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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices
P. D. Lebedevab, O. A. Kuvshinovab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Ural Federal University named after B.N. Yeltsin, ul. Mira, 19, Yekaterinburg, 620002, Russia
Abstract:
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 $M$.
Keywords:
covering, circle, Bravais lattice, Hausdorff deviation, minimization.
Received: 01.03.2023 Accepted: 20.04.2023
Citation:
P. D. Lebedev, O. A. Kuvshinov, “Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices”, Izv. IMI UdGU, 61 (2023), 76–93
Linking options:
https://www.mathnet.ru/eng/iimi443 https://www.mathnet.ru/eng/iimi/v61/p76
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Abstract page: | 163 | Full-text PDF : | 77 | References: | 25 |
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