Singularity analysis, Hadamard products, and tree recurrences

Authors:
James Allen Fill;Philippe Flajolet;Nevin Kapur
Affiliations:
Department of Applied Mathematics and Statistics, The Johns Hopkins University, 34th and Charles Streets, Baltimore, MD;Algorithms Project, INRIA, F-78153 Rocquencourt, France;Department of Computer Science, California Institute of Technology, MC 256-80, 1200 E California Blvd., Pasadena, CA
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relations.