Abstract
Hard problems of discrete geometry may be formulated as a global optimization problems, which may be solved by general purpose solvers implementing branch-and-bound (B&B) algorithm. A problem of densest packing of N equal circles in special geometrical object, so called Square Flat Torus, \(\mathbb {R}^2/\mathbb {Z}^2\), with the induced metric, is considered. It is formulated as mixed-integer problem with linear and nonconvex quadratic constraints. The open-source B&B-solver SCIP and its parallel implementation ParaSCIP have been used to find optimal arrangements for \(N \,{\leqslant }\,9\). The main result is a confirmation of the conjecture on optimal packing for \(N = 9\) that was published in 2012 by O. Musin and A. Nikitenko.
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