3 * mtp is the ``Multi Tracked Paths'', an implementation of the
4 * k-shortest paths algorithm for multi-target tracking.
6 * Copyright (c) 2012 Idiap Research Institute, http://www.idiap.ch/
7 * Written by Francois Fleuret <francois.fleuret@idiap.ch>
9 * This file is part of mtp.
11 * mtp is free software: you can redistribute it and/or modify it
12 * under the terms of the GNU General Public License version 3 as
13 * published by the Free Software Foundation.
15 * mtp is distributed in the hope that it will be useful, but WITHOUT
16 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
17 * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
18 * License for more details.
20 * You should have received a copy of the GNU General Public License
21 * along with selector. If not, see <http://www.gnu.org/licenses/>.
25 #include "mtp_graph.h"
34 scalar_t length, positivized_length;
35 Vertex *origin_vertex, *terminal_vertex;
37 // These fields are used for the linked list of a vertex's leaving
38 // edge list. We have to do insertions / deletions.
39 Edge *next_leaving_edge, *pred_leaving_edge;
47 scalar_t distance_from_source;
48 Edge *pred_edge_toward_source;
53 inline void add_leaving_edge(Edge *e);
54 inline void del_leaving_edge(Edge *e);
55 inline void decrease_distance_in_heap(Vertex **heap);
56 inline void increase_distance_in_heap(Vertex **heap, Vertex **heap_bottom);
59 //////////////////////////////////////////////////////////////////////
63 positivized_length = - positivized_length;
64 origin_vertex->del_leaving_edge(this);
65 terminal_vertex->add_leaving_edge(this);
66 swap(terminal_vertex, origin_vertex);
69 //////////////////////////////////////////////////////////////////////
75 void Vertex::add_leaving_edge(Edge *e) {
76 e->next_leaving_edge = leaving_edges;
77 e->pred_leaving_edge = 0;
78 if(leaving_edges) { leaving_edges->pred_leaving_edge = e; }
82 void Vertex::del_leaving_edge(Edge *e) {
83 if(e == leaving_edges) {
84 leaving_edges = e->next_leaving_edge;
86 if(e->pred_leaving_edge) {
87 e->pred_leaving_edge->next_leaving_edge = e->next_leaving_edge;
89 if(e->next_leaving_edge) {
90 e->next_leaving_edge->pred_leaving_edge = e->pred_leaving_edge;
94 void Vertex::decrease_distance_in_heap(Vertex **heap) {
96 // There is some beauty in that
99 (p = heap + (h - heap + 1) / 2 - 1,
100 (*p)->distance_from_source > (*h)->distance_from_source)) {
102 swap((*p)->heap_slot, (*h)->heap_slot);
107 void Vertex::increase_distance_in_heap(Vertex **heap, Vertex **heap_bottom) {
108 Vertex **c1, **c2, **h;
109 // omg, that's beautiful
111 while(c1 = heap + 2 * (h - heap) + 1,
114 (*c1)->distance_from_source < (*h)->distance_from_source
116 (c2 < heap_bottom && (*c2)->distance_from_source < (*h)->distance_from_source)
118 if(c2 < heap_bottom && (*c2)->distance_from_source <= (*c1)->distance_from_source) {
120 swap((*c2)->heap_slot, (*h)->heap_slot);
124 swap((*c1)->heap_slot, (*h)->heap_slot);
130 //////////////////////////////////////////////////////////////////////
132 static int compare_vertex(const void *v1, const void *v2) {
134 (*((Vertex **) v1))->distance_from_source -
135 (*((Vertex **) v2))->distance_from_source;
136 if(delta < 0) return -1;
137 else if(delta > 0) return 1;
141 MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
142 int *vertex_from, int *vertex_to,
143 int source, int sink) {
144 _nb_vertices = nb_vertices;
145 _nb_edges = nb_edges;
147 _edges = new Edge[_nb_edges];
148 _vertices = new Vertex[_nb_vertices];
149 _heap = new Vertex *[_nb_vertices];
150 _dp_order = new Vertex *[_nb_vertices];
152 _source = &_vertices[source];
153 _sink = &_vertices[sink];
155 for(int e = 0; e < nb_edges; e++) {
156 _vertices[vertex_from[e]].add_leaving_edge(_edges + e);
157 _edges[e].occupied = 0;
158 _edges[e].origin_vertex = _vertices + vertex_from[e];
159 _edges[e].terminal_vertex = _vertices + vertex_to[e];
162 for(int v = 0; v < _nb_vertices; v++) {
163 _heap[v] = &_vertices[v];
164 _vertices[v].heap_slot = &_heap[v];
170 if(compute_dp_ranks()) {
171 // Here the distance_from_source field of every vertex is the
172 // number of DP iterations needed to update it. Hence we only have
173 // to process the vertex in that order.
174 for(int v = 0; v < _nb_vertices; v++) { _dp_order[v] = &_vertices[v]; }
175 qsort(_dp_order, _nb_vertices, sizeof(Vertex *), compare_vertex);
177 cerr << __FILE__ << ": This graph is not a DAG." << endl;
182 MTPGraph::~MTPGraph() {
187 for(int p = 0; p < nb_paths; p++) delete paths[p];
191 int MTPGraph::compute_dp_ranks() {
195 // This procedure computes for each node the longest link from the
196 // source and abort if the graph is not a DAG. It works by removing
197 // successively nodes without predecessor: At the first iteration it
198 // removes the source, then the nodes with incoming edge only from
199 // the source, etc. If it can remove all the nodes that way, the
200 // graph is a DAG. If at some point it can not remove node anymore
201 // and there are some remaining nodes, the graph is not a DAG. The
202 // rank of a node is the iteration at which is it removed, and we
203 // set the distance_from_source fields to this value.
205 Vertex **with_predecessor = new Vertex *[_nb_vertices];
207 // All the nodes are with_predecessor at first
208 for(int k = 0; k < _nb_vertices; k++) {
209 _vertices[k].distance_from_source = 0;
210 with_predecessor[k] = &_vertices[k];
214 int nb_with_predecessor = _nb_vertices, pred_nb_with_predecessor;
217 // We set the distance_from_source field of all the vertices with incoming
218 // edges to the current rank value
219 for(int f = 0; f < nb_with_predecessor; f++) {
220 v = with_predecessor[f];
221 for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
222 e->terminal_vertex->distance_from_source = rank;
226 pred_nb_with_predecessor = nb_with_predecessor;
227 nb_with_predecessor = 0;
229 // We keep all the vertices with incoming nodes
230 for(int f = 0; f < pred_nb_with_predecessor; f++) {
231 v = with_predecessor[f];
232 if(v->distance_from_source == rank) {
233 with_predecessor[nb_with_predecessor++] = v;
238 } while(nb_with_predecessor < pred_nb_with_predecessor);
240 delete[] with_predecessor;
242 return nb_with_predecessor == 0;
245 //////////////////////////////////////////////////////////////////////
247 void MTPGraph::print(ostream *os) {
248 for(int k = 0; k < _nb_edges; k++) {
249 Edge *e = _edges + k;
250 (*os) << e->origin_vertex - _vertices
252 << e->terminal_vertex - _vertices
262 void MTPGraph::print_dot(ostream *os) {
263 (*os) << "digraph {" << endl;
264 (*os) << " rankdir=\"LR\";" << endl;
265 (*os) << " node [shape=circle,width=0.75,fixedsize=true];" << endl;
266 (*os) << " edge [color=gray,arrowhead=open]" << endl;
267 (*os) << " " << _source - _vertices << " [peripheries=2];" << endl;
268 (*os) << " " << _sink - _vertices << " [peripheries=2];" << endl;
269 for(int k = 0; k < _nb_edges; k++) {
270 Edge *e = _edges + k;
272 << e->origin_vertex - _vertices
274 << e->terminal_vertex - _vertices
277 (*os) << "style=bold,color=black,";
279 (*os) << "label=\"" << e->length << "\"];" << endl;
281 (*os) << "}" << endl;
284 //////////////////////////////////////////////////////////////////////
286 void MTPGraph::update_positivized_lengths() {
287 for(int k = 0; k < _nb_edges; k++) {
288 Edge *e = _edges + k;
289 e->positivized_length +=
290 e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
294 void MTPGraph::force_positivized_lengths() {
296 scalar_t residual_error = 0.0;
297 scalar_t max_error = 0.0;
299 for(int k = 0; k < _nb_edges; k++) {
300 Edge *e = _edges + k;
302 if(e->positivized_length < 0) {
304 residual_error -= e->positivized_length;
305 max_error = max(max_error, - e->positivized_length);
307 e->positivized_length = 0.0;
311 cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << residual_error << endl;
315 void MTPGraph::dp_compute_distances() {
320 for(int k = 0; k < _nb_vertices; k++) {
321 _vertices[k].distance_from_source = FLT_MAX;
322 _vertices[k].pred_edge_toward_source = 0;
325 _source->distance_from_source = 0;
327 for(int k = 0; k < _nb_vertices; k++) {
329 for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
330 d = v->distance_from_source + e->positivized_length;
331 tv = e->terminal_vertex;
332 if(d < tv->distance_from_source) {
333 tv->distance_from_source = d;
334 tv->pred_edge_toward_source = e;
340 // This method does not change the edge occupation. It only sets
341 // properly, for every vertex, the fields distance_from_source and
342 // pred_edge_toward_source.
344 void MTPGraph::find_shortest_path() {
345 Vertex *v, *tv, **last_slot;
349 for(int k = 0; k < _nb_vertices; k++) {
350 _vertices[k].distance_from_source = FLT_MAX;
351 _vertices[k].pred_edge_toward_source = 0;
354 _heap_size = _nb_vertices;
355 _source->distance_from_source = 0;
356 _source->decrease_distance_in_heap(_heap);
359 // Get the closest to the source
362 // Remove it from the heap (swap it with the last_slot in the heap, and
363 // update the distance of that one)
365 last_slot = _heap + _heap_size;
366 swap(*_heap, *last_slot); swap((*_heap)->heap_slot, (*last_slot)->heap_slot);
367 _heap[0]->increase_distance_in_heap(_heap, _heap + _heap_size);
369 // Now update the neighbors of the node currently closest to the
371 for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
372 d = v->distance_from_source + e->positivized_length;
373 tv = e->terminal_vertex;
374 if(d < tv->distance_from_source) {
375 ASSERT(tv->heap_slot - _heap < _heap_size);
376 tv->distance_from_source = d;
377 tv->pred_edge_toward_source = e;
378 tv->decrease_distance_in_heap(_heap);
381 } while(_heap_size > 0);
384 void MTPGraph::find_best_paths(scalar_t *lengths) {
385 scalar_t shortest_path_length;
389 for(int e = 0; e < _nb_edges; e++) {
390 _edges[e].length = lengths[e];
391 _edges[e].occupied = 0;
392 _edges[e].positivized_length = _edges[e].length;
395 // Compute the distance of all the nodes from the source by just
396 // visiting them in the proper DAG ordering we computed when
397 // building the graph
398 dp_compute_distances();
401 // Use the current distance from the source to make all edge
403 update_positivized_lengths();
404 // Fix numerical errors
405 force_positivized_lengths();
407 find_shortest_path();
409 shortest_path_length = 0.0;
411 // Do we reach the sink?
412 if(_sink->pred_edge_toward_source) {
413 // If yes, compute the length of the best path according to the
414 // original edge lengths
416 while(v->pred_edge_toward_source) {
417 shortest_path_length += v->pred_edge_toward_source->length;
418 v = v->pred_edge_toward_source->origin_vertex;
420 // If that length is negative
421 if(shortest_path_length < 0.0) {
423 cerr << __FILE__ << ": Found a path of length " << shortest_path_length << endl;
425 // Invert all the edges along the best path
427 while(v->pred_edge_toward_source) {
428 e = v->pred_edge_toward_source;
429 v = e->origin_vertex;
431 // This is the only place where we change the occupations of
433 e->occupied = 1 - e->occupied;
438 } while(shortest_path_length < 0.0);
440 // Put back the graph in its original state (i.e. invert edges which
441 // have been inverted in the process)
442 for(int k = 0; k < _nb_edges; k++) {
444 if(e->occupied) { e->invert(); }
448 int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
450 int l = 0, nb_occupied_next;
453 path->nodes[l++] = e->origin_vertex - _vertices;
454 path->length = e->length;
457 while(e->terminal_vertex != _sink) {
459 path->nodes[l++] = e->terminal_vertex - _vertices;
460 path->length += e->length;
463 nb_occupied_next = 0;
464 for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
465 if(f->occupied) { nb_occupied_next++; next = f; }
469 if(nb_occupied_next == 0) {
470 cerr << __FILE__ << ": retrieve_one_path: Non-sink end point." << endl;
474 else if(nb_occupied_next > 1) {
475 cerr << __FILE__ << ": retrieve_one_path: Non node-disjoint paths." << endl;
484 path->nodes[l++] = e->terminal_vertex - _vertices;
485 path->length += e->length;
491 void MTPGraph::retrieve_disjoint_paths() {
495 for(int p = 0; p < nb_paths; p++) delete paths[p];
499 for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
500 if(e->occupied) { nb_paths++; }
503 paths = new Path *[nb_paths];
506 for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
508 l = retrieve_one_path(e, 0);
509 paths[p] = new Path(l);
510 retrieve_one_path(e, paths[p]);