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Stochastic Analysis of ‘Simultaneous Merge–Sort'

  • M. Cramer (a1)

Abstract

The asymptotic behaviour of the recursion is investigated; Yk describes the number of comparisons which have to be carried out to merge two sorted subsequences of length 2k –1 and Mk can be interpreted as the number of comparisons of ‘Simultaneous Merge–Sort'. The challenging problem in the analysis of the above recursion lies in the fact that it contains a maximum as well as a sum. This demands different ideal properties for the metric in the contraction method. By use of the weighted Kolmogorov metric it is shown that an exponential normalization provides the recursion's convergence. Furthermore, one can show that any sequence of linear normalizations of Mk must converge towards a constant if it converges in distribution at all.

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Postal address: Institut für Mathematische Stochastik, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany.

References

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Knuth, D. E. (1973) The Art of Computer Programming. Vol. 3: Sorting and Searching. Addison-Wesley, Reading, MA
Rachev, S. T. (1991) Probability Metrics and the Stability of Stochastic Models. Wiley, New York.
Rachev, S. T. and Rüschendorf, L. (1995) Probability metrics and recursive algorithms. Adv. Appl. Prob. 27, 770799.

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Stochastic Analysis of ‘Simultaneous Merge–Sort'

  • M. Cramer (a1)

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