X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?a=blobdiff_plain;f=mtp_graph.cc;h=343ebf79a60a98d145138891d286ec70915280e0;hb=9aa2c8c57bbe0ac533d081fa3917aa037e65c766;hp=d3b921b791e6acfc2728702b0b593d0dc2cacdf0;hpb=abbaf6b4b4b8d10ee8e9054a3b8d262a2f242920;p=mtp.git

diff --git a/mtp_graph.cc b/mtp_graph.cc
index d3b921b..343ebf7 100644
--- a/mtp_graph.cc
+++ b/mtp_graph.cc
@@ -24,19 +24,18 @@
 
 #include "mtp_graph.h"
 
-#include <iostream>
 #include <float.h>
-#include <stdlib.h>
 
 using namespace std;
 
 class Edge {
 public:
-  int id, occupied;
+  int occupied;
   scalar_t length, positivized_length;
   Vertex *origin_vertex, *terminal_vertex;
 
-  // These are the links in the origin_vertex leaving edge list
+  // 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();
@@ -44,23 +43,24 @@ public:
 
 class Vertex {
 public:
-  int id;
   Edge *leaving_edges;
   scalar_t distance_from_source;
   Edge *pred_edge_toward_source;
+  Vertex **heap_slot;
 
-  int iteration; // Used in find_shortest_path to know if we already
-                 // added this vertex to the front
   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, int heap_size);
 };
 
 //////////////////////////////////////////////////////////////////////
 
 void Edge::invert() {
   length = - length;
-  positivized_length = 0;
+  positivized_length = - positivized_length;
   origin_vertex->del_leaving_edge(this);
   terminal_vertex->add_leaving_edge(this);
   Vertex *t = terminal_vertex;
@@ -93,8 +93,53 @@ 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, int heap_size) {
+  Vertex **c1, **c2, **h;
+  // omg, that's beautiful
+  h = heap_slot;
+  while(c1 = heap + 2 * (h - heap) + 1,
+        c1 < heap + heap_size &&
+        (c2 = c1 + 1,
+         (*c1)->distance_from_source < (*h)->distance_from_source
+         ||
+         (c2 < heap + heap_size && (*c2)->distance_from_source < (*h)->distance_from_source)
+         )) {
+    if(c2 < heap + heap_size && (*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_vertex(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,
                    int *vertex_from, int *vertex_to,
                    int source, int sink) {
@@ -103,33 +148,44 @@ 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];
 
-  for(int k = 0; k < _nb_vertices; k++) {
-    _vertices[k].id = k;
-  }
-
   for(int e = 0; e < nb_edges; e++) {
     _vertices[vertex_from[e]].add_leaving_edge(_edges + e);
     _edges[e].occupied = 0;
-    _edges[e].id = 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_slot = &_heap[v];
+  }
+
   paths = 0;
   nb_paths = 0;
+
+  if(compute_dp_ranks()) {
+    // Here the distance_from_source field of every vertex is the
+    // number of DP iterations needed to update 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[] _dp_order;
+  delete[] _heap;
   delete[] _edges;
-  delete[] _front;
-  delete[] _new_front;
   for(int p = 0; p < nb_paths; p++) delete paths[p];
   delete[] paths;
 }
@@ -139,9 +195,9 @@ MTPGraph::~MTPGraph() {
 void MTPGraph::print(ostream *os) {
   for(int k = 0; k < _nb_edges; k++) {
     Edge *e = _edges + k;
-    (*os) << e->origin_vertex->id
+    (*os) << e->origin_vertex - _vertices
          << " -> "
-         << e->terminal_vertex->id
+         << e->terminal_vertex - _vertices
          << " "
          << e->length;
     if(e->occupied) {
@@ -156,14 +212,14 @@ void MTPGraph::print_dot(ostream *os) {
   (*os) << "        rankdir=\"LR\";" << endl;
   (*os) << "        node [shape=circle,width=0.75,fixedsize=true];" << endl;
   (*os) << "        edge [color=gray,arrowhead=open]" << endl;
-  (*os) << "        " << _source->id << " [peripheries=2];" << endl;
-  (*os) << "        " << _sink->id << " [peripheries=2];" << 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->id << " -> " << e->terminal_vertex->id
-    // << ";"
-    // << endl;
-    (*os) << "        " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
+    (*os) << "        "
+          << e->origin_vertex - _vertices
+          << " -> "
+          << e->terminal_vertex - _vertices
           << " [";
     if(e->occupied) {
       (*os) << "style=bold,color=black,";
@@ -188,119 +244,145 @@ void MTPGraph::force_positivized_lengths() {
   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].leaving_edges; e; e = e->next_leaving_edge) {
-      if(e->positivized_length < 0) {
+  for(int k = 0; k < _nb_edges; k++) {
+    Edge *e = _edges + k;
+
+    if(e->positivized_length < 0) {
+
 #ifdef VERBOSE
-        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;
-      }
+      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() {
+int MTPGraph::compute_dp_ranks() {
   Vertex *v;
   Edge *e;
 
-  // We put everybody in the front
+  // 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 **active = new Vertex *[_nb_vertices];
+
+  // All the nodes are active at first
   for(int k = 0; k < _nb_vertices; k++) {
-    _vertices[k].iteration = 0;
-    _front[k] = &_vertices[k];
+    _vertices[k].distance_from_source = 0;
+    active[k] = &_vertices[k];
   }
 
-  int iteration = 0;
-  int front_size = _nb_vertices, pred_front_size;
+  scalar_t rank = 1;
+  int nb_active = _nb_vertices, pred_nb_active;
 
   do {
-    iteration++;
-
-    // We set the iteration field of all vertex with incoming edges to
-    // the current iteration value
-    for(int f = 0; f < front_size; f++) {
-      v = _front[f];
+    // 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_active; f++) {
+      v = active[f];
       for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
-        e->terminal_vertex->iteration = iteration;
+        e->terminal_vertex->distance_from_source = rank;
       }
     }
 
-    pred_front_size = front_size;
-    front_size = 0;
+    pred_nb_active = nb_active;
+    nb_active = 0;
 
-    // We remove all the vertices without incoming edge
-    for(int f = 0; f < pred_front_size; f++) {
-      v = _front[f];
-      if(v->iteration == iteration) {
-        _front[front_size++] = v;
+    // We keep all the vertices with incoming nodes
+    for(int f = 0; f < pred_nb_active; f++) {
+      v = active[f];
+      if(v->distance_from_source == rank) {
+        active[nb_active++] = v;
       }
     }
-  } while(front_size < pred_front_size);
 
-  return front_size == 0;
-}
+    rank++;
+  } while(nb_active < pred_nb_active);
 
-// 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.
+  delete[] active;
 
-void MTPGraph::find_shortest_path() {
-  Vertex **tmp_front;
+  return nb_active == 0;
+}
+
+void MTPGraph::dp_compute_distances() {
   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();
+  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;
+        tv->decrease_distance_in_heap(_heap);
+      }
     }
-    cout << "find_shortest_path: All positivized_length are positive -> ok" << endl;
   }
-#endif
+}
+
+// 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, **a, **b;
+  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;
-    _vertices[k].iteration = 0;
   }
 
-  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;
-    iteration++;
-
-    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->iteration < iteration) {
-            _new_front[new_front_size++] = tv;
-            tv->iteration = iteration;
-          }
-        }
+    // Get the closest to the source
+    v = _heap[0];
+
+    // Remove it from the heap (swap it with the last in the heap, and
+    // update the distance of that one)
+    _heap_size--;
+    a = _heap;
+    b = _heap + _heap_size;
+    swap(*a, *b); swap((*a)->heap_slot, (*b)->heap_slot);
+    _heap[0]->increase_distance_in_heap(_heap, _heap_size);
+
+    // Now update the neighbors of the currently closest to the source
+    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_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;
-  } while(front_size > 0);
+  } while(_heap_size > 0);
 }
 
 void MTPGraph::find_best_paths(scalar_t *lengths) {
@@ -314,10 +396,8 @@ 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();
+  // Update the distances to the source in "good order"
+  dp_compute_distances();
 
   do {
     update_positivized_lengths();
@@ -328,7 +408,8 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
 
     // Do we reach the sink?
     if(_sink->pred_edge_toward_source) {
-      // If yes, compute the length of the best path
+      // 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;
@@ -337,7 +418,7 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
       // If that length is negative
       if(total_length < 0.0) {
 #ifdef VERBOSE
-        cerr << "Found a path of length " << total_length << endl;
+        cerr << __FILE__ << ": Found a path of length " << total_length << endl;
 #endif
         // Invert all the edges along the best path
         v = _sink;
@@ -357,42 +438,48 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
   // 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++) {
-    Edge *e = _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;
+  int l = 0, nb_occupied_next;
 
   if(path) {
-    path->nodes[l++] = e->origin_vertex->id;
+    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->id;
+      path->nodes[l++] = e->terminal_vertex - _vertices;
       path->length += e->length;
     } else l++;
-    int nb_choices = 0;
+
+    nb_occupied_next = 0;
     for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
-      if(f->occupied) { nb_choices++; next = f; }
-      if(nb_choices == 0) {
-        cerr << "retrieve_one_path: Non-sink end point." << endl;
-        abort();
-      }
-      if(nb_choices > 1) {
-        cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
-        abort();
-      }
+      if(f->occupied) { nb_occupied_next++; next = f; }
+    }
+
+#ifdef DEBUG
+    if(nb_occupied_next == 0) {
+      cerr << __FILE__ << ": retrieve_one_path: Non-sink end point." << endl;
+      abort();
     }
+
+    else if(nb_occupied_next > 1) {
+      cerr << __FILE__ << ": retrieve_one_path: Non node-disjoint paths." << endl;
+      abort();
+    }
+#endif
+
     e = next;
   }
 
   if(path) {
-    path->nodes[l++] = e->terminal_vertex->id;
+    path->nodes[l++] = e->terminal_vertex - _vertices;
     path->length += e->length;
   } else l++;
 
@@ -401,6 +488,7 @@ int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
 
 void MTPGraph::retrieve_disjoint_paths() {
   Edge *e;
+  int p, l;
 
   for(int p = 0; p < nb_paths; p++) delete paths[p];
   delete[] paths;
@@ -412,10 +500,10 @@ void MTPGraph::retrieve_disjoint_paths() {
 
   paths = new Path *[nb_paths];
 
-  int p = 0;
+  p = 0;
   for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
     if(e->occupied) {
-      int l = retrieve_one_path(e, 0);
+      l = retrieve_one_path(e, 0);
       paths[p] = new Path(l);
       retrieve_one_path(e, paths[p]);
       p++;