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Sphere Packing with Limited Overlap

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Kerber,  Michael
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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arXiv:1401.0468.pdf
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Citation

Iglesias-Ham, M., Kerber, M., & Uhler, C. (2014). Sphere Packing with Limited Overlap. Retrieved from http://arxiv.org/abs/1401.0468.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-4781-B
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.