5 research outputs found
Leader election: A Markov chain approach
Full text linkA well-studied randomized election algorithm proceeds as follows: In each
round the remaining candidates each toss a coin and leave the competition if
they obtain heads. Of interest is the number of rounds required and the number
of winners, both related to maxima of geometric random samples, as well as the
number of remaining participants as a function of the number of rounds. We
introduce two related Markov chains and use ideas and methods from discrete
potential theory to analyse the respective asymptotic behaviour as the initial
number of participants grows. One of the tools used is the approach via the
R\'enyi-Sukhatme representation of exponential order statistics, which was
first used in the leader election context by Bruss and Gr\"ubel in
\cite{BrGr03}
