Optimal packings of congruent circles on a square flat torus Journal Article

Author(s): Musin, Oleg R; Nikitenko, Anton V
Article Title: Optimal packings of congruent circles on a square flat torus
Affiliation IST Austria
Abstract: We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs.
Keywords: Circle packing; Contact graph; Flat torus; Graph enumeration
Journal Title: Discrete & Computational Geometry
Volume: 55
Issue 1
ISSN: 0179-5376
Publisher: Springer  
Date Published: 2016-01-01
Start Page: 1
End Page: 20
DOI: 10.1007/s00454-015-9742-6
Notes: We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01- 99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.
Open access: yes (repository)
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