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 substantially improves (for any fixed dimension \(d \geqslant 3\)) the best previous algorithm for this problem that uses O(1/ε d − (3/2)) space, presented by Agarwal and Yu at SoCG’07. Our algorithm immediately improves the space complexity of the best previous streaming algorithms for a number of fundamental geometric optimization problems in fixed dimensions, including width, minimum enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc.
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Zarrabi-Zadeh, H. (2008). An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_68
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DOI: https://doi.org/10.1007/978-3-540-87744-8_68
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