#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;
+
+ 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, int heap_size);
+ 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)) {
+ while(1) {
+ if(h <= heap) break;
+ p = heap + ((h - heap + 1) >> 1) - 1;
+ if((*p)->distance_from_source <= distance_from_source) break;
+ swap((*p)->heap_slot, heap_slot);
swap(*p, *h);
- swap((*p)->heap_slot, (*h)->heap_slot);
h = p;
}
}
-void Vertex::increase_distance_in_heap(Vertex **heap, int heap_size) {
+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 + 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;
+ while(1) {
+ c1 = heap + 2 * (h - heap) + 1;
+ if(c1 >= heap_bottom) break;
+ c2 = c1 + 1;
+ if((*c1)->distance_from_source < distance_from_source) {
+ if(c2 < heap_bottom && (*c2)->distance_from_source < (*c1)->distance_from_source) {
+ swap((*c2)->heap_slot, heap_slot);
+ swap(*c2, *h);
+ h = c2;
+ } else {
+ swap((*c1)->heap_slot, heap_slot);
+ swap(*c1, *h);
+ h = c1;
+ }
} else {
- swap(*c1, *h);
- swap((*c1)->heap_slot, (*h)->heap_slot);
- h = c1;
+ if(c2 < heap_bottom && (*c2)->distance_from_source < distance_from_source) {
+ swap((*c2)->heap_slot, heap_slot);
+ swap(*c2, *h);
+ h = c2;
+ } else break;
}
}
}
//////////////////////////////////////////////////////////////////////
-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) {
_sink = &_vertices[sink];
for(int e = 0; e < nb_edges; e++) {
- _vertices[vertex_from[e]].add_leaving_edge(_edges + e);
+ _vertices[vertex_from[e]].add_leaving_edge(&_edges[e]);
_edges[e].occupied = 0;
- _edges[e].origin_vertex = _vertices + vertex_from[e];
- _edges[e].terminal_vertex = _vertices + vertex_to[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++) {
paths = 0;
nb_paths = 0;
- if(compute_dp_distances()) {
- // 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();
- }
+ compute_dp_ordering();
}
MTPGraph::~MTPGraph() {
void MTPGraph::print(ostream *os) {
for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _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;
}
}
(*os) << " " << _source - _vertices << " [peripheries=2];" << endl;
(*os) << " " << _sink - _vertices << " [peripheries=2];" << endl;
for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _edges + k;
+ Edge *e = &_edges[k];
(*os) << " "
<< e->origin_vertex - _vertices
<< " -> "
void MTPGraph::update_positivized_lengths() {
for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _edges + k;
+ Edge *e = &_edges[k];
e->positivized_length +=
e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
}
scalar_t max_error = 0.0;
#endif
for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _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);
}
}
#ifdef VERBOSE
- cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << residual_error << endl;
+ cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << max_error << endl;
#endif
}
-int MTPGraph::compute_dp_distances() {
- 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.
-
- Vertex **active = new Vertex *[_nb_vertices];
-
- // All the nodes are active at first
- for(int k = 0; k < _nb_vertices; k++) {
- _vertices[k].distance_from_source = 0;
- active[k] = &_vertices[k];
- }
-
- scalar_t nb_iterations = 1;
- int nb_active = _nb_vertices, pred_nb_active;
-
- do {
- // We set the distance_from_source field of all the vertices with incoming
- // edges to the current nb_iterations 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->distance_from_source = nb_iterations;
- }
- }
-
- 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->distance_from_source == nb_iterations) {
- active[nb_active++] = v;
- }
- }
-
- nb_iterations++;
- } while(nb_active < pred_nb_active);
-
- delete[] active;
-
- return nb_active == 0;
-}
-
void MTPGraph::dp_compute_distances() {
Vertex *v, *tv;
Edge *e;
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;
- tv->decrease_distance_in_heap(_heap);
}
}
}
// pred_edge_toward_source.
void MTPGraph::find_shortest_path() {
- Vertex *v, *tv, **a, **b;
+ int heap_size;
+ Vertex *v, *tv, **last_slot;
Edge *e;
scalar_t d;
_vertices[k].pred_edge_toward_source = 0;
}
- _heap_size = _nb_vertices;
+ heap_size = _nb_vertices;
_source->distance_from_source = 0;
_source->decrease_distance_in_heap(_heap);
- do {
+ while(heap_size > 1) {
// Get the closest to the source
v = _heap[0];
- // Remove it from the heap (swap it with the last in the heap, and
+ // Remove it from the heap (swap it with the last_slot 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) {
+ heap_size--;
+ last_slot = _heap + heap_size;
+ swap(*_heap, *last_slot); swap((*_heap)->heap_slot, (*last_slot)->heap_slot);
+ (*_heap)->increase_distance_in_heap(_heap, last_slot);
+
+ // 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);
+ ASSERT(tv->heap_slot < last_slot);
tv->distance_from_source = d;
tv->pred_edge_toward_source = e;
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 distances to the source in "good order"
+ // 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 << __FILE__ << ": 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)
for(int k = 0; k < _nb_edges; k++) {
- e = _edges + k;
+ e = &_edges[k];
if(e->occupied) { e->invert(); }
}
}
-int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
+int MTPGraph::retrieve_one_path(Edge *e, Path *path, int *used_edges) {
Edge *f, *next = 0;
int l = 0, nb_occupied_next;
if(path) {
- path->nodes[l++] = e->origin_vertex - _vertices;
+ path->nodes[l++] = int(e->origin_vertex - _vertices);
path->length = e->length;
} else l++;
while(e->terminal_vertex != _sink) {
if(path) {
- path->nodes[l++] = e->terminal_vertex - _vertices;
+ path->nodes[l++] = int(e->terminal_vertex - _vertices);
path->length += e->length;
} else l++;
nb_occupied_next = 0;
- for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
- if(f->occupied) { nb_occupied_next++; next = f; }
+ for(f = e->terminal_vertex->leaving_edge_list_root; f; f = f->next_leaving_edge) {
+ if(f->occupied && !used_edges[f - _edges]) {
+ nb_occupied_next++; next = f;
+ }
}
#ifdef DEBUG
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
+ if(path) { used_edges[next - _edges] = 1; }
+
e = next;
}
if(path) {
- path->nodes[l++] = e->terminal_vertex - _vertices;
+ path->nodes[l++] = int(e->terminal_vertex - _vertices);
path->length += e->length;
} else l++;
return l;
}
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::compute_dp_ordering() {
+ Vertex *v;
+ Edge *e;
+ int ntv;
+
+ // This method orders the nodes by putting first the ones with no
+ // predecessors, then going on adding nodes whose predecessors have
+ // all been already added. Computing the distances from the source
+ // by visiting nodes in that order is equivalent to DP.
+
+ int *nb_predecessors = new int[_nb_vertices];
+
+ Vertex **already_processed = _dp_order, **front = _dp_order, **new_front = _dp_order;
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ nb_predecessors[k] = 0;
+ }
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ v = &_vertices[k];
+ for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+ ntv = int(e->terminal_vertex - _vertices);
+ nb_predecessors[ntv]++;
+ }
+ }
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ if(nb_predecessors[k] == 0) {
+ *(front++) = _vertices + k;
+ }
+ }
+
+ while(already_processed < front) {
+ // Here, nodes before already_processed can be ignored, nodes
+ // before front were set to 0 predecessors during the previous
+ // iteration. During this new iteration, we have to visit the
+ // successors of these ones only, since they are the only ones
+ // which may end up with no predecessors.
+ new_front = front;
+ while(already_processed < front) {
+ v = *(already_processed++);
+ for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+ ntv = int(e->terminal_vertex - _vertices);
+ nb_predecessors[ntv]--;
+ ASSERT(nb_predecessors[ntv] >= 0);
+ if(nb_predecessors[ntv] == 0) {
+ *(new_front++) = e->terminal_vertex;
+ }
+ }
+ }
+ front = new_front;
+ }
+
+ if(already_processed < _dp_order + _nb_vertices) {
+ cerr << __FILE__ << ": The graph is not a DAG." << endl;
+ abort();
+ }
+
+ delete[] nb_predecessors;
+}
+
+//////////////////////////////////////////////////////////////////////
+
void MTPGraph::retrieve_disjoint_paths() {
Edge *e;
int p, l;
+ int *used_edges;
for(int p = 0; p < nb_paths; p++) delete paths[p];
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];
+ used_edges = new int[_nb_edges];
+ for(int e = 0; e < _nb_edges; e++) {
+ used_edges[e] = 0;
+ }
p = 0;
- for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
- if(e->occupied) {
- l = retrieve_one_path(e, 0);
+ for(e = _source->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+ if(e->occupied && !used_edges[e - _edges]) {
+ l = retrieve_one_path(e, 0, used_edges);
paths[p] = new Path(l);
- retrieve_one_path(e, paths[p]);
+ retrieve_one_path(e, paths[p], used_edges);
+ used_edges[e - _edges] = 1;
p++;
}
}
+
+ delete[] used_edges;
}
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