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...

• Type: Conference
• Year: 1993
• Where: ICALP
• Authors: Philippe Flajolet, Mordecai J. Golin
• Keywords: ICALP 1993, Programming Languages, Recurrences, Recursive Mergesort Algorithm, Top-down Recursive Mergesort