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arXiv · 1401.0468

Sphere Packing with Limited Overlap

Mabel Iglesias-Ham·Michael Kerber·Caroline Uhler
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Abstract

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.

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Mabel Iglesias-Ham, Michael Kerber, Caroline Uhler. 2014-01-02. Sphere Packing with Limited Overlap. https://arxiv.org/abs/1401.0468

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