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

  • Authors:

  • F. Dehne;X. Deng;P. Dymond;A. Fabri;A. A. Khokhar

  • Affiliations:

  • School of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6 dehne@scs.carleton.ca, CA;Department of Computer Science, York University, North York, Ontario, Canada M3J 1P3 deng@cs.yorku.ca, dymond@cs.yorku.ca, CA;Department of Computer Science, York University, North York, Ontario, Canada M3J 1P3 deng@cs.yorku.ca, dymond@cs.yorku.ca, CA;Department of Computer Science, Utrecht University, 3508 TB Utrecht, The Netherlands andreas@cs.ruu.nl, NL;School of EE and Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA ashfaq@cs.purdue.edu, US

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 1997

Quantified Score

Hi-index 0.00

Visualization

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 驴 p 2+驴 (for some arbitrarily small 驴 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 驴 p 2+驴 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).