Distance Labeling in Hyperbolic Graphs

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 dG(u, v) + dG(x, y), dG(u, x) + dG(v, y), dG(u, y) + dG(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 nε . 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 lo...

• Type: Conference
• Year: 2005
• Where: ISAAC
• Authors: Cyril Gavoille, Olivier Ly
• Keywords: Distance Labeling Scheme, Distance Sums, Hyperbolicity Graphs, ISAAC 2005