Abstract
A file ofn records can be sorted in linear time givenO(log(n)) processors. Four such algorithms are presented and analyzed. All of them have reasonable hardware requirements; no memory access conflicts are generated; a constant number of communication lines per processor are needed (except for one case); and the space requirements areO(n) orO(n log(log(n))).
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References
A. V. Aho, J. E. Hopcroft and J. D. Ullman,The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.
K. E. Batcher,Sorting networks and their applications, Proceedings of the AFIPS Spring Joint Conference 32, pp. 307–314, 1968.
M. Blum, R. W. Floyd, V. Pratt, R. L. Rivest and R. E. Tarjan,Time bounds for selection, Journal of Computer and System Sciences 7, pp. 448–461, 1973.
L. Devroye,Exponential bounds for the running time of a selection algorithm, Manuscript, McGill University, Montreal, 1982.
L. Devroye and T. Klincsek,Average time behaviour of distributive sorting algorithms, Computing 26, pp. 107, 1981.
W. Dobosiewicz,Sorting by distributive partitioning, Information Processing Letters 7, pp. 1–6, 1978.
R. W. Floyd and R. L. Rivest,Expected time bounds for selection, Communications of the ACM 18, pp. 165–173, 1975.
D. S. Hirschberg,Fast parallel sorting algorithms, Communications of the ACM 21, pp. 657–661, 1978.
C. A. R. Hoare,Quicksort, Computer Journal 5, pp. 10–15, 1962.
C. A. R. Hoare,FIND (Algorithm 65), Communications of the ACM 4, pp. 321–322, 1961.
D. E. Knuth,The Art of Computer Programming, Vol. 3. Sorting and Scarching, Addison-Wesley, Reading, Mass., 1975.
F. P. Preparata,New parallel-sorting schemes, IEEE Transactions on Computers, C-27, pp. 669–673, 1978.
A. Schonhage, M. Paterson and N. Pippenger,Finding the median, Journal of Computer and System Sciences 13, pp. 184–199, 1976.
R. Sedgewick,The analysis of quicksort programs, Acta Informatica 7, pp. 327–355, 1977.
P. G. Sorenson, J. P. Tremblay and R. F. Deutscher,Key-to-address transformation techniques, INFOR 16, pp. 1–34, 1978.
S. Todd,Algorithm and hardware for a mergesort using multiple processors, IBM Journal of Research and Development 22, pp. 509–517, 1978.
R. L. Wheeden and A. Zygmund,Measure and Integral, Marcel Dekker, New York, 1977.
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Orenstein, J.A., Merrett, T.H. & Devroye, L. Linear sorting withO(logn) processors. BIT 23, 170–180 (1983). https://doi.org/10.1007/BF02218438
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DOI: https://doi.org/10.1007/BF02218438