Finding next-to-shortest paths in a graph

Authors:
I. Krasikov;S. D. Noble
Affiliations:
Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, UK;Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, UK
Venue:
Information Processing Letters
Year:
2004

Citing 3
Cited 0

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Abstract

We study the problem of finding the next-to-shortest paths in a graph. A next-to-shortest (u,v)-path is a shortest (u,v)-path amongst (u,v)-paths with length strictly greater than the length of the shortest (u,v)-path. In contrast to the situation in directed graphs, where the problem has been shown to be NP-hard, providing edges of length zero are allowed, we prove the somewhat surprising result that there is a polynomial time algorithm for the undirected version of the problem.