Fast, precise and dynamic distance queries
Abstract
We present an approximate distance oracle for a point set S with n points and doubling dimension {\lambda}. For every {\epsilon}>0, the oracle supports (1+{\epsilon})-approximate distance queries in (universal) constant time, occupies space [{\epsilon}^{-O({\lambda})} + 2^{O({\lambda} log {\lambda})}]n, and can be constructed in [2^{O({\lambda})} log3 n + {\epsilon}^{-O({\lambda})} + 2^{O({\lambda} log {\lambda})}]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 2^{O({\lambda})} log n + {\epsilon}^{-O({\lambda})} + 2^{O({\lambda} log {\lambda})} update time. This is the first fully dynamic (1+{\epsilon})-distance oracle.
Cite
@article{arxiv.1008.1480,
title = {Fast, precise and dynamic distance queries},
author = {Yair Bartal and Lee-Ad Gottlieb and Tsvi Kopelowitz and Moshe Lewenstein and Liam Roditty},
journal= {arXiv preprint arXiv:1008.1480},
year = {2010}
}