X-Git-Url: https://www.fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=mtp.git;a=blobdiff_plain;f=mtp_graph.cc;h=2cbb33848a3589007528a6e3b1098357dbf3d3df;hp=04b84aaf534aeab753a7f57c2b05004166904163;hb=HEAD;hpb=b33d04fc473e7de0f9d404b014fb694b7ee6c661

diff --git a/mtp_graph.cc b/mtp_graph.cc
index 04b84aa..2cbb338 100644
--- a/mtp_graph.cc
+++ b/mtp_graph.cc
@@ -1,275 +1,520 @@
 
-///////////////////////////////////////////////////////////////////////////
-// This program is free software: you can redistribute it and/or modify  //
-// it under the terms of the version 3 of the GNU General Public License //
-// as published by the Free Software Foundation.                         //
-//                                                                       //
-// 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/>.  //
-//                                                                       //
-// Written by and Copyright (C) Francois Fleuret                         //
-// Contact <francois.fleuret@idiap.ch> for comments & bug reports        //
-///////////////////////////////////////////////////////////////////////////
+/*
+ *  mtp is the ``Multi Tracked Paths'', an implementation of the
+ *  k-shortest paths algorithm for multi-target tracking.
+ *
+ *  Copyright (c) 2012 Idiap Research Institute, http://www.idiap.ch/
+ *  Written by Francois Fleuret <francois.fleuret@idiap.ch>
+ *
+ *  This file is part of mtp.
+ *
+ *  mtp is free software: you can redistribute it and/or modify it
+ *  under the terms of the GNU General Public License version 3 as
+ *  published by the Free Software Foundation.
+ *
+ *  mtp 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 selector.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ */
 
 #include "mtp_graph.h"
 
-#include <iostream>
+#include <cmath>
 #include <float.h>
 
 using namespace std;
 
 class Edge {
 public:
-  int id, occupied;
-  scalar_t length, work_length;
-  Vertex *terminal_vertex;
-  Edge *next, *pred;
+  int occupied;
+  scalar_t length, positivized_length;
+  Vertex *origin_vertex, *terminal_vertex;
+
+  // These fields are used for the linked list of a vertex's leaving
+  // edge list. We have to do insertions / deletions.
+  Edge *next_leaving_edge, *pred_leaving_edge;
+
+  inline void invert();
 };
 
 class Vertex {
 public:
-  int id, iteration;
-  Edge *root_edge;
   scalar_t distance_from_source;
-  Vertex *pred_vertex;
-  Edge *pred_edge;
+  Edge *pred_edge_toward_source;
+
+  Edge *leaving_edge_list_root;
+  Vertex **heap_slot;
+
+  Vertex();
+
+  inline void add_leaving_edge(Edge *e);
+  inline void del_leaving_edge(Edge *e);
+  inline void decrease_distance_in_heap(Vertex **heap);
+  inline void increase_distance_in_heap(Vertex **heap, Vertex **heap_bottom);
+};
 
-  Vertex() { root_edge = 0; }
+//////////////////////////////////////////////////////////////////////
 
-  inline void add_edge(Edge *e) {
-    e->next = root_edge;
-    e->pred = 0;
-    if(root_edge) { root_edge->pred = e; }
-    root_edge = e;
+void Edge::invert() {
+  length = - length;
+  positivized_length = - positivized_length;
+  origin_vertex->del_leaving_edge(this);
+  terminal_vertex->add_leaving_edge(this);
+  swap(terminal_vertex, origin_vertex);
+}
+
+//////////////////////////////////////////////////////////////////////
+
+Vertex::Vertex() {
+  leaving_edge_list_root = 0;
+}
+
+void Vertex::add_leaving_edge(Edge *e) {
+  e->next_leaving_edge = leaving_edge_list_root;
+  e->pred_leaving_edge = 0;
+  if(leaving_edge_list_root) {
+    leaving_edge_list_root->pred_leaving_edge = e;
   }
+  leaving_edge_list_root = e;
+}
 
-  inline void del_edge(Edge *e) {
-    if(e == root_edge) { root_edge = e->next; }
-    if(e->pred) { e->pred->next = e->next; }
-    if(e->next) { e->next->pred = e->pred; }
+void Vertex::del_leaving_edge(Edge *e) {
+  if(e == leaving_edge_list_root) {
+    leaving_edge_list_root = e->next_leaving_edge;
   }
-};
+  if(e->pred_leaving_edge) {
+    e->pred_leaving_edge->next_leaving_edge = e->next_leaving_edge;
+  }
+  if(e->next_leaving_edge) {
+    e->next_leaving_edge->pred_leaving_edge = e->pred_leaving_edge;
+  }
+}
 
-void MTPGraph::print() {
-  for(int n = 0; n < _nb_vertices; n++) {
-    for(Edge *e = vertices[n].root_edge; e; e = e->next) {
-      cout << n << " -> " << e->terminal_vertex->id << " " << e->length;
-      if(e->occupied) {
-        cout << " *";
-      }
-      cout << endl;
-    }
+void Vertex::decrease_distance_in_heap(Vertex **heap) {
+  Vertex **p, **h;
+  h = heap_slot;
+  while(1) {
+    if(h <= heap) break;
+    p = heap + ((h - heap + 1) >> 1) - 1;
+    if((*p)->distance_from_source <= distance_from_source) break;
+    swap((*p)->heap_slot, heap_slot);
+    swap(*p, *h);
+    h = p;
   }
 }
 
-void MTPGraph::print_dot() {
-  cout << "digraph {" << endl;
-  cout << "  node[shape=circle];" << endl;
-  for(int n = 0; n < _nb_vertices; n++) {
-    int a = vertices[n].id;
-    for(Edge *e = vertices[n].root_edge; e; e = e->next) {
-      int b = e->terminal_vertex->id;
-      if(e->occupied) {
-        cout << "  " << b << " -> " << a << " [style=bold,color=black,label=\"" << -e->length << "\"];" << endl;
+void Vertex::increase_distance_in_heap(Vertex **heap, Vertex **heap_bottom) {
+  Vertex **c1, **c2, **h;
+  h = heap_slot;
+  while(1) {
+    c1 = heap + 2 * (h - heap) + 1;
+    if(c1 >= heap_bottom) break;
+    c2 = c1 + 1;
+    if((*c1)->distance_from_source < distance_from_source) {
+      if(c2 < heap_bottom && (*c2)->distance_from_source < (*c1)->distance_from_source) {
+        swap((*c2)->heap_slot, heap_slot);
+        swap(*c2, *h);
+        h = c2;
       } else {
-        cout << "  " << a << " -> " << b << " [color=gray,label=\"" << e->length << "\"];" << endl;
+        swap((*c1)->heap_slot, heap_slot);
+        swap(*c1, *h);
+        h = c1;
       }
+    } else {
+      if(c2 < heap_bottom && (*c2)->distance_from_source < distance_from_source) {
+        swap((*c2)->heap_slot, heap_slot);
+        swap(*c2, *h);
+        h = c2;
+      } else break;
     }
   }
-  cout << "}" << endl;
 }
 
+//////////////////////////////////////////////////////////////////////
+
 MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
-                   int *from, int *to,
-                   int src, int snk) {
+                   int *vertex_from, int *vertex_to,
+                   int source, int sink) {
   _nb_vertices = nb_vertices;
   _nb_edges = nb_edges;
 
-  edges = new Edge[_nb_edges];
-  vertices = new Vertex[_nb_vertices];
-  _front = new Vertex *[_nb_vertices];
-  _new_front = new Vertex *[_nb_vertices];
+  _edges = new Edge[_nb_edges];
+  _vertices = new Vertex[_nb_vertices];
+  _heap = new Vertex *[_nb_vertices];
+  _dp_order = new Vertex *[_nb_vertices];
 
-  _source = &vertices[src];
-  _sink = &vertices[snk];
+  _source = &_vertices[source];
+  _sink = &_vertices[sink];
 
-  for(int v = 0; v < _nb_vertices; v++) {
-    vertices[v].id = v;
+  for(int e = 0; e < nb_edges; e++) {
+    _vertices[vertex_from[e]].add_leaving_edge(&_edges[e]);
+    _edges[e].occupied = 0;
+    _edges[e].origin_vertex = &_vertices[vertex_from[e]];
+    _edges[e].terminal_vertex = &_vertices[vertex_to[e]];
   }
 
-  for(int e = 0; e < nb_edges; e++) {
-    vertices[from[e]].add_edge(&edges[e]);
-    edges[e].occupied = 0;
-    edges[e].id = e;
-    edges[e].terminal_vertex = &vertices[to[e]];
+  for(int v = 0; v < _nb_vertices; v++) {
+    _heap[v] = &_vertices[v];
+    _vertices[v].heap_slot = &_heap[v];
   }
 
+  paths = 0;
+  nb_paths = 0;
+
+  compute_dp_ordering();
 }
 
 MTPGraph::~MTPGraph() {
-  delete[] vertices;
-  delete[] edges;
-  delete[] _front;
-  delete[] _new_front;
+  delete[] _vertices;
+  delete[] _dp_order;
+  delete[] _heap;
+  delete[] _edges;
+  for(int p = 0; p < nb_paths; p++) delete paths[p];
+  delete[] paths;
 }
 
-void MTPGraph::initialize_work_lengths() {
-  scalar_t length_min = 0;
-  for(int n = 0; n < _nb_vertices; n++) {
-    for(Edge *e = vertices[n].root_edge; e; e = e->next) {
-      length_min = min(e->length, length_min);
-    }
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::print(ostream *os) {
+  for(int k = 0; k < _nb_edges; k++) {
+    Edge *e = &_edges[k];
+    (*os) << e->origin_vertex - _vertices
+          << " -> "
+          << e->terminal_vertex - _vertices
+          << " (" << e->length << ")";
+    if(e->occupied) { (*os) << " *"; }
+    (*os) << endl;
   }
-  for(int n = 0; n < _nb_vertices; n++) {
-    for(Edge *e = vertices[n].root_edge; e; e = e->next) {
-      e->work_length = e->length - length_min;
+}
+
+void MTPGraph::print_dot(ostream *os) {
+  (*os) << "digraph {" << endl;
+  (*os) << "        rankdir=\"LR\";" << endl;
+  (*os) << "        node [shape=circle,width=0.75,fixedsize=true];" << endl;
+  (*os) << "        edge [color=gray,arrowhead=open]" << endl;
+  (*os) << "        " << _source - _vertices << " [peripheries=2];" << endl;
+  (*os) << "        " << _sink - _vertices << " [peripheries=2];" << endl;
+  for(int k = 0; k < _nb_edges; k++) {
+    Edge *e = &_edges[k];
+    (*os) << "        "
+          << e->origin_vertex - _vertices
+          << " -> "
+          << e->terminal_vertex - _vertices
+          << " [";
+    if(e->occupied) {
+      (*os) << "style=bold,color=black,";
     }
+    (*os) << "label=\"" << e->length << "\"];" << endl;
   }
+  (*os) << "}" << endl;
 }
 
-void MTPGraph::update_work_lengths() {
-  for(int n = 0; n < _nb_vertices; n++) {
-    scalar_t d = vertices[n].distance_from_source;
-    for(Edge *e = vertices[n].root_edge; e; e = e->next) {
-      e->work_length += d - e->terminal_vertex->distance_from_source;
-    }
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::update_positivized_lengths() {
+  for(int k = 0; k < _nb_edges; k++) {
+    Edge *e = &_edges[k];
+    e->positivized_length +=
+      e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
   }
 }
 
-void MTPGraph::force_positive_work_lengths() {
+void MTPGraph::force_positivized_lengths() {
 #ifdef VERBOSE
   scalar_t residual_error = 0.0;
+  scalar_t max_error = 0.0;
 #endif
-  for(int n = 0; n < _nb_vertices; n++) {
-    for(Edge *e = vertices[n].root_edge; e; e = e->next) {
-      if(e->work_length < 0) {
+  for(int k = 0; k < _nb_edges; k++) {
+    Edge *e = &_edges[k];
+
+    if(e->positivized_length < 0) {
 #ifdef VERBOSE
-        residual_error -= e->work_length;
+      residual_error -= e->positivized_length;
+      max_error = max(max_error, - e->positivized_length);
 #endif
-        e->work_length = 0.0;
-      }
+      e->positivized_length = 0.0;
     }
   }
 #ifdef VERBOSE
-  cerr << "residual_error " << residual_error << endl;
+  cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << max_error << endl;
 #endif
 }
 
-void MTPGraph::find_shortest_path(Vertex **_front, Vertex **_new_front) {
-  Vertex **tmp_front;
-  int tmp_front_size;
+void MTPGraph::dp_compute_distances() {
   Vertex *v, *tv;
+  Edge *e;
   scalar_t d;
 
-  for(int v = 0; v < _nb_vertices; v++) {
-    vertices[v].distance_from_source = FLT_MAX;
-    vertices[v].pred_vertex = 0;
-    vertices[v].pred_edge = 0;
-    vertices[v].iteration = 0;
+  for(int k = 0; k < _nb_vertices; k++) {
+    _vertices[k].distance_from_source = FLT_MAX;
+    _vertices[k].pred_edge_toward_source = 0;
   }
 
-  int iteration = 0;
-
-  int _front_size = 0, _new_front_size;
-  _front[_front_size++] = _source;
   _source->distance_from_source = 0;
 
-  do {
-    _new_front_size = 0;
-    iteration++;
-    for(int f = 0; f < _front_size; f++) {
-      v = _front[f];
-      for(Edge *e = v->root_edge; e; e = e->next) {
-        d = v->distance_from_source + e->work_length;
-        tv = e->terminal_vertex;
-        if(d < tv->distance_from_source) {
-          tv->distance_from_source = d;
-          tv->pred_vertex = v;
-          tv->pred_edge = e;
-          if(tv->iteration < iteration) {
-            _new_front[_new_front_size++] = tv;
-            tv->iteration = iteration;
-          }
-        }
+  for(int k = 0; k < _nb_vertices; k++) {
+    v = _dp_order[k];
+    for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+      d = v->distance_from_source + e->positivized_length;
+      tv = e->terminal_vertex;
+      if(d < tv->distance_from_source) {
+        tv->distance_from_source = d;
+        tv->pred_edge_toward_source = e;
       }
     }
+  }
+}
+
+// This method does not change the edge occupation. It only sets
+// properly, for every vertex, the fields distance_from_source and
+// pred_edge_toward_source.
 
-    tmp_front = _new_front;
-    _new_front = _front;
-    _front = tmp_front;
+void MTPGraph::find_shortest_path() {
+  int heap_size;
+  Vertex *v, *tv, **last_slot;
+  Edge *e;
+  scalar_t d;
+
+  for(int k = 0; k < _nb_vertices; k++) {
+    _vertices[k].distance_from_source = FLT_MAX;
+    _vertices[k].pred_edge_toward_source = 0;
+  }
 
-    tmp_front_size = _new_front_size;
-    _new_front_size = _front_size;
-    _front_size = tmp_front_size;
-  } while(_front_size > 0);
+  heap_size = _nb_vertices;
+  _source->distance_from_source = 0;
+  _source->decrease_distance_in_heap(_heap);
+
+  while(heap_size > 1) {
+    // Get the closest to the source
+    v = _heap[0];
+
+    // Remove it from the heap (swap it with the last_slot in the heap, and
+    // update the distance of that one)
+    heap_size--;
+    last_slot = _heap + heap_size;
+    swap(*_heap, *last_slot); swap((*_heap)->heap_slot, (*last_slot)->heap_slot);
+    (*_heap)->increase_distance_in_heap(_heap, last_slot);
+
+    // Now update the neighbors of the node currently closest to the
+    // source
+    for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+      d = v->distance_from_source + e->positivized_length;
+      tv = e->terminal_vertex;
+      if(d < tv->distance_from_source) {
+        ASSERT(tv->heap_slot < last_slot);
+        tv->distance_from_source = d;
+        tv->pred_edge_toward_source = e;
+        tv->decrease_distance_in_heap(_heap);
+      }
+    }
+  }
 }
 
-void MTPGraph::find_best_paths(scalar_t *lengths, int *result_edge_occupation) {
-  scalar_t total_length;
+void MTPGraph::find_best_paths(scalar_t *lengths) {
+  scalar_t shortest_path_length;
+  Vertex *v;
+  Edge *e;
 
   for(int e = 0; e < _nb_edges; e++) {
-    edges[e].length = lengths[e];
-    edges[e].work_length = edges[e].length;
+    _edges[e].length = lengths[e];
+    _edges[e].occupied = 0;
+    _edges[e].positivized_length = _edges[e].length;
   }
 
-  find_shortest_path(_front, _new_front);
-  update_work_lengths();
-
-  // initialize_work_lengths();
+  // Compute the distance of all the nodes from the source by just
+  // visiting them in the proper DAG ordering we computed when
+  // building the graph
+  dp_compute_distances();
 
   do {
-    force_positive_work_lengths();
-    find_shortest_path(_front, _new_front);
-    update_work_lengths();
-
-    total_length = 0.0;
-
-    // Do we reach the _sink?
-    if(_sink->pred_edge) {
-
-      // If yes, compute the length of the best path
-      for(Vertex *v = _sink; v->pred_edge; v = v->pred_vertex) {
-        total_length += v->pred_edge->length;
+    // Use the current distance from the source to make all edge
+    // lengths positive
+    update_positivized_lengths();
+    // Fix numerical errors
+    force_positivized_lengths();
+
+    find_shortest_path();
+
+    shortest_path_length = 0.0;
+
+    // Do we reach the sink?
+    if(_sink->pred_edge_toward_source) {
+      // If yes, compute the length of the best path according to the
+      // original edge lengths
+      v = _sink;
+      while(v->pred_edge_toward_source) {
+        shortest_path_length += v->pred_edge_toward_source->length;
+        v = v->pred_edge_toward_source->origin_vertex;
       }
-
       // If that length is negative
-      if(total_length < 0.0) {
+      if(shortest_path_length < 0.0) {
+#ifdef VERBOSE
+        cerr << __FILE__ << ": Found a path of length " << shortest_path_length << endl;
+#endif
         // Invert all the edges along the best path
-        for(Vertex *v = _sink; v->pred_edge; v = v->pred_vertex) {
-          Edge *e = v->pred_edge;
-          e->terminal_vertex = v->pred_vertex;
+        v = _sink;
+        while(v->pred_edge_toward_source) {
+          e = v->pred_edge_toward_source;
+          v = e->origin_vertex;
+          e->invert();
+          // This is the only place where we change the occupations of
+          // edges
           e->occupied = 1 - e->occupied;
-          e->length = - e->length;
-          e->work_length = - e->work_length;
-          v->pred_vertex->del_edge(e);
-          v->add_edge(e);
         }
       }
     }
 
-  } while(total_length < 0.0);
+  } while(shortest_path_length < 0.0);
 
-  for(Edge *e = _sink->root_edge; e; e = e->next) {
-    if(e->occupied) {
-      Edge *f = e;
-      cout << "PATH " << _sink->id;
-      while(f) {
-        cout << " " << f->terminal_vertex->id;
-        for(f = f->terminal_vertex->root_edge; f && !f->occupied; f = f->next);
+  // Put back the graph in its original state (i.e. invert edges which
+  // have been inverted in the process)
+  for(int k = 0; k < _nb_edges; k++) {
+    e = &_edges[k];
+    if(e->occupied) { e->invert(); }
+  }
+}
+
+int MTPGraph::retrieve_one_path(Edge *e, Path *path, int *used_edges) {
+  Edge *f, *next = 0;
+  int l = 0, nb_occupied_next;
+
+  if(path) {
+    path->nodes[l++] = int(e->origin_vertex - _vertices);
+    path->length = e->length;
+  } else l++;
+
+  while(e->terminal_vertex != _sink) {
+    if(path) {
+      path->nodes[l++] = int(e->terminal_vertex - _vertices);
+      path->length += e->length;
+    } else l++;
+
+    nb_occupied_next = 0;
+    for(f = e->terminal_vertex->leaving_edge_list_root; f; f = f->next_leaving_edge) {
+      if(f->occupied && !used_edges[f - _edges]) {
+        nb_occupied_next++; next = f;
+      }
+    }
+
+#ifdef DEBUG
+    if(nb_occupied_next == 0) {
+      cerr << __FILE__ << ": retrieve_one_path: Non-sink end point." << endl;
+      abort();
+    }
+#endif
+
+    if(path) { used_edges[next - _edges] = 1; }
+
+    e = next;
+  }
+
+  if(path) {
+    path->nodes[l++] = int(e->terminal_vertex - _vertices);
+    path->length += e->length;
+  } else l++;
+
+  return l;
+}
+
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::compute_dp_ordering() {
+  Vertex *v;
+  Edge *e;
+  int ntv;
+
+  // This method orders the nodes by putting first the ones with no
+  // predecessors, then going on adding nodes whose predecessors have
+  // all been already added. Computing the distances from the source
+  // by visiting nodes in that order is equivalent to DP.
+
+  int *nb_predecessors = new int[_nb_vertices];
+
+  Vertex **already_processed = _dp_order, **front = _dp_order, **new_front = _dp_order;
+
+  for(int k = 0; k < _nb_vertices; k++) {
+    nb_predecessors[k] = 0;
+  }
+
+  for(int k = 0; k < _nb_vertices; k++) {
+    v = &_vertices[k];
+    for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+      ntv = int(e->terminal_vertex - _vertices);
+      nb_predecessors[ntv]++;
+    }
+  }
+
+  for(int k = 0; k < _nb_vertices; k++) {
+    if(nb_predecessors[k] == 0) {
+      *(front++) = _vertices + k;
+    }
+  }
+
+  while(already_processed < front) {
+    // Here, nodes before already_processed can be ignored, nodes
+    // before front were set to 0 predecessors during the previous
+    // iteration. During this new iteration, we have to visit the
+    // successors of these ones only, since they are the only ones
+    // which may end up with no predecessors.
+    new_front = front;
+    while(already_processed < front) {
+      v = *(already_processed++);
+      for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+        ntv = int(e->terminal_vertex - _vertices);
+        nb_predecessors[ntv]--;
+        ASSERT(nb_predecessors[ntv] >= 0);
+        if(nb_predecessors[ntv] == 0) {
+          *(new_front++) = e->terminal_vertex;
+        }
       }
-      cout << endl;
     }
+    front = new_front;
+  }
+
+  if(already_processed < _dp_order + _nb_vertices) {
+    cerr << __FILE__ << ": The graph is not a DAG." << endl;
+    abort();
+  }
+
+  delete[] nb_predecessors;
+}
+
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::retrieve_disjoint_paths() {
+  Edge *e;
+  int p, l;
+  int *used_edges;
+
+  for(int p = 0; p < nb_paths; p++) delete paths[p];
+  delete[] paths;
+
+  nb_paths = 0;
+  for(e = _source->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+    if(e->occupied) { nb_paths++; }
+  }
+
+  paths = new Path *[nb_paths];
+  used_edges = new int[_nb_edges];
+  for(int e = 0; e < _nb_edges; e++) {
+    used_edges[e] = 0;
   }
 
-  for(int n = 0; n < _nb_vertices; n++) {
-    Vertex *v = &vertices[n];
-    for(Edge *e = v->root_edge; e; e = e->next) {
-      result_edge_occupation[e->id] = e->occupied;
+  p = 0;
+  for(e = _source->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+    if(e->occupied && !used_edges[e - _edges]) {
+      l = retrieve_one_path(e, 0, used_edges);
+      paths[p] = new Path(l);
+      retrieve_one_path(e, paths[p], used_edges);
+      used_edges[e - _edges] = 1;
+      p++;
     }
   }
+
+  delete[] used_edges;
 }