Relaxed Disk Packing

Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configura...

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Bibliographic Details
Published in:arXiv.org 2015-05
Main Authors: Edelsbrunner, Herbert, Iglesias-Ham, Mabel, Kurlin, Vitaliy
Format: Article
Language:English
Subjects:
Configurations
Disks
Euclidean geometry
Online Access:Get full text
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Summary:Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations.
ISSN:2331-8422