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;
+ 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);
};
//////////////////////////////////////////////////////////////////////
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);
}
//////////////////////////////////////////////////////////////////////
}
}
+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_vertex(const void *v1, const void *v2) {
- return (*((Vertex **) v1))->last_change - (*((Vertex **) v2))->last_change;
+ 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,
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(check_DAG_and_set_last_change()) {
- // 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.
+ 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 {
delete[] paths;
}
+int 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 **unreached = new Vertex *[_nb_vertices];
+
+ // All the nodes are unreached at first
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].distance_from_source = 0;
+ unreached[k] = &_vertices[k];
+ }
+
+ scalar_t rank = 1;
+ int nb_unreached = _nb_vertices, pred_nb_unreached;
+
+ 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_unreached; f++) {
+ v = unreached[f];
+ for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+ e->terminal_vertex->distance_from_source = rank;
+ }
+ }
+
+ pred_nb_unreached = nb_unreached;
+ nb_unreached = 0;
+
+ // We keep all the vertices with incoming nodes
+ for(int f = 0; f < pred_nb_unreached; f++) {
+ v = unreached[f];
+ if(v->distance_from_source == rank) {
+ unreached[nb_unreached++] = v;
+ }
+ }
+
+ rank++;
+ } while(nb_unreached < pred_nb_unreached);
+
+ delete[] unreached;
+
+ return nb_unreached == 0;
+}
+
//////////////////////////////////////////////////////////////////////
void MTPGraph::print(ostream *os) {
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::check_DAG_and_set_last_change() {
- 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;
-}
-
-void MTPGraph::decrease_distance_in_heap(Vertex *v) {
- 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)) {
- swap(*p, *h);
- swap((*p)->heap_position, (*h)->heap_position);
- h = p;
- }
-}
-
-void MTPGraph::increase_distance_in_heap(Vertex *v) {
- 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;
- }
- }
-}
-
-void MTPGraph::dp_distance_propagation() {
+void MTPGraph::dp_compute_distances() {
Vertex *v, *tv;
Edge *e;
scalar_t d;
if(d < tv->distance_from_source) {
tv->distance_from_source = d;
tv->pred_edge_toward_source = e;
- decrease_distance_in_heap(tv);
+ tv->decrease_distance_in_heap(_heap);
}
}
}
_heap_size = _nb_vertices;
_source->distance_from_source = 0;
- decrease_distance_in_heap(_source);
+ _source->decrease_distance_in_heap(_heap);
do {
// Get the closest to the source
_heap_size--;
a = _heap;
b = _heap + _heap_size;
- swap(*a, *b); swap((*a)->heap_position, (*b)->heap_position);
- increase_distance_in_heap(_heap[0]);
+ swap(*a, *b); swap((*a)->heap_slot, (*b)->heap_slot);
+ _heap[0]->increase_distance_in_heap(_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_position - _heap < _heap_size);
+ ASSERT(tv->heap_slot - _heap < _heap_size);
tv->distance_from_source = d;
tv->pred_edge_toward_source = e;
- decrease_distance_in_heap(tv);
+ tv->decrease_distance_in_heap(_heap);
}
}
} 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;
_edges[e].positivized_length = _edges[e].length;
}
- // Update the distance to the source in "good order"
-
- dp_distance_propagation();
+ // Compute the distance of every node 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) {
// 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;
}
}
- } 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)
#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