Covering Spheres with Spheres

نویسنده

  • Ilya Dumer
چکیده

Given a sphere of radius r > 1 in the n-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growing n, we obtain the covering density of (n lnn)/2. This new upper bound is half the order n lnn established in the classical Rogers bound.

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عنوان ژورنال:
  • Discrete & Computational Geometry

دوره 38  شماره 

صفحات  -

تاریخ انتشار 2007