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A Space-Optimal Data-Stream Algorithm for Coresets in the Plane
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Pankaj Agarwal, et al.
| Citations: | 19 - 5 self |
BibTeX
@MISC{Agarwal_aspace-optimal,
author = {Pankaj Agarwal and et al.},
title = {A Space-Optimal Data-Stream Algorithm for Coresets in the Plane },
year = {}
}
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Abstract
Given a point set P ⊆ R², a subset Q ⊆ P is an ε-kernel of P if for every slab W containing Q, the (1+ε)-expansion of W also contains P. We present a data-stream algorithm for maintaining an ε-kernel of a stream of points in R² that uses O(1/√ε) space and takes O(log(1/ε)) amortized time to process each point. This is the first space-optimal data-stream algorithm for this problem. As a consequence, we obtain improved data-stream approximation algorithms for other extent measures, such as width, robust kernels, as well as ε-kernels in higher dimensions.
