Iterative Methods for Constructing Approximations to Optimal Coverings of Nonconvex Polygons

The paper proposes algorithms for the iterative construction of optimal coverings of nonconvex flat figures using sets of circles. These algorithms are based on the procedures of dividing the figure into zones of influence of points that serve as the centers of the initial coverings and finding the...

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Bibliographic Details
Published inMathematical Optimization Theory and Operations Research pp. 244 - 254
Main Authors Lebedev, Pavel, Ushakov, Vladimir
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing
SeriesCommunications in Computer and Information Science
Subjects
Chebyshev center
Dirichlet domain
Nonconvex polygon
Optimal covering
Voronoi diagram
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Summary:The paper proposes algorithms for the iterative construction of optimal coverings of nonconvex flat figures using sets of circles. These algorithms are based on the procedures of dividing the figure into zones of influence of points that serve as the centers of the initial coverings and finding the Chebyshev centers of these zones. To generate the initial array of points, we use stochastic procedures based on the synthesis of optimal hexagonal grids and random vectors.
Bibliography:The work was supported by the Decree no. 211 of the Government of the Russian Federation, contract no. 02.A03.21.0006.
ISBN:9783030333935
3030333930
ISSN:1865-0929
1865-0937
DOI:10.1007/978-3-030-33394-2_19