Fast, precise and dynamic distance queries

Yair Bartal*, Lee Ad Gottlieb, Tsvi Kopelowitz, Moshe Lewenstein, Liam Roditty

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

15 Scopus citations


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.

Original languageAmerican English
Title of host publicationProceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011
PublisherAssociation for Computing Machinery
Number of pages14
ISBN (Print)9780898719932
StatePublished - 2011

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


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