Mellin transforms and asymptotics. The mergesort recurrence. (English) Zbl 0818.68064

Summary: Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divide-and-conquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard top-down recursive mergesort algorithm, in the average case, as well as in the worst and best cases. It also derives the variance and shows that the cost of mergesort has a Gaussian limiting distribution. The approach is applicable to a number of divide-and-conquer recurrences.


68P10 Searching and sorting
44A15 Special integral transforms (Legendre, Hilbert, etc.)
68Q25 Analysis of algorithms and problem complexity
Full Text: DOI


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