Covering and packing with spheres by diagonal distortion in Rn

Authors:
Herbert Edelsbrunner;Michael Kerber
Affiliations:
Institute of Science and Technology Austria, Klosterneuburg, Austria and Departments of Computer Science and of Mathematics, Duke University, Durham, North Carolina and Geomagic, North Carolina;Institute of Science and Technology Austria, Klosterneuburg, Austria
Venue:
Rainbow of computer science
Year:
2011

Citing 3
Cited 0

Sphere-packings, lattices, and groups

Sphere-packings, lattices, and groups
Geometry and topology for mesh generation

Geometry and topology for mesh generation
Some combinatorial Lemmas in topology

IBM Journal of Research and Development

Quantified Score

Hi-index	0.00

Visualization

Abstract

We address the problem of covering Rn 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 Rn, 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.