Fast, precise and dynamic distance queries [chapter]

Yair Bartal, Lee-Ad Gottlieb, Tsvi Kopelowitz, Moshe Lewenstein, Liam Roditty
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
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 . Furthermore, the oracle can be made fully dynamic with expected O(1) query time and only 2
more » ... y 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.
doi:10.1137/1.9781611973082.66 dblp:conf/soda/BartalGKLR11 fatcat:snahqxbz3jh3dfeqkrnjjz5ham