Solution of continuous problems of optimal covering with spheres using optimal set-partition theory. (English. Russian original) Zbl 1182.49045
Cybern. Syst. Anal. 45, No. 3, 421-437 (2009); translation from Kibern. Sist. Anal. 2009, No. 3, 98-117 (2009).
Summary: The paper considers a continuous problem of optimal \(c\)-sphere covering of a compact set \(\Omega \) of \(\mathbb E_n\) with a given number of spheres of minimum radius and a problem of covering a set with the minimum number of spheres of given radius. Algorithms are proposed and substantiated to solve the problems using optimal set-partition theory and Shor’s \(r\)-algorithm.
MSC:
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
| 81P68 | Quantum computation |
Keywords:
optimal covering; minimum radius of covering spheres; optimal partition; metrics; Dirichlet-Voronoi diagram; Shor’s \(r\)-algorithmReferences:
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