#include "mtp_graph.h"
+#include <cmath>
#include <float.h>
using namespace std;
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);
};
//////////////////////////////////////////////////////////////////////
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;
}
}
+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;
+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,
int *vertex_from, int *vertex_to,
int source, int sink) {
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_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() {
//////////////////////////////////////////////////////////////////////
+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;
}
}
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;
-#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);
+ cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << residual_error << endl;
#endif
}
-void MTPGraph::dp_distance_propagation() {
+void MTPGraph::dp_compute_distances() {
Vertex *v, *tv;
Edge *e;
scalar_t d;
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;
+ 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;
_source->distance_from_source = 0;
- decrease_distance_in_heap(_source);
+ _source->decrease_distance_in_heap(_heap);
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
-
+ // 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--;
- Vertex **a = _heap, **b = _heap + _heap_size;
- swap(*a, *b); swap((*a)->heap_position, (*b)->heap_position);
- increase_distance_in_heap(_heap[0]);
+ 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);
- for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+ // 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 - _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);
}
-#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;
_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) {
// 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)
} 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
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);
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