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.
We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper. The second author has been supported by the Max Planck Center for Visual Computing and Communication
Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/arXiv.1401.0468
Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468
Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.
M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. .
Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.
Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468.
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