Constructing Delaunay triangulations along space-filling curves

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Abstract

Incremental construction con BRIO using a space-filling curve order for insertion is a popular algorithm for constructing Delaunay triangulations. So far, it has only been analyzed for the case that a worst-case optimal point location data structure is used which is often avoided in implementations. In this paper, we analyze its running time for the more typical case that points are located by walking. We show that in the worst-case the algorithm needs quadratic time, but that this can only happen in degenerate cases. We show that the algorithm runs in O(n logn) time under realistic assumptions. Furthermore, we show that it runs in expected linear time for many random point distributions. This research was supported by the Deutsche Forschungsgemeinschaft within the European graduate program ’Combinatorics, Geometry, and Computation’ (No. GRK 588/2) and by the Netherlands’ Organisation for Scientific Research (NWO) under BRICKS/FOCUS grant number 642.065.503 and project no. 639.022.707.
Original languageEnglish
Title of host publicationAlgorithms - ESA 2009 (17th Annual European Symposium, Copenhagen, Denmark, September 7-9, 2009. Proceedings)
EditorsA. Fiat, P. Sanders
Place of PublicationBerlin
PublisherSpringer
Pages119-130
ISBN (Print)978-3-642-04127-3
DOIs
Publication statusPublished - 2009

Publication series

NameLecture Notes in Computer Science
Volume5757
ISSN (Print)0302-9743

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  • Cite this

    Buchin, K. (2009). Constructing Delaunay triangulations along space-filling curves. In A. Fiat, & P. Sanders (Eds.), Algorithms - ESA 2009 (17th Annual European Symposium, Copenhagen, Denmark, September 7-9, 2009. Proceedings) (pp. 119-130). (Lecture Notes in Computer Science; Vol. 5757). Springer. https://doi.org/10.1007/978-3-642-04128-0_11