-///////////////////////////////////////////////////////////////////////////
-// This program is free software: you can redistribute it and/or modify //
-// it under the terms of the version 3 of the GNU General Public License //
-// as published by the Free Software Foundation. //
-// //
-// This program is distributed in the hope that it will be useful, but //
-// WITHOUT ANY WARRANTY; without even the implied warranty of //
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU //
-// General Public License for more details. //
-// //
-// You should have received a copy of the GNU General Public License //
-// along with this program. If not, see <http://www.gnu.org/licenses/>. //
-// //
-// Written by and Copyright (C) Francois Fleuret //
-// Contact <francois.fleuret@idiap.ch> for comments & bug reports //
-///////////////////////////////////////////////////////////////////////////
+/*
+ * mtp is the ``Multi Tracked Paths'', an implementation of the
+ * k-shortest paths algorithm for multi-target tracking.
+ *
+ * Copyright (c) 2012 Idiap Research Institute, http://www.idiap.ch/
+ * Written by Francois Fleuret <francois.fleuret@idiap.ch>
+ *
+ * This file is part of mtp.
+ *
+ * mtp is free software: you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 3 as
+ * published by the Free Software Foundation.
+ *
+ * mtp is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+ * License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with selector. If not, see <http://www.gnu.org/licenses/>.
+ *
+ */
#include "mtp_graph.h"
-#include <iostream>
+#include <cmath>
#include <float.h>
using namespace std;
class Edge {
public:
- int id, occupied;
- scalar_t length, work_length;
+ int occupied;
+ scalar_t length, positivized_length;
Vertex *origin_vertex, *terminal_vertex;
- Edge *next, *pred;
- inline void revert();
+ // These fields are used for the linked list of a vertex's leaving
+ // edge list. We have to do insertions / deletions.
+ Edge *next_leaving_edge, *pred_leaving_edge;
+
+ inline void invert();
};
class Vertex {
public:
- int id, iteration;
- Edge *root_edge;
scalar_t distance_from_source;
- Edge *pred_edge;
+ Edge *pred_edge_toward_source;
+
+ Edge *leaving_edge_list_root;
+ Vertex **heap_slot;
Vertex();
- inline void add_edge(Edge *e);
- inline void del_edge(Edge *e);
+
+ 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);
};
//////////////////////////////////////////////////////////////////////
-void Edge::revert() {
+void Edge::invert() {
length = - length;
- work_length = 0;
- origin_vertex->del_edge(this);
- terminal_vertex->add_edge(this);
- Vertex *t = terminal_vertex;
- terminal_vertex = origin_vertex;
- origin_vertex = t;
+ positivized_length = - positivized_length;
+ origin_vertex->del_leaving_edge(this);
+ terminal_vertex->add_leaving_edge(this);
+ swap(terminal_vertex, origin_vertex);
}
//////////////////////////////////////////////////////////////////////
Vertex::Vertex() {
- root_edge = 0;
+ leaving_edge_list_root = 0;
}
-void Vertex::add_edge(Edge *e) {
- e->next = root_edge;
- e->pred = 0;
- if(root_edge) { root_edge->pred = e; }
- root_edge = e;
+void Vertex::add_leaving_edge(Edge *e) {
+ e->next_leaving_edge = leaving_edge_list_root;
+ e->pred_leaving_edge = 0;
+ if(leaving_edge_list_root) {
+ leaving_edge_list_root->pred_leaving_edge = e;
+ }
+ leaving_edge_list_root = e;
}
-void Vertex::del_edge(Edge *e) {
- if(e == root_edge) { root_edge = e->next; }
- if(e->pred) { e->pred->next = e->next; }
- if(e->next) { e->next->pred = e->pred; }
+void Vertex::del_leaving_edge(Edge *e) {
+ 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;
+ }
+ if(e->next_leaving_edge) {
+ e->next_leaving_edge->pred_leaving_edge = e->pred_leaving_edge;
+ }
}
-//////////////////////////////////////////////////////////////////////
-
-void MTPGraph::print() {
- for(int k = 0; k < _nb_edges; k++) {
- Edge *e = edges + k;
- cout << e->origin_vertex->id
- << " -> "
- << e->terminal_vertex->id
- << " "
- << e->length;
- if(e->occupied) {
- cout << " *";
- }
- cout << endl;
+void Vertex::decrease_distance_in_heap(Vertex **heap) {
+ Vertex **p, **h;
+ h = heap_slot;
+ 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);
+ h = p;
}
}
-void MTPGraph::print_dot() {
- cout << "digraph {" << endl;
- cout << " node[shape=circle];" << endl;
- for(int k = 0; k < _nb_edges; k++) {
- Edge *e = edges + k;
- if(e->occupied) {
- cout << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
- << " [style=bold,color=black,label=\"" << -e->length << "\"];" << endl;
+void Vertex::increase_distance_in_heap(Vertex **heap, Vertex **heap_bottom) {
+ Vertex **c1, **c2, **h;
+ h = heap_slot;
+ 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 {
- cout << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
- << " [color=gray,label=\"" << e->length << "\"];" << endl;
+ if(c2 < heap_bottom && (*c2)->distance_from_source < distance_from_source) {
+ swap((*c2)->heap_slot, heap_slot);
+ swap(*c2, *h);
+ h = c2;
+ } else break;
}
}
- cout << "}" << endl;
}
+//////////////////////////////////////////////////////////////////////
+
MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
- int *from, int *to,
- int src, int snk) {
+ int *vertex_from, int *vertex_to,
+ int source, int sink) {
_nb_vertices = nb_vertices;
_nb_edges = nb_edges;
- edges = new Edge[_nb_edges];
- vertices = new Vertex[_nb_vertices];
- _front = new Vertex *[_nb_vertices];
- _new_front = new Vertex *[_nb_vertices];
+ _edges = new Edge[_nb_edges];
+ _vertices = new Vertex[_nb_vertices];
+ _heap = new Vertex *[_nb_vertices];
+ _dp_order = new Vertex *[_nb_vertices];
- _source = &vertices[src];
- _sink = &vertices[snk];
+ _source = &_vertices[source];
+ _sink = &_vertices[sink];
- for(int v = 0; v < _nb_vertices; v++) {
- vertices[v].id = v;
+ for(int e = 0; e < nb_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]];
}
- for(int e = 0; e < nb_edges; e++) {
- vertices[from[e]].add_edge(&edges[e]);
- edges[e].occupied = 0;
- edges[e].id = e;
- edges[e].origin_vertex = &vertices[from[e]];
- edges[e].terminal_vertex = &vertices[to[e]];
+ for(int v = 0; v < _nb_vertices; v++) {
+ _heap[v] = &_vertices[v];
+ _vertices[v].heap_slot = &_heap[v];
}
+ paths = 0;
+ nb_paths = 0;
+
+ compute_dp_ordering();
}
MTPGraph::~MTPGraph() {
- delete[] vertices;
- delete[] edges;
- delete[] _front;
- delete[] _new_front;
+ delete[] _vertices;
+ delete[] _dp_order;
+ delete[] _heap;
+ delete[] _edges;
+ for(int p = 0; p < nb_paths; p++) delete paths[p];
+ delete[] paths;
}
-void MTPGraph::initialize_work_lengths() {
- scalar_t length_min = 0;
- for(int n = 0; n < _nb_vertices; n++) {
- for(Edge *e = vertices[n].root_edge; e; e = e->next) {
- length_min = min(e->length, length_min);
- }
+//////////////////////////////////////////////////////////////////////
+
+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) << " *"; }
+ (*os) << endl;
}
- for(int n = 0; n < _nb_vertices; n++) {
- for(Edge *e = vertices[n].root_edge; e; e = e->next) {
- e->work_length = e->length - length_min;
+}
+
+void MTPGraph::print_dot(ostream *os) {
+ (*os) << "digraph {" << endl;
+ (*os) << " rankdir=\"LR\";" << endl;
+ (*os) << " node [shape=circle,width=0.75,fixedsize=true];" << endl;
+ (*os) << " edge [color=gray,arrowhead=open]" << 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];
+ (*os) << " "
+ << e->origin_vertex - _vertices
+ << " -> "
+ << e->terminal_vertex - _vertices
+ << " [";
+ if(e->occupied) {
+ (*os) << "style=bold,color=black,";
}
+ (*os) << "label=\"" << e->length << "\"];" << endl;
}
+ (*os) << "}" << endl;
}
-void MTPGraph::update_work_lengths() {
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::update_positivized_lengths() {
for(int k = 0; k < _nb_edges; k++) {
- Edge *e = edges + k;
- e->work_length += e->terminal_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
+ Edge *e = &_edges[k];
+ e->positivized_length +=
+ e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
}
}
-void MTPGraph::force_positive_work_lengths() {
+void MTPGraph::force_positivized_lengths() {
#ifdef VERBOSE
scalar_t residual_error = 0.0;
+ scalar_t max_error = 0.0;
#endif
- for(int n = 0; n < _nb_vertices; n++) {
- for(Edge *e = vertices[n].root_edge; e; e = e->next) {
- if(e->work_length < 0) {
+ for(int k = 0; k < _nb_edges; k++) {
+ Edge *e = &_edges[k];
+
+ if(e->positivized_length < 0) {
#ifdef VERBOSE
- residual_error -= e->work_length;
+ residual_error -= e->positivized_length;
+ max_error = max(max_error, - e->positivized_length);
#endif
- e->work_length = 0.0;
- }
+ e->positivized_length = 0.0;
}
}
#ifdef VERBOSE
- cerr << "residual_error " << residual_error << endl;
+ cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << max_error << endl;
#endif
}
-void MTPGraph::find_shortest_path(Vertex **_front, Vertex **_new_front) {
- Vertex **tmp_front;
- int tmp_front_size;
+void MTPGraph::dp_compute_distances() {
Vertex *v, *tv;
+ Edge *e;
scalar_t d;
- for(int v = 0; v < _nb_vertices; v++) {
- vertices[v].distance_from_source = FLT_MAX;
- vertices[v].pred_edge = 0;
- vertices[v].iteration = 0;
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].distance_from_source = FLT_MAX;
+ _vertices[k].pred_edge_toward_source = 0;
}
- int iteration = 0;
-
- int _front_size = 0, _new_front_size;
- _front[_front_size++] = _source;
_source->distance_from_source = 0;
- do {
- _new_front_size = 0;
- iteration++;
- for(int f = 0; f < _front_size; f++) {
- v = _front[f];
- for(Edge *e = v->root_edge; e; e = e->next) {
- d = v->distance_from_source + e->work_length;
- tv = e->terminal_vertex;
- if(d < tv->distance_from_source) {
- tv->distance_from_source = d;
- tv->pred_edge = e;
- if(tv->iteration < iteration) {
- _new_front[_new_front_size++] = tv;
- tv->iteration = iteration;
- }
- }
+ for(int k = 0; k < _nb_vertices; k++) {
+ v = _dp_order[k];
+ 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;
}
}
+ }
+}
+
+// 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() {
+ int heap_size;
+ Vertex *v, *tv, **last_slot;
+ Edge *e;
+ scalar_t d;
- tmp_front = _new_front;
- _new_front = _front;
- _front = tmp_front;
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].distance_from_source = FLT_MAX;
+ _vertices[k].pred_edge_toward_source = 0;
+ }
- tmp_front_size = _new_front_size;
- _new_front_size = _front_size;
- _front_size = tmp_front_size;
- } while(_front_size > 0);
+ heap_size = _nb_vertices;
+ _source->distance_from_source = 0;
+ _source->decrease_distance_in_heap(_heap);
+
+ while(heap_size > 1) {
+ // 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--;
+ 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 < last_slot);
+ tv->distance_from_source = d;
+ tv->pred_edge_toward_source = e;
+ tv->decrease_distance_in_heap(_heap);
+ }
+ }
+ }
}
-void MTPGraph::find_best_paths(scalar_t *lengths, int *result_edge_occupation) {
- scalar_t total_length;
+void MTPGraph::find_best_paths(scalar_t *lengths) {
+ scalar_t shortest_path_length;
Vertex *v;
Edge *e;
for(int e = 0; e < _nb_edges; e++) {
- edges[e].length = lengths[e];
- edges[e].work_length = edges[e].length;
+ _edges[e].length = lengths[e];
+ _edges[e].occupied = 0;
+ _edges[e].positivized_length = _edges[e].length;
}
- find_shortest_path(_front, _new_front);
- update_work_lengths();
-
- // #warning
- // initialize_work_lengths();
+ // 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 {
- force_positive_work_lengths();
- find_shortest_path(_front, _new_front);
- update_work_lengths();
+ // 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) {
- // If yes, compute the length of the best path
+ // Do we reach the sink?
+ if(_sink->pred_edge_toward_source) {
+ // If yes, compute the length of the best path according to the
+ // original edge lengths
v = _sink;
- while(v->pred_edge) {
- total_length += v->pred_edge->length;
- v = v->pred_edge->origin_vertex;
+ while(v->pred_edge_toward_source) {
+ 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
- cout << "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(v->pred_edge) {
- e = v->pred_edge;
+ while(v->pred_edge_toward_source) {
+ e = v->pred_edge_toward_source;
v = e->origin_vertex;
- e->revert();
+ e->invert();
+ // This is the only place where we change the occupations of
+ // edges
e->occupied = 1 - e->occupied;
}
}
}
- } 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++) {
- Edge *e = edges + k;
- if(e->occupied) { e->revert(); }
+ e = &_edges[k];
+ if(e->occupied) { e->invert(); }
+ }
+}
+
+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++] = int(e->origin_vertex - _vertices);
+ path->length = e->length;
+ } else l++;
+
+ while(e->terminal_vertex != _sink) {
+ if(path) {
+ path->nodes[l++] = int(e->terminal_vertex - _vertices);
+ path->length += e->length;
+ } else l++;
+
+ nb_occupied_next = 0;
+ 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
+ if(nb_occupied_next == 0) {
+ cerr << __FILE__ << ": retrieve_one_path: Non-sink end point." << endl;
+ abort();
+ }
+#endif
+
+ if(path) { used_edges[next - _edges] = 1; }
+
+ e = next;
+ }
+
+ if(path) {
+ 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 n = 0; n < _nb_vertices; n++) {
- Vertex *v = &vertices[n];
- for(Edge *e = v->root_edge; e; e = e->next) {
- result_edge_occupation[e->id] = e->occupied;
+ 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_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_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], used_edges);
+ used_edges[e - _edges] = 1;
+ p++;
+ }
+ }
+
+ delete[] used_edges;
}
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