From approximate balls to approximate ellipses

Asish Mukhopadhyay (), Eugene Greene, Animesh Sarker and Tom Switzer

Journal of Global Optimization, 2013, vol. 56, issue 1, 27-42

Abstract: A ball spans a set of n points when none of the points lie outside it. In Zarrabi-Zadeh and Chan (Proceedings of the 18th Canadian conference on computational geometry (CCCG’06), pp 139–142, 2006 ) proposed an algorithm to compute an approximate spanning ball in the streaming model of computation, and showed that the radius of the approximate ball is within 3/2 of the minimum. Spurred by this, in this paper we consider the 2-dimensional extension of this result: computation of spanning ellipses. The ball algorithm is simple to the point of being trivial, but the extension of the algorithm to ellipses is non-trivial. Surprisingly, the area of the approximate ellipse computed by this approach is not within a constant factor of the minimum and we provide an elegant proof of this. We have implemented this algorithm, and experiments with a variety of inputs, except for a very pathological one, show that it can nevertheless serve as a good heuristic for computing an approximate ellipse. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Computational geometry; Streaming algorithms; Approximation schemes; Approximate ellipses (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9932-1

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