A probabilistic analysis of a leader election algorithm

TL;DR

This paper analyzes the probabilistic behavior and cost of a leader election algorithm, especially in biased cases, linking its asymptotic performance to hitting times of random sequences.

Contribution

It provides a probabilistic analysis of the biased leader election algorithm's asymptotic cost, connecting it to hitting times of random sequences.

Findings

Asymptotic behavior related to hitting times of random sequences

Analysis of biased leader election process

Probabilistic approach to algorithm cost

Abstract

A {\em leader election} algorithm is an elimination process that divides recursively into tow subgroups an initial group of n items, eliminates one subgroup and continues the procedure until a subgroup is of size 1. In this paper the biased case is analyzed. We are interested in the {\em cost} of the algorithm, i.e. the number of operations needed until the algorithm stops. Using a probabilistic approach, the asymptotic behavior of the algorithm is shown to be related to the behavior of a hitting time of two random sequences on [0,1].