An optimal dynamic spanner for doubling metric spaces

Abstract

A t-spanner is a graph on a set of points S with the following property: Between any pair of points there is a path in the spanner whose total length is at most t times the actual distance between the points. In this paper, we consider points residing in a metric space equipped with doubling dimension λ, and show how to construct a dynamic (1 + ε)-spanner with degree ε-O(λ) in O( log n/εO(λ))update time. When λ and ε are taken as constants, the degree and update times are optimal. © 2008 Springer-Verlag Berlin Heidelberg.