Improved algorithm for finding next-to-shortest paths

Authors:
Shisheng Li;Guangzhong Sun;Guoliang Chen
Affiliations:
National High Performance Computing Center at Hefei, Department of Computer Science, University of Science and Technology of China, Anhui, Hefei, PR China;National High Performance Computing Center at Hefei, Department of Computer Science, University of Science and Technology of China, Anhui, Hefei, PR China;National High Performance Computing Center at Hefei, Department of Computer Science, University of Science and Technology of China, Anhui, Hefei, PR China
Venue:
Information Processing Letters
Year:
2006

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Abstract

We study the problem of finding the next-to-shortest paths in a weighted undirected 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. The first polynomial algorithm for this problem was presented in [I. Krasikov, S.D. Noble, Finding next-to-shortest paths in a graph, Inform. Process. Lett. 92 (2004) 117-119]. We improve the upper bound from O(n3m) to O(n3).