Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space
- Authors: Ushakov V.N.1,2, Lebedev P.D.1
-
Affiliations:
- Krasovskii Institute of Mathematics and Mechanics
- Ural Federal University
- Issue: Vol 293, No Suppl 1 (2016)
- Pages: 225-237
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/173626
- DOI: https://doi.org/10.1134/S0081543816050205
- ID: 173626
Cite item
Abstract
The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented.
Keywords
About the authors
V. N. Ushakov
Krasovskii Institute of Mathematics and Mechanics; Ural Federal University
Author for correspondence.
Email: ushak@imm.uran.ru
Russian Federation, ul. S. Kovalevskoi 16, Yekaterinburg, 620990; ul. Mira 32, Yekaterinburg, 620002
P. D. Lebedev
Krasovskii Institute of Mathematics and Mechanics
Email: ushak@imm.uran.ru
Russian Federation, ul. S. Kovalevskoi 16, Yekaterinburg, 620990
Supplementary files
