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29 p, 554.8 KB On the structure of higher order Voronoi cells / Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona) ; Roshchina, Vera (University of New South Wales (Australia)) ; Todorov, Maxim (Universidad de las Américas Puebla)
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 order Voronoi cells for four points.
2019 - 10.1007/s10957-019-01555-2
Journal of optimization theory and applications, Vol. 183 (2019) , p. 24-49  

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