Asymptotics of Divide-and-Conquer Recurrences: Batcher's Sorting Algorithm and a Minimum Euclidean Matching Heuristic

Abstract

We examine in detail the asymptotic behaviors of the number of comparisons used in Batcher's sorting algorithm and a quantity arising in analyzing the rectangle heuristic for finding minimum Euclidean matching due to Supowit and Reingold. We put forth methods (elementary and analytic) for computing the Fourier coefficients of periodic functions appearing in the asymptotic expansions of these quantities. The methods consist of the approach by Flajolet and Golin for divide-and-conquer recurrences and van der Corput's method from analytic number theory for exponential sums.