@inproceedings{f397d74dedfa4d5e85943ac89d486c08,

title = "Fast, precise and dynamic distance queries",

abstract = "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 [13]. 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.",

author = "Yair Bartal and Gottlieb, {Lee Ad} and Tsvi Kopelowitz and Moshe Lewenstein and Liam Roditty",

year = "2011",

doi = "10.1137/1.9781611973082.66",

language = "American English",

isbn = "9780898719932",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "840--853",

booktitle = "Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011",

}