Abstract
We consider the leader election problem in a ring whose nodes have possibly nonunique labels. Every node knows a priori its own label and two integers, m and M, which are, respectively, a lower and an upper bound on the (unknown) size n of the ring. The aim is to decide whether leader election is possible and to perform it, if so. We consider both the synchronous and the asynchronous version of the problem and we are interested in message complexity in both cases. For the synchronous version we present an algorithm using O(n log n) messages and working in time O(M). Moreover, our algorithm uses O(n) messages when all identifiers are distinct. For the asynchronous version we show an Ω(nM) lower bound on message complexity for this problem, and present an algorithm for it using O(nM) messages.