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Distance Labeling in Hyperbolic Graphs

  • Cyril Gavoille
  • Olivier Ly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)

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).

Keywords

Distance queries distance labeling scheme hyperbolic graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cyril Gavoille
    • 1
  • Olivier Ly
    • 1
  1. 1.LaBRIBordeaux University 

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