On the Structure of Higher Order Voronoi Cells

J. E. Martínez Legaz, V. Roshchina, M. Todorov

The classic Voronoi cells can be generalized to a higher-order version by considering the cells of points for which a given k-element subset of the set of sites consists of the k closest sites. We study the structure of the k-order Voronoi cells and illustrate our theoretical findings with a case study of two-dimensional higher-orderVoronoi cells for four points.

Keywords: Voronoi diagrams Convex sets

B. Jiménez, V. Novo, A. Vílchez Medina

M. A. Melguizo Padial, F. García Castaño

J. Parra López, M. J. Cánovas Cánovas, M. A. López Cerdá, B. Mordukhovich