X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=mtp.git;a=blobdiff_plain;f=mtp_graph.cc;h=dc383210e450711218fc69232d112320d61acc28;hp=5371732a03e9c85e3b357f16464e36773535a0b7;hb=23dae2d97cfbc14f63d3d2c9050d3d4f1ef7bd66;hpb=6c727bc27f1b594b5f3e5a756a0a01c3cb9b1cec

diff --git a/mtp_graph.cc b/mtp_graph.cc
index 5371732..dc38321 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;
@@ -43,17 +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
+  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);
 };
 
 //////////////////////////////////////////////////////////////////////
@@ -63,27 +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;
@@ -93,6 +95,53 @@ void Vertex::del_leaving_edge(Edge *e) {
   }
 }
 
+void Vertex::decrease_distance_in_heap(Vertex **heap) {
+  Vertex **p, **h;
+  // There is some beauty in that
+  h = heap_slot;
+  while(h > heap &&
+        (p = heap + (h - heap + 1) / 2 - 1,
+         (*p)->distance_from_source > (*h)->distance_from_source)) {
+    swap(*p, *h);
+    swap((*p)->heap_slot, (*h)->heap_slot);
+    h = p;
+  }
+}
+
+void Vertex::increase_distance_in_heap(Vertex **heap, Vertex **heap_bottom) {
+  Vertex **c1, **c2, **h;
+  // omg, that's beautiful
+  h = heap_slot;
+  while(c1 = heap + 2 * (h - heap) + 1,
+        c1 < heap_bottom &&
+        (c2 = c1 + 1,
+         (*c1)->distance_from_source < (*h)->distance_from_source
+         ||
+         (c2 < heap_bottom && (*c2)->distance_from_source < (*h)->distance_from_source)
+         )) {
+    if(c2 < heap_bottom && (*c2)->distance_from_source <= (*c1)->distance_from_source) {
+      swap(*c2, *h);
+      swap((*c2)->heap_slot, (*h)->heap_slot);
+      h = c2;
+    } else {
+      swap(*c1, *h);
+      swap((*c1)->heap_slot, (*h)->heap_slot);
+      h = c1;
+    }
+  }
+}
+
+//////////////////////////////////////////////////////////////////////
+
+static int compare_vertices_on_distance(const void *v1, const void *v2) {
+  scalar_t delta =
+    (*((Vertex **) v1))->distance_from_source -
+    (*((Vertex **) v2))->distance_from_source;
+  if(delta < 0) return -1;
+  else if(delta > 0) return 1;
+  else return 0;
+}
+
 //////////////////////////////////////////////////////////////////////
 
 MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
@@ -103,8 +152,8 @@ MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
 
   _edges = new Edge[_nb_edges];
   _vertices = new Vertex[_nb_vertices];
-  _front = new Vertex *[_nb_vertices];
-  _new_front = new Vertex *[_nb_vertices];
+  _heap = new Vertex *[_nb_vertices];
+  _dp_order = new Vertex *[_nb_vertices];
 
   _source = &_vertices[source];
   _sink = &_vertices[sink];
@@ -116,32 +165,97 @@ MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
     _edges[e].terminal_vertex = _vertices + vertex_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_ranks();
+  for(int v = 0; v < _nb_vertices; v++) { _dp_order[v] = &_vertices[v]; }
+  qsort(_dp_order, _nb_vertices, sizeof(Vertex *), compare_vertices_on_distance);
 }
 
 MTPGraph::~MTPGraph() {
   delete[] _vertices;
+  delete[] _dp_order;
+  delete[] _heap;
   delete[] _edges;
-  delete[] _front;
-  delete[] _new_front;
   for(int p = 0; p < nb_paths; p++) delete paths[p];
   delete[] paths;
 }
 
 //////////////////////////////////////////////////////////////////////
 
+void MTPGraph::compute_dp_ranks() {
+  Vertex *v;
+  Edge *e;
+
+  // This procedure computes for each node the longest link from the
+  // source and abort if the graph is not a DAG. It works by removing
+  // successively nodes without predecessor: At the first iteration it
+  // removes the source, then the nodes with incoming edge only from
+  // the source, etc. If it can remove all the nodes that way, the
+  // graph is a DAG. If at some point it can not remove node anymore
+  // and there are some remaining nodes, the graph is not a DAG. The
+  // rank of a node is the iteration at which is it removed, and we
+  // set the distance_from_source fields to this value.
+
+  Vertex **with_predecessor = new Vertex *[_nb_vertices];
+
+  // All the nodes are with_predecessor at first
+  for(int k = 0; k < _nb_vertices; k++) {
+    _vertices[k].distance_from_source = 0;
+    with_predecessor[k] = &_vertices[k];
+  }
+
+  scalar_t rank = 1;
+  int nb_with_predecessor = _nb_vertices, pred_nb_with_predecessor;
+
+  do {
+    // We set the distance_from_source field of all the vertices with incoming
+    // edges to the current rank value
+    for(int f = 0; f < nb_with_predecessor; f++) {
+      v = with_predecessor[f];
+      for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+        e->terminal_vertex->distance_from_source = rank;
+      }
+    }
+
+    pred_nb_with_predecessor = nb_with_predecessor;
+    nb_with_predecessor = 0;
+
+    // We keep all the vertices with incoming nodes
+    for(int f = 0; f < pred_nb_with_predecessor; f++) {
+      v = with_predecessor[f];
+      if(v->distance_from_source == rank) {
+        with_predecessor[nb_with_predecessor++] = v;
+      }
+    }
+
+    rank++;
+  } while(nb_with_predecessor < pred_nb_with_predecessor);
+
+  delete[] with_predecessor;
+
+  if(nb_with_predecessor > 0) {
+    cerr << __FILE__ << ": The graph is not a DAG." << endl;
+    abort();
+  }
+}
+
+//////////////////////////////////////////////////////////////////////
+
 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) << " *";
-    }
+          << " -> "
+          << e->terminal_vertex - _vertices
+          << " (" << e->length << ")";
+    if(e->occupied) { (*os) << " *"; }
     (*os) << endl;
   }
 }
@@ -187,130 +301,89 @@ void MTPGraph::force_positivized_lengths() {
     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 " << residual_error << endl;
 #endif
 }
 
-int MTPGraph::is_dag() {
-  Vertex *v;
+void MTPGraph::dp_compute_distances() {
+  Vertex *v, *tv;
   Edge *e;
+  scalar_t d;
 
-  // We put everybody in the front
   for(int k = 0; k < _nb_vertices; k++) {
-    _vertices[k].last_change = -1;
-    _front[k] = &_vertices[k];
+    _vertices[k].distance_from_source = FLT_MAX;
+    _vertices[k].pred_edge_toward_source = 0;
   }
 
-  int iteration = 0;
-  int front_size = _nb_vertices, pred_front_size;
-
-  do {
-    // We set the last_change field of all the vertices with incoming
-    // edges to the current iteration value
-    for(int f = 0; f < front_size; f++) {
-      v = _front[f];
-      for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
-        e->terminal_vertex->last_change = iteration;
-      }
-    }
-
-    pred_front_size = front_size;
-    front_size = 0;
+  _source->distance_from_source = 0;
 
-    // We keep all the vertices with incoming nodes
-    for(int f = 0; f < pred_front_size; f++) {
-      v = _front[f];
-      if(v->last_change == iteration) {
-        _front[front_size++] = v;
+  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;
       }
     }
-
-    iteration++;
-  } while(front_size < pred_front_size);
-
-  return front_size == 0;
+  }
 }
 
-// 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 **tmp_front;
-  Vertex *v, *tv;
+  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;
-    _vertices[k].last_change = -1;
   }
 
-  int iteration = 0;
-
-  int front_size = 0, new_front_size;
-  _front[front_size++] = _source;
+  _heap_size = _nb_vertices;
   _source->distance_from_source = 0;
+  _source->decrease_distance_in_heap(_heap);
 
   do {
-    new_front_size = 0;
-
-    for(int f = 0; f < front_size; f++) {
-      v = _front[f];
-      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;
-          if(tv->last_change < iteration) {
-            _new_front[new_front_size++] = tv;
-            tv->last_change = iteration;
-          }
-        }
+    // 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[0]->increase_distance_in_heap(_heap, _heap + _heap_size);
+
+    // 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 - _heap < _heap_size);
+        tv->distance_from_source = d;
+        tv->pred_edge_toward_source = e;
+        tv->decrease_distance_in_heap(_heap);
       }
     }
-
-    tmp_front = _new_front; _new_front = _front; _front = tmp_front;
-
-    front_size = new_front_size;
-
-    iteration++;
-  } while(front_size > 0);
+  } while(_heap_size > 0);
 }
 
 void MTPGraph::find_best_paths(scalar_t *lengths) {
-  scalar_t total_length;
+  scalar_t shortest_path_length;
   Vertex *v;
   Edge *e;
 
@@ -320,17 +393,21 @@ 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();
+  // 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) {
@@ -338,13 +415,13 @@ 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;
@@ -359,7 +436,7 @@ 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)
@@ -385,18 +462,18 @@ int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
     } else l++;
 
     nb_occupied_next = 0;
-    for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
+    for(f = e->terminal_vertex->leaving_edge_list_root; 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;
+      cerr << __FILE__ << ": 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 node-disjoint paths." << endl;
       abort();
     }
 #endif
@@ -420,14 +497,14 @@ void MTPGraph::retrieve_disjoint_paths() {
   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];
 
   p = 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) {
       l = retrieve_one_path(e, 0);
       paths[p] = new Path(l);