Authors: Nancy M. Amato and Franco P. Preparata

Venue: Proceedings of the Ninth Annual Symposium on Computational Geometry
DOI: 10.1145/160985.161152
Link to Publication

Abstract:
In this paper we present an O(log n) time parallel algorithm for computing the convex hull of n points in R3. This algorithm uses O(n^(1+α)) processors on a CREW PRAM, for any constant 0 < α ≤ 1. So far, all adequately documented parallel algorithms proposed for this problem use time at least O (log^2 n). In addition, the algorithm presented here is the first parallel algorithm for the three-dimensional convex hull problem that is not based on the serial divide-and-conquer algorithm of Preparata and Hong, whose crucial operation is the merging of the convex hulls of two linearly separated point sets. The contributions of this paper are therefore (i) an O(logn) time parallel algorithm for the three-dimensional convex hull problem, and (ii) a parallel algorithm for this problem that does not follow the traditional divide-and-conquer paradigm. 

@inproceedings{Preparata-anp3ch-1993, 
 author = {N. M. Amato and F. P. Preparata}, 
 booktitle = {Proceedings of the 9th Annual {ACM} Symposium on Computational Geometry}, 
 pages = {289--297}, 
 title = {An {NC}$^1$ Parallel {3D} Convex Hull Algorithm}, 
 year = {1993} 
}