Analysis of an Asymmetric Leader Election Algorithm

We consider a leader election algorithm in which a set ofdistributed 'ob· jects (people, computers, elc.) try to identify one object as their leader. The election process is randomized, that is, at every stage of the algorithm. those objects that survived so far flip abiased coin, and those who received, say a tail. survive for the next round. The process .continues until only one objects remains. OUf interest is in evaluating the limiting distribution and the first two moments of the number of rounds needed to select a ]ea'der: 'We establish precise asymptotics for the first two moments, and show that the asymptotic"expression for the duration of the algotithm exhibits some perioPic fluctuatiobs'an:d consequently no limiting distribution exists. These results are proved by analytical techniques of the precise analysis ofalgorithms such as: analytical poissonization and depoissonization. Mellin transfonn. and complex analysis. Key~words: Election algorithm; Asympto~c analysisj Complex analysis; Mellin transform.