A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers

F. Dehne, X. Deng, P. Dymond, A. Fabri, A. A. Khokhar
1997 Theory of Computing Systems  
We present a randomized parallel algorithm for constructing the threedimensional 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
more » ... ent/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 + n, p ), where 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 = ((n log n)/ p), computation cost O((n log n)/ p), and communication cost O((n/ p)g).
doi:10.1007/s002240000067 fatcat:outcwc7vqfdzlmlod7wriubpza