Leader Election in Rings with Homonyms.

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.