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

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