A note on Conway's parallel sorting algorithm

  • Kazem U. Ahmed
  • Der-Yun Yeh
Track 3: Parallel Processing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)


This paper presents an improved lower bound on Conway's parallel sorting algorithm. It is shown that Conway's parallel sorting algorithm sorts N keys in (N+[N/2]-2) cycles, where [X] denotes the smallest integer which is larger than or equal to X. The original result proposed by Warshauer is (2N-3) cycles. With this improvement it can be saved (N-[N/2]-1) cycles for N keys. Consequently it is shown that 50(1-2/N) percent of cycles can be saved on the sorting process. Also with this improvement the modified algorithm for average behavior proposed by the authors in an earlier paper will become more efficient.


Final Position Average Behavior Finite State Machine Original Algorithm Original Result 
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  1. [1]
    K. U. Ahmed and D. Y. Yeh. Time Efficient Implementation of Conway's Parallel Sorting Algorithm. 1988 International Computer Symposium, Tamkang University, Taipei, Taiwan, Dec 15–17, 1988.Google Scholar
  2. [2]
    D. E. Knuth. Sorting and Searching. In the Art of Computer Programming Vol 3, Addison-Wesley, Reading, Mass. 1973.Google Scholar
  3. [3]
    M. L. Warshauer. Conway's Parallel Sorting Algorithm. Journal of Algorithms 7 (1986), 270–276.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Kazem U. Ahmed
    • 1
  • Der-Yun Yeh
    • 1
  1. 1.Computer Science DepartmentArizona State UniversityTempe

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