A Quadratic Algorithm for Finding Next-to-Shortest Paths in Graphs

Authors:
Kuo-Hua Kao;Jou-Ming Chang;Yue-Li Wang;Justie Su-Tzu Juan
Affiliations:
National Chi Nan University, Department of Computer Science and Information Engineering, Nantou, Taiwan, ROC;National Taipei College of Business, Institute of Information Science and Management, Taipei, Taiwan, ROC;National Taiwan University of Science and Technology, Department of Information Management, Taipei, Taiwan, ROC;National Chi Nan University, Department of Computer Science and Information Engineering, Nantou, Taiwan, ROC
Venue:
Algorithmica
Year:
2011

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Abstract

Given an edge-weighted undirected graph G and two prescribed vertices u and v, a next-to-shortest (u,v)-path is a shortest (u,v)-path amongst all (u,v)-paths having length strictly greater than the length of a shortest (u,v)-path. In this paper, we deal with the problem of computing a next-to-shortest (u,v)-path. We propose an ${\mathcal{O}}(n^{2})$ time algorithm for solving this problem, which significantly improves the bound of a previous one in ${\mathcal{O}}(n^{3})$ time where n is the number of vertices in G.