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

  • W. Preilowski
  • E. Dahlhaus
  • G. Wechsung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)


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.


Convex Hull Parallel Algorithm Vertex Versus Internal Edge Convex Hull Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • W. Preilowski
    • 1
  • E. Dahlhaus
    • 2
  • G. Wechsung
    • 3
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornBrazil
  2. 2.Department of Computer ScienceUniversity of SidneyAustralia
  3. 3.Department of MathematicsFriedrich-Schiller-University of JenaGermany

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