caa a22 4500 605518831 CHVBK 20210128105158.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10559-015-9725-x doi (NATIONALLICENCE)springer-10.1007/s10559-015-9725-x Theory of Continuous Optimal Set Partitioning Problems as a Universal Mathematical Formalism for Constructing Voronoi Diagrams and Their Generalizations. I. Theoretical Foundations [Elektronische Daten] [E. Kiseleva, L. Koriashkina] This article considers a method for constructing Voronoi diagrams and their generalizations on the basis of the unified approach that consists of formulating a continuous optimal set partitioning problem with a partition quality criterion that provides appropriate types of Voronoi diagrams and applying the mathematical and algorithmic apparatus to solve such problems. This approach provides the ability not only to construct well-known Voronoi diagrams but also to design new ones. Springer Science+Business Media New York, 2015 Voronoi diagram nationallicence continuous problem of optimal partitioning of sets from E n nationallicence Shor's r-algorithm nationallicence Kiseleva E. Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine aut Koriashkina L. Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine aut Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/3(2015-05-01), 325-335 1060-0396 51:3<325 2015 51 10559 https://doi.org/10.1007/s10559-015-9725-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10559-015-9725-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kiseleva E. Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine aut NATIONALLICENCE 700 1- Koriashkina L. Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine aut NATIONALLICENCE 773 0- Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/3(2015-05-01), 325-335 1060-0396 51:3<325 2015 51 10559 SWISSBIB 605518831