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.
Similar content being viewed by others
References
Akl, S. G., Meijer, H.: The design and analysis of a new hybrid sorting algorithm. Information Processing Lett.10, 213–218 (1980).
Billingsley, P.: Probability and measure. New York: Wiley 1979.
Breiman, L.: Probability. Reading, Mass.: Addison-Wesley 1968.
Devroye, L., Klincsek, T.: Average time behavior of distributive sorting algorithms. Computing26, 1–7 (1981).
Dobosiewicz, W.: Sorting by distributive partitioning. Information Processing Lett.7, 1–6 (1978).
Feller, W.: An introduction to probability theory and its applications, Vol. I. New York: Wiley 1970.
Kawata, T.: Fourier analysis in probability theory. New York: Academic Press 1972.
Knuth, D. E.: The art of computer programming. Reading, Mass.: Addison-Wesley 1973.
Van der Nat, M.: A fast sorting algorithm, a hybrid of distributive and merge sorting. Information Processing Lett.10, 163–167 (1980).
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02251234