Fast, precise and dynamic distance queries

This is the authors' abstract. We don't add key points for this paper.

We present an approximate distance oracle for a point set S with n points and doubling dimension λ. For every ε>0, the oracle supports (1+ε)-approximate distance queries in (universal) constant time, occupies space [ε-O(λ) + 2O(λ log λ)]n, and can be constructed in [2O(λ) log3 n + ε-O(λ) + 2O(λ log λ)]n expected time. This improves upon the best previously known constructions, presented by Har-Peled and Mendel. Furthermore, the oracle can be made fully dynamic with expected O(1) query time and only 2O(λ) log n + ε-O(λ) + 2O(λ log λ) update time. This is the first fully dynamic (1+ε)-distance oracle.