Theory of continuous optimal set partitioning problems as a universal mathematical formalism for constructing Voronoi diagrams and their generalizations. I. Theoretical foundations

DOI10.1007/s10559-015-9725-xzbMath1327.90261OpenAlexW588514424MaRDI QIDQ891710

E. M. Kiseleva, L. S. Koriashkina

Publication date: 17 November 2015

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10559-015-9725-x

zbMATH Keywords

Voronoi diagramShor's \(r\)-algorithmcontinuous problem of optimal partitioning of sets from \(E_n\)

Mathematics Subject Classification ID

Combinatorial optimization (90C27)

Related Items (5)

Optimal placement of irradiation sources in the planning of radiotherapy: mathematical models and methods of solving ⋮ Configuration space of geometric objects ⋮ Formalizing spatial configuration optimization problems with the use of a special function class ⋮ 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 ⋮ Application of the theory of optimal set partitioning for constructing fuzzy Voronoi diagrams

Cites Work

• The Zermelo-Voronoi diagram: a dynamic partition problem
• Stable marker-particle method for the Voronoi diagram in a flow field
• Uncertain Voronoi diagram
• Solution of continuous problems of optimal covering with spheres using optimal set-partition theory
• Concrete and abstract Voronoi diagrams
• Modified \(r\)-algorithm to find the global minimum of polynomial functions
• A geometrical solution for quadratic bicriteria location models
• Nonsmooth-optimization methods in problems of stochastic programming
• Multiple packing and covering of spheres
• A continuous problem of optimal partition with a nondifferentiable functional
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