Computing Minimum-Volume Enclosing Axis-Aligned Ellipsoids
نویسندگان
چکیده
Given a set of points S = {x1, . . . , xm} ⊂ R and > 0, we propose and analyze an algorithm for the problem of computing a (1 + )-approximation to the minimum-volume axis-aligned ellipsoid enclosing S . We establish that our algorithm is polynomial for fixed . 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.
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