TY - GEN

T1 - Fast, precise and dynamic distance queries

AU - Bartal, Yair

AU - Gottlieb, Lee Ad

AU - Kopelowitz, Tsvi

AU - Lewenstein, Moshe

AU - Roditty, Liam

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79955711185&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973082.66

DO - 10.1137/1.9781611973082.66

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AN - SCOPUS:79955711185

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 840

EP - 853

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

PB - Association for Computing Machinery

ER -