C&SA | Contents

Volume 51>№ 4 JULY — AUGUST 2015

UDC 519.8

Kiseleva E.M., Koriashkina L.S.

THE THEORY OF CONTINUOUS OPTIMAL SET PARTITIONING PROBLEMS AS A UNIVERSAL MATHEMATICAL
FORMALISM FOR CONSTRUCTING THE VORONOI DIAGRAM AND ITS GENERALIZATIONS.
II. ALGORITHMS FOR CONSTRUCTING VORONOI DIAGRAMS BASED ON THE THEORY OF OPTIMAL
PARTITIONING OF SETS

Abstract. Аn algorithm is presented for solving the continuous linear problem of optimal partitioning of the set from E_n into its disjoint subsets under constraints with finding the coordinates of the relevant subset centers. This algorithm and its special cases are applied to construct the classical Voronoi diagram and its various generalizations both for a fixed set of generator points and for finding their optimal location in the given set.

Keywords: Voronoi diagram, continuous problem of optimal partitioning of sets from Е_n, Shor’s r-algorithm.

FULL TEXT

Киселева Елена Михайловна,
чл.-кор. НАН Украины, профессор, декан, заведующая кафедрой Днепропетровского национального университета имени Олеся Гончара, e-mail: kiseleva47@mail.ru.

Коряшкина Лариса Сергеевна,
кандидат физ.-мат. наук, доцент Днепропетровского национального университета имени Олеся Гончара, e-mail: koryashkinals@mail.ru.

UDC 519.8

THE THEORY OF CONTINUOUS OPTIMAL SET PARTITIONING PROBLEMS AS A UNIVERSAL MATHEMATICAL FORMALISM FOR CONSTRUCTING THE VORONOI DIAGRAM AND ITS GENERALIZATIONS. II. ALGORITHMS FOR CONSTRUCTING VORONOI DIAGRAMS BASED ON THE THEORY OF OPTIMAL PARTITIONING OF SETS

THE THEORY OF CONTINUOUS OPTIMAL SET PARTITIONING PROBLEMS AS A UNIVERSAL MATHEMATICAL
FORMALISM FOR CONSTRUCTING THE VORONOI DIAGRAM AND ITS GENERALIZATIONS.
II. ALGORITHMS FOR CONSTRUCTING VORONOI DIAGRAMS BASED ON THE THEORY OF OPTIMAL
PARTITIONING OF SETS