A note on shortest path problems with forbidden paths

We consider the variant of the shortest path problem in which a given set of paths is forbidden to occur as a subpath in an optimal path. We establish that the most-efficient algorithm for its solution, a dynamic programming algorithm, has polynomial time complexity; it had previously been conjectured that the algorithm has pseudo-polynomial time complexity. Furthermore, we show that this algorithm can be extended, without increasing its time complexity, to handle non elementary forbidden paths