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.Keywords: Voronoi diagram, continuous problem of optimal partitioning of sets from Å n , Shor's r-algorithm.
This paper proposes and analyses a mathematical model for the problem of distribution of a finite number of irradiation sources during radiotherapy in continuous environments to maximize the minimal cumulative effects. A new algorithm based on nondifferentiable optimization techniques has been developed to solve this problem.
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