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Distance Labeling in Hyperbolic Graphs

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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Abstract

A graph G is δ-hyperbolic if for any four vertices u,v,x,y of G the two larger of the three distance sums d G (u,v) + d G (x,y), d G (u,x) + d G (v,y), d G (u,y) + d G (v,x) differ by at most δ, and the smallest δ ≥ 0 for which G is δ-hyperbolic is called the hyperbolicity of G.

In this paper, we construct a distance labeling scheme for bounded hyperbolicity graphs, that is a vertex labeling such that the distance between any two vertices of G can be estimated from their labels, without any other source of information. More precisely, our scheme assigns labels of O(log2 n) bits for bounded hyperbolicity graphs with n vertices such that distances can be approximated within an additive error of O(log n). The label length is optimal for every additive error up to n ε. We also show a lower bound of Ω(log log n) on the approximation factor, namely every s-multiplicative approximate distance labeling scheme on bounded hyperbolicity graphs with polylogarithmic labels requires s = Ω(log log n).

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Author information

Authors and Affiliations

  1. LaBRI, Bordeaux University,  

    Cyril Gavoille & Olivier Ly

Authors
  1. Cyril Gavoille
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  2. Olivier Ly
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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Gavoille, C., Ly, O. (2005). Distance Labeling in Hyperbolic Graphs. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_106

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  • DOI: https://doi.org/10.1007/11602613_106

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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