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Solution of continuous problems of optimal covering with spheres using optimal set-partition theory

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Cybernetics and Systems Analysis Aims and scope

The paper considers a continuous problem of optimal c-sphere covering of a compact set from Ω from 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.

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Authors and Affiliations

  1. O. Gonchar Dnepropetrovsk National University, Dnepropetrovsk, Ukraine

    E. M. Kiseleva, L. I. Lozovskaya & E. V. Timoshenko

Authors
  1. E. M. Kiseleva
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  2. L. I. Lozovskaya
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  3. E. V. Timoshenko
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Corresponding author

Correspondence to E. M. Kiseleva.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 98–117, May–June 2009.

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Kiseleva, E.M., Lozovskaya, L.I. & Timoshenko, E.V. Solution of continuous problems of optimal covering with spheres using optimal set-partition theory. Cybern Syst Anal 45, 421–437 (2009). https://doi.org/10.1007/s10559-009-9113-5

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  • DOI: https://doi.org/10.1007/s10559-009-9113-5

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