We consider the optimal covering of the unit square by N circles. By optimal, we mean the covering that can be done with N circles of minimum radius. Equivalently, we study the problem of the optimal placement of N points such that the maximum over all locations in the square of the distance of the location to the set of points is minimized. We propose a new algorithm that can identify optimal coverings to high precision. Numerical predictions of optimal coverings for N = 1 to 16 agree with the best known results in the literature. We use the optimal designs in approximations to two novel, related problems involving the optimal placement of curves.
|Number of pages||11|
|Journal||Canadian Applied Mathematics Quarterly|
|Publication status||Published - 2013|