Algorithms of the best approximations of the flat sets by the union of circles

The article is devoted to the problem of constructing an optimal approximating circle-cover for the bounded flat set by the finite number of circles with equal radius. The problem is solved if the best $n$-net in meaning of Hausdorff metric is constructed for the considered set. Sufficient conditions of optimality of the $n$-nets are given. The best net-construction algorithm based on dividing of the set $M$ into subsets and finding their Chebyshev centers is realized. This algorithm is proved to be efficient with the examples of sets with different geometry.