Approximate ellipsoid in the streaming model

Authors:
Asish Mukhopadhyay;Animesh Sarker;Tom Switzer
Affiliations:
School of Computer Science, University of Windsor, ON, Canada;School of Computer Science, University of Windsor, ON, Canada;School of Computer Science, University of Windsor, ON, Canada
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Year:
2010

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Abstract

In this paper we consider the problem of computing an approximate ellipsoid in the streaming model of computation, motivated by a 3/2-factor approximation algorithm for computing approximate balls. Our contribution is twofold: first, we show how to compute an approximate ellipsoid as done in the approximate ball algorithm, and second, construct an input to show that the approximation factor can be unbounded, unlike the algorithm for computing approxinmate balls. Though the ratio of volumes can become unbounded, we show that there exists a direction in which the ratio of widths is bounded by a factor of 2.