ALCOMFT-TR-03-17

James A. Fill, Philippe Flajolet and Nevin Kapur
Singularity Analysis, Hadamard Products, and Tree Recurrences
INRIA. Work package 4. July 2003.

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.

Postscript file: ALCOMFT-TR-03-17.ps.gz (323 kb).