We study leader election in unidirectional rings of homonyms that have no a priori knowledge of the number of processes. In this context, we show that there exists no algorithm that solves the process-terminating leader election problem for the class of asymmetrically labeled unidirectional rings. More precisely, we prove that there is no process-terminating leader election algorithm even for the subclass of unidirectional rings where at least one label is unique. Message-terminating leader election is also impossible for the class of unidirectional rings where only a bound on multiplicity is known. However, we show that the process-terminating leader election is possible for two particular subclasses of asymmetrically labeled unidirectional rings where the multiplicity is bounded. We propose three efficient algorithms and analyze their complexities. We also give some non-trivial lower bounds.

我们在没有先验的同音单向环中研究领导者选举有关流程数量的知识。在这种情况下，我们表明，对于一类不对称标记的单向环，没有算法可以解决过程终止的领导者选举问题。更准确地说，我们证明即使对于至少一个标签都是唯一的单向环的子类，也没有终止过程的领导者选举算法。对于仅知道多重性界限的单向环类，也无法结束消息终止的领导者选举。但是，我们表明，对于多重性有界的不对称标记的单向环的两个特定子类，可以终止过程的领导者选举。我们提出了三种有效的算法并分析了它们的复杂性。我们还给出一些非平凡的下界。