Discrete & Computational Geometry

, Volume 42, Issue 3, pp 469–488

Dynamic Coresets

Article

DOI: 10.1007/s00454-009-9165-3

Cite this article as:
Chan, T.M. Discrete Comput Geom (2009) 42: 469. doi:10.1007/s00454-009-9165-3

Abstract

We give a dynamic data structure that can maintain an ε-coreset of n points, with respect to the extent measure, in O(log n) time per update for any constant ε>0 and any constant dimension. The previous method by Agarwal, Har-Peled, and Varadarajan requires polylogarithmic update time. For points with integer coordinates bounded by U, we alternatively get O(log log U) time. Numerous applications follow, for example, on dynamically approximating the width, smallest enclosing cylinder, minimum bounding box, or minimum-width annulus. We can also use the same approach to maintain approximate k-centers in time O(log n) (or O(log log U) if the spread is bounded by U) for any constant k and any constant dimension.

For the smallest enclosing cylinder problem, we also show that a constant-factor approximation can be maintained in O(1) randomized amortized time on the word RAM.

Keywords

Approximation algorithmsDynamic data structuresRandomizationGeometric optimizationWidthk-CenterWord RAM

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada