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On the Minimum Eccentricity Shortest Path Problem

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Algorithms and Data Structures (WADS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9214))

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Abstract

In this paper, we introduce and investigate the Minimum Eccentricity Shortest Path (MESP) problem in unweighted graphs. It asks for a given graph to find a shortest path with minimum eccentricity. We demonstrate that:

  • a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line;

  • the MESP-problem is NP-hard on general graphs;

  • a 2-approximation, a 3-approximation, and an 8-approximation for the MESP-problem can be computed in \(\mathcal {O}(n^3)\) time, in \(\mathcal {O}(nm)\) time, and in linear time, respectively;

  • a shortest path of minimum eccentricity k in general graphs can be computed in \(\mathcal {O}(n^{2k+2}m)\) time;

  • the MESP-problem can be solved in linear time for trees.

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Authors and Affiliations

  1. Department of Computer Science, Kent State University, Kent, Ohio, USA

    Feodor F. Dragan & Arne Leitert

Authors
  1. Feodor F. Dragan
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  2. Arne Leitert
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Correspondence to Arne Leitert .

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Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Carleton University, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. University of Victoria, Victoria, Canada

    Ulrike Stege

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Dragan, F.F., Leitert, A. (2015). On the Minimum Eccentricity Shortest Path Problem. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_23

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  • DOI: https://doi.org/10.1007/978-3-319-21840-3_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21839-7

  • Online ISBN: 978-3-319-21840-3

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