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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Covering and Packing with Spheres by Diagonal Distortion in ℝ n
verfasst von : Herbert Edelsbrunner, Michael Kerber
Erschienen in: Rainbow of Computer Science
Verlag: Springer Berlin Heidelberg
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We address the problem of covering ℝ
n
with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ
n
, for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3.