+void MTPGraph::compute_dp_ranks() {
+ Vertex *v;
+ Edge *e;
+ int tv;
+
+ // 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.
+
+ int *nb_predecessors = new int[_nb_vertices];
+ int *without_predecessors = new int[_nb_vertices];
+ int *new_without_predecessors = new int[_nb_vertices];
+ int nb_without_predecessors, new_nb_without_predecessors;
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ nb_predecessors[k] = 0;
+ }
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ v = _vertices + k;
+ for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+ tv = e->terminal_vertex - _vertices;
+ nb_predecessors[tv]++;
+ }
+ }
+
+ nb_without_predecessors = 0;
+ for(int k = 0; k < _nb_vertices; k++) {
+ if(nb_predecessors[k] == 0) {
+ without_predecessors[nb_without_predecessors++] = k;
+ }
+ }
+
+ scalar_t rank = 1;
+ while(nb_without_predecessors > 0) {
+ new_nb_without_predecessors = 0;
+ for(int l = 0; l < nb_without_predecessors; l++) {
+ v = _vertices + without_predecessors[l];
+ v->distance_from_source = rank;
+ for(e = v->leaving_edge_list_root; e; e = e->next_leaving_edge) {
+ tv = e->terminal_vertex - _vertices;
+ nb_predecessors[tv]--;
+ ASSERT(nb_predecessors[tv] >= 0);
+ if(nb_predecessors[tv] == 0) {
+ new_without_predecessors[new_nb_without_predecessors++] = tv;
+ }
+ }
+ }
+
+ swap(without_predecessors, new_without_predecessors);
+ nb_without_predecessors = new_nb_without_predecessors;
+ rank++;
+ }
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ if(nb_predecessors[k] > 0) {
+ cerr << __FILE__ << ": The graph is not a DAG." << endl;
+ abort();
+ }
+ }
+
+ delete[] nb_predecessors;
+ delete[] without_predecessors;
+ delete[] new_without_predecessors;
+}
+
+//////////////////////////////////////////////////////////////////////
+