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International Symposium on Mathematical Foundations of Computer Science

MFCS 1992: Mathematical Foundations of Computer Science 1992 pp 442–450Cite as

New parallel algorithms for convex hull and triangulation in 3-dimensional space

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 629))

Abstract

Let S be a set of n given points in 3-dimensional space. We present parallel algorithms for the construction of the convex hull and for triangulation of S on a CREW-PRAM. For 3-dim. convex hull our algorithm is time-optimal and uses time O(1/ε· log(n)) with O(n 1+e) processors. By duality parallel convex hull algorithms induce new ones for Voronoidiagrams in the plane, using the same time and processor bounds. A second parallel algorithm for Voronoi-diagrams presented here uses time O(log(n) 2) with O(n) processors.

For 3-dim. triangulation of S we give the first parallel algorithm for the generalized problem, using time O(log(n) 2) with O(n 1+e) processors. For the tangential-plane problem we give a parallel algorithm, needing time O(log(n)) with O(n) processors.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Paderborn, Brazil

    W. Preilowski

  2. Department of Computer Science, University of Sidney, Australia

    E. Dahlhaus

  3. Department of Mathematics, Friedrich-Schiller-University of Jena, Germany

    G. Wechsung

Authors
  1. W. Preilowski
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  2. E. Dahlhaus
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  3. G. Wechsung
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Editor information

Ivan M. Havel Václav Koubek

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© 1992 Springer-Verlag Berlin Heidelberg

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Preilowski, W., Dahlhaus, E., Wechsung, G. (1992). New parallel algorithms for convex hull and triangulation in 3-dimensional space. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_43

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  • DOI: https://doi.org/10.1007/3-540-55808-X_43

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55808-8

  • Online ISBN: 978-3-540-47291-9

  • eBook Packages: Springer Book Archive

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