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

  • Authors:

  • E. M. Kiseleva;L. I. Lozovskaya;E. V. Timoshenko

  • Affiliations:

  • O. Gonchar Dnepropetrovsk National University, Dnepropetrovsk, Ukraine;O. Gonchar Dnepropetrovsk National University, Dnepropetrovsk, Ukraine;O. Gonchar Dnepropetrovsk National University, Dnepropetrovsk, Ukraine

  • Venue:
  • Cybernetics and Systems Analysis
  • Year:
  • 2009

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Abstract

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