, Volume 5, Issue 1–4, pp 75–92 | Cite as

Improved sorting networks withO(logN) depth

  • M. S. Paterson


The sorting network described by Ajtaiet al. was the first to achieve a depth ofO(logn). The networks introduced here are simplifications and improvements based strongly on their work. While the constants obtained for the depth bound still prevent the construction being of practical value, the structure of the presentation offers a convenient basis for further development.

Key words

Sorting networks Comparators Parallel algorithm 


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  1. [1]
    M. Ajtai, J. Komlós, and E. Szemerédi, AnO(n logn) sorting network,Proc. 15th Ann. ACM Symp. on Theory of Computing, 1983, pp. 1–9.Google Scholar
  2. [2]
    M. Ajtai, J. Komlós, and E. Szemerédi, Sorting inC logN parallel steps,Combinatorial,3 (1983), 1–19.zbMATHCrossRefGoogle Scholar
  3. [3]
    K. Batcher, Sorting networks and their applications,Proc. AFIPS Spring Joint Computer Conference, 1968, pp. 307–314.Google Scholar
  4. [4]
    F. Chung, On concentrators, superconcentrators, generalizers, and nonblocking networks,Bell System Tech. J.,58 (1978), 1765–1777.Google Scholar
  5. [5]
    O. Gabber and Z. Galil, Explicit constructions of linear-sized superconcentrators,J. Comput. System Sci.,22 (1981), 407–420.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    D. E. Knuth,The Art of Computer Programming, Vol. 3, Addison-Wesley, Reading, MA, 1973.Google Scholar
  7. [7]
    A. Lubotzky, R. Phillips, and P. Sarnak, Explicit expanders and the Ramanujan conjectures,Proc. 18th Ann. ACM Symp. on Theory of Computing, 1986, pp. 240–246.Google Scholar
  8. [8]
    G. A. Margulis, Explicit construction of concentrators,Problemy Peredači Informacii,9 (1973), 71–80. English translation:Problems Inform. Transmission (1975), 325–332.zbMATHMathSciNetGoogle Scholar
  9. [9]
    H. Robbins, A remark on Stirling's formula,Amer. Math. Monthly,62 (1955), 26–29.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • M. S. Paterson
    • 1
  1. 1.Department of Computer ScienceUniversity of WarwickCoventryEngland

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