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An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions

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Abstract

We present a new streaming algorithm for maintaining an ε-kernel of a point set in ℝd using O((1/ε (d−1)/2)log (1/ε)) space. The space used by our algorithm is optimal up to a small logarithmic factor. This significantly improves (for any fixed dimension d ≥3) the best previous algorithm for this problem that uses O(1/ε d−(3/2)) space, presented by Agarwal and Yu. Our algorithm immediately improves the space complexity of the previous streaming algorithms for a number of fundamental geometric optimization problems in fixed dimensions, including width, minimum-volume bounding box, minimum-radius enclosing cylinder, minimum-width enclosing annulus, etc.

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  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    Hamid Zarrabi-Zadeh

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  1. Hamid Zarrabi-Zadeh
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Correspondence to Hamid Zarrabi-Zadeh.

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Zarrabi-Zadeh, H. An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions. Algorithmica 60, 46–59 (2011). https://doi.org/10.1007/s00453-010-9392-2

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  • DOI: https://doi.org/10.1007/s00453-010-9392-2

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