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Theory of Continuous Optimal Set Partitioning Problems as a Universal Mathematical Formalism for Constructing Voronoi Diagrams and Their Generalizations. I. Theoretical Foundations

  • Cybernetics
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Cybernetics and Systems Analysis Aims and scope

Abstract

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.

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Authors and Affiliations

  1. Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine

    E. M. Kiseleva & L. S. Koriashkina

Authors
  1. E. M. Kiseleva
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  2. L. S. Koriashkina
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Correspondence to E. M. Kiseleva.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–15, May–June, 2015.

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Kiseleva, E.M., Koriashkina, L.S. Theory of Continuous Optimal Set Partitioning Problems as a Universal Mathematical Formalism for Constructing Voronoi Diagrams and Their Generalizations. I. Theoretical Foundations. Cybern Syst Anal 51, 325–335 (2015). https://doi.org/10.1007/s10559-015-9725-x

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  • DOI: https://doi.org/10.1007/s10559-015-9725-x

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