An improved algorithm for constructing kth-order Voronoi diagrams

Authors:
Bernard Chazelle;Herbert Edelsbrunner
Affiliations:
Department of Computer Science, Brown University, Providence, RI;Institutes for Information Processing, Technical, University of Graz, SchieDstattgasse 4a., A-8010 Graz, Austria
Venue:
SCG '85 Proceedings of the first annual symposium on Computational geometry
Year:
1985

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Abstract

The kth-order Voronoi diagram of a set of points in E2 (called sites) subdivides E2 into maximal regions such that each point within a given region has the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in &Ogr;(n2logn+k(n-k)log2n) time, &Ogr;(k(n-k)) storage, and &Ogr;(n2+k(n-k)log2n) time, &Ogr;(n2) storage, respectively.