Fast, precise and dynamic distance queries
Yair Bartal, Lee-Ad J. Gottlieb, Tsvi Kopelowitz, Moshe Lewenstein, Liam Roditty · 2011
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) log 3 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 2O(λ) log n+ε−O(λ) O(λ log λ) +2 update time. This is the first fully dynamic (1 + ε)distance oracle. 1