Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices
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| Автор |
Lebedev, P. D.
Kuvshinov, O. A. |
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| Тематика |
BRAVAIS LATTICE
CIRCLE COVERING HAUSDORFF DEVIATION MINIMIZATION |
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| Описание |
The problem of covering a compact planar set M with a set of congruent disks is considered. It is assumed that the centers of the circles belong to some lattice. The criterion of optimality in one case is the minimum of the number of elements of the covering, and in the other case — the minimum of the Hausdorff deviation of the union of elements of the covering from the set M. To solve the problems, transformations of parallel transfer and rotation with the center at the origin can be applied to the lattice. Statements concerning sufficient conditions for sets of circles that provide solutions to the problems are proved. Numerical algorithms based on minimizing the Hausdorff deviation between two flat compacts are proposed. Solutions of a number of examples are given for various figures of M. © 2023 The Author(s).
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| Дата |
2024-04-05T16:26:13Z
2024-04-05T16:26:13Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Лебедев, ПД & Кувшинов, ОА 2023, 'АЛГОРИТМЫ ПОСТРОЕНИЯ СУБОПТИМАЛЬНЫХ ПОКРЫТИЙ ПЛОСКИХ ФИГУР КРУГАМИ В КЛАССАХ РЕГУЛЯРНЫХ РЕШЕТОК', Известия Института математики и информатики Удмуртского государственного университета, Том. 61, стр. 76-93. https://doi.org/10.35634/2226-3594-2023-61-05
Лебедев, П. Д., & Кувшинов, О. А. (2023). АЛГОРИТМЫ ПОСТРОЕНИЯ СУБОПТИМАЛЬНЫХ ПОКРЫТИЙ ПЛОСКИХ ФИГУР КРУГАМИ В КЛАССАХ РЕГУЛЯРНЫХ РЕШЕТОК. Известия Института математики и информатики Удмуртского государственного университета, 61, 76-93. https://doi.org/10.35634/2226-3594-2023-61-05 2226-3594 Final All Open Access, Bronze https://www.scopus.com/inward/record.uri?eid=2-s2.0-85162751544&doi=10.35634%2f2226-3594-2023-61-05&partnerID=40&md5=29d4183686e180b91d1098d5ccf189fc https://www.mathnet.ru/php/getFT.phtml?jrnid=iimi&paperid=443&what=fullt&option_lang=eng http://elar.urfu.ru/handle/10995/130566 53741290 10.35634/2226-3594-2023-61-05 85162751544 001005574800005 |
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| Язык |
ru
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Udmurt State University
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| Источник |
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta |
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