Optimization of the Number and Arrangement of Circles of Two Radii for Forming a k-Covering of a Bounded Set

Abstract

A numerical method for investigating k-coverings of a convex bounded closed set with nonempty interior with circles of two given radii is proposed. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. Cases with constraints on the distances between the covering circle centers and problems with a variable (given) covering multiplicity are also considered. Numerical results demonstrating the effectiveness of the proposed methods are presented.