Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning (Q1988465)

The problem of the construction of a generalized Voronoi diagram with optimal placement of a finite number of generator points in a bounded set of the \(n\)-dimensional Euclidean space is considered. A method to solve this problem based on the formulation of the corresponding continuous problem of optimal partitioning of a set with a partition quality criterion providing the corresponding form of the Voronoi diagram is proposed. The numerical method relies on Shor's \(r\)-algorithm.