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.
Key words:$k$-covering with circles of two radii, multiple coverings, estimation of density of a $k$-covering with circles of two radii.
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