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- W1535772777 abstract "The divide-and-conquer principle is a major 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 partitioning-merging 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." @default.
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- W1535772777 date "1993-01-01" @default.
- W1535772777 modified "2023-10-01" @default.
- W1535772777 title "Exact asymptotics of divide-and-conquer recurrences" @default.
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- W1535772777 doi "https://doi.org/10.1007/3-540-56939-1_68" @default.
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