We study leader election in unidirectional rings of homonym processes that have no a priori knowledge on the number of processes. We show that message-terminating leader election is impossible for any class of rings (K)_k with bounded multiplicity k ≥ 2. However, we show that process-terminating leader election is possible in the sub-class (U)~*∩(K)_k, where (U)~* is the class of rings which contain a process with a unique label.
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