Abstract
We present a randomized parallel algorithm for constructing the three-dimensional convex hull on a generic p-processor coarse-grained multicomputer with arbitrary interconnection network and n/p local memory per processor, where n/p ≥ p 2+ε (for some arbitrarily small ε > 0). For any given set of n points in 3-space, the algorithm computes the three-dimensional convex hull, with high probability, in \(O((n\log{n})/p)\) local computation time and O(1) communication phases with at most O(n/p) data sent/received by each processor. That is, with high probability, the algorithm computes the three-dimensional convex hull of an arbitrary point set in time \(O((n\log n)/{p} + \Gamma_{n,p})\) , where Γ n,p denotes the time complexity of one communication phase. The assumption n/p ≥ p 2+ε implies a coarse-grained, limited parallelism, model which is applicable to most commercially available multiprocessors.
In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps, synchronization period \(L = \Theta((n\log n)/{p})\) , computation cost \(O((n\log n)/{p})\) , and communication cost O((n/p) g).
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received October 30, 1995, and in revised form April 15, 1996, and in final form September 17, 1996.
Rights and permissions
About this article
Cite this article
Dehne, F., Deng, X., Dymond, P. et al. A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers. Theory Comput. Systems 30, 547–558 (1997). https://doi.org/10.1007/s002240000067
Published:
Issue Date:
DOI: https://doi.org/10.1007/s002240000067