Covering Spheres with Spheres

@article{Dumer2007CoveringSW,
  title={Covering Spheres with Spheres},
  author={I. Dumer},
  journal={Discrete & Computational Geometry},
  year={2007},
  volume={38},
  pages={665-679}
}
  • I. Dumer
  • Published 2007
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • Abstract Given a sphere of any radius r in an n-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average number of solid spheres covering a point in a bigger sphere. For growing dimension n, we design a covering that gives the covering density of order (nln n)/2 for a sphere of any radius r>1 and a complete Euclidean space. This new upper bound reduces two times… CONTINUE READING

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