Optimal Packings of Congruent Circles on a Square Flat Torus

Authors

Oleg R. Musin, The University of Texas Rio Grande Valley
Anton Nikitenko

Document Type

Article

Publication Date

11-2-2015

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.

Comments

Copyright © 2015, Springer Science Business Media New York

https://rdcu.be/c50Qo

Recommended Citation

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

Publication Title

Discrete Comput Geom

DOI

10.1007/s00454-015-9742-6