X-Git-Url: https://www.fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=mtp.git;a=blobdiff_plain;f=mtp_graph.cc;h=12017c20a1b9039e1e62ebd5a96ed9ee0a90ac92;hp=c2a7fa3e2a150ab06b575ddb84695cddf46f3984;hb=2b3a2e10ec226f1610b9c39abd20f0899a34a652;hpb=ea33e3e5dddbe3796d2361910e1e3ed98a19865c

diff --git a/mtp_graph.cc b/mtp_graph.cc
index c2a7fa3..12017c2 100644
--- a/mtp_graph.cc
+++ b/mtp_graph.cc
@@ -1,263 +1,605 @@
 
-///////////////////////////////////////////////////////////////////////////
-// 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 <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;
+  Edge *leaving_edges;
   scalar_t distance_from_source;
-  Vertex *pred_vertex;
-  Edge *pred_edge;
+  Edge *pred_edge_toward_source;
 
-  Vertex() { root_edge = 0; }
+  int last_change; // Used to mark which edges have already been
+                   // processed in some methods
 
-  inline void add_edge(Edge *e) {
-    e->next = root_edge;
-    e->pred = 0;
-    if(root_edge) { root_edge->pred = e; }
-    root_edge = e;
-  }
+  Vertex **heap_position;
 
-  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; }
-  }
+  Vertex();
+
+  inline void add_leaving_edge(Edge *e);
+  inline void del_leaving_edge(Edge *e);
 };
 
-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 Edge::invert() {
+  length = - length;
+  positivized_length = - positivized_length;
+  origin_vertex->del_leaving_edge(this);
+  terminal_vertex->add_leaving_edge(this);
+  Vertex *t = terminal_vertex;
+  terminal_vertex = origin_vertex;
+  origin_vertex = t;
 }
 
-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;
-      } else {
-        cout << "  " << a << " -> " << b << " [color=gray,label=\"" << e->length << "\"];" << endl;
-      }
-    }
-  }
-  cout << "}" << endl;
+//////////////////////////////////////////////////////////////////////
+
+Vertex::Vertex() {
+  leaving_edges = 0;
 }
 
+void Vertex::add_leaving_edge(Edge *e) {
+  e->next_leaving_edge = leaving_edges;
+  e->pred_leaving_edge = 0;
+  if(leaving_edges) { leaving_edges->pred_leaving_edge = e; }
+  leaving_edges = e;
+}
 
-void dot_print(int nb_vertices,
-               int nb_edges, int *ea, int *eb, scalar_t *el,
-               int _source, int _sink,
-               int *edge_occupation) {
-  for(int e = 0; e < nb_edges; e++) {
+void Vertex::del_leaving_edge(Edge *e) {
+  if(e == leaving_edges) {
+    leaving_edges = 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;
   }
-  cout << "}" << endl;
 }
+
+//////////////////////////////////////////////////////////////////////
+
+static int compare_vertex(const void *v1, const void *v2) {
+  return (*((Vertex **) v1))->last_change - (*((Vertex **) v2))->last_change;
+}
+
 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];
+  _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_position = &_heap[v];
   }
 
-  _front = new Vertex *[_nb_vertices];
-  _new_front = new Vertex *[_nb_vertices];
+  paths = 0;
+  nb_paths = 0;
+
+  if(is_dag()) {
+    // Here the last_change field of every vertex tells us how many
+    // iterations of DP we need to reach it. Hence we only have to
+    // process the vertex in that order.
+    for(int v = 0; v < _nb_vertices; v++) { _dp_order[v] = &_vertices[v]; }
+    qsort(_dp_order, _nb_vertices, sizeof(Vertex *), compare_vertex);
+  } else {
+    cerr << __FILE__ << ": This graph is not a DAG." << endl;
+    abort();
+  }
 }
 
 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);
-    }
-  }
-  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(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;
   }
 }
 
-void MTPGraph::update_work_length() {
-  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::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::find_shortest_path(Vertex **_front, Vertex **_new_front) {
-  Vertex **tmp_front;
-  int tmp_front_size;
-  Vertex *v, *tv;
-  scalar_t d;
+//////////////////////////////////////////////////////////////////////
+
+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_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;
-#endif
-        e->work_length = 0.0;
+      if((e->origin_vertex->last_change < 0 && e->terminal_vertex->last_change >= 0) ||
+         (e->origin_vertex->last_change >= 0 && e->terminal_vertex->last_change < 0)) {
+        cout << "Inconsistent non-connexity (this should never happen)." << endl;
+        abort();
+      }
+      if(e->origin_vertex->last_change >= 0 &&
+         e->terminal_vertex->last_change >= 0 &&
+         e->positivized_length < 0) {
+        residual_error -= e->positivized_length;
+        max_error = max(max_error, - e->positivized_length);
       }
+#endif
+      e->positivized_length = 0.0;
     }
   }
 #ifdef VERBOSE
-  cerr << "residual_error " << residual_error << endl;
+  cerr << "residual_error " << residual_error << " max_error " << residual_error << endl;
 #endif
+}
 
-  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;
-  }
+int MTPGraph::is_dag() {
+  Vertex *v;
+  Edge *e;
 
-  int iteration = 0;
+  Vertex **active = new Vertex *[_nb_vertices];
 
-  int _front_size = 0, _new_front_size;
-  _front[_front_size++] = _source;
-  _source->distance_from_source = 0;
+  // We put everybody in the active
+  for(int k = 0; k < _nb_vertices; k++) {
+    _vertices[k].last_change = 0;
+    active[k] = &_vertices[k];
+  }
+
+  int iteration = 1;
+  int nb_active = _nb_vertices, pred_nb_active;
 
   do {
-    _new_front_size = 0;
+    // We set the last_change field of all the vertices with incoming
+    // edges to the current iteration value
+    for(int f = 0; f < nb_active; f++) {
+      v = active[f];
+      for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+        e->terminal_vertex->last_change = iteration;
+      }
+    }
+
+    pred_nb_active = nb_active;
+    nb_active = 0;
+
+    // We keep all the vertices with incoming nodes
+    for(int f = 0; f < pred_nb_active; f++) {
+      v = active[f];
+      if(v->last_change == iteration) {
+        active[nb_active++] = v;
+      }
+    }
+
     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;
-          }
-        }
+  } while(nb_active < pred_nb_active);
+
+  delete[] active;
+
+  return nb_active == 0;
+}
+
+#ifdef DEBUG
+void print_heap(int first, int heap_size, Vertex **heap, int depth, Vertex *vertices) {
+  // if(depth == 0) cout << "** START_HEAP ********************************************************" << endl;
+  // if(first < heap_size) {
+    // print_heap((first + 1) * 2 - 1, heap_size, heap, depth + 1, vertices);
+    // for(int d = 0; d < depth; d++) cout << "  ";
+    // cout << "[" << heap[first] - vertices << "] ";
+    // if(heap[first]->distance_from_source == FLT_MAX) cout << "inf";
+    // else cout << heap[first]->distance_from_source;
+    // cout << endl;
+    // print_heap((first + 1) * 2, heap_size, heap, depth + 1, vertices);
+  // }
+  // if(depth == 0) cout << "** END_HEAP **********************************************************" << endl;
+}
+
+void check_heap(Vertex **heap, int heap_size, Vertex *vertices, int nb_vertices) {
+  Vertex **p, **h;
+  int *used = new int[nb_vertices];
+  for(int v = 0; v < nb_vertices; v++) used[v] = 0;
+  for(int k = 0; k < heap_size; k++) {
+    used[heap[k] - vertices]++;
+    h = heap + k;
+    if(h != (*h)->heap_position) abort();
+    if(k > 0) {
+      p = heap + (h - heap + 1) / 2 - 1;
+      if((*h)->distance_from_source < (*p)->distance_from_source) abort();
+    }
+  }
+  for(int v = 0; v < nb_vertices; v++) {
+    cout << used[v];
+    if(used[v] > 1) abort();
+  }
+  cout << endl;
+  delete[] used;
+}
+#endif
+
+void MTPGraph::decrease_distance_in_heap(Vertex *v) {
+#ifdef DEBUG
+  // cout << "START decrease_distance_in_heap" << endl;
+  // print_heap(0, _heap_size, _heap, 0, _vertices);
+#endif
+  Vertex **p, **h;
+  // There is some beauty in that
+  h = v->heap_position;
+  while(h > _heap &&
+        (p = _heap + (h - _heap + 1) / 2 - 1,
+         (*p)->distance_from_source > (*h)->distance_from_source)) {
+// #warning REMOVE
+    // cout << "SWAP [" << (*p) - _vertices << " | " << (*h) - _vertices << "]" << endl;
+    // if((*p) - _vertices == 6 && (*h) - _vertices == 96) abort();
+    swap(*p, *h);
+    swap((*p)->heap_position, (*h)->heap_position);
+    h = p;
+  }
+#ifdef DEBUG
+  // check_heap(_heap, _heap_size, _vertices, _nb_vertices);
+  // print_heap(0, _heap_size, _heap, 0, _vertices);
+#endif
+}
+
+void MTPGraph::increase_distance_in_heap(Vertex *v) {
+#ifdef DEBUG
+  // cout << "START increase_distance_in_heap" << endl;
+  // print_heap(0, _heap_size, _heap, 0, _vertices);
+#endif
+  Vertex **c1, **c2, **h;
+  // There is some beauty in that
+  h = v->heap_position;
+  while(c1 = _heap + 2 * (h - _heap + 1) - 1, c2 = c1 + 1,
+        (c1 < _heap + _heap_size &&
+         (*c1)->distance_from_source < (*h)->distance_from_source)
+        ||
+        (c2 < _heap + _heap_size &&
+          (*c2)->distance_from_source < (*h)->distance_from_source)
+        ) {
+    if(c1 < _heap + _heap_size &&
+       !(c2 < _heap + _heap_size &&
+         (*c2)->distance_from_source < (*c1)->distance_from_source)){
+      swap(*c1, *h);
+      swap((*c1)->heap_position, (*h)->heap_position);
+      h = c1;
+    } else {
+      swap(*c2, *h);
+      swap((*c2)->heap_position, (*h)->heap_position);
+      h = c2;
+    }
+  }
+#ifdef DEBUG
+  // check_heap(_heap, _heap_size, _vertices, _nb_vertices);
+  // print_heap(0, _heap_size, _heap, 0, _vertices);
+#endif
+}
+
+void MTPGraph::dp_distance_propagation() {
+  Vertex *v, *tv;
+  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;
+  }
+
+  _source->distance_from_source = 0;
+
+  for(int k = 0; k < _nb_vertices; k++) {
+    v = _dp_order[k];
+    for(e = v->leaving_edges; 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;
+        decrease_distance_in_heap(tv);
       }
     }
+  }
 
-    tmp_front = _new_front;
-    _new_front = _front;
-    _front = tmp_front;
+#ifdef DEBUG
+  for(int k = 0; k < _nb_vertices; k++) {
+    if(_vertices[k].distance_from_source == FLT_MAX) abort();
+  }
+#endif
+}
 
-    tmp_front_size = _new_front_size;
-    _new_front_size = _front_size;
-    _front_size = tmp_front_size;
-  } while(_front_size > 0);
+// This method does not change the edge occupation. It only set
+// properly, for every vertex, the fields distance_from_source and
+// pred_edge_toward_source.
+
+void MTPGraph::find_shortest_path() {
+  Vertex *v, *tv;
+  Edge *e;
+  scalar_t d;
+
+#ifdef DEBUG
+  if(is_dag()) {
+    cout << "find_shortest_path: DAG -> ok" << endl;
+  } else {
+    for(int e = 0; e < _nb_edges; e++) {
+      if(_edges[e].positivized_length < 0) abort();
+    }
+    cout << "find_shortest_path: All positivized_length are positive -> ok" << endl;
+  }
+#endif
+
+  for(int k = 0; k < _nb_vertices; k++) {
+    _vertices[k].distance_from_source = FLT_MAX;
+    _vertices[k].pred_edge_toward_source = 0;
+  }
+
+  _heap_size = _nb_vertices;
+  _source->distance_from_source = 0;
+  decrease_distance_in_heap(_source);
+
+  do {
+#ifdef DEBUG
+    for(int k = 0; k < _heap_size; k++) {
+      if(_heap[0]->distance_from_source > _heap[k]->distance_from_source) abort();
+    }
+    // cout << "OK!" << endl;
+#endif
+
+    v = _heap[0];
+    _heap_size--;
+    Vertex **a = _heap, **b = _heap + _heap_size;
+    swap(*a, *b); swap((*a)->heap_position, (*b)->heap_position);
+    increase_distance_in_heap(_heap[0]);
+
+    for(e = v->leaving_edges; 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_position - _heap < _heap_size);
+        tv->distance_from_source = d;
+        tv->pred_edge_toward_source = e;
+        decrease_distance_in_heap(tv);
+      }
+#ifdef DEBUG
+      for(int k = 0; k < _heap_size; k++) {
+        if(_heap[0]->distance_from_source > _heap[k]->distance_from_source) abort();
+      }
+#endif
+    }
+  } while(_heap_size > 0);
+
+#ifdef DEBUG
+  for(int k = 0; k < _nb_vertices; k++) {
+    v = &_vertices[k];
+    for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+      d = v->distance_from_source + e->positivized_length;
+      tv = e->terminal_vertex;
+      if(d < tv->distance_from_source) abort();
+    }
+  }
+#endif
+  cout << "DONE!" << endl;
 }
 
-void MTPGraph::find_best_paths(scalar_t *lengths, int *result_edge_occupation) {
+void MTPGraph::find_best_paths(scalar_t *lengths) {
   scalar_t total_length;
+  Vertex *v;
+  Edge *e;
 
   for(int e = 0; e < _nb_edges; e++) {
-    edges[e].length = lengths[e];
+    _edges[e].length = lengths[e];
+    _edges[e].occupied = 0;
+    _edges[e].positivized_length = _edges[e].length;
   }
 
-  initialize_work_lengths();
+  // // We call find_shortest_path here to set properly the distances to
+  // // the source, so that we can make all the edge lengths positive at
+  // // the first iteration.
+  // find_shortest_path();
+
+  dp_distance_propagation();
 
   do {
-    total_length = 0.0;
-    find_shortest_path(_front, _new_front);
-    update_work_length();
+    update_positivized_lengths();
+    force_positivized_lengths();
+    find_shortest_path();
 
-    // Do we reach the _sink?
-    if(_sink->pred_edge) {
+    total_length = 0.0;
 
-      // 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;
+    // 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) {
+        total_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) {
+#ifdef VERBOSE
+        cerr << "Found a path of length " << total_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);
 
-  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;
+  // 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) {
+  Edge *f, *next = 0;
+  int l = 0, nb_occupied_next;
+
+  if(path) {
+    path->nodes[l++] = e->origin_vertex - _vertices;
+    path->length = e->length;
+  } else l++;
+
+  while(e->terminal_vertex != _sink) {
+    if(path) {
+      path->nodes[l++] = e->terminal_vertex - _vertices;
+      path->length += e->length;
+    } else l++;
+
+    nb_occupied_next = 0;
+    for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
+      if(f->occupied) { nb_occupied_next++; next = f; }
+    }
+
+#ifdef DEBUG
+    if(nb_occupied_next == 0) {
+      cerr << "retrieve_one_path: Non-sink end point." << endl;
+      abort();
+    }
+
+    else if(nb_occupied_next > 1) {
+      cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
+      abort();
+    }
+#endif
+
+    e = next;
+  }
+
+  if(path) {
+    path->nodes[l++] = e->terminal_vertex - _vertices;
+    path->length += e->length;
+  } else l++;
+
+  return l;
+}
+
+void MTPGraph::retrieve_disjoint_paths() {
+  Edge *e;
+  int p, l;
+
+  for(int p = 0; p < nb_paths; p++) delete paths[p];
+  delete[] paths;
+
+  nb_paths = 0;
+  for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
+    if(e->occupied) { nb_paths++; }
+  }
+
+  paths = new Path *[nb_paths];
+
+  p = 0;
+  for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
+    if(e->occupied) {
+      l = retrieve_one_path(e, 0);
+      paths[p] = new Path(l);
+      retrieve_one_path(e, paths[p]);
+      p++;
     }
   }
 }