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Russia Yekaterinburg
Section Mathematics
Title Algorithms of the best approximations of the flat sets by the union of circles
Author(-s) Lebedev P.D.a, Uspenskii A.A.a, Ushakov V.N.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
Abstract 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
UDC 514.174.3
MSC 05B40
DOI 10.20537/vm130409
Received 30 October 2013
Language Russian
Citation Lebedev P.D., Uspenskii A.A., Ushakov V.N. Algorithms of the best approximations of the flat sets by the union of circles, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 88-99.
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