Sorting algorithms for broadcast communications: mathematical analysis

Assume that n persons communicate via a channel; to each person a certain number is attached, and the goal is to see the numbers of all persons, e. g. in order to sort them. In this paper three algorithms to achieve this are analyzed with respect to the average number of rounds. While a precise description of the algorithmic aspects can be found in the companion paper [14], we concentrate here on the mathematical aspects of the analysis. The quantities of interest can be written as certain contour integrals involving zeta functions. The numerical evaluation leads first via residues to extremely slowly converging series, and the acceleration of them is a nontrivial task that is done in a slightly more general fashion in order to fit all the applications.