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International Colloquium on Automata, Languages, and Programming

ICALP 1993: Automata, Languages and Programming pp 137–149Cite as

Exact asymptotics of divide-and-conquer recurrences

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 700))

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.

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Author information

Authors and Affiliations

  1. Algorithms Project, INRIA Rocquencourt, F-78153, Le Chesnay, France

    Philippe Flajolet

  2. Department of Computer Science, HKUST, Clear Water Bay, Kowloon, Hong Kong

    Mordecai Golin

Authors
  1. Philippe Flajolet
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  2. Mordecai Golin
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Editor information

Andrzej Lingas Rolf Karlsson Svante Carlsson

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© 1993 Springer-Verlag Berlin Heidelberg

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Flajolet, P., Golin, M. (1993). Exact asymptotics of divide-and-conquer recurrences. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_68

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  • DOI: https://doi.org/10.1007/3-540-56939-1_68

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56939-8

  • Online ISBN: 978-3-540-47826-3

  • eBook Packages: Springer Book Archive

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