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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 46

Algorithms for Constructing Optimal Covering of Planar Figures with Disks Sets of Linearly Different Radii

Author(s)
Pavel D. Lebedev1,2, Krasimir L. Stoychin1

1Ural Federal University named after B. N. Yeltsin, Yekaterinburg, Russian Federation

2N. N. Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russian Federation

Abstract
The problem of optimal covering of plane figures with sets of a fixed number of different circles is considered. We suppose that each circle has a radius equal to the sum of the parameter common to all and its individual number. The main aim of the paper is to develop algorithms that allow the construction of a covering with a minimum common parameter. It is proved that the problem can be reduced to minimizing a function of several variables depending on the coordinates of the centers of the circles. The zones of influence of points serving as the centers of circles for a fixed set of individual numbers have been studied. Iterative algorithm for solving the problem is proposed using the concepts of the Chebyshev center and a generalization of the Dirichlet zone. The possibilities of applying the results of the article to the construction of sensor networks are shown.
About the Authors

Pavel D. Lebedev, Cand. Sci. (Phys.Math.), Senior Researcher, Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, 620108, Russian Federation, Ural Federal University named after B. N. Yeltsin, Yekaterinburg, 620002, Russian Federation, pleb@yandex.ru

Krasimir L. Stoychin, Postgraduate, Ural Federal University named after B. N. Yeltsin, Yekaterinburg, 620002, Russian Federation, k001kk96@mail.ru

For citation
Lebedev P. D., Stoychin K. L. Algorithms for Constructing Optimal Covering of Planar Figures with Disks Sets of Linearly Different Radii. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 46, pp. 35–50. (in Russian) https://doi.org/10.26516/1997-7670.2023.46.35
Keywords
disks coverage, domain of dominance, Dirichlet zone, Chebyshev center, minimization
UDC
514.174.3
MSC
41A50, 52C15
DOI
https://doi.org/10.26516/1997-7670.2023.46.35
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