A simpler and more efficient algorithm for the next-to-shortest path problem

Authors:
Bang Ye Wu
Affiliations:
National Chung Cheng University, ChiaYi, Taiwan, R.O.C.
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Year:
2010

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Abstract

Given an undirected graph G = (V,E) with positive edge weights and two vertices s and t, the next-to-shortest path problem is to find an st-path which length is minimum among all st-paths of lengths strictly larger than the shortest path length. In this paper we give an O(|V| log |V|+|E|) time algorithm for this problem, which improves the previous result of O(|V|2) time for sparse graphs.