Exact Asymptotics of Divide-and-Conquer Recurrences

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Exact Asymptotics of Divide-and-Conquer Recurrences
The divide-and-conquer principle is a majoi paradigm of algorithms design. Corresponding cost functions satisfy recurrences that directly reflect the decomposition mechanism used in the algorithm. This work shows that periodicity phenomena, often of a fractal nature, are ubiquitous in the performances of these algorithms. Mellin transforms and Dirichlet series are used to attain precise asymptotic estimates. The method is illustrated by a detailed average case, variance and distribution analysis of the classic top-down recursive mergesort algorithm. The approach is applicable to a large number of divide-and-conquer recurrences, and a general theorem is obtained when the partitioningmerging toll of a divide-and-conquer algorithm is a sublinear function. As another illustration the method is also used to provide an exact analysis of an efficient maxima-finding algorithm. Many algorithms are based on a recursive divide-and-conquer strategy. Accordingly, their complexity is expressed by re...
Philippe Flajolet, Mordecai J. Golin
Added 09 Aug 2010
Updated 09 Aug 2010
Type Conference
Year 1993
Authors Philippe Flajolet, Mordecai J. Golin
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