> Dijkstra's algorithm does that in O(n^2) time, and we would have to do
> this for n origins and (n-1) receivers.
>
> Thus, worst case should be O(n^4).

I did not fully track the discussion, but for all-pair shortest path one may
use http://en.wikipedia.org/wiki/Floyd-Warshall_algorithm

Greetings
Marcin Mank