Algorithmica

, Volume 7, Issue 1–6, pp 91–117 | Cite as

Optimal randomized parallel algorithms for computational geometry

  • John H. Reif
  • Sandeep Sen
Article

Abstract

We present parallel algorithms for some fundamental problems in computational geometry which have a running time ofO(logn) usingn processors, with very high probability (approaching 1 asn → ∞). These include planar-point location, triangulation, and trapezoidal decomposition. We also present optimal algorithms for three-dimensional maxima and two-set dominance counting by an application of integer sorting. Most of these algorithms run on a CREW PRAM model and have optimal processor-time product which improve on the previously best-known algorithms of Atallah and Goodrich [5] for these problems. The crux of these algorithms is a useful data structure which emulates the plane-sweeping paradigm used for sequential algorithms. We extend some of the techniques used by Reischuk [26] and Reif and Valiant [25] for flashsort algorithm to perform divide and conquer in a plane very efficiently leading to the improved performance by our approach.

Key words

Randomized Parallel algorithm Computational geometry Point location Triangulation Trapezoidal decomposition 

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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • John H. Reif
    • 1
  • Sandeep Sen
    • 1
  1. 1.Computer Science DepartmentDuke UniversityDurhamUSA

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