2014/01/02 by Mabel Iglesias-Ham, Iglesias-Ham, Mabel, Michael Kerber +3
Engineering · Materials Science · Computer Science · #Optimization and Packing Problems #Quasicrystal Structures and Properties #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.1401.0468
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.