Skip to main content
SpringerLink
Log in

The asymptotic behaviour of a distributive sorting method

Zum asymptotischen Verhalten eines distributiven Suchverfahrens

  • Published:
Computing Aims and scope Submit manuscript

Abstract

In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned inton/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions.

Zusammenfassung

Bei dem distributiven Sortierverfahren von Dobosiewicz wird sowohl das Intervall zwischen Minimum und Median als auch das Intervall zwischen Median und Maximum inn/2 Teilintervalle gleicher Länge zerlegt; die Prozedur wird dann rekursiv in jedem, mindestens vier Zahlen enthaltenden Teilintervall angesetzt. In dieser Arbeit werden einige Aspekte des Verfahrens verfeinert und erweitert. Insbesondere wird das asymptotisch lineare Verhalten unter verschiedene Wahrscheinlichkeits-Annahmen untersucht.

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. Akl, S. G., Meijer, H.: The design and analysis of a new hybrid sorting algorithm. Information Processing Lett.10, 213–218 (1980).

    Google Scholar 

  2. Billingsley, P.: Probability and measure. New York: Wiley 1979.

    Google Scholar 

  3. Breiman, L.: Probability. Reading, Mass.: Addison-Wesley 1968.

    Google Scholar 

  4. Devroye, L., Klincsek, T.: Average time behavior of distributive sorting algorithms. Computing26, 1–7 (1981).

    Google Scholar 

  5. Dobosiewicz, W.: Sorting by distributive partitioning. Information Processing Lett.7, 1–6 (1978).

    Google Scholar 

  6. Feller, W.: An introduction to probability theory and its applications, Vol. I. New York: Wiley 1970.

    Google Scholar 

  7. Kawata, T.: Fourier analysis in probability theory. New York: Academic Press 1972.

    Google Scholar 

  8. Knuth, D. E.: The art of computer programming. Reading, Mass.: Addison-Wesley 1973.

    Google Scholar 

  9. Van der Nat, M.: A fast sorting algorithm, a hybrid of distributive and merge sorting. Information Processing Lett.10, 163–167 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management Science, Eindhoven University of Technology, P. O. Box 513, 5600 MB, Eindhoven, The Netherlands

    W. B. van Dam

  2. Department of Industrial Engineering and Operations Research, University of California, 94720, Berkeley, CA, USA

    J. B. G. Frenk

  3. Econometric Institute, Erasmus University Rotterdam, P. O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    A. H. G. Rinnooy Kan

Authors
  1. W. B. van Dam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. B. G. Frenk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. H. G. Rinnooy Kan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

van Dam, W.B., Frenk, J.B.G. & Rinnooy Kan, A.H.G. The asymptotic behaviour of a distributive sorting method. Computing 31, 287–303 (1983). https://doi.org/10.1007/BF02251234

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02251234

AMS Subject Classifications

Key words

Search

Navigation