Shortest Paths Avoiding Forbidden Subpaths

Mustaq Ahmed (1) , Anna Lubiw (1)

1 David R. Cheriton School of Computer Science

In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P . Path P is allowed to repeat vertices and edges. We call each path in X an exception, and our desired path a shortest exception avoiding path. We formulate a new version of the problem where the algorithm has no a priori knowledge of X, and finds out about an exception x ∈ X only when a path containing x fails. This situation arises in computing shortest paths in optical networks. We give an algorithm that finds a shortest exception avoiding path in time polynomial in |G| and |X|. The main idea is to run Dijkstra's algorithm incrementally after replicating vertices when an exception is discovered.

Mots clés: Algorithms and data structures; Graph algorithms; Optical networks

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Mustaq Ahmed, Anna Lubiw. Shortest Paths Avoiding Forbidden Subpaths. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.63-74. ⟨inria-00359710⟩