Given a directed cyclic graph where the weight of each edge may be negative the concept of a "shortest path" only makes sense if there are no negative cycles, and in that case you can apply the Bellman-Ford algorithm.
However, I'm interested in finding the shortest-path between two vertices that doesn't involve cycling (ie. under the constraint that you may not visit the same vertex twice). Is this problem well studied? Can a variant of the Bellman-Ford algorithm be employed, and if not is there another solution?
I'm also interested in the equivalent all-pairs problem, for which I might otherwise apply Floyd–Warshall.