TY - JOUR AU - Kiseleva, E.M. AU - Hart, L.L. AU - Prytomanova , O.M. AU - Zhuravel, S.V. PY - 2020/03/17 Y2 - 2024/03/29 TI - Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning JF - Matematychni Studii JA - Mat. Stud. VL - 53 IS - 1 SE - Problem Section DO - 10.30970/ms.53.1.109-112 UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/12 SP - 109-112 AB - The problem of construction of a generalized Voronoi diagram with optimal placement of a finite number of generator points in a bounded set of \textit{n}-dimensional Euclidean space is considered. A method is proposed for solving such a problem based on the formulation of the corresponding continuous problem of optimal partitioning of a set in \textit{n}-dimensional Euclidean space with a partition quality criterion that provides the corresponding form of the Voronoi diagram. Further, to solve such a problem, the developed mathematical and algorithmic apparatus is used, the part of which is Shor's \textit{r}-algorithm. ER -