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Optimal randomized parallel algorithms for computational geometry
J.H. Reif,
Published in Springer-Verlag
Volume: 7
Issue: 1
Pages: 91 - 117
We present parallel algorithms for some fundamental problems in computational geometry which have a running time of O(log n) using n processors, with very high probability (approaching 1 as n → ∞). 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. © 1992 Springer-Verlag New York Inc.
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