Publications [#236950] of John H. Reif

Journal articles or Book chapters PUBLISHED

1. Reif, JH; Sen, S, Optimal randomized parallel algorithms for computational geometry, Algorithmica, vol. 7 no. 1-6 (June, 1992), pp. 91-117, Springer Nature, ISSN 0178-4617 [pdf], [doi]
   (last updated on 2026/01/14)

   Abstract:
   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.