Computing strictly-second shortest paths
Information Processing Letters
SIAM Journal on Computing
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Improved algorithm for finding next-to-shortest paths
Information Processing Letters
On the small cycle transversal of planar graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A simpler and more efficient algorithm for the next-to-shortest path problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
On the small cycle transversal of planar graphs
Theoretical Computer Science
The next-to-shortest path in undirected graphs with nonnegative weights
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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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.