Fast, precise and dynamic distance queries

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) + 2^{O(λ log λ)}]n, and can be constructed in [2^O(λ) log³ n + ε^-O(λ) + 2^{O(λ log λ)}]n expected time. This improves upon the best previously known constructions, presented by Har-Peled and Mendel [13]. Furthermore, the oracle can be made fully dynamic with expected O(1) query time and only 2^O(λ) log n+ε^-O(λ)+2^{O(λ log λ)} update time. This is the first fully dynamic (1 + ε)- distance oracle.