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

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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.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Chi Nan University, Nantou, Taiwan, ROC

    Kuo-Hua Kao & Justie Su-Tzu Juan

  2. Institute of Information Science and Management, National Taipei College of Business, Taipei, Taiwan, ROC

    Jou-Ming Chang

  3. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC

    Yue-Li Wang

Authors
  1. Kuo-Hua Kao
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  2. Jou-Ming Chang
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  3. Yue-Li Wang
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  4. Justie Su-Tzu Juan
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Corresponding author

Correspondence to Yue-Li Wang.

Additional information

This research was partially supported by National Science Council of Taiwan under the Grants NSC96-2221-E-260-014 and NSC97-2115-M-141-001-MY2.

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Kao, KH., Chang, JM., Wang, YL. et al. A Quadratic Algorithm for Finding Next-to-Shortest Paths in Graphs. Algorithmica 61, 402–418 (2011). https://doi.org/10.1007/s00453-010-9402-4

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  • DOI: https://doi.org/10.1007/s00453-010-9402-4

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