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JOURNALS // Avtomatika i Telemekhanika // Archive

Avtomat. i Telemekh., 2012 Issue 3, Pages 79–90 (Mi at3779)

This article is cited in 10 papers

Applications of Mathematical Programming

Approximating sets on a plane with optimal sets of circles

P. D. Lebedev, A. V. Ushakov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles.

Presented by the member of Editorial Board: A. I. Kibzun

Received: 06.06.2011


 English version:
Automation and Remote Control, 2012, 73:3, 485–493

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