X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?a=blobdiff_plain;ds=inline;f=mtp_graph.cc;h=33d5a4ff0d8bdd191467b5cdaf8fc607108fb5a3;hb=86c860c0f43a9130e4121072620961fc892ed83f;hp=4608b82f428fe252c96aec1fbf6656f753f3238b;hpb=6afe91234d7807ce82b96a071087decb2f7aead3;p=mtp.git
diff --git a/mtp_graph.cc b/mtp_graph.cc
index 4608b82..33d5a4f 100644
--- a/mtp_graph.cc
+++ b/mtp_graph.cc
@@ -1,36 +1,41 @@
-///////////////////////////////////////////////////////////////////////////
-// 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 . //
-// //
-// Written by and Copyright (C) Francois Fleuret //
-// Contact 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
+ *
+ * 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 .
+ *
+ */
#include "mtp_graph.h"
-#include
#include
-#include
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();
@@ -38,23 +43,24 @@ public:
class Vertex {
public:
- int id;
Edge *leaving_edges;
scalar_t distance_from_source;
Edge *pred_edge_toward_source;
+ Vertex **heap_slot;
- int iteration; // Used in find_shortest_path to know if we already
- // added this vertex to the front
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);
};
//////////////////////////////////////////////////////////////////////
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;
@@ -87,43 +93,98 @@ void Vertex::del_leaving_edge(Edge *e) {
}
}
+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)) {
+ swap(*p, *h);
+ swap((*p)->heap_slot, (*h)->heap_slot);
+ h = p;
+ }
+}
+
+void Vertex::increase_distance_in_heap(Vertex **heap, int heap_size) {
+ Vertex **c1, **c2, **h;
+ // omg, that's beautiful
+ h = heap_slot;
+ 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_slot, (*h)->heap_slot);
+ h = c1;
+ } else {
+ swap(*c2, *h);
+ swap((*c2)->heap_slot, (*h)->heap_slot);
+ h = c2;
+ }
+ }
+}
+
//////////////////////////////////////////////////////////////////////
+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 *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_slot = &_heap[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();
+ }
}
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;
}
@@ -133,9 +194,9 @@ MTPGraph::~MTPGraph() {
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) {
@@ -147,22 +208,22 @@ void MTPGraph::print(ostream *os) {
void MTPGraph::print_dot(ostream *os) {
(*os) << "digraph {" << endl;
- // (*os) << " node [shape=circle];" << endl;
- (*os) << " edge [color=gray]" << endl;
- (*os) << " " << _source->id << " [peripheries=2];" << endl;
- (*os) << " " << _sink->id << " [peripheries=2];" << 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->id << " -> " << e->terminal_vertex->id
- // << ";"
- // << endl;
+ (*os) << " "
+ << e->origin_vertex - _vertices
+ << " -> "
+ << e->terminal_vertex - _vertices
+ << " [";
if(e->occupied) {
- (*os) << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
- << " [style=bold,color=black,label=\"" << e->length << "\"];" << endl;
- } else {
- (*os) << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
- << " [label=\"" << e->length << "\"];" << endl;
+ (*os) << "style=bold,color=black,";
}
+ (*os) << "label=\"" << e->length << "\"];" << endl;
}
(*os) << "}" << endl;
}
@@ -182,71 +243,143 @@ void MTPGraph::force_positivized_lengths() {
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
- residual_error -= e->positivized_length;
- max_error = max(max_error, - e->positivized_length);
+ residual_error -= e->positivized_length;
+ max_error = max(max_error, - e->positivized_length);
#endif
- e->positivized_length = 0.0;
- }
+ e->positivized_length = 0.0;
}
}
#ifdef VERBOSE
- cerr << "residual_error " << residual_error << " max_error " << residual_error << endl;
+ cerr << __FILE__ << ": residual_error " << residual_error << " max_error " << residual_error << endl;
#endif
}
-// This method does not change the edge occupation. It update
-// distance_from_source and pred_edge_toward_source.
-void MTPGraph::find_shortest_path() {
- Vertex **tmp_front;
- int tmp_front_size;
+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;
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;
+ 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(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;
- }
- }
+ 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;
+ tv->decrease_distance_in_heap(_heap);
}
}
+ }
+}
+
+// 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() {
+ Vertex *v, *tv, **a, **b;
+ 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;
+ }
- tmp_front = _new_front;
- _new_front = _front;
- _front = tmp_front;
+ _heap_size = _nb_vertices;
+ _source->distance_from_source = 0;
+ _source->decrease_distance_in_heap(_heap);
- tmp_front_size = _new_front_size;
- _new_front_size = _front_size;
- _front_size = tmp_front_size;
- } while(_front_size > 0);
+ do {
+ // Get the closest to the source
+ v = _heap[0];
+
+ // Remove it from the heap (swap it with the last 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) {
+ 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);
+ 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) {
@@ -260,9 +393,8 @@ 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();
+ // Update the distances to the source in "good order"
+ dp_compute_distances();
do {
update_positivized_lengths();
@@ -271,9 +403,10 @@ void MTPGraph::find_best_paths(scalar_t *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;
@@ -282,7 +415,7 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
// If that length is negative
if(total_length < 0.0) {
#ifdef VERBOSE
- cerr << "Found a path of length " << total_length << endl;
+ cerr << __FILE__ << ": Found a path of length " << total_length << endl;
#endif
// Invert all the edges along the best path
v = _sink;
@@ -302,42 +435,48 @@ void MTPGraph::find_best_paths(scalar_t *lengths) {
// 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 << __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
+
e = next;
}
if(path) {
- path->nodes[l++] = e->terminal_vertex->id;
+ path->nodes[l++] = e->terminal_vertex - _vertices;
path->length += e->length;
} else l++;
@@ -346,6 +485,7 @@ int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
void MTPGraph::retrieve_disjoint_paths() {
Edge *e;
+ int p, l;
for(int p = 0; p < nb_paths; p++) delete paths[p];
delete[] paths;
@@ -357,10 +497,10 @@ void MTPGraph::retrieve_disjoint_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++;