Capacity-Constrained Voronoi Diagrams in Finite Spaces

Balzer, Michael; Heck, Daniel

Capacity-Constrained Voronoi Diagrams in Finite Spaces

Dateien

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Datum

2008

Autor:innen

Balzer, Michael

Heck, Daniel

URI (zitierfähiger Link)

http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-66425

Link zur Lizenz

Attribution-NonCommercial-NoDerivs 2.0 Generic

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Beitrag zu einem Konferenzband

Publikationsstatus

Published

Erschienen in

Proceedings of the 5 th Annual International Symposium on Voronoi Diagrams in Science and Engineering, 22 - 28 September, 2008, Kiev, Ukraine. 2008

Zusammenfassung

A Voronoi diagram of a set of n sites partitions a finite set of m points into regions of different areas, called the capacities of the sites. In this paper we are interested in Voronoi diagrams in which the capacities are given as constraints. We compute such capacity-constrained Voronoi diagrams in finite spaces by starting with an arbitrary partition that fulfills the capacity constraint without representing a valid Voronoi diagram. We then iteratively swap the assignment of points to sites guided by an energy minimization that is related to the distance function of the Voronoi diagram. This optimization converges towards a valid Voronoi diagram that fulfills the capacity constraint due to the restriction to swap operations. The straightforward structure of our algorithm makes it easy to implement and flexible. The computational time complexity for each iteration step is O(n2+nmlog m/n). We provide examples for extensions of our algorithm such as applying different energy functions, or generating Voronoi diagrams with centroidal and/or void regions.

Fachgebiet (DDC)

004 Informatik

Schlagwörter

Voronoi diagram, capacity constraint, finite space, power diagram, leastsquares, centroidal Voronoi diagram

Konferenz

Voronoi Diagrams in Science and Engineering, 22. Sep. 2008 - 28. Sep. 2008, Kiev, Ukraine

Zitieren

ISO 690

BALZER, Michael, Daniel HECK, 2008. Capacity-Constrained Voronoi Diagrams in Finite Spaces. Voronoi Diagrams in Science and Engineering. Kiev, Ukraine, 22. Sep. 2008 - 28. Sep. 2008. In: Proceedings of the 5 th Annual International Symposium on Voronoi Diagrams in Science and Engineering, 22 - 28 September, 2008, Kiev, Ukraine. 2008

BibTex

@inproceedings{Balzer2008Capac-5419,
  year={2008},
  title={Capacity-Constrained Voronoi Diagrams in Finite Spaces},
  booktitle={Proceedings of the 5 th Annual International Symposium on Voronoi Diagrams in Science and Engineering, 22 - 28 September, 2008, Kiev, Ukraine},
  author={Balzer, Michael and Heck, Daniel}
}

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Universitätsbibliographie

Ja