Computing minimum-volume enclosing axis-aligned ellipsoids

Date
2008
Authors
Kumar, P.
Yıldırım, E. A.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Journal of Optimization Theory and Applications
Print ISSN
0022-3239
Electronic ISSN
1573-2878
Publisher
Springer
Volume
136
Issue
2
Pages
211 - 228
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
Abstract

Given a set of points S = {x1 ,..., xm}⊂ ℝn 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 S. We establish that our algorithm is polynomial for fixed ε. In addition, the algorithm returns a small core set X ⊆ S, whose size is independent of the number of points m, with the property that the minimum-volume axis-aligned ellipsoid enclosing X is a good approximation of the minimum-volume axis-aligned ellipsoid enclosing S. Our computational results indicate that the algorithm exhibits significantly better performance than the theoretical worst-case complexity estimate.

Course
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Book Title
Keywords
Approximation algorithms, Axis-aligned ellipsoids, Core sets, Enclosing ellipsoids
Citation
Published Version (Please cite this version)