Abstract. The authors demonstrate the way of constructing the Voronoi diagram and its various generalizations based on a unified approach: formulating a continuous optimal set partitioning problem with the partition quality criterion that provides the appropriate type of Voronoi diagrams and applying the mathematical and algorithmic apparatus to solve such problems. The result of this approach is 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 Е_n, Shor’s r-algorithm.