Authors: Kari J. Nurmela and Patric R. J. Östergård

Title: Optimal Packings of Equal Circles in a Square

Appeared in: Y. Alavi, D. R. Lick, and A. Schwenk (eds.), Combinatorics, Graph Theory, and Algorithms (Proceedings of the Eighth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms, and Applications) (1999), 671-680.

The problem of finding the maximum radius of n non-overlapping equal circles in a unit square is considered. A computer-aided method for proving global optimality of such packings is presented. This method is based on recent results by De Groot, Monagan, Peikert, and Würtz. As an example, it is shown how the method can be used to get an optimality proof for the case n=7, which has not earlier been published.