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From approximate balls to approximate ellipses

Author

Listed:
  • Asish Mukhopadhyay
  • Eugene Greene
  • Animesh Sarker
  • Tom Switzer

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

Suggested Citation

  • Asish Mukhopadhyay & Eugene Greene & Animesh Sarker & Tom Switzer, 2013. "From approximate balls to approximate ellipses," Journal of Global Optimization, Springer, vol. 56(1), pages 27-42, May.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:1:p:27-42
    DOI: 10.1007/s10898-012-9932-1
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