#include "mtp_graph.h"
-// #include <iostream>
+#include <cmath>
#include <float.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 last_change; // Used to mark which edges have already been
- // processed in some methods
+ Edge *leaving_edge_list_root;
+ Vertex **heap_slot;
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, Vertex **heap_bottom);
};
//////////////////////////////////////////////////////////////////////
positivized_length = - positivized_length;
origin_vertex->del_leaving_edge(this);
terminal_vertex->add_leaving_edge(this);
- Vertex *t = terminal_vertex;
- terminal_vertex = origin_vertex;
- origin_vertex = t;
+ swap(terminal_vertex, origin_vertex);
}
//////////////////////////////////////////////////////////////////////
Vertex::Vertex() {
- leaving_edges = 0;
+ leaving_edge_list_root = 0;
}
void Vertex::add_leaving_edge(Edge *e) {
- e->next_leaving_edge = leaving_edges;
+ e->next_leaving_edge = leaving_edge_list_root;
e->pred_leaving_edge = 0;
- if(leaving_edges) { leaving_edges->pred_leaving_edge = e; }
- leaving_edges = e;
+ if(leaving_edge_list_root) {
+ leaving_edge_list_root->pred_leaving_edge = e;
+ }
+ leaving_edge_list_root = e;
}
void Vertex::del_leaving_edge(Edge *e) {
- if(e == leaving_edges) {
- leaving_edges = e->next_leaving_edge;
+ 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;
}
}
+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, Vertex **heap_bottom) {
+ Vertex **c1, **c2, **h;
+ // omg, that's beautiful
+ h = heap_slot;
+ while(c1 = heap + 2 * (h - heap) + 1,
+ c1 < heap_bottom &&
+ (c2 = c1 + 1,
+ (*c1)->distance_from_source < (*h)->distance_from_source
+ ||
+ (c2 < heap_bottom && (*c2)->distance_from_source < (*h)->distance_from_source)
+ )) {
+ if(c2 < heap_bottom && (*c2)->distance_from_source <= (*c1)->distance_from_source) {
+ swap(*c2, *h);
+ swap((*c2)->heap_slot, (*h)->heap_slot);
+ h = c2;
+ } else {
+ swap(*c1, *h);
+ swap((*c1)->heap_slot, (*h)->heap_slot);
+ h = c1;
+ }
+ }
+}
+
+//////////////////////////////////////////////////////////////////////
+
+static int compare_vertices_on_distance(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,
_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 k = 0; k < _nb_vertices; k++) {
- _vertices[k].id = k;
- }
-
for(int e = 0; e < nb_edges; e++) {
_vertices[vertex_from[e]].add_leaving_edge(_edges + e);
_edges[e].occupied = 0;
- _edges[e].id = 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;
+
+ compute_dp_ranks();
+ for(int v = 0; v < _nb_vertices; v++) { _dp_order[v] = &_vertices[v]; }
+ qsort(_dp_order, _nb_vertices, sizeof(Vertex *), compare_vertices_on_distance);
}
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::compute_dp_ranks() {
+ 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. The
+ // rank of a node is the iteration at which is it removed, and we
+ // set the distance_from_source fields to this value.
+
+ Vertex **with_predecessor = new Vertex *[_nb_vertices];
+
+ // All the nodes are with_predecessor at first
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].distance_from_source = 0;
+ with_predecessor[k] = &_vertices[k];
+ }
+
+ scalar_t rank = 1;
+ int nb_with_predecessor = _nb_vertices, pred_nb_with_predecessor;
+
+ do {
+ // We set the distance_from_source field of all the vertices with incoming
+ // edges to the current rank value
+ for(int f = 0; f < nb_with_predecessor; f++) {
+ v = with_predecessor[f];
+ for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+ e->terminal_vertex->distance_from_source = rank;
+ }
+ }
+
+ pred_nb_with_predecessor = nb_with_predecessor;
+ nb_with_predecessor = 0;
+
+ // We keep all the vertices with incoming nodes
+ for(int f = 0; f < pred_nb_with_predecessor; f++) {
+ v = with_predecessor[f];
+ if(v->distance_from_source == rank) {
+ with_predecessor[nb_with_predecessor++] = v;
+ }
+ }
+
+ rank++;
+ } while(nb_with_predecessor < pred_nb_with_predecessor);
+
+ delete[] with_predecessor;
+
+ if(nb_with_predecessor > 0) {
+ cerr << __FILE__ << ": The graph is not a DAG." << endl;
+ abort();
+ }
+}
+
+//////////////////////////////////////////////////////////////////////
+
void MTPGraph::print(ostream *os) {
for(int k = 0; k < _nb_edges; k++) {
Edge *e = _edges + k;
- (*os) << e->origin_vertex->id
- << " -> "
- << e->terminal_vertex->id
- << " "
- << e->length;
- if(e->occupied) {
- (*os) << " *";
- }
+ (*os) << e->origin_vertex - _vertices
+ << " -> "
+ << e->terminal_vertex - _vertices
+ << " (" << e->length << ")";
+ if(e->occupied) { (*os) << " *"; }
(*os) << 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 - _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,";
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);
- }
+ residual_error -= e->positivized_length;
+ max_error = max(max_error, - e->positivized_length);
#endif
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
}
-int MTPGraph::is_dag() {
- Vertex *v;
+void MTPGraph::dp_compute_distances() {
+ Vertex *v, *tv;
Edge *e;
+ scalar_t d;
- // We put everybody in the front
for(int k = 0; k < _nb_vertices; k++) {
- _vertices[k].last_change = -1;
- _front[k] = &_vertices[k];
+ _vertices[k].distance_from_source = FLT_MAX;
+ _vertices[k].pred_edge_toward_source = 0;
}
- int iteration = 0;
- int front_size = _nb_vertices, pred_front_size;
-
- do {
- // We set the last_change field of all the vertices with incoming
- // edges to the current iteration value
- for(int f = 0; f < front_size; f++) {
- v = _front[f];
- for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
- e->terminal_vertex->last_change = iteration;
- }
- }
-
- pred_front_size = front_size;
- front_size = 0;
+ _source->distance_from_source = 0;
- // We keep all the vertices with incoming nodes
- for(int f = 0; f < pred_front_size; f++) {
- v = _front[f];
- if(v->last_change == iteration) {
- _front[front_size++] = v;
+ 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;
}
}
-
- iteration++;
- } while(front_size < pred_front_size);
-
- return front_size == 0;
+ }
}
-// This method does not change the edge occupation. It only set
+// 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 **tmp_front;
- Vertex *v, *tv;
+ Vertex *v, *tv, **last_slot;
Edge *e;
scalar_t d;
-#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
-
for(int k = 0; k < _nb_vertices; k++) {
_vertices[k].distance_from_source = FLT_MAX;
_vertices[k].pred_edge_toward_source = 0;
- _vertices[k].last_change = -1;
}
- int iteration = 0;
-
- int front_size = 0, new_front_size;
- _front[front_size++] = _source;
+ _heap_size = _nb_vertices;
_source->distance_from_source = 0;
+ _source->decrease_distance_in_heap(_heap);
do {
- new_front_size = 0;
-
- 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->last_change < iteration) {
- _new_front[new_front_size++] = tv;
- tv->last_change = iteration;
- }
- }
+ // 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[0]->increase_distance_in_heap(_heap, _heap + _heap_size);
+
+ // 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 - _heap < _heap_size);
+ tv->distance_from_source = d;
+ tv->pred_edge_toward_source = e;
+ tv->decrease_distance_in_heap(_heap);
}
}
-
- tmp_front = _new_front; _new_front = _front; _front = tmp_front;
-
- front_size = new_front_size;
-
- iteration++;
- } while(front_size > 0);
+ } while(_heap_size > 0);
}
void MTPGraph::find_best_paths(scalar_t *lengths) {
- scalar_t total_length;
+ scalar_t shortest_path_length;
Vertex *v;
Edge *e;
_edges[e].positivized_length = _edges[e].length;
}
- // 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();
+ // 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 {
+ // 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_toward_source) {
// original edge lengths
v = _sink;
while(v->pred_edge_toward_source) {
- total_length += v->pred_edge_toward_source->length;
+ 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
- cerr << "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(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)
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;
- for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
- if(f->occupied) { nb_choices++; next = f; }
+
+ nb_occupied_next = 0;
+ for(f = e->terminal_vertex->leaving_edge_list_root; f; f = f->next_leaving_edge) {
+ if(f->occupied) { nb_occupied_next++; next = f; }
}
#ifdef DEBUG
- if(nb_choices == 0) {
- cerr << "retrieve_one_path: Non-sink end point." << endl;
+ if(nb_occupied_next == 0) {
+ cerr << __FILE__ << ": retrieve_one_path: Non-sink end point." << endl;
abort();
}
- if(nb_choices > 1) {
- cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
+
+ else if(nb_occupied_next > 1) {
+ cerr << __FILE__ << ": retrieve_one_path: Non node-disjoint paths." << endl;
abort();
}
#endif
}
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;
nb_paths = 0;
- for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
+ for(e = _source->leaving_edge_list_root; e; e = e->next_leaving_edge) {
if(e->occupied) { nb_paths++; }
}
paths = new Path *[nb_paths];
- int p = 0;
- for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
+ p = 0;
+ for(e = _source->leaving_edge_list_root; 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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