Abstract : Considering the case of homonyms processes (some processes
may share the same identifier) on a ring, we give here a necessary and
sufficient condition on the number of identifiers to enable leader election.
We prove that if l is the number of identifiers then message-terminating
election is possible if and only if l is greater than the greatest proper
divisor of the ring size even if the processes do not know the ring size.
If the ring size is known, we propose a process-terminating algorithm
exchanging O(n log(n)) messages that is optimal.