X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=mtp.git;a=blobdiff_plain;f=mtp_graph.cc;h=2cbb33848a3589007528a6e3b1098357dbf3d3df;hp=12017c20a1b9039e1e62ebd5a96ed9ee0a90ac92;hb=HEAD;hpb=2b3a2e10ec226f1610b9c39abd20f0899a34a652

diff --git a/mtp_graph.cc b/mtp_graph.cc
index 12017c2..2cbb338 100644
--- a/mtp_graph.cc
+++ b/mtp_graph.cc
@@ -24,6 +24,7 @@
 
 #include "mtp_graph.h"
 
+#include <cmath>
 #include <float.h>
 
 using namespace std;
@@ -43,19 +44,18 @@ public:
 
 class Vertex {
 public:
-  Edge *leaving_edges;
   scalar_t distance_from_source;
   Edge *pred_edge_toward_source;
 
-  int last_change; // Used to mark which edges have already been
-                   // processed in some methods
-
-  Vertex **heap_position;
+  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);
 };
 
 //////////////////////////////////////////////////////////////////////
@@ -65,27 +65,27 @@ void Edge::invert() {
   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;
+  swap(terminal_vertex, origin_vertex);
 }
 
 //////////////////////////////////////////////////////////////////////
 
 Vertex::Vertex() {
-  leaving_edges = 0;
+  leaving_edge_list_root = 0;
 }
 
 void Vertex::add_leaving_edge(Edge *e) {
-  e->next_leaving_edge = leaving_edges;
+  e->next_leaving_edge = leaving_edge_list_root;
   e->pred_leaving_edge = 0;
-  if(leaving_edges) { leaving_edges->pred_leaving_edge = e; }
-  leaving_edges = e;
+  if(leaving_edge_list_root) {
+    leaving_edge_list_root->pred_leaving_edge = e;
+  }
+  leaving_edge_list_root = e;
 }
 
 void Vertex::del_leaving_edge(Edge *e) {
-  if(e == leaving_edges) {
-    leaving_edges = e->next_leaving_edge;
+  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;
@@ -95,12 +95,48 @@ void Vertex::del_leaving_edge(Edge *e) {
   }
 }
 
-//////////////////////////////////////////////////////////////////////
+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;
+  }
+}
 
-static int compare_vertex(const void *v1, const void *v2) {
-  return (*((Vertex **) v1))->last_change - (*((Vertex **) v2))->last_change;
+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 {
+        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;
+    }
+  }
 }
 
+//////////////////////////////////////////////////////////////////////
+
 MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
                    int *vertex_from, int *vertex_to,
                    int source, int sink) {
@@ -116,30 +152,21 @@ MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
   _sink = &_vertices[sink];
 
   for(int e = 0; e < nb_edges; e++) {
-    _vertices[vertex_from[e]].add_leaving_edge(_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];
+    _edges[e].origin_vertex = &_vertices[vertex_from[e]];
+    _edges[e].terminal_vertex = &_vertices[vertex_to[e]];
   }
 
   for(int v = 0; v < _nb_vertices; v++) {
     _heap[v] = &_vertices[v];
-    _vertices[v].heap_position = &_heap[v];
+    _vertices[v].heap_slot = &_heap[v];
   }
 
   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();
-  }
+  compute_dp_ordering();
 }
 
 MTPGraph::~MTPGraph() {
@@ -155,15 +182,12 @@ MTPGraph::~MTPGraph() {
 
 void MTPGraph::print(ostream *os) {
   for(int k = 0; k < _nb_edges; k++) {
-    Edge *e = _edges + k;
+    Edge *e = &_edges[k];
     (*os) << e->origin_vertex - _vertices
-         << " -> "
-         << e->terminal_vertex - _vertices
-         << " "
-         << e->length;
-    if(e->occupied) {
-      (*os) << " *";
-    }
+          << " -> "
+          << e->terminal_vertex - _vertices
+          << " (" << e->length << ")";
+    if(e->occupied) { (*os) << " *"; }
     (*os) << endl;
   }
 }
@@ -176,7 +200,7 @@ void MTPGraph::print_dot(ostream *os) {
   (*os) << "        " << _source - _vertices << " [peripheries=2];" << endl;
   (*os) << "        " << _sink - _vertices << " [peripheries=2];" << endl;
   for(int k = 0; k < _nb_edges; k++) {
-    Edge *e = _edges + k;
+    Edge *e = &_edges[k];
     (*os) << "        "
           << e->origin_vertex - _vertices
           << " -> "
@@ -194,7 +218,7 @@ void MTPGraph::print_dot(ostream *os) {
 
 void MTPGraph::update_positivized_lengths() {
   for(int k = 0; k < _nb_edges; k++) {
-    Edge *e = _edges + k;
+    Edge *e = &_edges[k];
     e->positivized_length +=
       e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
   }
@@ -206,170 +230,22 @@ void MTPGraph::force_positivized_lengths() {
   scalar_t max_error = 0.0;
 #endif
   for(int k = 0; k < _nb_edges; k++) {
-    Edge *e = _edges + k;
+    Edge *e = &_edges[k];
 
     if(e->positivized_length < 0) {
-
 #ifdef VERBOSE
-      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);
-      }
+      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 << " max_error " << residual_error << endl;
+  cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << max_error << endl;
 #endif
 }
 
-int MTPGraph::is_dag() {
-  Vertex *v;
-  Edge *e;
-
-  Vertex **active = new Vertex *[_nb_vertices];
-
-  // 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 {
-    // 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++;
-  } 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() {
+void MTPGraph::dp_compute_distances() {
   Vertex *v, *tv;
   Edge *e;
   scalar_t d;
@@ -383,99 +259,64 @@ void MTPGraph::dp_distance_propagation() {
 
   for(int k = 0; k < _nb_vertices; k++) {
     v = _dp_order[k];
-    for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+    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;
-        decrease_distance_in_heap(tv);
       }
     }
   }
-
-#ifdef DEBUG
-  for(int k = 0; k < _nb_vertices; k++) {
-    if(_vertices[k].distance_from_source == FLT_MAX) abort();
-  }
-#endif
 }
 
-// This method does not change the edge occupation. It only set
+// 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.
 
 void MTPGraph::find_shortest_path() {
-  Vertex *v, *tv;
+  int heap_size;
+  Vertex *v, *tv, **last_slot;
   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;
+  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
+  _source->decrease_distance_in_heap(_heap);
 
+  while(heap_size > 1) {
+    // Get the closest to the source
     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) {
+    // 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_position - _heap < _heap_size);
+        ASSERT(tv->heap_slot < last_slot);
         tv->distance_from_source = d;
         tv->pred_edge_toward_source = e;
-        decrease_distance_in_heap(tv);
+        tv->decrease_distance_in_heap(_heap);
       }
-#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) {
-  scalar_t total_length;
+  scalar_t shortest_path_length;
   Vertex *v;
   Edge *e;
 
@@ -485,19 +326,21 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
     _edges[e].positivized_length = _edges[e].length;
   }
 
-  // // 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();
+  // 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 {
+    // 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();
 
-    total_length = 0.0;
+    shortest_path_length = 0.0;
 
     // Do we reach the sink?
     if(_sink->pred_edge_toward_source) {
@@ -505,13 +348,13 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
       // original edge lengths
       v = _sink;
       while(v->pred_edge_toward_source) {
-        total_length += v->pred_edge_toward_source->length;
+        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 << "Found a path of length " << total_length << endl;
+        cerr << __FILE__ << ": Found a path of length " << shortest_path_length << endl;
 #endif
         // Invert all the edges along the best path
         v = _sink;
@@ -526,80 +369,152 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
       }
     }
 
-  } while(total_length < 0.0);
+  } while(shortest_path_length < 0.0);
 
   // 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;
+    e = &_edges[k];
     if(e->occupied) { e->invert(); }
   }
 }
 
-int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
+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++] = e->origin_vertex - _vertices;
+    path->nodes[l++] = int(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->nodes[l++] = int(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; }
+    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 << "retrieve_one_path: Non-sink end point." << endl;
-      abort();
-    }
-
-    else if(nb_occupied_next > 1) {
-      cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
+      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++] = e->terminal_vertex - _vertices;
+    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;
+        }
+      }
+    }
+    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_edges; e; e = e->next_leaving_edge) {
+  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;
+  }
 
   p = 0;
-  for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
-    if(e->occupied) {
-      l = retrieve_one_path(e, 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]);
+      retrieve_one_path(e, paths[p], used_edges);
+      used_edges[e - _edges] = 1;
       p++;
     }
   }
+
+  delete[] used_edges;
 }