Abstract
The computational complexity of a parallel algorithm depends critically on the model of computation. We describe a simple and elegant rule-based model of computation in which processors apply rules asynchronously to pairs of objects from a global object space. Application of a rule to a pair of objects results in the creation of a new object if the objects satisfy the guard of the rule. The model can be efficiently implemented as a novel MIMD array processor architecture, the Intersecting Broadcast Machine. For this model of computation, we describe an efficient parallel sorting algorithm based on mergesort. The computational complexity of the sorting algorithm isO(nlog2 n), comparable to that for specialized sorting networks and an improvement on theO(n 1.5) complexity of conventional mesh-connected array processors.
Similar content being viewed by others
References
S. G. Akl,Parallel Sorting Algorithms, Academic Press (1985).
D. Bitton, D. J. DeWitt, D. K. Hsaio, and J. Menon,ACM Computing Surveys,16(3):287–318 (September 1984).
K. E. Batcher, Sorting Networks and Their Applications,Proc. of the AFIPS Spring Joint Computer Conf., pp. 307–314 (1968).
H. S. Stone, Parallel Processing with the Perfect Shuffle,IEEE Trans. on Computers,C-20(2):153–161 (February 1971).
M. Ajtai, J. Komlos, and E. Szemeredi, AnO(nlogn) Sorting Network,Proc. of the 15th Annual Symp. on the Theory of Computing, pp. 1–9 (1983).
D. J. Evans, A Parallel Sorting-Merging Algorithm for Tightly Coupled Multiprocessors,Parallel Computing,14:111–121 (1990).
J. Huang and L. Kleinrock, Distributed Selectsort Sorting Algorithms on Broadcast Communication Networks,Parallel Computing,16:183–190 (1990).
I. D. Scherson, S. Sen, and A. Shamir, Shear Sort: A True Two-Dimensional Sorting Technique for VLSI Networks,Proc. of the Int'l. Conf. on Parallel Processing, pp. 903–908 (August 1986).
C. P. Schnorr and A. Shamir, An Optimal Sorting Algorithm for Mesh-Connected Computers,Proc. of the 18th Annual Symp. on Theory of Computing, pp. 255–263, Berkeley, California (1986).
M. Kunde, Lower Bounds for Sorting on Mesh-Connected Architectures,Acta Informatica,24:121–130 (1987).
C. D. Thompson and H. T. Kung, Sorting on a Mesh-Connected Parallel Computer,Communications of the ACM 20(4):263–271 (April 1977).
Y. Han and Y. Igarashi, Time Lower Bounds for Parallel Sorting on a Mesh-Connected Processor Array,Acta Informatica,26:643–655 (1990).
M. Kunde, Routing and Sorting on Mesh-Connected Arrays,Proc. of the AWOC Conference, Lecture Notes in Computer Science 319, Springer-Verlag, pp. 423–433 (1988).
Y. Ma, S. Sen and I. D. Scherson, The Distance Bound for Sorting on Mesh-Connected Processor Arrays is Tight,Proc. Foundations of Computer Science, pp. 255–263 (August 1986).
S. K. Nayudu and K. A. Teague, Parallel Sorting on the iPSC/2 Hypercube Computer,Proc. of the Fourth Conf. on Hypercubes, Concurrent Computers, and Applications,1:429–431 (March 1989).
B. Wagar, Hyperquicksort: A Fast Sorting Algorithm for Hypercubes,Proc. of the Second Conf. on Hypercube Multiprocessors, pp. 292–299 (1986).
P. M. Melliar-Smith, L. e. Moser, A. Das, and C. Ye, A Fault-Tolerant Array Processor Architecture,Proc. of the Fifth Int'l. Conf. on Parallel and Distributed Computing and Systems (October 1992).
N. Carriero, D. Gelernter, and J. Leichter, Distributed Data Structures in Linda,Proc. of the Thirteenth Annual ACM Symp. on Principles Programming Languages, pp. 236–242 (January 1986).
D. Gelernter, N. Carriero, S. Chandran, and S. Chang, Parallel Programming in Linda,Proc. of the IEEE Int'l. Conf. on Parallel Processing, pp. 255–263 (August 1985).
K. M. Chandy and J. Misra,Parallel Program Design: A Foundation, Addison Wesley (1988).
D. Nassimi and S. Sahni, Bitonic Sort on a Mesh-Connected Parallel Computer,IEEE Transactions on Computers,C-27(1):2–7 (January 1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Das, A., Moser, L.E. & Melliar-Smith, P.M. A parallel sorting algorithm for a novel model of computation. Int J Parallel Prog 20, 403–419 (1991). https://doi.org/10.1007/BF01407814
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01407814