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Computing Giant Graph Diameters

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Combinatorial Algorithms (IWOCA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9843))

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Abstract

This paper is devoted to the fast and exact diameter computation in graphs with n vertices and m edges, if the diameter is a large fraction of n. We give an optimal \(O(m+n)\) time algorithm for diameters above n / 2. The problem changes its structure at diameter value n / 2, as large cycles may be present. We propose a randomized \(O(m+n\log n)\) time algorithm for diameters above \((1/3+\epsilon )n\) for constant \(\epsilon >0\).

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Acknowledgment

The author would like to thank the anonymous referees for careful remarks which helped erase a number of small inaccuracies.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Chalmers University, 41296, Göteborg, Sweden

    Peter Damaschke

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  1. Peter Damaschke
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Correspondence to Peter Damaschke .

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Editors and Affiliations

  1. University of Helsinki, Helsinki, Finland

    Veli Mäkinen

  2. University of Helsinki, Helsinki, Finland

    Simon J. Puglisi

  3. University of Helsinki, Helsinki, Finland

    Leena Salmela

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Damaschke, P. (2016). Computing Giant Graph Diameters. In: Mäkinen, V., Puglisi, S., Salmela, L. (eds) Combinatorial Algorithms. IWOCA 2016. Lecture Notes in Computer Science(), vol 9843. Springer, Cham. https://doi.org/10.1007/978-3-319-44543-4_29

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  • DOI: https://doi.org/10.1007/978-3-319-44543-4_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44542-7

  • Online ISBN: 978-3-319-44543-4

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