
+{
+  std::cout << "Enter landmark choice to kd tree\n";
+  //std::vector<Point_d> landmarks;
+  int chosen_landmark;
+  //std::pair<Point_etiquette_map::iterator,bool> res = std::make_pair(L_i.begin(),false);
+  Point_d* p;
+  CGAL::Random rand;
+  for (int i = 0; i < nbL; i++)
+    {
+      //      while (!res.second)
+      //  {
+      do chosen_landmark = rand.get_int(0,nbP);
+      while (std::find(landmarks_ind.begin(), landmarks_ind.end(), chosen_landmark) != landmarks_ind.end());
+      //rand++;
+      //std::cout << "Chose " << chosen_landmark << std::endl;
+      p = &W[chosen_landmark];
+      //L_i.emplace(chosen_landmark,i);
+      //  }
+      landmarks.push_back(*p);
+      landmarks_ind.push_back(chosen_landmark);
+      //std::cout << "Added landmark " << chosen_landmark << std::endl;
+    }
+ }
+
+
+void landmarks_to_witness_complex(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, FT alpha)
+{
+  //********************Preface: origin point
+  unsigned D = W[0].size();
+  std::vector<FT> orig_vector;
+  for (unsigned i = 0; i < D; i++)
+    orig_vector.push_back(0);
+  Point_d origin(orig_vector);
+  //Distance dist;
+  //dist.transformed_distance(0,1);
+  //******************** Constructing a WL matrix
+  int nbP = W.size();
+  int nbL = landmarks.size();
+  STraits traits(&(landmarks[0]));
+  Euclidean_distance ed;
+  std::vector< std::vector <int> > WL(nbP);
+  std::vector< std::vector< typename std::vector<int>::iterator > > ope_limits(nbP);
+  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
+         boost::counting_iterator<std::ptrdiff_t>(nbL),
+         typename Tree::Splitter(),
+         traits);
+
+  std::cout << "Enter (D+1) nearest landmarks\n";
+  //std::cout << "Size of the tree is " << L.size() << std::endl;
+  for (int i = 0; i < nbP; i++)
+    {
+      //std::cout << "Entered witness number " << i << std::endl;
+      Point_d& w = W[i];
+      std::queue< typename std::vector<int>::iterator > ope_queue; // queue of points at (1+epsilon) distance to current landmark
+      Neighbor_search search(L, w, FT(0), true, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks[0])));
+      Neighbor_search::iterator search_it = search.begin();
+      
+      //Incremental search and filling WL
+      while (WL[i].size() < D)
+        WL[i].push_back((search_it++)->first);
+      FT dtow = ed.transformed_distance(w, landmarks[WL[i][D-1]]);
+      while (search_it->second < dtow + alpha)
+        WL[i].push_back((search_it++)->first);
+
+      //Filling the (1+epsilon)-limits table
+      for (std::vector<int>::iterator wl_it = WL[i].begin(); wl_it != WL[i].end(); ++wl_it)
+        {
+          ope_queue.push(wl_it);
+          FT d_to_curr_l = ed.transformed_distance(w, landmarks[*wl_it]);
+          //std::cout << "d_to_curr_l=" << d_to_curr_l << std::endl;
+          //std::cout << "d_to_front+alpha=" << d_to_curr_l << std::endl;
+          while (d_to_curr_l > alpha + ed.transformed_distance(w, landmarks[*(ope_queue.front())]))
+            {
+              ope_limits[i].push_back(wl_it);
+              ope_queue.pop();
+            }
+        }
+      while (ope_queue.size() > 0)
+        {
+          ope_limits[i].push_back(WL[i].end());
+          ope_queue.pop();
+        }
+      //std::cout << "Safely constructed a point\n";
+      ////Search D+1 nearest neighbours from the tree of landmarks L
+      /*
+      if (w[0]>0.95)
+        std::cout << i << std::endl;
+      */
+      //K_neighbor_search search(L, w, D, FT(0), true,
+      //                         CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks[0])) );
+      //std::cout << "Safely found nearest landmarks\n";
+      /* 
+      for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it)
+        {
+          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
+          //Point_etiquette_map::iterator itm = L_i.find(it->first);
+          //assert(itm != L_i.end());
+          //std::cout << "Entered KNN_it with point at distance " << it->second << "\n";
+          WL[i].push_back(it->first);
+          //std::cout << "ITFIRST " << it->first << std::endl;
+          //std::cout << i << " " << it->first << ": " << it->second << std::endl; 
+        }
+      */
+    }
+  //std::cout << "\n";
+  
+  //std::string out_file = "wl_result";
+  write_wl("wl_result",WL);
+  write_rl("rl_result",ope_limits);
+  
+  //******************** Constructng a witness complex
+  std::cout << "Entered witness complex construction\n";
+  Witness_complex<> witnessComplex;
+  witnessComplex.setNbL(nbL);
+  witnessComplex.relaxed_witness_complex(WL, ope_limits);
+  char buffer[100];
+  int i = sprintf(buffer,"stree_result.txt");
+  
+  if (i >= 0)
+    {
+      std::string out_file = (std::string)buffer;
+      std::ofstream ofs (out_file, std::ofstream::out);
+      witnessComplex.st_to_file(ofs);
+      ofs.close();
+    }
+  write_edges("landmarks/edges", witnessComplex, landmarks);
+  std::cout << Distance().transformed_distance(Point_d(std::vector<double>({0.1,0.1})), Point_d(std::vector<double>({1.9,1.9}))) << std::endl;
+}
+
+
+int main (int argc, char * const argv[])
+{
+  
+  if (argc != 5)
+    {
+      std::cerr << "Usage: " << argv[0]
+                << " nbP nbL dim alpha\n";
+      return 0;
+    }
+  /*
+  boost::filesystem::path p;
+  for (; argc > 2; --argc, ++argv)
+    p /= argv[1];
+  */
+  
+  int nbP       = atoi(argv[1]);
+  int nbL       = atoi(argv[2]);
+  int dim       = atoi(argv[3]);
+  double alpha  = atof(argv[4]);
+  //clock_t start, end;
+  //Construct the Simplex Tree
+  Witness_complex<> witnessComplex;
+ 
+  std::cout << "Let the carnage begin!\n";
+  Point_Vector point_vector;
+  //read_points_cust(file_name, point_vector);
+  generate_points_sphere(point_vector, nbP, dim);
+  /*
+  for (auto &p: point_vector)
+    {
+      assert(std::count(point_vector.begin(),point_vector.end(),p) == 1);
+    }
+  */
+  //std::cout << "Successfully read the points\n";
+  //witnessComplex.setNbL(nbL);
+  Point_Vector L;
+  std::vector<int> chosen_landmarks;
+  landmark_choice(point_vector, nbP, nbL, L, chosen_landmarks);
+  //start = clock();
+  
+  write_points("landmarks/initial_pointset",point_vector);
+  write_points("landmarks/initial_landmarks",L);
+  
+  landmarks_to_witness_complex(point_vector, L, chosen_landmarks, alpha);
+  //end = clock();
+  
+  /*
+  std::cout << "Landmark choice took "
+            << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
+  start = clock();
+  witnessComplex.witness_complex(WL);
+  //
+  end = clock();
+  std::cout << "Howdy world! The process took "
+       << (double)(end-start)/CLOCKS_PER_SEC << " s. \n";
+  */
+  
+  /*
+  out_file = "output/"+file_name+"_"+argv[2]+".stree";
+  std::ofstream ofs (out_file, std::ofstream::out);
+  witnessComplex.st_to_file(ofs);
+  ofs.close();
+
+  out_file = "output/"+file_name+"_"+argv[2]+".badlinks";
+  std::ofstream ofs2(out_file, std::ofstream::out);
+  witnessComplex.write_bad_links(ofs2);
+  ofs2.close();
+  */
+}
diff --git a/src/Witness_complex/example/relaxed_witness_persistence.cpp b/src/Witness_complex/example/relaxed_witness_persistence.cpp
index b8e4866f..b4837594 100644
--- a/src/Witness_complex/example/relaxed_witness_persistence.cpp
+++ b/src/Witness_complex/example/relaxed_witness_persistence.cpp
@@ -4,7 +4,7 @@
  *
  *    Author(s):       Siargey Kachanovich
  *
- *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (France)
+ *    Copyright (C) 2016  INRIA Sophia Antipolis-Méditerranée (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
@@ -22,9 +22,11 @@
 
 #include <gudhi/Simplex_tree.h>
 #include <gudhi/Relaxed_witness_complex.h>
+#include <gudhi/Dim_lists.h>
 #include <gudhi/reader_utils.h>
 #include <gudhi/Persistent_cohomology.h>
 #include "Landmark_choice_random_knn.h"
+#include "Landmark_choice_sparsification.h"
 
 #include <iostream>
 #include <fstream>
@@ -34,6 +36,7 @@
 #include <set>
 #include <queue>
 #include <iterator>
+#include <string>
 
 #include <boost/tuple/tuple.hpp>
 #include <boost/iterator/zip_iterator.hpp>
@@ -49,6 +52,7 @@ using namespace Gudhi::persistent_cohomology;
 
 typedef std::vector<Point_d> Point_Vector;
 typedef Relaxed_witness_complex< Simplex_tree<> > RelaxedWitnessComplex;
+typedef Simplex_tree<>::Simplex_handle Simplex_handle;
 
 /**
  * \brief Customized version of read_points
@@ -81,7 +85,7 @@ void output_experiment_information(char * const file_name)
     std::cout << "Enter a valid experiment number. Usage: "
               << file_name << " exp_no options\n";
     std::cout << "Experiment description:\n"
-              << "0 nbP nbL dim alpha limD: "
+              << "0 nbP nbL dim alpha limD mu_epsilon: "
               << "Build persistence diagram on relaxed witness complex "
               << "built from a point cloud on (dim-1)-dimensional sphere "
               << "consisting of nbP witnesses and nbL landmarks. "
@@ -93,7 +97,7 @@ void output_experiment_information(char * const file_name)
               << "The maximal relaxation is alpha and the limit on simplicial complex dimension is limD\n";
 }
 
-void rw_experiment(Point_Vector & point_vector, int nbL, FT alpha, int limD)
+void rw_experiment(Point_Vector & point_vector, int nbL, FT alpha, int limD, FT mu_epsilon = 0.1)
 {
   clock_t start, end;
   Simplex_tree<> simplex_tree;
@@ -102,81 +106,60 @@ void rw_experiment(Point_Vector & point_vector, int nbL, FT alpha, int limD)
   std::vector<std::vector< int > > knn;
   std::vector<std::vector< FT > > distances;
   start = clock();
-  Gudhi::witness_complex::landmark_choice_by_random_knn(point_vector, nbL, alpha, limD, knn, distances);
+  //Gudhi::witness_complex::landmark_choice_by_random_knn(point_vector, nbL, alpha, limD, knn, distances);
+  std::vector<Point_d> landmarks;
+  Gudhi::witness_complex::landmark_choice_by_sparsification(point_vector, nbL, mu_epsilon, landmarks);
+  Gudhi::witness_complex::build_distance_matrix(point_vector,   // aka witnesses
+                                                landmarks,  // aka landmarks
+                                                alpha,
+                                                limD,
+                                                knn,
+                                                distances);
   end = clock();
   double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
   std::cout << "Choice of " << nbL << " landmarks took "
             << time << " s. \n";
   // Compute witness complex
   start = clock();
-  RelaxedWitnessComplex(distances,
-                        knn,
-                        simplex_tree,
-                        nbL,
-                        alpha,
-                        limD);
+  RelaxedWitnessComplex rw(distances,
+                           knn,
+                           simplex_tree,
+                           nbL,
+                           alpha,
+                           limD);
   end = clock();
   time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
-  std::cout << "Witness complex for " << nbL << " landmarks took "
+  std::cout << "Relaxed witness complex for " << nbL << " landmarks took "
             << time << " s. \n";
   std::cout << "The complex contains " << simplex_tree.num_simplices() << " simplices \n";
   // std::cout << simplex_tree << "\n";
   
   // Compute the persistence diagram of the complex
-  persistent_cohomology::Persistent_cohomology< Simplex_tree<>, Field_Zp > pcoh(simplex_tree, false);
+  simplex_tree.set_dimension(limD);
+  persistent_cohomology::Persistent_cohomology< Simplex_tree<>, Field_Zp > pcoh(simplex_tree, true);
   int p = 3;
   pcoh.init_coefficients( p ); //initilizes the coefficient field for homology
   start = clock();
-  pcoh.compute_persistent_cohomology( alpha/5 );
+  pcoh.compute_persistent_cohomology( alpha/1000 );
   end = clock();
   time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
   std::cout << "Persistence diagram took "
             << time << " s. \n";
   pcoh.output_diagram();
-}
-
-void rips_experiment(Point_Vector & points, double threshold, int dim_max)
-{
-  typedef std::vector<double> Point_t;
-  typedef Simplex_tree<Simplex_tree_options_fast_persistence> ST;
-  clock_t start, end;
-  ST st;
-
-  // Compute the proximity graph of the points
-  start = clock();
-  Graph_t prox_graph = compute_proximity_graph(points, threshold
-                                               , euclidean_distance<Point_t>);
-  // Construct the Rips complex in a Simplex Tree
-  // insert the proximity graph in the simplex tree
-  st.insert_graph(prox_graph);
-  // expand the graph until dimension dim_max
-  st.expansion(dim_max);
-  end = clock();
-  
-  double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
-  std::cout << "Rips complex took "
-            << time << " s. \n";
-  std::cout << "The complex contains " << st.num_simplices() << " simplices \n";
-  //std::cout << "   and has dimension " << st.dimension() << " \n";
 
-  // Sort the simplices in the order of the filtration
-  st.initialize_filtration();
+  int chi = 0;
+  for (auto sh: simplex_tree.complex_simplex_range())
+    chi += 1-2*(simplex_tree.dimension(sh)%2);
+  std::cout << "Euler characteristic is " << chi << std::endl;
 
-  // Compute the persistence diagram of the complex
-  persistent_cohomology::Persistent_cohomology<ST, Field_Zp > pcoh(st);
-  // initializes the coefficient field for homology
-  int p = 3;
-  double min_persistence = threshold/5;
-  pcoh.init_coefficients(p);
-  pcoh.compute_persistent_cohomology(min_persistence);
-  pcoh.output_diagram();
 }
 
+
 int experiment0 (int argc, char * const argv[])
 {
-  if (argc != 7) {
+  if (argc != 8) {
     std::cerr << "Usage: " << argv[0]
-              << " 0 nbP nbL dim alpha limD\n";
+              << " 0 nbP nbL dim alpha limD mu_epsilon\n";
     return 0;
   }
   /*
@@ -190,6 +173,7 @@ int experiment0 (int argc, char * const argv[])
   int dim       = atoi(argv[4]);
   double alpha  = atof(argv[5]);
   int limD      = atoi(argv[6]);
+  double mu_epsilon = atof(argv[7]);
 
   // Read the point file
   Point_Vector point_vector;
@@ -244,25 +228,25 @@ int experiment1 (int argc, char * const argv[])
       ok = true; break;
     }
   }
-  ok = false;
-  while (!ok) {
-    std::cout << "Rips complex: parameters threshold, limD.\n";
-    std::cout << "Enter threshold: ";
-    std::cin >> alpha;
-    std::cout << "Enter limD: ";
-    std::cin >> limD;
-    std::cout << "Start Rips complex...\n";
-    rips_experiment(point_vector, alpha, limD);
-    std::cout << "Is the result correct? [y/n]: ";
-    char answer;
-    std::cin >> answer;
-    switch (answer) {
-    case 'n':
-      ok = false; break;
-    default :
-      ok = true; break;
-    }
-  }
+  // ok = false;
+  // while (!ok) {
+  //   std::cout << "Rips complex: parameters threshold, limD.\n";
+  //   std::cout << "Enter threshold: ";
+  //   std::cin >> alpha;
+  //   std::cout << "Enter limD: ";
+  //   std::cin >> limD;
+  //   std::cout << "Start Rips complex...\n";
+  //   rips_experiment(point_vector, alpha, limD);
+  //   std::cout << "Is the result correct? [y/n]: ";
+  //   char answer;
+  //   std::cin >> answer;
+  //   switch (answer) {
+  //   case 'n':
+  //     ok = false; break;
+  //   default :
+  //     ok = true; break;
+  //   }
+  // }
 }
 
 int main (int argc, char * const argv[])
diff --git a/src/Witness_complex/example/strange_sphere.cpp b/src/Witness_complex/example/strange_sphere.cpp
new file mode 100644
index 00000000..9188bd8e
--- /dev/null
+++ b/src/Witness_complex/example/strange_sphere.cpp
@@ -0,0 +1,219 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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/>.
+ */
+#define BOOST_PARAMETER_MAX_ARITY 12
+
+
+#include <sys/types.h>
+#include <sys/stat.h>
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Strange_witness_complex.h>
+#include <gudhi/Landmark_choice_by_random_point.h>
+#include <gudhi/reader_utils.h>
+#include "output.h"
+
+#include <iostream>
+#include <fstream>
+#include <ctime>
+#include <utility>
+#include <string>
+#include <vector>
+
+#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_incremental_neighbor_search.h>
+#include <CGAL/Kd_tree.h>
+#include <CGAL/Euclidean_distance.h>
+
+#include <CGAL/Kernel_d/Vector_d.h>
+#include <CGAL/point_generators_d.h>
+#include <CGAL/constructions_d.h>
+#include <CGAL/Fuzzy_sphere.h>
+#include <CGAL/Random.h>
+
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+
+#include "generators.h"
+
+using namespace Gudhi;
+using namespace Gudhi::witness_complex;
+
+typedef std::vector< Vertex_handle > typeVectorVertex;
+typedef Strange_witness_complex< Simplex_tree<> > WitnessComplex;
+
+typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
+typedef K::FT FT;
+typedef K::Point_d Point_d;
+typedef CGAL::Search_traits<
+  FT, Point_d,
+  typename K::Cartesian_const_iterator_d,
+  typename K::Construct_cartesian_const_iterator_d> Traits_base;
+typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance;
+
+typedef CGAL::Search_traits_adapter<
+  std::ptrdiff_t, Point_d*, Traits_base> STraits;
+typedef CGAL::Orthogonal_incremental_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> Neighbor_search;
+typedef Neighbor_search::Tree Tree;
+typedef Neighbor_search::Distance Distance;
+typedef Neighbor_search::iterator KNS_iterator;
+typedef Neighbor_search::iterator KNS_range;
+typedef boost::container::flat_map<int, int> Point_etiquette_map;
+typedef CGAL::Kd_tree<STraits> Tree2;
+typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere;
+typedef std::vector<Point_d> Point_Vector;
+
+/** Function that chooses landmarks from W and place it in the kd-tree L.
+ *  Note: nbL hould be removed if the code moves to Witness_complex
+ */
+void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind)
+{
+  std::cout << "Enter landmark choice to kd tree\n";
+  //std::vector<Point_d> landmarks;
+  int chosen_landmark;
+  //std::pair<Point_etiquette_map::iterator,bool> res = std::make_pair(L_i.begin(),false);
+  Point_d* p;
+  CGAL::Random rand;
+  for (int i = 0; i < nbL; i++)
+    {
+      //      while (!res.second)
+      //  {
+      do chosen_landmark = rand.get_int(0,nbP);
+      while (std::find(landmarks_ind.begin(), landmarks_ind.end(), chosen_landmark) != landmarks_ind.end());
+      //rand++;
+      //std::cout << "Chose " << chosen_landmark << std::endl;
+      p = &W[chosen_landmark];
+      //L_i.emplace(chosen_landmark,i);
+      //  }
+      landmarks.push_back(*p);
+      landmarks_ind.push_back(chosen_landmark);
+      //std::cout << "Added landmark " << chosen_landmark << std::endl;
+    }
+ }
+
+void landmarks_to_witness_complex(Point_Vector &W, int nbL)
+{
+  //********************Preface: origin point
+  unsigned D = W[0].size();
+  std::vector<FT> orig_vector;
+  for (unsigned i = 0; i < D; i++)
+    orig_vector.push_back(0);
+  Point_d origin(orig_vector);
+  //Distance dist;
+  //dist.transformed_distance(0,1);
+  //******************** Constructing a WL matrix
+  int nbP = W.size();
+  Point_Vector landmarks;
+  std::vector<int> landmarks_ind;
+  landmark_choice(W, nbP, nbL, landmarks, landmarks_ind);
+  
+  
+  STraits traits(&(landmarks[0]));
+  Euclidean_distance ed;
+  std::vector< std::vector <int> > WL(nbP);
+  std::vector< std::vector< typename std::vector<int>::iterator > > ope_limits(nbP);
+  Tree L(boost::counting_iterator<std::ptrdiff_t>(0),
+         boost::counting_iterator<std::ptrdiff_t>(nbL),
+         typename Tree::Splitter(),
+         traits);
+
+  std::cout << "Enter (D+1) nearest landmarks\n";
+  //std::cout << "Size of the tree is " << L.size() << std::endl;
+  for (int i = 0; i < nbP; i++) {
+    //std::cout << "Entered witness number " << i << std::endl;
+    Point_d& w = W[i];
+    std::queue< typename std::vector<int>::iterator > ope_queue; // queue of points at (1+epsilon) distance to current landmark
+    Neighbor_search search(L, w, FT(0), true, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks[0])));
+    Neighbor_search::iterator search_it = search.begin();
+      
+    //Incremental search and filling WL
+    while (WL[i].size() < D)
+      WL[i].push_back((search_it++)->first);
+  }
+  write_wl("WL.txt", WL); //!
+  //******************** Constructng a witness complex
+  std::cout << "Entered witness complex construction\n";
+
+  Simplex_tree<> simplex_tree;
+  WitnessComplex(WL, simplex_tree, nbL, W[0].size()-1);
+  //std::cout << simplex_tree << "\n"; //!
+  write_witness_mesh(W, landmarks_ind, simplex_tree, false, true);
+}
+
+
+
+/** Write a gnuplot readable file.
+ *  Data range is a random access range of pairs (arg, value)
+ */
+template < typename Data_range >
+void write_data(Data_range & data, std::string filename) {
+  std::ofstream ofs(filename, std::ofstream::out);
+  for (auto entry : data)
+    ofs << entry.first << ", " << entry.second << "\n";
+  ofs.close();
+}
+
+
+
+int main(int argc, char * const argv[]) {
+  if (argc != 4) {
+    std::cerr << "Usage: " << argv[0]
+        << " nbP nbL dim\n";
+    return 0;
+  }
+
+  int nbP = atoi(argv[1]);
+  int nbL = atoi(argv[2]);
+  int dim = atoi(argv[3]);
+  clock_t start, end;
+
+  // Construct the Simplex Tree
+  Simplex_tree<> simplex_tree;
+
+  std::vector< std::pair<int, double> > l_time;
+
+  // Read the point file
+  Point_Vector point_vector;
+  generate_points_sphere(point_vector, nbP, dim);
+  std::cout << "Successfully generated " << point_vector.size() << " points.\n";
+  std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n";
+
+  // Choose landmarks
+  start = clock();
+  std::vector<std::vector< int > > knn;
+  
+  landmarks_to_witness_complex(point_vector, nbL);
+
+  end = clock();
+  double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
+  std::cout << "Witness complex for " << nbL << " landmarks took "
+            << time << " s. \n";
+  l_time.push_back(std::make_pair(nbP, time));
+  //write_data(l_time, "w_time.dat");
+}
diff --git a/src/Witness_complex/include/gudhi/A0_complex.h b/src/Witness_complex/include/gudhi/A0_complex.h
new file mode 100644
index 00000000..2018e1c8
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/A0_complex.h
@@ -0,0 +1,337 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 A0_COMPLEX_H_
+#define A0_COMPLEX_H_
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <algorithm>
+#include <utility>
+#include "gudhi/reader_utils.h"
+#include "gudhi/distance_functions.h"
+#include "gudhi/Simplex_tree.h"
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <math.h>
+#include <ctime>
+#include <iostream>
+
+// Needed for nearest neighbours
+#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_k_neighbor_search.h>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  /** \addtogroup simplex_tree
+   *  Witness complex is a simplicial complex defined on two sets of points in \f$\mathbf{R}^D\f$:
+   *  \f$W\f$ set of witnesses and \f$L \subseteq W\f$ set of landmarks. The simplices are based on points in \f$L\f$
+   *  and a simplex belongs to the witness complex if and only if it is witnessed (there exists a point \f$w \in W\f$ such that
+   *  w is closer to the vertices of this simplex than others) and all of its faces are witnessed as well. 
+   */
+template< class Simplicial_complex >
+class A0_complex {
+
+private:    
+  struct Active_witness {
+    int witness_id;
+    int landmark_id;
+    
+    Active_witness(int witness_id_, int landmark_id_)
+      : witness_id(witness_id_),
+        landmark_id(landmark_id_) { }
+    };
+
+private:
+  typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
+  typedef typename Simplicial_complex::Vertex_handle Vertex_handle;
+  typedef typename Simplicial_complex::Filtration_value FT;
+
+  typedef std::vector< double > Point_t;
+  typedef std::vector< Point_t > Point_Vector;
+
+  // typedef typename Simplicial_complex::Filtration_value Filtration_value;
+  typedef std::vector< Vertex_handle > typeVectorVertex;
+  typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
+  typedef std::pair< Simplex_handle, bool > typePairSimplexBool;
+
+  typedef int Witness_id;
+  typedef int Landmark_id;
+  typedef std::list< Vertex_handle > ActiveWitnessList;
+
+ private:
+  int nbL;  // Number of landmarks
+  Simplicial_complex& sc;  // Simplicial complex
+  
+  public:
+    /** @name Constructor
+     */
+
+    //@{
+  
+    /**
+     *  \brief Iterative construction of the relaxed witness complex.
+     *  \details The witness complex is written in sc_ basing on a matrix knn
+     *  of k nearest neighbours of the form {witnesses}x{landmarks} and 
+     *  and a matrix distances of distances to these landmarks from witnesses.
+     *  The parameter alpha defines relaxation and
+     *  limD defines the 
+     *
+     *  The line lengths in one given matrix can differ, 
+     *  however both matrices have the same corresponding line lengths.
+     *
+     *  The type KNearestNeighbors can be seen as 
+     *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+     *  Witness_range and Closest_landmark_range are random access ranges.
+     *
+     *  Constructor takes into account at most (dim+1) 
+     *  first landmarks from each landmark range to construct simplices.
+     *
+     *  Landmarks are supposed to be in [0,nbL_-1]
+     */
+    
+    template< typename KNearestNeighbours >
+    A0_complex(std::vector< std::vector<double> > const & distances,
+                            KNearestNeighbours const & knn,
+                            Simplicial_complex & sc_, 
+                            int nbL_,
+                            double alpha2,
+                            unsigned limD) : nbL(nbL_), sc(sc_) {
+      int nbW = knn.size();
+      typeVectorVertex vv;
+      //int counter = 0;
+      /* The list of still useful witnesses
+       * it will diminuish in the course of iterations
+       */
+      ActiveWitnessList active_w;// = new ActiveWitnessList();
+      for (int i = 0; i != nbL; ++i) {
+        // initial fill of 0-dimensional simplices
+        // by doing it we don't assume that landmarks are necessarily witnesses themselves anymore
+        //counter++;
+        vv = {i};
+        sc.insert_simplex(vv, Filtration_value(0.0));
+        /* TODO Error if not inserted : normally no need here though*/
+      }
+      for (int i=0; i != nbW; ++i) {
+        // int i_end = limD+1;
+        // if (knn[i].size() < limD+1)
+        //   i_end = knn[i].size();
+        // double dist_wL = *(distances[i].begin());
+        // while (distances[i][i_end] > dist_wL + alpha2)
+        //   i_end--;
+        // add_all_witnessed_faces(distances[i].begin(),
+        //                         knn[i].begin(),
+        //                         knn[i].begin() + i_end + 1);
+        unsigned j_end = 0;
+        while (j_end < distances[i].size() && j_end <= limD && distances[i][j_end] <= distances[i][0] + alpha2) {
+          std::vector<int> simplex;
+          for (unsigned j = 0; j <= j_end; ++j)
+            simplex.push_back(knn[i][j]);
+          assert(distances[i][j_end] - distances[i][0] >= 0);
+          sc.insert_simplex_and_subfaces(simplex, distances[i][j_end] - distances[i][0]);
+          j_end++; 
+        }
+      }
+      sc.set_dimension(limD);
+    }
+
+  //@}
+  
+private:
+  /* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness
+   * Iterator is needed to know until how far we can take landmarks to form simplexes
+   * simplex is the prefix of the simplexes to insert
+   * The output value indicates if the witness rests active or not
+   */
+  void add_all_witnessed_faces(std::vector<double>::const_iterator curr_d,
+                               std::vector<int>::const_iterator curr_l,
+                               std::vector<int>::const_iterator end)
+  {
+    std::vector<int> simplex;
+    std::vector<int>::const_iterator l_end = curr_l;
+    for (; l_end != end; ++l_end) {
+      std::vector<int>::const_iterator l_it = curr_l;
+      std::vector<double>::const_iterator d_it = curr_d;
+      simplex = {};
+      for (; l_it != l_end; ++l_it, ++d_it)
+        simplex.push_back(*l_it);
+      sc.insert_simplex_and_subfaces(simplex, *(d_it--) - *curr_d);
+    }
+  }
+  
+  /** \brief Check if the facets of the k-dimensional simplex witnessed 
+   *  by witness witness_id are already in the complex.
+   *  inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
+   */
+  bool all_faces_in(std::vector<int>& simplex, double* filtration_value)
+  {
+    std::vector< int > facet;
+    for (std::vector<int>::iterator not_it = simplex.begin(); not_it != simplex.end(); ++not_it)
+      {
+        facet.clear();
+        for (std::vector<int>::iterator it = simplex.begin(); it != simplex.end(); ++it)
+          if (it != not_it)
+            facet.push_back(*it);
+        Simplex_handle facet_sh = sc.find(facet);
+        if (facet_sh == sc.null_simplex())
+          return false;
+        else if (sc.filtration(facet_sh) > *filtration_value)
+          *filtration_value = sc.filtration(facet_sh);
+      }
+    return true;
+  }
+
+  bool is_face(Simplex_handle face, Simplex_handle coface)
+  {
+    // vertex range is sorted in decreasing order
+    auto fvr = sc.simplex_vertex_range(face);
+    auto cfvr = sc.simplex_vertex_range(coface);
+    auto fv_it = fvr.begin();
+    auto cfv_it = cfvr.begin();
+    while (fv_it != fvr.end() && cfv_it != cfvr.end()) {
+      if (*fv_it < *cfv_it)
+        ++cfv_it;
+      else if (*fv_it == *cfv_it) {
+        ++cfv_it;
+        ++fv_it;
+      }
+      else
+        return false;
+      
+    }
+    return (fv_it == fvr.end());
+  }
+
+  // void erase_simplex(Simplex_handle sh)
+  // {
+  //   auto siblings = sc.self_siblings(sh);
+  //   auto oncles = siblings->oncles();
+  //   int prev_vertex = siblings->parent();
+  //   siblings->members().erase(sh->first);
+  //   if (siblings->members().empty()) {
+  //     typename typedef Simplicial_complex::Siblings Siblings;
+  //     oncles->members().find(prev_vertex)->second.assign_children(new Siblings(oncles, prev_vertex));
+  //     assert(!sc.has_children(oncles->members().find(prev_vertex)));
+  //     //delete siblings;
+  //   }
+
+  // }
+  
+  void elementary_collapse(Simplex_handle face_sh, Simplex_handle coface_sh)
+  {
+    erase_simplex(coface_sh);
+    erase_simplex(face_sh);
+  }
+
+public:
+  // void collapse(std::vector<Simplex_handle>& simplices)
+  // {
+  //   // Get a vector of simplex handles ordered by filtration value
+  //   std::cout << sc << std::endl;
+  //   //std::vector<Simplex_handle> simplices;
+  //   for (Simplex_handle sh: sc.filtration_simplex_range())
+  //     simplices.push_back(sh);
+  //   // std::sort(simplices.begin(),
+  //   //           simplices.end(),
+  //   //           [&](Simplex_handle sh1, Simplex_handle sh2)
+  //   //           { double f1 = sc.filtration(sh1), f2 = sc.filtration(sh2);
+  //   //             return (f1 > f2) || (f1 >= f2 && sc.dimension(sh1) > sc.dimension(sh2)); });
+  //   // Double iteration
+  //   auto face_it = simplices.rbegin();
+  //   while (face_it != simplices.rend() && sc.filtration(*face_it) != 0) {
+  //     int coface_count = 0;
+  //     auto reduced_coface = simplices.rbegin();
+  //     for (auto coface_it = simplices.rbegin(); coface_it != simplices.rend() && sc.filtration(*coface_it) != 0; ++coface_it)
+  //       if (face_it != coface_it && is_face(*face_it, *coface_it)) {
+  //         coface_count++;
+  //         if (coface_count == 1)
+  //           reduced_coface = coface_it;
+  //         else
+  //           break;
+  //       }
+  //     if (coface_count == 1) {
+  //       std::cout << "Erase ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--reduced_coface.base())))
+  //         std::cout << v << " ";
+        
+  //       simplices.erase(--(reduced_coface.base()));
+  //       //elementary_collapse(*face_it, *reduced_coface);
+  //       std::cout << ") and then ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--face_it.base())))
+  //         std::cout << v << " ";
+  //       std::cout << ")\n";
+  //       simplices.erase(--((face_it++).base()));
+  //       //face_it = simplices.rbegin();
+  //       //std::cout << "Size of vector: " << simplices.size() << "\n";
+  //     } 
+  //     else
+  //       face_it++;
+  //   }
+  //   sc.initialize_filtration();
+  //   //std::cout << sc << std::endl;
+  // }
+
+  template <class Dim_lists>
+  void collapse(Dim_lists& dim_lists)
+  {
+    dim_lists.collapse();
+  }
+  
+private:
+  
+  /** Collapse recursively boundary faces of the given simplex
+   *  if its filtration is bigger than alpha_lim.  
+   */
+  void rec_boundary_collapse(Simplex_handle sh, FT alpha_lim)
+  {
+    for (Simplex_handle face_it : sc.boundary_simplex_range()) {
+      
+    }
+      
+  }
+  
+}; //class Relaxed_witness_complex
+
+} // namespace witness_complex
+  
+} // namespace Gudhi
+
+#endif
diff --git a/src/Witness_complex/include/gudhi/Dim_list_iterator.h b/src/Witness_complex/include/gudhi/Dim_list_iterator.h
new file mode 100644
index 00000000..3f23e8c9
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Dim_list_iterator.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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 DIM_LISTS_ITERATOR_H_
+#define DIM_LISTS_ITERATOR_H_
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <algorithm>
+#include <utility>
+#include "gudhi/reader_utils.h"
+#include "gudhi/distance_functions.h"
+#include "gudhi/Simplex_tree.h"
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <math.h>
+#include <ctime>
+#include <iostream>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  /** \addtogroup simplex_tree
+   *  Witness complex is a simplicial complex defined on two sets of points in \f$\mathbf{R}^D\f$:
+   *  \f$W\f$ set of witnesses and \f$L \subseteq W\f$ set of landmarks. The simplices are based on points in \f$L\f$
+   *  and a simplex belongs to the witness complex if and only if it is witnessed (there exists a point \f$w \in W\f$ such that
+   *  w is closer to the vertices of this simplex than others) and all of its faces are witnessed as well. 
+   */
+template< class Simplex_handle >
+class Dim_lists_iterator {
+
+private:
+
+  typedef typename std::list<Simplex_handle>::iterator List_iterator;
+  typedef typename std::vector<std::list<Simplex_handle>>::reverse_iterator Vector_iterator;
+  typedef typename Gudhi::witness_complex::Dim_lists_iterator<Simplex_handle> Iterator;
+  
+  
+  List_iterator sh_;
+  Vector_iterator curr_list_;
+  typename std::vector<std::list<Simplex_handle>>& table_;
+
+public:
+
+  Dim_lists_iterator(List_iterator sh,
+                     Vector_iterator curr_list,
+                     typename std::vector<std::list<Simplex_handle>>& table)
+    : sh_(sh), curr_list_(curr_list), table_(table)
+  {
+  }
+
+  Simplex_handle operator*()
+  {
+    return *sh_;
+  }
+  
+  Iterator operator++()
+  {
+    increment();
+    return (*this);
+  }
+
+  Iterator operator++(int)
+  {
+    Iterator prev_it(sh_, curr_list_, table_);
+    increment();
+    return prev_it;
+  }
+
+  Iterator dim_begin()
+  {
+    return Iterator(curr_list_->begin(), curr_list_, table_);
+  }  
+
+  Iterator dim_end()
+  {
+    return Iterator(curr_list_->end(), curr_list_, table_);
+  }
+  
+  Iterator dimp1_begin()
+  {
+    return Iterator((curr_list_-1)->begin(), curr_list_-1, table_); 
+  }
+
+  Iterator dimp1_end()
+  {
+    return Iterator((curr_list_-1)->end(), curr_list_-1, table_); 
+  }
+  
+  bool operator==(const Iterator& it2) const
+  {
+    return (sh_ == it2.sh_);
+  }
+
+  bool operator!=(const Iterator& it2) const
+  {
+    return (sh_ != it2.sh_);
+  }
+
+  void remove_incr()
+  {
+    
+  }
+  
+private:
+  
+  void increment()
+  {
+    if (++sh_ == curr_list_->end())
+      if (++curr_list_ != table_.rend())
+        sh_ = curr_list_->begin();
+    // The iterator of the end of the table is the end of the last list
+  }
+
+  
+}; //class Dim_lists_iterator
+
+} // namespace witness_complex
+  
+} // namespace Gudhi
+
+#endif
diff --git a/src/Witness_complex/include/gudhi/Dim_lists.h b/src/Witness_complex/include/gudhi/Dim_lists.h
new file mode 100644
index 00000000..1d1b03c3
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Dim_lists.h
@@ -0,0 +1,195 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 DIM_LISTS_H_
+#define DIM_LISTS_H_
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <algorithm>
+#include <utility>
+#include "gudhi/reader_utils.h"
+#include "gudhi/distance_functions.h"
+#include <gudhi/Dim_list_iterator.h>
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <math.h>
+#include <ctime>
+#include <iostream>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  /** \addtogroup simplex_tree
+   *  Witness complex is a simplicial complex defined on two sets of points in \f$\mathbf{R}^D\f$:
+   *  \f$W\f$ set of witnesses and \f$L \subseteq W\f$ set of landmarks. The simplices are based on points in \f$L\f$
+   *  and a simplex belongs to the witness complex if and only if it is witnessed (there exists a point \f$w \in W\f$ such that
+   *  w is closer to the vertices of this simplex than others) and all of its faces are witnessed as well. 
+   */
+template< class Simplicial_complex >
+class Dim_lists {
+
+private:
+
+  typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
+  typedef typename Gudhi::witness_complex::Dim_lists_iterator<Simplex_handle> Iterator;
+  
+  std::vector<std::list<Simplex_handle>> table_;
+  Simplicial_complex& sc_;
+
+public:
+
+  Dim_lists(Simplicial_complex & sc, int dim, double alpha_max = 100)
+    : sc_(sc)
+  {
+    table_ = std::vector<std::list<Simplex_handle>>(dim+1);
+    for (auto sh: sc.filtration_simplex_range()) {
+      if (sc_.filtration(sh) < alpha_max)
+        table_[sc.dimension(sh)].push_front(sh);
+    }
+    auto t_it = table_.rbegin();
+    while (t_it->empty()) {
+      t_it++;
+      table_.pop_back();
+    }
+  }
+
+  Iterator begin()
+  {
+    return Iterator(table_.rbegin()->begin(), table_.rbegin(), table_);
+  }
+
+  Iterator end()
+  {
+    return Iterator(table_[0].end(), table_.rend(), table_);
+  }
+  
+  unsigned size()
+  {
+    unsigned curr_size = 0;
+    for (auto l: table_)
+      curr_size += l.size();
+    return curr_size;
+  }
+  
+  bool is_face(Simplex_handle face, Simplex_handle coface)
+  {
+    // vertex range is sorted in decreasing order
+    auto fvr = sc_.simplex_vertex_range(face);
+    auto cfvr = sc_.simplex_vertex_range(coface);
+    auto fv_it = fvr.begin();
+    auto cfv_it = cfvr.begin();
+    while (fv_it != fvr.end() && cfv_it != cfvr.end()) {
+      if (*fv_it < *cfv_it)
+        ++cfv_it;
+      else if (*fv_it == *cfv_it) {
+        ++cfv_it;
+        ++fv_it;
+      }
+      else
+        return false;
+      
+    }
+    return (fv_it == fvr.end());
+  }
+
+  void output_simplices() {
+    std::cout << "Size of vector: " << size() << std::endl;
+    for (auto line_it = table_.rbegin(); line_it != table_.rend(); ++line_it)
+      for (auto sh: *line_it) {
+        std::cout << sc_.dimension(sh) << " ";
+        for (auto v : sc_.simplex_vertex_range(sh))
+          std::cout << v << " ";
+        std::cout << sc_.filtration(sh) << "\n";
+      }
+  }
+  
+  void collapse()
+  {
+    auto coface_list_it = table_.rbegin();
+    auto face_list_it = table_.rbegin()+1;
+    for ( ;
+          face_list_it != table_.rend();
+          ++face_list_it) {
+      auto face_it = face_list_it->begin();
+      while (face_it != face_list_it->end() && sc_.filtration(*face_it) != 0) {
+        int coface_count = 0;
+        auto reduced_coface = coface_list_it->begin();
+        for (auto coface_it = coface_list_it->begin(); coface_it != coface_list_it->end() && sc_.filtration(*coface_it) != 0; ++coface_it)
+          if (is_face(*face_it, *coface_it)) {
+            coface_count++;
+            if (coface_count == 1)
+              reduced_coface = coface_it;
+            else
+              break;
+          }
+        if (coface_count == 1) {
+          /*
+          std::cout << "Erase ( ";
+          for (auto v: sc_.simplex_vertex_range(*reduced_coface))
+            std::cout << v << " ";        
+          */
+          coface_list_it->erase(reduced_coface);
+          /*
+          std::cout << ") and then ( ";
+          for (auto v: sc_.simplex_vertex_range(*face_it))
+            std::cout << v << " ";
+          std::cout << ")\n";
+          */
+          face_list_it->erase(face_it);
+          face_it = face_list_it->begin();
+        } 
+        else
+          face_it++;
+      }
+      if ((coface_list_it++)->empty())
+        table_.pop_back();
+    }
+  }
+  
+  bool is_pseudomanifold()
+  {
+
+    return true;
+  }
+  
+}; //class Dim_lists
+
+} // namespace witness_complex
+  
+} // namespace Gudhi
+
+#endif
diff --git a/src/Witness_complex/include/gudhi/Good_links.h b/src/Witness_complex/include/gudhi/Good_links.h
new file mode 100644
index 00000000..a011c032
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Good_links.h
@@ -0,0 +1,72 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 GOOD_LINKS_H_
+#define GOOD_LINKS_H_
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <algorithm>
+#include <utility>
+#include "gudhi/reader_utils.h"
+#include "gudhi/distance_functions.h"
+#include <gudhi/Dim_list_iterator.h>
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <math.h>
+#include <ctime>
+#include <iostream>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  /** \addtogroup simplex_tree
+   *  Witness complex is a simplicial complex defined on two sets of points in \f$\mathbf{R}^D\f$:
+   *  \f$W\f$ set of witnesses and \f$L \subseteq W\f$ set of landmarks. The simplices are based on points in \f$L\f$
+   *  and a simplex belongs to the witness complex if and only if it is witnessed (there exists a point \f$w \in W\f$ such that
+   *  w is closer to the vertices of this simplex than others) and all of its faces are witnessed as well. 
+   */
+template< class Simplicial_complex >
+bool good_links(Simplicial_complex& sc_)
+{
+
+}
+  
+} // namespace witness_complex
+  
+} // namespace Gudhi
+
+#endif
diff --git a/src/Witness_complex/include/gudhi/Relaxed_witness_complex.h b/src/Witness_complex/include/gudhi/Relaxed_witness_complex.h
index 04dc37d4..2971149a 100644
--- a/src/Witness_complex/include/gudhi/Relaxed_witness_complex.h
+++ b/src/Witness_complex/include/gudhi/Relaxed_witness_complex.h
@@ -83,6 +83,7 @@ private:
 private:
   typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
   typedef typename Simplicial_complex::Vertex_handle Vertex_handle;
+  typedef typename Simplicial_complex::Filtration_value FT;
 
   typedef std::vector< double > Point_t;
   typedef std::vector< Point_t > Point_Vector;
@@ -197,7 +198,7 @@ private:
     std::vector<int>::const_iterator l_it = curr_l;
     std::vector<double>::const_iterator d_it = curr_d;
     if (dim > 0)
-      for (; *d_it - alpha < norelax_dist && l_it != end; ++l_it, ++d_it) {
+      for (; *d_it - alpha <= norelax_dist && l_it != end; ++l_it, ++d_it) {
         simplex.push_back(*l_it);
         if (sc.find(simplex) != sc.null_simplex())
           will_be_active = add_all_faces_of_dimension(dim-1,
@@ -209,7 +210,7 @@ private:
                                                       end) || will_be_active;
         simplex.pop_back();
         // If norelax_dist is infinity, change to first omitted distance
-        if (*d_it < norelax_dist)
+        if (*d_it <= norelax_dist)
           norelax_dist = *d_it;
         will_be_active = add_all_faces_of_dimension(dim-1,
                                                     alpha,
@@ -220,17 +221,16 @@ private:
                                                     end) || will_be_active;
       } 
     else if (dim == 0)
-      for (; *d_it - alpha < norelax_dist && l_it != end; ++l_it, ++d_it) {
+      for (; *d_it - alpha <= norelax_dist && l_it != end; ++l_it, ++d_it) {
         simplex.push_back(*l_it);
         double filtration_value = 0;
         // if norelax_dist is infinite, relaxation is 0.
         if (*d_it > norelax_dist) 
           filtration_value = *d_it - norelax_dist; 
-        if (all_faces_in(simplex, &filtration_value)) 
-          {
-            will_be_active = true;
-            sc.insert_simplex(simplex, filtration_value);
-          }
+        if (all_faces_in(simplex, &filtration_value)) {
+          will_be_active = true;
+          sc.insert_simplex(simplex, filtration_value);
+        }
         simplex.pop_back();
         // If norelax_dist is infinity, change to first omitted distance
         if (*d_it < norelax_dist)
@@ -260,11 +260,120 @@ private:
       }
     return true;
   }
-    
-}; //class Witness_complex
+
+  bool is_face(Simplex_handle face, Simplex_handle coface)
+  {
+    // vertex range is sorted in decreasing order
+    auto fvr = sc.simplex_vertex_range(face);
+    auto cfvr = sc.simplex_vertex_range(coface);
+    auto fv_it = fvr.begin();
+    auto cfv_it = cfvr.begin();
+    while (fv_it != fvr.end() && cfv_it != cfvr.end()) {
+      if (*fv_it < *cfv_it)
+        ++cfv_it;
+      else if (*fv_it == *cfv_it) {
+        ++cfv_it;
+        ++fv_it;
+      }
+      else
+        return false;
+      
+    }
+    return (fv_it == fvr.end());
+  }
+
+  // void erase_simplex(Simplex_handle sh)
+  // {
+  //   auto siblings = sc.self_siblings(sh);
+  //   auto oncles = siblings->oncles();
+  //   int prev_vertex = siblings->parent();
+  //   siblings->members().erase(sh->first);
+  //   if (siblings->members().empty()) {
+  //     typename typedef Simplicial_complex::Siblings Siblings;
+  //     oncles->members().find(prev_vertex)->second.assign_children(new Siblings(oncles, prev_vertex));
+  //     assert(!sc.has_children(oncles->members().find(prev_vertex)));
+  //     //delete siblings;
+  //   }
+
+  // }
+  
+  void elementary_collapse(Simplex_handle face_sh, Simplex_handle coface_sh)
+  {
+    erase_simplex(coface_sh);
+    erase_simplex(face_sh);
+  }
+
+public:
+  // void collapse(std::vector<Simplex_handle>& simplices)
+  // {
+  //   // Get a vector of simplex handles ordered by filtration value
+  //   std::cout << sc << std::endl;
+  //   //std::vector<Simplex_handle> simplices;
+  //   for (Simplex_handle sh: sc.filtration_simplex_range())
+  //     simplices.push_back(sh);
+  //   // std::sort(simplices.begin(),
+  //   //           simplices.end(),
+  //   //           [&](Simplex_handle sh1, Simplex_handle sh2)
+  //   //           { double f1 = sc.filtration(sh1), f2 = sc.filtration(sh2);
+  //   //             return (f1 > f2) || (f1 >= f2 && sc.dimension(sh1) > sc.dimension(sh2)); });
+  //   // Double iteration
+  //   auto face_it = simplices.rbegin();
+  //   while (face_it != simplices.rend() && sc.filtration(*face_it) != 0) {
+  //     int coface_count = 0;
+  //     auto reduced_coface = simplices.rbegin();
+  //     for (auto coface_it = simplices.rbegin(); coface_it != simplices.rend() && sc.filtration(*coface_it) != 0; ++coface_it)
+  //       if (face_it != coface_it && is_face(*face_it, *coface_it)) {
+  //         coface_count++;
+  //         if (coface_count == 1)
+  //           reduced_coface = coface_it;
+  //         else
+  //           break;
+  //       }
+  //     if (coface_count == 1) {
+  //       std::cout << "Erase ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--reduced_coface.base())))
+  //         std::cout << v << " ";
+        
+  //       simplices.erase(--(reduced_coface.base()));
+  //       //elementary_collapse(*face_it, *reduced_coface);
+  //       std::cout << ") and then ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--face_it.base())))
+  //         std::cout << v << " ";
+  //       std::cout << ")\n";
+  //       simplices.erase(--((face_it++).base()));
+  //       //face_it = simplices.rbegin();
+  //       //std::cout << "Size of vector: " << simplices.size() << "\n";
+  //     } 
+  //     else
+  //       face_it++;
+  //   }
+  //   sc.initialize_filtration();
+  //   //std::cout << sc << std::endl;
+  // }
+
+  template <class Dim_lists>
+  void collapse(Dim_lists& dim_lists)
+  {
+    dim_lists.collapse();
+  }
+  
+private:
+  
+  /** Collapse recursively boundary faces of the given simplex
+   *  if its filtration is bigger than alpha_lim.  
+   */
+  void rec_boundary_collapse(Simplex_handle sh, FT alpha_lim)
+  {
+    for (Simplex_handle face_it : sc.boundary_simplex_range()) {
+      
+    }
+      
+  }
+  
+}; //class Relaxed_witness_complex
 
 } // namespace witness_complex
   
-} // namespace Guhdi
+} // namespace Gudhi
 
 #endif
diff --git a/src/Witness_complex/include/gudhi/Strange_witness_complex.h b/src/Witness_complex/include/gudhi/Strange_witness_complex.h
new file mode 100644
index 00000000..c1c2912b
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Strange_witness_complex.h
@@ -0,0 +1,232 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 WITNESS_COMPLEX_H_
+#define WITNESS_COMPLEX_H_
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+
+#include <gudhi/distance_functions.h>
+
+#include <algorithm>
+#include <utility>
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <ctime>
+#include <iostream>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+/** 
+    \class Witness_complex
+    \brief Constructs the witness complex for the given set of witnesses and landmarks.
+    \ingroup witness_complex
+ */
+template< class Simplicial_complex>
+class Strange_witness_complex {
+ private:
+  struct Active_witness {
+    int witness_id;
+    int landmark_id;
+
+    Active_witness(int witness_id_, int landmark_id_)
+        : witness_id(witness_id_),
+        landmark_id(landmark_id_) { }
+  };
+
+ private:
+  typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
+  typedef typename Simplicial_complex::Vertex_handle Vertex_handle;
+
+  typedef std::vector< double > Point_t;
+  typedef std::vector< Point_t > Point_Vector;
+
+  // typedef typename Simplicial_complex::Filtration_value Filtration_value;
+  typedef std::vector< Vertex_handle > typeVectorVertex;
+  typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
+  typedef std::pair< Simplex_handle, bool > typePairSimplexBool;
+
+  typedef int Witness_id;
+  typedef int Landmark_id;
+  typedef std::list< Vertex_handle > ActiveWitnessList;
+
+ private:
+  int nbL;  // Number of landmarks
+  Simplicial_complex& sc;  // Simplicial complex
+
+ public:
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  /** @name Constructor
+   */
+
+  //@{
+
+  // Witness_range<Closest_landmark_range<Vertex_handle>>
+
+  /**
+   *  \brief Iterative construction of the witness complex.
+   *  \details The witness complex is written in sc_ basing on a matrix knn of
+   *  nearest neighbours of the form {witnesses}x{landmarks}.
+   *
+   *  The type KNearestNeighbors can be seen as 
+   *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+   *  Witness_range and Closest_landmark_range are random access ranges.
+   *
+   *  Constructor takes into account at most (dim+1) 
+   *  first landmarks from each landmark range to construct simplices.
+   *
+   *  Landmarks are supposed to be in [0,nbL_-1]
+   */
+  template< typename KNearestNeighbors >
+  Strange_witness_complex(KNearestNeighbors const & knn,
+                  Simplicial_complex & sc_,
+                  int nbL_,
+                  int dim) : nbL(nbL_), sc(sc_) {
+    // Construction of the active witness list
+    int nbW = knn.size();
+    typeVectorVertex vv;
+    int counter = 0;
+    /* The list of still useful witnesses
+     * it will diminuish in the course of iterations
+     */
+    for (int i = 0; i != nbL; ++i) {
+      // initial fill of 0-dimensional simplices
+      // by doing it we don't assume that landmarks are necessarily witnesses themselves anymore
+      counter++;
+      vv = {i};
+      sc.insert_simplex(vv);
+      // TODO(SK) Error if not inserted : normally no need here though
+    }
+    for (int i = 0; i != nbW; ++i) {
+      std::vector<int> simplex;
+      simplex.reserve(dim+1);
+      for (int j = 0; j <= dim; j++)
+        simplex.push_back(knn[i][j]);
+      sc.insert_simplex_and_subfaces(simplex);
+    }
+  }
+
+  //@}
+
+ private:
+  /** \brief Check if the facets of the k-dimensional simplex witnessed 
+   *  by witness witness_id are already in the complex.
+   *  inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
+   */
+  template <typename KNearestNeighbors>
+  bool all_faces_in(KNearestNeighbors const &knn, int witness_id, int k) {
+    // std::cout << "All face in with the landmark " << inserted_vertex << std::endl;
+    std::vector< Vertex_handle > facet;
+    // Vertex_handle curr_vh = curr_sh->first;
+    // CHECK ALL THE FACETS
+    for (int i = 0; i != k + 1; ++i) {
+      facet = {};
+      for (int j = 0; j != k + 1; ++j) {
+        if (j != i) {
+          facet.push_back(knn[witness_id][j]);
+        }
+      }  // endfor
+      if (sc.find(facet) == sc.null_simplex())
+        return false;
+      // std::cout << "++++ finished loop safely\n";
+    }  // endfor
+    return true;
+  }
+
+  template <typename T>
+  static void print_vector(const std::vector<T>& v) {
+    std::cout << "[";
+    if (!v.empty()) {
+      std::cout << *(v.begin());
+      for (auto it = v.begin() + 1; it != v.end(); ++it) {
+        std::cout << ",";
+        std::cout << *it;
+      }
+    }
+    std::cout << "]";
+  }
+
+ public:
+  /**
+   *  \brief Verification if every simplex in the complex is witnessed by witnesses in knn.
+   *  \param print_output =true will print the witnesses for each simplex
+   *  \remark Added for debugging purposes.
+   */
+  template< class KNearestNeighbors >
+  bool is_witness_complex(KNearestNeighbors const & knn, bool print_output) {
+    // bool final_result = true;
+    for (Simplex_handle sh : sc.complex_simplex_range()) {
+      bool is_witnessed = false;
+      typeVectorVertex simplex;
+      int nbV = 0;  // number of verticed in the simplex
+      for (int v : sc.simplex_vertex_range(sh))
+        simplex.push_back(v);
+      nbV = simplex.size();
+      for (typeVectorVertex w : knn) {
+        bool has_vertices = true;
+        for (int v : simplex)
+          if (std::find(w.begin(), w.begin() + nbV, v) == w.begin() + nbV) {
+            has_vertices = false;
+            // break;
+          }
+        if (has_vertices) {
+          is_witnessed = true;
+          if (print_output) {
+            std::cout << "The simplex ";
+            print_vector(simplex);
+            std::cout << " is witnessed by the witness ";
+            print_vector(w);
+            std::cout << std::endl;
+          }
+          break;
+        }
+      }
+      if (!is_witnessed) {
+        if (print_output) {
+          std::cout << "The following simplex is not witnessed ";
+          print_vector(simplex);
+          std::cout << std::endl;
+        }
+        assert(is_witnessed);
+        return false;
+      }
+    }
+    return true;
+  }
+};
+
+}  // namespace witness_complex
+
+}  // namespace Gudhi
+
+#endif  // WITNESS_COMPLEX_H_
diff --git a/src/Witness_complex/include/gudhi/Strong_relaxed_witness_complex.h b/src/Witness_complex/include/gudhi/Strong_relaxed_witness_complex.h
new file mode 100644
index 00000000..ee863a42
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Strong_relaxed_witness_complex.h
@@ -0,0 +1,337 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 STRONG_RELAXED_WITNESS_COMPLEX_H_
+#define STRONG_RELAXED_WITNESS_COMPLEX_H_
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <algorithm>
+#include <utility>
+#include "gudhi/reader_utils.h"
+#include "gudhi/distance_functions.h"
+#include "gudhi/Simplex_tree.h"
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <math.h>
+#include <ctime>
+#include <iostream>
+
+// Needed for nearest neighbours
+#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_k_neighbor_search.h>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  /** \addtogroup simplex_tree
+   *  Witness complex is a simplicial complex defined on two sets of points in \f$\mathbf{R}^D\f$:
+   *  \f$W\f$ set of witnesses and \f$L \subseteq W\f$ set of landmarks. The simplices are based on points in \f$L\f$
+   *  and a simplex belongs to the witness complex if and only if it is witnessed (there exists a point \f$w \in W\f$ such that
+   *  w is closer to the vertices of this simplex than others) and all of its faces are witnessed as well. 
+   */
+template< class Simplicial_complex >
+class Strong_relaxed_witness_complex {
+
+private:    
+  struct Active_witness {
+    int witness_id;
+    int landmark_id;
+    
+    Active_witness(int witness_id_, int landmark_id_)
+      : witness_id(witness_id_),
+        landmark_id(landmark_id_) { }
+    };
+
+private:
+  typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
+  typedef typename Simplicial_complex::Vertex_handle Vertex_handle;
+  typedef typename Simplicial_complex::Filtration_value FT;
+
+  typedef std::vector< double > Point_t;
+  typedef std::vector< Point_t > Point_Vector;
+
+  // typedef typename Simplicial_complex::Filtration_value Filtration_value;
+  typedef std::vector< Vertex_handle > typeVectorVertex;
+  typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
+  typedef std::pair< Simplex_handle, bool > typePairSimplexBool;
+
+  typedef int Witness_id;
+  typedef int Landmark_id;
+  typedef std::list< Vertex_handle > ActiveWitnessList;
+
+ private:
+  int nbL;  // Number of landmarks
+  Simplicial_complex& sc;  // Simplicial complex
+  
+  public:
+    /** @name Constructor
+     */
+
+    //@{
+  
+    /**
+     *  \brief Iterative construction of the relaxed witness complex.
+     *  \details The witness complex is written in sc_ basing on a matrix knn
+     *  of k nearest neighbours of the form {witnesses}x{landmarks} and 
+     *  and a matrix distances of distances to these landmarks from witnesses.
+     *  The parameter alpha defines relaxation and
+     *  limD defines the 
+     *
+     *  The line lengths in one given matrix can differ, 
+     *  however both matrices have the same corresponding line lengths.
+     *
+     *  The type KNearestNeighbors can be seen as 
+     *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+     *  Witness_range and Closest_landmark_range are random access ranges.
+     *
+     *  Constructor takes into account at most (dim+1) 
+     *  first landmarks from each landmark range to construct simplices.
+     *
+     *  Landmarks are supposed to be in [0,nbL_-1]
+     */
+    
+    template< typename KNearestNeighbours >
+    Strong_relaxed_witness_complex(std::vector< std::vector<double> > const & distances,
+                            KNearestNeighbours const & knn,
+                            Simplicial_complex & sc_, 
+                            int nbL_,
+                            double alpha2,
+                            unsigned limD) : nbL(nbL_), sc(sc_) {
+      int nbW = knn.size();
+      typeVectorVertex vv;
+      //int counter = 0;
+      /* The list of still useful witnesses
+       * it will diminuish in the course of iterations
+       */
+      ActiveWitnessList active_w;// = new ActiveWitnessList();
+      for (int i = 0; i != nbL; ++i) {
+        // initial fill of 0-dimensional simplices
+        // by doing it we don't assume that landmarks are necessarily witnesses themselves anymore
+        //counter++;
+        vv = {i};
+        sc.insert_simplex(vv, Filtration_value(0.0));
+        /* TODO Error if not inserted : normally no need here though*/
+      }
+      for (int i=0; i != nbW; ++i) {
+        // int i_end = limD+1;
+        // if (knn[i].size() < limD+1)
+        //   i_end = knn[i].size();
+        // double dist_wL = *(distances[i].begin());
+        // while (distances[i][i_end] > dist_wL + alpha2)
+        //   i_end--;
+        // add_all_witnessed_faces(distances[i].begin(),
+        //                         knn[i].begin(),
+        //                         knn[i].begin() + i_end + 1);
+        unsigned j_end = 0;
+        while (j_end < distances[i].size() && j_end <= limD && distances[i][j_end] <= distances[i][0] + alpha2) {
+          std::vector<int> simplex;
+          for (unsigned j = 0; j <= j_end; ++j)
+            simplex.push_back(knn[i][j]);
+          assert(distances[i][j_end] - distances[i][0] >= 0);
+          sc.insert_simplex_and_subfaces(simplex, distances[i][j_end] - distances[i][0]);
+          j_end++; 
+        }
+      }
+      sc.set_dimension(limD);
+    }
+
+  //@}
+  
+private:
+  /* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness
+   * Iterator is needed to know until how far we can take landmarks to form simplexes
+   * simplex is the prefix of the simplexes to insert
+   * The output value indicates if the witness rests active or not
+   */
+  void add_all_witnessed_faces(std::vector<double>::const_iterator curr_d,
+                               std::vector<int>::const_iterator curr_l,
+                               std::vector<int>::const_iterator end)
+  {
+    std::vector<int> simplex;
+    std::vector<int>::const_iterator l_end = curr_l;
+    for (; l_end != end; ++l_end) {
+      std::vector<int>::const_iterator l_it = curr_l;
+      std::vector<double>::const_iterator d_it = curr_d;
+      simplex = {};
+      for (; l_it != l_end; ++l_it, ++d_it)
+        simplex.push_back(*l_it);
+      sc.insert_simplex_and_subfaces(simplex, *(d_it--) - *curr_d);
+    }
+  }
+  
+  /** \brief Check if the facets of the k-dimensional simplex witnessed 
+   *  by witness witness_id are already in the complex.
+   *  inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
+   */
+  bool all_faces_in(std::vector<int>& simplex, double* filtration_value)
+  {
+    std::vector< int > facet;
+    for (std::vector<int>::iterator not_it = simplex.begin(); not_it != simplex.end(); ++not_it)
+      {
+        facet.clear();
+        for (std::vector<int>::iterator it = simplex.begin(); it != simplex.end(); ++it)
+          if (it != not_it)
+            facet.push_back(*it);
+        Simplex_handle facet_sh = sc.find(facet);
+        if (facet_sh == sc.null_simplex())
+          return false;
+        else if (sc.filtration(facet_sh) > *filtration_value)
+          *filtration_value = sc.filtration(facet_sh);
+      }
+    return true;
+  }
+
+  bool is_face(Simplex_handle face, Simplex_handle coface)
+  {
+    // vertex range is sorted in decreasing order
+    auto fvr = sc.simplex_vertex_range(face);
+    auto cfvr = sc.simplex_vertex_range(coface);
+    auto fv_it = fvr.begin();
+    auto cfv_it = cfvr.begin();
+    while (fv_it != fvr.end() && cfv_it != cfvr.end()) {
+      if (*fv_it < *cfv_it)
+        ++cfv_it;
+      else if (*fv_it == *cfv_it) {
+        ++cfv_it;
+        ++fv_it;
+      }
+      else
+        return false;
+      
+    }
+    return (fv_it == fvr.end());
+  }
+
+  // void erase_simplex(Simplex_handle sh)
+  // {
+  //   auto siblings = sc.self_siblings(sh);
+  //   auto oncles = siblings->oncles();
+  //   int prev_vertex = siblings->parent();
+  //   siblings->members().erase(sh->first);
+  //   if (siblings->members().empty()) {
+  //     typename typedef Simplicial_complex::Siblings Siblings;
+  //     oncles->members().find(prev_vertex)->second.assign_children(new Siblings(oncles, prev_vertex));
+  //     assert(!sc.has_children(oncles->members().find(prev_vertex)));
+  //     //delete siblings;
+  //   }
+
+  // }
+  
+  void elementary_collapse(Simplex_handle face_sh, Simplex_handle coface_sh)
+  {
+    erase_simplex(coface_sh);
+    erase_simplex(face_sh);
+  }
+
+public:
+  // void collapse(std::vector<Simplex_handle>& simplices)
+  // {
+  //   // Get a vector of simplex handles ordered by filtration value
+  //   std::cout << sc << std::endl;
+  //   //std::vector<Simplex_handle> simplices;
+  //   for (Simplex_handle sh: sc.filtration_simplex_range())
+  //     simplices.push_back(sh);
+  //   // std::sort(simplices.begin(),
+  //   //           simplices.end(),
+  //   //           [&](Simplex_handle sh1, Simplex_handle sh2)
+  //   //           { double f1 = sc.filtration(sh1), f2 = sc.filtration(sh2);
+  //   //             return (f1 > f2) || (f1 >= f2 && sc.dimension(sh1) > sc.dimension(sh2)); });
+  //   // Double iteration
+  //   auto face_it = simplices.rbegin();
+  //   while (face_it != simplices.rend() && sc.filtration(*face_it) != 0) {
+  //     int coface_count = 0;
+  //     auto reduced_coface = simplices.rbegin();
+  //     for (auto coface_it = simplices.rbegin(); coface_it != simplices.rend() && sc.filtration(*coface_it) != 0; ++coface_it)
+  //       if (face_it != coface_it && is_face(*face_it, *coface_it)) {
+  //         coface_count++;
+  //         if (coface_count == 1)
+  //           reduced_coface = coface_it;
+  //         else
+  //           break;
+  //       }
+  //     if (coface_count == 1) {
+  //       std::cout << "Erase ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--reduced_coface.base())))
+  //         std::cout << v << " ";
+        
+  //       simplices.erase(--(reduced_coface.base()));
+  //       //elementary_collapse(*face_it, *reduced_coface);
+  //       std::cout << ") and then ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--face_it.base())))
+  //         std::cout << v << " ";
+  //       std::cout << ")\n";
+  //       simplices.erase(--((face_it++).base()));
+  //       //face_it = simplices.rbegin();
+  //       //std::cout << "Size of vector: " << simplices.size() << "\n";
+  //     } 
+  //     else
+  //       face_it++;
+  //   }
+  //   sc.initialize_filtration();
+  //   //std::cout << sc << std::endl;
+  // }
+
+  template <class Dim_lists>
+  void collapse(Dim_lists& dim_lists)
+  {
+    dim_lists.collapse();
+  }
+  
+private:
+  
+  /** Collapse recursively boundary faces of the given simplex
+   *  if its filtration is bigger than alpha_lim.  
+   */
+  void rec_boundary_collapse(Simplex_handle sh, FT alpha_lim)
+  {
+    for (Simplex_handle face_it : sc.boundary_simplex_range()) {
+      
+    }
+      
+  }
+  
+}; //class Strong_relaxed_witness_complex
+
+} // namespace witness_complex
+  
+} // namespace Gudhi
+
+#endif
diff --git a/src/Witness_complex/include/gudhi/Weak_relaxed_witness_complex.h b/src/Witness_complex/include/gudhi/Weak_relaxed_witness_complex.h
new file mode 100644
index 00000000..a1aedd8e
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Weak_relaxed_witness_complex.h
@@ -0,0 +1,379 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA Sophia Antipolis-Méditerranée (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 WEAK_RELAXED_WITNESS_COMPLEX_H_
+#define WEAK_RELAXED_WITNESS_COMPLEX_H_
+
+#include <boost/container/flat_map.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <algorithm>
+#include <utility>
+#include "gudhi/reader_utils.h"
+#include "gudhi/distance_functions.h"
+#include "gudhi/Simplex_tree.h"
+#include <vector>
+#include <list>
+#include <set>
+#include <queue>
+#include <limits>
+#include <math.h>
+#include <ctime>
+#include <iostream>
+
+// Needed for nearest neighbours
+#include <CGAL/Cartesian_d.h>
+#include <CGAL/Search_traits.h>
+#include <CGAL/Search_traits_adapter.h>
+#include <CGAL/property_map.h>
+#include <CGAL/Epick_d.h>
+#include <CGAL/Orthogonal_k_neighbor_search.h>
+
+#include <boost/tuple/tuple.hpp>
+#include <boost/iterator/zip_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/range/iterator_range.hpp>
+
+// Needed for the adjacency graph in bad link search
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/connected_components.hpp>
+
+namespace Gudhi {
+
+namespace witness_complex {
+
+  /** \addtogroup simplex_tree
+   *  Witness complex is a simplicial complex defined on two sets of points in \f$\mathbf{R}^D\f$:
+   *  \f$W\f$ set of witnesses and \f$L \subseteq W\f$ set of landmarks. The simplices are based on points in \f$L\f$
+   *  and a simplex belongs to the witness complex if and only if it is witnessed (there exists a point \f$w \in W\f$ such that
+   *  w is closer to the vertices of this simplex than others) and all of its faces are witnessed as well. 
+   */
+template< class Simplicial_complex >
+class Weak_relaxed_witness_complex {
+
+private:    
+  struct Active_witness {
+    int witness_id;
+    int landmark_id;
+    
+    Active_witness(int witness_id_, int landmark_id_)
+      : witness_id(witness_id_),
+        landmark_id(landmark_id_) { }
+    };
+
+private:
+  typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
+  typedef typename Simplicial_complex::Vertex_handle Vertex_handle;
+  typedef typename Simplicial_complex::Filtration_value FT;
+
+  typedef std::vector< double > Point_t;
+  typedef std::vector< Point_t > Point_Vector;
+
+  // typedef typename Simplicial_complex::Filtration_value Filtration_value;
+  typedef std::vector< Vertex_handle > typeVectorVertex;
+  typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
+  typedef std::pair< Simplex_handle, bool > typePairSimplexBool;
+
+  typedef int Witness_id;
+  typedef int Landmark_id;
+  typedef std::list< Vertex_handle > ActiveWitnessList;
+
+ private:
+  int nbL;  // Number of landmarks
+  Simplicial_complex& sc;  // Simplicial complex
+  
+  public:
+    /** @name Constructor
+     */
+
+    //@{
+  
+    /**
+     *  \brief Iterative construction of the relaxed witness complex.
+     *  \details The witness complex is written in sc_ basing on a matrix knn
+     *  of k nearest neighbours of the form {witnesses}x{landmarks} and 
+     *  and a matrix distances of distances to these landmarks from witnesses.
+     *  The parameter alpha defines relaxation and
+     *  limD defines the 
+     *
+     *  The line lengths in one given matrix can differ, 
+     *  however both matrices have the same corresponding line lengths.
+     *
+     *  The type KNearestNeighbors can be seen as 
+     *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+     *  Witness_range and Closest_landmark_range are random access ranges.
+     *
+     *  Constructor takes into account at most (dim+1) 
+     *  first landmarks from each landmark range to construct simplices.
+     *
+     *  Landmarks are supposed to be in [0,nbL_-1]
+     */
+    
+    template< typename KNearestNeighbours >
+    Weak_relaxed_witness_complex(std::vector< std::vector<double> > const & distances,
+                            KNearestNeighbours const & knn,
+                            Simplicial_complex & sc_, 
+                            int nbL_,
+                            double alpha,
+                            int limD) : nbL(nbL_), sc(sc_) {
+      int nbW = knn.size();
+      typeVectorVertex vv;
+      //int counter = 0;
+      /* The list of still useful witnesses
+       * it will diminuish in the course of iterations
+       */
+      ActiveWitnessList active_w;// = new ActiveWitnessList();
+      for (int i = 0; i != nbL; ++i) {
+        // initial fill of 0-dimensional simplices
+        // by doing it we don't assume that landmarks are necessarily witnesses themselves anymore
+        //counter++;
+        vv = {i};
+        sc.insert_simplex(vv, Filtration_value(0.0));
+        /* TODO Error if not inserted : normally no need here though*/
+      }
+      int k = 1; /* current dimension in iterative construction */
+      for (int i=0; i != nbW; ++i)
+        active_w.push_back(i);
+      while (!active_w.empty() && k <= limD && k < nbL )
+        {
+          typename ActiveWitnessList::iterator aw_it = active_w.begin();
+          while (aw_it != active_w.end())
+            {
+              std::vector<int> simplex;
+              bool ok = add_all_faces_of_dimension(k,
+                                                   alpha,
+                                                   std::numeric_limits<double>::infinity(),
+                                                   distances[*aw_it].begin(),
+                                                   knn[*aw_it].begin(),
+                                                   simplex,
+                                                   knn[*aw_it].end());
+              if (!ok)
+                active_w.erase(aw_it++); //First increase the iterator and then erase the previous element
+              else
+                aw_it++;
+            }
+          k++;
+        }
+      sc.set_dimension(limD);
+    }
+
+  //@}
+  
+private:
+  /* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness
+   * Iterator is needed to know until how far we can take landmarks to form simplexes
+   * simplex is the prefix of the simplexes to insert
+   * The output value indicates if the witness rests active or not
+   */
+  bool add_all_faces_of_dimension(int dim,
+                                  double alpha,
+                                  double norelax_dist,
+                                  std::vector<double>::const_iterator curr_d,
+                                  std::vector<int>::const_iterator curr_l,
+                                  std::vector<int>& simplex,
+                                  std::vector<int>::const_iterator end)
+  {
+    if (curr_l == end)
+      return false;
+    bool will_be_active = false;
+    std::vector<int>::const_iterator l_it = curr_l;
+    std::vector<double>::const_iterator d_it = curr_d;
+    if (dim > 0)
+      for (; *d_it - alpha <= norelax_dist && l_it != end; ++l_it, ++d_it) {
+        simplex.push_back(*l_it);
+        if (sc.find(simplex) != sc.null_simplex())
+          will_be_active = add_all_faces_of_dimension(dim-1,
+                                                      alpha,
+                                                      norelax_dist,
+                                                      d_it+1,
+                                                      l_it+1,
+                                                      simplex,
+                                                      end) || will_be_active;
+        simplex.pop_back();
+        // If norelax_dist is infinity, change to first omitted distance
+        if (*d_it <= norelax_dist)
+          norelax_dist = *d_it;
+        will_be_active = add_all_faces_of_dimension(dim-1,
+                                                    alpha,
+                                                    norelax_dist,
+                                                    d_it+1,
+                                                    l_it+1,
+                                                    simplex,
+                                                    end) || will_be_active;
+      } 
+    else if (dim == 0)
+      for (; *d_it - alpha <= norelax_dist && l_it != end; ++l_it, ++d_it) {
+        simplex.push_back(*l_it);
+        double filtration_value = 0;
+        // if norelax_dist is infinite, relaxation is 0.
+        if (*d_it > norelax_dist) 
+          filtration_value = *d_it - norelax_dist; 
+        if (all_faces_in(simplex, &filtration_value)) {
+          will_be_active = true;
+          sc.insert_simplex(simplex, filtration_value);
+        }
+        simplex.pop_back();
+        // If norelax_dist is infinity, change to first omitted distance
+        if (*d_it < norelax_dist)
+          norelax_dist = *d_it;
+      } 
+    return will_be_active;
+  }
+  
+  /** \brief Check if the facets of the k-dimensional simplex witnessed 
+   *  by witness witness_id are already in the complex.
+   *  inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
+   */
+  bool all_faces_in(std::vector<int>& simplex, double* filtration_value)
+  {
+    std::vector< int > facet;
+    for (std::vector<int>::iterator not_it = simplex.begin(); not_it != simplex.end(); ++not_it)
+      {
+        facet.clear();
+        for (std::vector<int>::iterator it = simplex.begin(); it != simplex.end(); ++it)
+          if (it != not_it)
+            facet.push_back(*it);
+        Simplex_handle facet_sh = sc.find(facet);
+        if (facet_sh == sc.null_simplex())
+          return false;
+        else if (sc.filtration(facet_sh) > *filtration_value)
+          *filtration_value = sc.filtration(facet_sh);
+      }
+    return true;
+  }
+
+  bool is_face(Simplex_handle face, Simplex_handle coface)
+  {
+    // vertex range is sorted in decreasing order
+    auto fvr = sc.simplex_vertex_range(face);
+    auto cfvr = sc.simplex_vertex_range(coface);
+    auto fv_it = fvr.begin();
+    auto cfv_it = cfvr.begin();
+    while (fv_it != fvr.end() && cfv_it != cfvr.end()) {
+      if (*fv_it < *cfv_it)
+        ++cfv_it;
+      else if (*fv_it == *cfv_it) {
+        ++cfv_it;
+        ++fv_it;
+      }
+      else
+        return false;
+      
+    }
+    return (fv_it == fvr.end());
+  }
+
+  // void erase_simplex(Simplex_handle sh)
+  // {
+  //   auto siblings = sc.self_siblings(sh);
+  //   auto oncles = siblings->oncles();
+  //   int prev_vertex = siblings->parent();
+  //   siblings->members().erase(sh->first);
+  //   if (siblings->members().empty()) {
+  //     typename typedef Simplicial_complex::Siblings Siblings;
+  //     oncles->members().find(prev_vertex)->second.assign_children(new Siblings(oncles, prev_vertex));
+  //     assert(!sc.has_children(oncles->members().find(prev_vertex)));
+  //     //delete siblings;
+  //   }
+
+  // }
+  
+  void elementary_collapse(Simplex_handle face_sh, Simplex_handle coface_sh)
+  {
+    erase_simplex(coface_sh);
+    erase_simplex(face_sh);
+  }
+
+public:
+  // void collapse(std::vector<Simplex_handle>& simplices)
+  // {
+  //   // Get a vector of simplex handles ordered by filtration value
+  //   std::cout << sc << std::endl;
+  //   //std::vector<Simplex_handle> simplices;
+  //   for (Simplex_handle sh: sc.filtration_simplex_range())
+  //     simplices.push_back(sh);
+  //   // std::sort(simplices.begin(),
+  //   //           simplices.end(),
+  //   //           [&](Simplex_handle sh1, Simplex_handle sh2)
+  //   //           { double f1 = sc.filtration(sh1), f2 = sc.filtration(sh2);
+  //   //             return (f1 > f2) || (f1 >= f2 && sc.dimension(sh1) > sc.dimension(sh2)); });
+  //   // Double iteration
+  //   auto face_it = simplices.rbegin();
+  //   while (face_it != simplices.rend() && sc.filtration(*face_it) != 0) {
+  //     int coface_count = 0;
+  //     auto reduced_coface = simplices.rbegin();
+  //     for (auto coface_it = simplices.rbegin(); coface_it != simplices.rend() && sc.filtration(*coface_it) != 0; ++coface_it)
+  //       if (face_it != coface_it && is_face(*face_it, *coface_it)) {
+  //         coface_count++;
+  //         if (coface_count == 1)
+  //           reduced_coface = coface_it;
+  //         else
+  //           break;
+  //       }
+  //     if (coface_count == 1) {
+  //       std::cout << "Erase ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--reduced_coface.base())))
+  //         std::cout << v << " ";
+        
+  //       simplices.erase(--(reduced_coface.base()));
+  //       //elementary_collapse(*face_it, *reduced_coface);
+  //       std::cout << ") and then ( ";
+  //       for (auto v: sc.simplex_vertex_range(*(--face_it.base())))
+  //         std::cout << v << " ";
+  //       std::cout << ")\n";
+  //       simplices.erase(--((face_it++).base()));
+  //       //face_it = simplices.rbegin();
+  //       //std::cout << "Size of vector: " << simplices.size() << "\n";
+  //     } 
+  //     else
+  //       face_it++;
+  //   }
+  //   sc.initialize_filtration();
+  //   //std::cout << sc << std::endl;
+  // }
+
+  template <class Dim_lists>
+  void collapse(Dim_lists& dim_lists)
+  {
+    dim_lists.collapse();
+  }
+  
+private:
+  
+  /** Collapse recursively boundary faces of the given simplex
+   *  if its filtration is bigger than alpha_lim.  
+   */
+  void rec_boundary_collapse(Simplex_handle sh, FT alpha_lim)
+  {
+    for (Simplex_handle face_it : sc.boundary_simplex_range()) {
+      
+    }
+      
+  }
+  
+}; //class Weak_relaxed_witness_complex
+
+} // namespace witness_complex
+  
+} // namespace Gudhi
+
+#endif