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Sphere Packing with Limited Overlap

The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice.

preprint2014arXivOpen access
Mabel Iglesias-HamMichael KerberCaroline Uhler
Computational Geometry
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Mabel Iglesias-HamMichael KerberCaroline Uhler

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