TY - JOUR
AU - Kiseleva, E.M.
AU - Hart, L.L.
AU - Prytomanova , O.M.
AU - Zhuravel, S.V.
PY - 2020/03/17
Y2 - 2021/12/09
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 -