论文信息 - Covering an ellipsoid with equal balls

Covering an ellipsoid with equal balls

The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension n. Given any ellipsoid, our goal is to find the minimum number of unit balls needed to cover this ellipsoid. A tight asymptotic bound on the logarithm of this number is obtained.

Ilya Dumer | I. Dumer

[1] K. Böröczky. Finite Packing and Covering , 2004 .

[2] Martin Henk. FINITE PACKING AND COVERING (Cambridge Tracts in Mathematics 154) , 2006 .

[3] N. J. A. Sloane,et al. Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[4] Jörg M. Wills,et al. Convexity and its applications , 1983 .

[5] Mark Semenovich Pinsker,et al. On coverings of ellipsoids in Euclidean spaces , 2004, IEEE Transactions on Information Theory.

[6] B. Bollobás. THE VOLUME OF CONVEX BODIES AND BANACH SPACE GEOMETRY (Cambridge Tracts in Mathematics 94) , 1991 .

[7] L. Tóth,et al. New Results in the Theory of Packing and Covering , 1983 .

[8] G. Pisier. The volume of convex bodies and Banach space geometry , 1989 .

[9] Jean-Louis Verger-Gaugry,et al. Covering a Ball with Smaller Equal Balls in ℝn , 2005, Discret. Comput. Geom..

[10] C. A. Rogers. Covering a sphere with spheres , 1963 .

[11] V. Tikhomirov,et al. ε-Entropy and ε-Capacity , 1993 .