School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Optimal Packings of Congruent Circles on a Square Flat Torus
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.
Musin, O.R., Nikitenko, A.V. Optimal Packings of Congruent Circles on a Square Flat Torus. Discrete Comput Geom 55, 1–20 (2016). https://doi.org/10.1007/s00454-015-9742-6
Discrete Comput Geom
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