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_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, int heap_size);
};
//////////////////////////////////////////////////////////////////////
}
}
+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) {
_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];
_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;
}
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() {
+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].last_change = -1;
- _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 {
- // 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];
+ // 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->last_change = 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 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 f = 0; f < pred_nb_active; f++) {
+ v = active[f];
+ if(v->distance_from_source == rank) {
+ active[nb_active++] = v;
}
}
- iteration++;
- } while(front_size < pred_front_size);
+ rank++;
+ } while(nb_active < pred_nb_active);
- return front_size == 0;
-}
+ delete[] 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.
+ return nb_active == 0;
+}
-void MTPGraph::find_shortest_path() {
- Vertex **tmp_front;
+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].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 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;
-
- iteration++;
- } while(front_size > 0);
+ } while(_heap_size > 0);
}
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();
// 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;
#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
projects / mtp.git / blobdiff