Skip to main content
SpringerLink
Log in

A new parallel sorting algorithm based upon min-mid-max operations

  • Part I Computer Science
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

In this paper we propose a new parallel sorting algorithm which is based upon an operation which sorts three elements. This algorithm is similar to the parallel odd-even merge sorting algorithm proposed by Batcher, except in the latter, the basic operation sorts only two elements. The correctness of our algorithm is also proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Aigner,Parallel complexity of sorting problems, J. of Algorithms 3, (1982), pp. 79–88.

    Google Scholar 

  2. H. Barlow, D. J. Evans and J. Shanehchi,A parallel merging algorithm, Information Processing Letters 13, No. 3, Dec. 1981, pp. 103–106.

    Google Scholar 

  3. K. W. Batcher,Sorting networks and their applications, AFIPS Conf. 32, (1968), pp. 307–314.

    Google Scholar 

  4. G. Baudet and D. Stevenson,Optimal sorting algorithms for parallel computers, IEEE Trans. Comput. C-27, No. 1, Jan. 1978, pp. 84–87.

    Google Scholar 

  5. H. K. Brock, B. J. Brooks and F. Sullivan,Diamond, a sorting method for vector machines, BIT 21; 2, (1981), pp. 142–152.

    Google Scholar 

  6. T. C. Chen, K. P. Eswaran, V. Y. Lum and C. Tung,Simplified odd-even sort using multiple shift-register loops, IJCIS 7, No. 3, 1978, pp. 293–314.

    Google Scholar 

  7. F. Y. Chin and K. S. Fok,Fast sorting algorithms on uniform ladders (multiple shift-register loops), IEEE Trans. Comput. C-27, No. 7, July 1980, pp. 618–631.

    Google Scholar 

  8. F. Gavril,Merging with parallel processors, Comm. ACM 18; 10, Oct. 1975, pp. 588–591.

    Google Scholar 

  9. R. Haggkvist and P. Hell,Parallel sorting with constant time for comparisons, SIAM J. Comput. 10; 3, Aug. 1981, pp. 465–472.

    Google Scholar 

  10. D.S. Hirschberg,Fast parallel sorting algorithms, Comm. ACM 21; 8, Aug. 1978, pp. 657–661.

    Google Scholar 

  11. R. W. Hockney and C. R. Jesshope,Parallel Computers, Adam Hilger Ltd., Bristol (1981).

    Google Scholar 

  12. D. E. Knuth,Sorting and Searching, Vol. 3, The Art of Computer Programming, Addison-Wesley, Reading, MA. (1973).

    Google Scholar 

  13. M. Kumar and D. S. Hirschberg,An efficient implementation of Batcher's odd-even merge algorithm and its application in parallel sorting schemes, IEEE Trans. Comput. C-32, No. 3, March 1983.

  14. D. J. Kuck,The Structure of Computers and Computations, Vol. 1, (1978), Wiley.

  15. D. T. Lee, H. Chang and C. K. Wong,An on-chip compare/steer bubble sorter, IEEE Trans. Comput. C-27, No. 6, June 1981, pp. 396–404.

    Google Scholar 

  16. C. L. Liu,Elements of Discrete Mathematics, (1977), McGraw Hill, New York.

    Google Scholar 

  17. D. E. Muller and F. P. Preparata,Bounds to complexities of networks for sorting and for switching, J. Assoc. Comput. Math. 22; 2, April 1975, pp. 195–201.

    Google Scholar 

  18. D. Nassimi and S. Sahni,Bitonic sort on a mesh-connected parallel computer, IEEE Trans. Comput. C-27, No. 1, Jan. 1979, pp. 2–7.

    Google Scholar 

  19. D. Nassimi and S. Sahni,Parallel permutation and sorting algorithms and a new generalized connection network, J. Assoc. Comput. Math. 29; 3, July 1982, pp. 642–667.

    Google Scholar 

  20. F. P. Preparata,Parallelism in sorting, Proc. of 1977 International Conf. on Parallel Processing, pp. 202–206.

  21. F. P. Preparata,New parallel sorting schemes, IEEE Trans. Comput. C-27, No. 7, July 1978, pp. 669–773.

    Google Scholar 

  22. R. Reischuk,A fast probabilistic parallel sorting algorithm, IEEE 1981 Symposium on Foundation of Computer Science, pp. 212–219.

  23. Y. Shiloach and U. Vishkin,Finding the maximum, merging, and sorting in a parallel computation model, J. of Algorithms 2, (1981), pp. 88–102.

    Google Scholar 

  24. H. S. Stone,Parallel processing perfect shuffle, IEEE Trans. Comput. C-20, Feb. 1971, pp. 153–161.

    Google Scholar 

  25. H. S. Stone,Sorting on STAR, IEEE Trans. Software Engineering SE-4, No. 2, Mar. 1978, pp. 138–146.

    Google Scholar 

  26. C. D. Thompson and H. T. Kung,Sorting on a mesh-connected parallel computer, Comm. ACM 20; 4, April 1977, pp. 263–271.

    Google Scholar 

  27. S. Todd,Algorithm and hardware for a merge sort using multiple processors, IBM J. Res. Develop. 22; 5, Sep. 1978, pp. 509–517.

    Google Scholar 

  28. L. G. Valiant,Parallelism in comparison problems, SIAM J. Comput. 4; 3, Sep. 1975, pp. 348–355.

    Google Scholar 

  29. A. C. Yao and F. F. Yao,Lower bounds on merging networks, J. Assoc. Comput. Math. 23; 3, July 1976, pp. 566–571.

    Google Scholar 

  30. H. Yasuura, N. Takagi and S. Yajima,The parallel enumeration sorting scheme for VLSI, IEEE Trans. Comput. C-3, No. 12, Dec. 1982, pp. 1192–1201.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate Institute of Computer Engineering, National Chiao Tung University, Hsinchu, Taiwan 300, Republic of China

    S. S. Tseng & R. C. T. Lee

  2. Graduate Institute of Computer and Decision Sciences, National Tsing, Hua University, Hsinchu, Taiwan 300, Republic of China

    S. S. Tseng & R. C. T. Lee

Authors
  1. S. S. Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. C. T. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research work was partially supported by a grant from the National Science Council, Republic of China under the contract NSC73-0201-E007-01.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tseng, S.S., Lee, R.C.T. A new parallel sorting algorithm based upon min-mid-max operations. BIT 24, 187–195 (1984). https://doi.org/10.1007/BF01937485

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01937485

Keywords

Search

Navigation