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

E. M. Kiseleva; L. S. Koriashkina

首页> 外文期刊>Cybernetics and Systems Analysis >THEORY OF CONTINUOUS OPTIMAL SET PARTITIONING PROBLEMS AS A UNIVERSAL MATHEMATICAL FORMALISM FOR CONSTRUCTING VORONOI DIAGRAMS AND THEIR GENERALIZATIONS. Ⅱ. ALGORITHMS FOR CONSTRUCTING VORONOI DIAGRAMS BASED ON THE THEORY OF OPTIMAL SET PARTITIONING

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

机译：连续最优集划分理论作为构造Vorono图及其通用化的通用数学形式。 Ⅱ。基于最优集合划分理论的Voroni图构造算法

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An algorithm is presented for solving the continuous linear problem of optimal partitioning of a set from E_n into its disjoint subsets under constraints with finding the coordinates of the centers of the subsets. The described algorithm and its special cases are used to construct the classical Voronoi diagram and its various generalizations for a fixed collection of generating points and to find an optimal placement of these points in a given set.

机译：提出了一种算法，用于求解在约束条件下找到一个子集的中心坐标，从而将一个集合从E_n最佳划分为其不相交的子集的连续线性问题。所描述的算法及其特殊情况用于构造经典的Voronoi图及其对生成点的固定集合的各种概括，并在给定集中找到这些点的最佳位置。

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来源
《Cybernetics and Systems Analysis》 |2015年第4期|489-499|共11页
作者
E. M. Kiseleva; L. S. Koriashkina;
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作者单位

Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine;

Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine;

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收录信息美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Voronoi diagram; continuous problem of optimal partitioning of sets from E_n; Shor's r-algorithm;

机译：Voronoi图;从E_n进行集的最佳划分的连续问题;索尔的r算法;

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专利

1. THEORY OF CONTINUOUS OPTIMAL SET PARTITIONING PROBLEMS AS A UNIVERSAL MATHEMATICAL FORMALISM FOR CONSTRUCTING VORONOI DIAGRAMS AND THEIR GENERALIZATIONS. I. THEORETICAL FOUNDATIONS [J] . E. M. Kiseleva, L. S. Koriashkina Cybernetics and Systems Analysis . 2015,第3期

机译：连续最优集划分理论作为构造Vorono图及其通用化的通用数学形式。一，理论基础
2. Algorithm for Constructing Voronoi Diagrams with Optimal Placement of Generator Points Based on Theory of Optimal Set Partitioning [J] . Elena M. Kiseleva, Lyudmila L. Hart, Olga M. Prytomanova Journal of automation and information sciences . 2020,第3期

机译：基于最优设置分区理论的发电点最优放置voronoi图的算法
3. A parallel algorithm for constructing Voronoi diagrams based on point-set adaptive grouping [J] . Jiechen Wang, Can Cui, Yikang Rui, Concurrency and computation: practice and experience . 2014,第2期

机译：基于点集自适应分组的Voronoi图并行构建算法
4. Voronoi Diagram of a Circle Set Constructed from Voronoi Diagram of a Point Set [C] . Deok-Soo Kim, Donguk Kim, Kokichi Sugihara Algorithms and Computation . 2000

机译：由点集的Voronoi图构造的圆集的Voronoi图
5. A parallel algorithm of constructing a Voronoi diagram on hypercube connected computer networks [D] . Chai, Wenmao 1994

机译：在超立方体连接的计算机网络上构造Voronoi图的并行算法
6. New Algorithms Based on the Voronoi Diagram Applied in a Pilot Study on Normal Mucosa and Carcinomas [O] . J. Sudbø, R. Marcelpoil, A. Reith 2000

机译：基于Voronoi图的新算法在正常粘膜和癌的初步研究中的应用
7. A parallel algorithm of constructing a Voronoi diagram on hypercube connected computer networks [O] . Chai Wenmao 1963- 1994

机译：在超立方体连接的计算机网络上构建Voronoi图的并行算法
8. Expected O(N) and O(N sup 4/3) Algorithms for Constructing Voronoi Diagrams in Two and Three Dimensions [R] . Bernal, J. 1987

机译：预期O（N）和O（N sup 4/3）算法构造二维和三维Voronoi图

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

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