Bidirectional Bfs and Dijkstra

[Peter Kovacs]

It would be nice to have bidirectional Bfs and Dijkstra implementation in LEMON for the s-t shortest path problem.

Theoretically it is simple: the algorithm should be started "in parallel" from the source node s on the original graph and from the target node t on the reversed graph. As soon as we have a node u for which both direction have set the final dist and pred values, we can finish searching and construct the s->t path form the s->u path and the opposite of the t->u path. It could be faster by about a factor of two due to smaller search spaces.

However it is not clear for me how difficult it would be to implement it.

[Alpar Juttner]

Replying to kpeter:

It would be nice to have bidirectional Bfs and Dijkstra implementation in LEMON for the s-t shortest path problem.

Theoretically it is simple: the algorithm should be started "in parallel" from the source node s on the original graph and from the target node t on the reversed graph. As soon as we have a node u for which both direction have set the final dist and pred values, we can finish searching and construct the s->t path form the s->u path and the opposite of the t->u path.

It is a bit more difficult, even theoretically (it may be that the path s->u->t is not the shortest one).

[Peter Kovacs]

Replying to alpar:

It is a bit more difficult, even theoretically (it may be that the path s->u->t is not the shortest one).

Oops, I'm sorry. You are right. I've heard (or studied?) this method in this way, but it's wrong.

E.g. G = ({s,u,v,w,t},{su,ut,sv,vw,wt}), c(su)=c(ut)=80, c(sv)=c(w,t)=10, c(vw)=100. Here the shortest path is <sv,vw,wt>, not <su,ut>.

[Peter Kovacs]

Tamas Bibok implemented bidirectional Dijkstra and A* (A-star) algorithms for LEMON. These codes and his BSc thesis (in Hungarian) can be found in this repository:
​http://lime.cs.elte.hu/~kpeter/hg/hgwebdir.cgi/lemon-astar/