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Localizing the Delaunay Triangulation and Its Parallel Implementation

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Transactions on Computational Science XX

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 8110))

Abstract

We show how to localize the Delaunay triangulation of a given planar point set, namely, bound the set of points which are possible Delaunay neighbors of a given point. We then exploit this observation in an algorithm for constructing the Delaunay triangulation (and its dual Voronoi diagram) by computing the Delaunay neighbors (and Voronoi cell) of each point independently. While this does not lead to the fastest serial algorithm possible for Delaunay triangulation, it does lead to an efficient parallelization strategy which achieves almost perfect speedups on multicore machines.

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Author information

Authors and Affiliations

  1. Technion - Israel Inistitute of Technology, Haifa, Israel

    Renjie Chen & Craig Gotsman

Authors
  1. Renjie Chen
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  2. Craig Gotsman
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Editor information

Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina L. Gavrilova

  2. CloudFabriQ Ltd., Warnford Court, 29 Throgmorton Street, EC2N 2AT, London, UK

    C. J. Kenneth Tan

  3. Rutgers University, New Brunswick, NJ, USA

    Bahman Kalantari

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Chen, R., Gotsman, C. (2013). Localizing the Delaunay Triangulation and Its Parallel Implementation. In: Gavrilova, M.L., Tan, C.J.K., Kalantari, B. (eds) Transactions on Computational Science XX. Lecture Notes in Computer Science, vol 8110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41905-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-41905-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41904-1

  • Online ISBN: 978-3-642-41905-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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