Symmetry breaking in asynchronous rings with O(N) messages

Abstract

The symmetry breaking problem is the problem of electing a leader in a network of indistinguishable processes. There is no deterministic solution for this problem. We provide here efficient probabilistic protocols for breaking symmetry in a unidirectional ring. For rings of unrestricted asynchrony, we provide a protocol needing only O(n) messages in the average. Yet, the average bit complexity of the protocol is still O(nlogn). We manage to get a message complexity below the Ω(nlogn) lower bound of [Burns, 80], by allowing our protocol to deadlock, with arbitrarily small probability, controllable by the implementer. The possibility of more than one leaders being elected is not allowed by our protocol.