Geodesic
Algorithms for constructing optimal covering of planar figures with disks sets of linearly different radii
The Bulletin of Irkutsk State University. Series Mathematics, Tome 46 (2023), pp. 35-50

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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.
Keywords: disks coverage, Dirichlet zone, Chebyshev center, minimization.
Mots-clés : domain of dominance 
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     author = {Pavel D. Lebedev and Krasimir L. Stoychin},
     title = {Algorithms for constructing optimal covering of planar figures with disks sets of linearly different radii},
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Pavel D. Lebedev; Krasimir L. Stoychin. Algorithms for constructing optimal covering of planar figures with disks sets of linearly different radii. The Bulletin of Irkutsk State University. Series Mathematics, Tome 46 (2023), pp. 35-50. http://geodesic.mathdoc.fr/item/IIGUM_2023_46_a2/