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 ov...

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Bibliographic Details
Published in:arXiv.org 2014-01
Main Authors: Iglesias-Ham, Mabel, Kerber, Michael, Uhler, Caroline
Format: Article
Language:English
Subjects:
Body centered cubic lattice
Face centered cubic lattice
Online Access:Get full text
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Summary: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.
ISSN:2331-8422