Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning
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 continuou...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2020-03-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/12 |
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| author | E.M. Kiseleva L.L. Hart O.M. Prytomanova S.V. Zhuravel |
| author_facet | E.M. Kiseleva L.L. Hart O.M. Prytomanova S.V. Zhuravel |
| author_sort | E.M. Kiseleva |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d88b1f91a0f84b7381e931bb2ac3cc3d |
| institution | DOAJ |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2020-03-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-d88b1f91a0f84b7381e931bb2ac3cc3d2025-08-20T02:41:33ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202020-03-0153110911210.30970/ms.53.1.109-11212Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioningE.M. Kiseleva0L.L. Hart1O.M. Prytomanova2S.V. Zhuravel3Oles Honchar Dnipro National University, Dnipro, UkraineOles Honchar Dnipro National University, Dnipro, UkraineOles Honchar Dnipro National University, Dnipro, UkraineOles Honchar Dnipro National University, Dnipro, UkraineThe 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.http://matstud.org.ua/ojs/index.php/matstud/article/view/12voronoi diagram; continuous problems of optimal set partitioning; shor's r-algorithm |
| spellingShingle | E.M. Kiseleva L.L. Hart O.M. Prytomanova S.V. Zhuravel Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning Математичні Студії voronoi diagram; continuous problems of optimal set partitioning; shor's r-algorithm |
| title | Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning |
| title_full | Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning |
| title_fullStr | Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning |
| title_full_unstemmed | Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning |
| title_short | Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning |
| title_sort | construction of a generalized voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning |
| topic | voronoi diagram; continuous problems of optimal set partitioning; shor's r-algorithm |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/12 |
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