Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices

被引：1

作者：

Lebedev, Pavel Dmitrievich ^{[1
,2
,3
]}

Kuvshinov, Oleg Aleksandrovich ^{[3
,4
]}

机构：

[1] Russian Acad Sci, NN Krasovskii Inst Math & Mech, Ural Branch, Dept Dynam Syst, Ul S Kovalevskoi 16, Ekaterinburg 620108, Russia

[2] Russian Acad Sci, NN Krasovskii Inst Math & Mech, Ural Branch, Phys & Math, Ul S Kovalevskoi 16, Ekaterinburg 620108, Russia

[3] Ural Fed Univ, Ul Mira 19, Ekaterinburg 620002, Russia

[4] Russian Acad Sci, Inst Math & Mech, Ural Branch, Dept Dynam Syst, Ul S Kovalevskoi 16, Ekaterinburg 620219, Russia

来源：

IZVESTIYA INSTITUTA MATEMATIKI I INFORMATIKI-UDMURTSKOGO GOSUDARSTVENNOGO UNIVERSITETA | 2023年 / 61卷

关键词：

covering; circle; Bravais lattice; Hausdorff deviation; minimization; PACKING;

D O I：

10.35634/2226-3594-2023-61-05

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：76 / 93

页数：18