On the Structure of Higher Order Voronoi Cells

Juan Enrique Martínez-Legaz, Vera Roshchina, Maxim Todorov

Research output: Contribution to journalArticleResearch

1 Citation (Scopus)


© 2019, Springer Science+Business Media, LLC, part of Springer Nature. 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.
Original languageEnglish
Pages (from-to)24-49
JournalJournal of Optimization Theory and Applications
Publication statusPublished - 15 Oct 2019


  • Higher order Voronoi cells
  • Structure of Voronoi cells


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