Skip to main content
SpringerLink
Log in

Best Increments for the Average Case of Shellsort

  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

Included in the following conference series:

Abstract

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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Ghoshdastidar, D., Roy, M. K.: A study on the evaluation of Shell’s sorting technique. Computer Journal 18 (1975), 234–235.

    Article  MATH  MathSciNet  Google Scholar 

  3. Hibbard, T. N.: An empirical study of minimal storage sorting. Communications of the ACM 6 (1963), 206–213.

    Article  MATH  Google Scholar 

  4. Incerpi, J., Sedgewick, R.: Improved upper bounds on Shellsort. Journal of Computer and System Sciences 31 (1985), 210–224.

    Article  MATH  MathSciNet  Google Scholar 

  5. Janson, S., Knuth, D. E.: Shellsort with three increments. Random Structures and Algorithms 10 (1997), 125–142.

    Article  MATH  MathSciNet  Google Scholar 

  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. Knuth, D.E.: The Art of Computer Programming. Vol. 3: Sorting and Searching. Addison-Wesley, Reading, MA, 1998.

    Google Scholar 

  8. Pratt, V. R.: Shellsort and Sorting Networks. Garland, New York, 1979, PhD thesis, Stanford University, Department of Computer Science, 1971.

    Google Scholar 

  9. Sedgewick, R: A new upper bound for Shellsort. Journal of Algorithms 7 (1986), 159–173.

    Article  MATH  MathSciNet  Google Scholar 

  10. Sedgewick, R.: Analysis of Shellsort and related algorithms. Lecture Notes in Computer Science 1136 (1996), 1–11.

    Google Scholar 

  11. Shell, D. L.: A high-speed sorting procedure. Communications of the ACM 2 (1959), 30–32.

    Article  Google Scholar 

  12. Tokuda, N: An improved Shellsort. IFIP Transactions A-12 (1992), 449–457.

    Google Scholar 

  13. Wald, A.: Sequential Analysis. J. Wiley & Sons, New York, 1947.

    MATH  Google Scholar 

  14. Yao, A. C.: An analysis of (h, k, 1)-Shellsort. Journal of Algorithms 1 (1980), 14–50.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Silesian Institute of Technology, Akademicka 16, PL-44-100, Gliwice, Poland

    Marcin Ciura

Authors
  1. Marcin Ciura
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ciura, M. (2001). Best Increments for the Average Case of Shellsort. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-44669-9_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation