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"
36 scalar_t length, positivized_length;
37 Vertex *origin_vertex, *terminal_vertex;
39 // These are the links in the origin_vertex leaving edge list
40 Edge *next_leaving_edge, *pred_leaving_edge;
49 scalar_t distance_from_source;
50 Edge *pred_edge_toward_source;
52 int iteration; // Used in find_shortest_path to know if we already
53 // added this vertex to the front
55 inline void add_leaving_edge(Edge *e);
56 inline void del_leaving_edge(Edge *e);
59 //////////////////////////////////////////////////////////////////////
63 positivized_length = 0;
64 origin_vertex->del_leaving_edge(this);
65 terminal_vertex->add_leaving_edge(this);
66 Vertex *t = terminal_vertex;
67 terminal_vertex = origin_vertex;
71 //////////////////////////////////////////////////////////////////////
77 void Vertex::add_leaving_edge(Edge *e) {
78 e->next_leaving_edge = leaving_edges;
79 e->pred_leaving_edge = 0;
80 if(leaving_edges) { leaving_edges->pred_leaving_edge = e; }
84 void Vertex::del_leaving_edge(Edge *e) {
85 if(e == leaving_edges) {
86 leaving_edges = e->next_leaving_edge;
88 if(e->pred_leaving_edge) {
89 e->pred_leaving_edge->next_leaving_edge = e->next_leaving_edge;
91 if(e->next_leaving_edge) {
92 e->next_leaving_edge->pred_leaving_edge = e->pred_leaving_edge;
96 //////////////////////////////////////////////////////////////////////
98 MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
99 int *vertex_from, int *vertex_to,
100 int source, int sink) {
101 _nb_vertices = nb_vertices;
102 _nb_edges = nb_edges;
104 _edges = new Edge[_nb_edges];
105 _vertices = new Vertex[_nb_vertices];
106 _front = new Vertex *[_nb_vertices];
107 _new_front = new Vertex *[_nb_vertices];
109 _source = &_vertices[source];
110 _sink = &_vertices[sink];
112 for(int k = 0; k < _nb_vertices; k++) {
116 for(int e = 0; e < nb_edges; e++) {
117 _vertices[vertex_from[e]].add_leaving_edge(_edges + e);
118 _edges[e].occupied = 0;
120 _edges[e].origin_vertex = _vertices + vertex_from[e];
121 _edges[e].terminal_vertex = _vertices + vertex_to[e];
128 MTPGraph::~MTPGraph() {
133 for(int p = 0; p < nb_paths; p++) delete paths[p];
137 //////////////////////////////////////////////////////////////////////
139 void MTPGraph::print(ostream *os) {
140 for(int k = 0; k < _nb_edges; k++) {
141 Edge *e = _edges + k;
142 (*os) << e->origin_vertex->id
144 << e->terminal_vertex->id
154 void MTPGraph::print_dot(ostream *os) {
155 (*os) << "digraph {" << endl;
156 (*os) << " rankdir=\"LR\";" << endl;
157 (*os) << " node [shape=circle,width=0.75,fixedsize=true];" << endl;
158 (*os) << " edge [color=gray,arrowhead=open]" << endl;
159 (*os) << " " << _source->id << " [peripheries=2];" << endl;
160 (*os) << " " << _sink->id << " [peripheries=2];" << endl;
161 for(int k = 0; k < _nb_edges; k++) {
162 Edge *e = _edges + k;
163 // (*os) << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
166 (*os) << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
169 (*os) << "style=bold,color=black,";
171 (*os) << "label=\"" << e->length << "\"];" << endl;
173 (*os) << "}" << endl;
176 //////////////////////////////////////////////////////////////////////
178 void MTPGraph::update_positivized_lengths() {
179 for(int k = 0; k < _nb_edges; k++) {
180 Edge *e = _edges + k;
181 e->positivized_length +=
182 e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
186 void MTPGraph::force_positivized_lengths() {
188 scalar_t residual_error = 0.0;
189 scalar_t max_error = 0.0;
191 for(int n = 0; n < _nb_vertices; n++) {
192 for(Edge *e = _vertices[n].leaving_edges; e; e = e->next_leaving_edge) {
193 if(e->positivized_length < 0) {
195 residual_error -= e->positivized_length;
196 max_error = max(max_error, - e->positivized_length);
198 e->positivized_length = 0.0;
203 cerr << "residual_error " << residual_error << " max_error " << residual_error << endl;
207 int MTPGraph::is_dag() {
211 // We put everybody in the front
212 for(int k = 0; k < _nb_vertices; k++) {
213 _vertices[k].iteration = 0;
214 _front[k] = &_vertices[k];
217 int front_size = _nb_vertices, nb_with_incoming;
219 int new_front_size, pred_front_size;
223 nb_with_incoming = 0;
225 // We set the iteration field of all vertex with incoming edges to
226 // the current iteration value
227 for(int f = 0; f < front_size; f++) {
229 for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
230 tv = e->terminal_vertex;
231 tv->iteration = iteration;
236 // We remove all the vertices without incoming edge
237 for(int f = 0; f < front_size; f++) {
239 if(v->iteration == iteration) {
240 _front[new_front_size++] = v;
244 pred_front_size = front_size;
245 front_size = new_front_size;
246 } while(front_size < pred_front_size);
248 return front_size == 0;
251 // This method does not change the edge occupation. It only set
252 // properly for every vertex the fields distance_from_source and
253 // pred_edge_toward_source.
255 void MTPGraph::find_shortest_path() {
262 for(int k = 0; k < _nb_vertices; k++) {
263 _vertices[k].distance_from_source = FLT_MAX;
264 _vertices[k].pred_edge_toward_source = 0;
265 _vertices[k].iteration = 0;
270 int front_size = 0, new_front_size;
271 _front[front_size++] = _source;
272 _source->distance_from_source = 0;
278 for(int f = 0; f < front_size; f++) {
280 for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
281 d = v->distance_from_source + e->positivized_length;
282 tv = e->terminal_vertex;
283 if(d < tv->distance_from_source) {
284 tv->distance_from_source = d;
285 tv->pred_edge_toward_source = e;
286 if(tv->iteration < iteration) {
287 _new_front[new_front_size++] = tv;
288 tv->iteration = iteration;
294 tmp_front = _new_front;
298 tmp_front_size = new_front_size;
299 new_front_size = front_size;
300 front_size = tmp_front_size;
301 } while(front_size > 0);
304 void MTPGraph::find_best_paths(scalar_t *lengths) {
305 scalar_t total_length;
309 for(int e = 0; e < _nb_edges; e++) {
310 _edges[e].length = lengths[e];
311 _edges[e].occupied = 0;
312 _edges[e].positivized_length = _edges[e].length;
315 // Let's be a bit paranoid
318 // We use call find_shortest_path here to set properly the distance,
319 // so that we can make all the edge lengths positive at the first
321 find_shortest_path();
324 update_positivized_lengths();
325 force_positivized_lengths();
326 find_shortest_path();
330 // Do we reach the sink?
331 if(_sink->pred_edge_toward_source) {
332 // If yes, compute the length of the best path
334 while(v->pred_edge_toward_source) {
335 total_length += v->pred_edge_toward_source->length;
336 v = v->pred_edge_toward_source->origin_vertex;
338 // If that length is negative
339 if(total_length < 0.0) {
341 cerr << "Found a path of length " << total_length << endl;
343 // Invert all the edges along the best path
345 while(v->pred_edge_toward_source) {
346 e = v->pred_edge_toward_source;
347 v = e->origin_vertex;
349 // This is the only place where we change the occupations of
351 e->occupied = 1 - e->occupied;
356 } while(total_length < 0.0);
358 // Put back the graph in its original state (i.e. invert edges which
359 // have been inverted in the process)
360 for(int k = 0; k < _nb_edges; k++) {
361 Edge *e = _edges + k;
362 if(e->occupied) { e->invert(); }
366 int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
371 path->nodes[l++] = e->origin_vertex->id;
372 path->length = e->length;
375 while(e->terminal_vertex != _sink) {
377 path->nodes[l++] = e->terminal_vertex->id;
378 path->length += e->length;
381 for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
382 if(f->occupied) { nb_choices++; next = f; }
383 if(nb_choices == 0) {
384 cerr << "retrieve_one_path: Non-sink end point." << endl;
388 cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
396 path->nodes[l++] = e->terminal_vertex->id;
397 path->length += e->length;
403 void MTPGraph::retrieve_disjoint_paths() {
406 for(int p = 0; p < nb_paths; p++) delete paths[p];
410 for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
411 if(e->occupied) { nb_paths++; }
414 paths = new Path *[nb_paths];
417 for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
419 int l = retrieve_one_path(e, 0);
420 paths[p] = new Path(l);
421 retrieve_one_path(e, paths[p]);