Geodesic
Algorithms of the best approximations of the flat sets by the union of circles
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 88-99

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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.
Keywords: Chebyshev center, the best net, circle cover. 
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     author = {P. D. Lebedev and A. A. Uspenskii and V. N. Ushakov},
     title = {Algorithms of the best approximations of the flat sets by the union of circles},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {88--99},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_4_a8/}
}
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P. D. Lebedev; A. A. Uspenskii; V. N. Ushakov. Algorithms of the best approximations of the flat sets by the union of circles. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 88-99. http://geodesic.mathdoc.fr/item/VUU_2013_4_a8/