Best Increments for the Average Case of Shellsort

  • Marcin Ciura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2138)


This paper presents the results of using sequential analysis to find increment sequences that minimize the average running time of Shellsort, for array sizes up to several thousand elements. The obtained sequences outperform by about 3% the best ones known so far, and there is a plausible evidence that they are the optimal ones.


Sequential Test Average Running Time Good Sequence Linear Recurrence Dominant Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    ’Aρиστοτέλη: ’Aναλυτиκά, πρτέρα, 64b28-65a37; Σοφιστικοὶ ἔλεγχοι, 181 a 15. In: Aristotelis Opera. Vol. 1: Aristoteles græce, Academia Regia Borussica, Berolini, 1831.Google Scholar
  2. 2.
    Ghoshdastidar, D., Roy, M. K.: A study on the evaluation of Shell’s sorting technique. Computer Journal 18 (1975), 234–235.CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Hibbard, T. N.: An empirical study of minimal storage sorting. Communications of the ACM 6 (1963), 206–213.MATHCrossRefGoogle Scholar
  4. 4.
    Incerpi, J., Sedgewick, R.: Improved upper bounds on Shellsort. Journal of Computer and System Sciences 31 (1985), 210–224.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Janson, S., Knuth, D. E.: Shellsort with three increments. Random Structures and Algorithms 10 (1997), 125–142.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jiang, T., Li, M., Vitányi, P.: The average-case complexity of Shellsort. Lecture Notes in Computer Science 1644 (1999), 453–462.Google Scholar
  7. 7.
    Knuth, D.E.: The Art of Computer Programming. Vol. 3: Sorting and Searching. Addison-Wesley, Reading, MA, 1998.Google Scholar
  8. 8.
    Pratt, V. R.: Shellsort and Sorting Networks. Garland, New York, 1979, PhD thesis, Stanford University, Department of Computer Science, 1971.Google Scholar
  9. 9.
    Sedgewick, R: A new upper bound for Shellsort. Journal of Algorithms 7 (1986), 159–173.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Sedgewick, R.: Analysis of Shellsort and related algorithms. Lecture Notes in Computer Science 1136 (1996), 1–11.Google Scholar
  11. 11.
    Shell, D. L.: A high-speed sorting procedure. Communications of the ACM 2 (1959), 30–32.CrossRefGoogle Scholar
  12. 12.
    Tokuda, N: An improved Shellsort. IFIP Transactions A-12 (1992), 449–457.Google Scholar
  13. 13.
    Wald, A.: Sequential Analysis. J. Wiley & Sons, New York, 1947.MATHGoogle Scholar
  14. 14.
    Yao, A. C.: An analysis of (h, k, 1)-Shellsort. Journal of Algorithms 1 (1980), 14–50.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marcin Ciura
    • 1
  1. 1.Department of Computer ScienceSilesian Institute of TechnologyGliwicePoland

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