/*
- * mtp is the ``Multi Tracked Path'', an implementation of the
- * k-shortest path algorithm for multi-target tracking.
+ * 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>
#include "mtp_graph.h"
-#include <iostream>
#include <float.h>
-#include <stdlib.h>
using namespace std;
class Edge {
public:
- int id, occupied;
+ int occupied;
scalar_t length, positivized_length;
Vertex *origin_vertex, *terminal_vertex;
- // These are the links in the origin_vertex leaving edge list
+ // 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;
Edge *leaving_edges;
scalar_t distance_from_source;
Edge *pred_edge_toward_source;
- int iteration; // Used in find_shortest_path to know if we already
- // added this vertex to the front
+ int last_change; // Used to mark which edges have already been
+ // processed in some methods
+
+ Vertex **heap_position;
+
Vertex();
+
inline void add_leaving_edge(Edge *e);
inline void del_leaving_edge(Edge *e);
};
void Edge::invert() {
length = - length;
- positivized_length = 0;
+ positivized_length = - positivized_length;
origin_vertex->del_leaving_edge(this);
terminal_vertex->add_leaving_edge(this);
Vertex *t = terminal_vertex;
//////////////////////////////////////////////////////////////////////
+static int compare_vertex(const void *v1, const void *v2) {
+ return (*((Vertex **) v1))->last_change - (*((Vertex **) v2))->last_change;
+}
+
MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
- int *from, int *to,
+ 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];
+ _heap = new Vertex *[_nb_vertices];
+ _dp_order = new Vertex *[_nb_vertices];
_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[from[e]].add_leaving_edge(_edges + e);
+ _vertices[vertex_from[e]].add_leaving_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];
+ _edges[e].origin_vertex = _vertices + vertex_from[e];
+ _edges[e].terminal_vertex = _vertices + vertex_to[e];
+ }
+
+ for(int v = 0; v < _nb_vertices; v++) {
+ _heap[v] = &_vertices[v];
+ _vertices[v].heap_position = &_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();
+ }
}
MTPGraph::~MTPGraph() {
delete[] _vertices;
+ delete[] _dp_order;
+ delete[] _heap;
delete[] _edges;
- delete[] _front;
- delete[] _new_front;
for(int p = 0; p < nb_paths; p++) delete paths[p];
delete[] paths;
}
void MTPGraph::print(ostream *os) {
for(int k = 0; k < _nb_edges; k++) {
Edge *e = _edges + k;
- (*os) << e->origin_vertex->id
+ (*os) << e->origin_vertex - _vertices
<< " -> "
- << e->terminal_vertex->id
+ << e->terminal_vertex - _vertices
<< " "
<< e->length;
if(e->occupied) {
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->id << " [peripheries=2];" << endl;
- (*os) << " " << _sink->id << " [peripheries=2];" << endl;
- // (*os) << " " << _source->id << " [style=bold,color=red];" << endl;
- // (*os) << " " << _sink->id << " [style=bold,color=green];" << 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->id << " -> " << e->terminal_vertex->id
- // << ";"
- // << endl;
- (*os) << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
+ (*os) << " "
+ << e->origin_vertex - _vertices
+ << " -> "
+ << e->terminal_vertex - _vertices
<< " [";
if(e->occupied) {
(*os) << "style=bold,color=black,";
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].leaving_edges; e; e = e->next_leaving_edge) {
- if(e->positivized_length < 0) {
+ for(int k = 0; k < _nb_edges; k++) {
+ 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);
-#endif
- e->positivized_length = 0.0;
}
+#endif
+ e->positivized_length = 0.0;
}
}
#ifdef VERBOSE
#endif
}
-// This method does not change the edge occupation. It update
-// distance_from_source and pred_edge_toward_source.
+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);
+#endif
+}
+
+void MTPGraph::dp_distance_propagation() {
+ Vertex *v, *tv;
+ Edge *e;
+ scalar_t d;
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].distance_from_source = FLT_MAX;
+ _vertices[k].pred_edge_toward_source = 0;
+ }
+
+ _source->distance_from_source = 0;
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ v = _dp_order[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) {
+ 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
+// properly, for every vertex, the fields distance_from_source and
+// pred_edge_toward_source.
+
void MTPGraph::find_shortest_path() {
- Vertex **tmp_front;
- int tmp_front_size;
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_toward_source = 0;
- _vertices[v].iteration = 0;
+#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
- int 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 _front_size = 0, _new_front_size;
- _front[_front_size++] = _source;
+ _heap_size = _nb_vertices;
_source->distance_from_source = 0;
+ decrease_distance_in_heap(_source);
do {
- _new_front_size = 0;
- iteration++;
+#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
- for(int f = 0; f < _front_size; f++) {
- v = _front[f];
- 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) {
- tv->distance_from_source = d;
- tv->pred_edge_toward_source = e;
- if(tv->iteration < iteration) {
- _new_front[_new_front_size++] = tv;
- tv->iteration = iteration;
- }
- }
+ v = _heap[0];
+ _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]);
+
+ 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) {
+ ASSERT(tv->heap_position - _heap < _heap_size);
+ tv->distance_from_source = d;
+ tv->pred_edge_toward_source = e;
+ decrease_distance_in_heap(tv);
+ }
+#ifdef DEBUG
+ for(int k = 0; k < _heap_size; k++) {
+ if(_heap[0]->distance_from_source > _heap[k]->distance_from_source) abort();
}
+#endif
}
-
- tmp_front = _new_front;
- _new_front = _front;
- _front = tmp_front;
-
- tmp_front_size = _new_front_size;
- _new_front_size = _front_size;
- _front_size = tmp_front_size;
- } while(_front_size > 0);
+ } 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) {
_edges[e].positivized_length = _edges[e].length;
}
- // We use one iteration of find_shortest_path simply to propagate
- // the distance to make all the edge lengths positive.
- find_shortest_path();
+ // // 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();
do {
update_positivized_lengths();
total_length = 0.0;
- // Do we reach the _sink?
+ // Do we reach the sink?
if(_sink->pred_edge_toward_source) {
- // If yes, compute the length of the best path
+ // If yes, compute the length of the best path according to the
+ // original edge lengths
v = _sink;
while(v->pred_edge_toward_source) {
total_length += v->pred_edge_toward_source->length;
// 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;
+ e = _edges + k;
if(e->occupied) { e->invert(); }
}
}
int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
Edge *f, *next = 0;
- int l = 0;
+ int l = 0, nb_occupied_next;
if(path) {
- path->nodes[l++] = e->origin_vertex->id;
+ path->nodes[l++] = e->origin_vertex - _vertices;
path->length = e->length;
} else l++;
while(e->terminal_vertex != _sink) {
if(path) {
- path->nodes[l++] = e->terminal_vertex->id;
+ path->nodes[l++] = e->terminal_vertex - _vertices;
path->length += e->length;
} else l++;
- int nb_choices = 0;
+
+ nb_occupied_next = 0;
for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
- if(f->occupied) { nb_choices++; next = f; }
- if(nb_choices == 0) {
- cerr << "retrieve_one_path: Non-sink end point." << endl;
- abort();
- }
- if(nb_choices > 1) {
- cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
- abort();
- }
+ if(f->occupied) { nb_occupied_next++; next = f; }
}
+
+#ifdef DEBUG
+ if(nb_occupied_next == 0) {
+ cerr << "retrieve_one_path: Non-sink end point." << endl;
+ abort();
+ }
+
+ else if(nb_occupied_next > 1) {
+ cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
+ abort();
+ }
+#endif
+
e = next;
}
if(path) {
- path->nodes[l++] = e->terminal_vertex->id;
+ path->nodes[l++] = e->terminal_vertex - _vertices;
path->length += e->length;
} else l++;
void MTPGraph::retrieve_disjoint_paths() {
Edge *e;
+ int p, l;
for(int p = 0; p < nb_paths; p++) delete paths[p];
delete[] paths;
paths = new Path *[nb_paths];
- int p = 0;
+ p = 0;
for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
if(e->occupied) {
- int l = retrieve_one_path(e, 0);
+ l = retrieve_one_path(e, 0);
paths[p] = new Path(l);
retrieve_one_path(e, paths[p]);
p++;
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