Computing Minimum-Volume Enclosing Axis-Aligned Ellipsoids

P. Kumar () and E. A. Yıldırım ()
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P. Kumar: Florida State University
E. A. Yıldırım: Bilkent University

Journal of Optimization Theory and Applications, 2008, vol. 136, issue 2, No 4, 228 pages

Abstract: Abstract Given a set of points $\mathcal{S}=\{x^{1},\ldots,x^{m}\}\subset \mathbb{R}^{n}$ and ε>0, we propose and analyze an algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume axis-aligned ellipsoid enclosing $\mathcal{S}$ . We establish that our algorithm is polynomial for fixed ε. In addition, the algorithm returns a small core set $\mathcal{X}\subseteq \mathcal{S}$ , whose size is independent of the number of points m, with the property that the minimum-volume axis-aligned ellipsoid enclosing $\mathcal{X}$ is a good approximation of the minimum-volume axis-aligned ellipsoid enclosing $\mathcal{S}$ . Our computational results indicate that the algorithm exhibits significantly better performance than the theoretical worst-case complexity estimate.

Keywords: Axis-aligned ellipsoids; Enclosing ellipsoids; Core sets; Approximation algorithms (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-007-9295-9

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