Leader election and renaming with optimal message complexity

Abstract

Asynchronous message-passing system is a standard distributed model, where n processors communicate over unreliable channels, controlled by a strong adaptive adversary. The asynchronous nature of the system and the fact that t<n2 processors may fail by crashing are the great obstacles for designing efficient algorithms. Leader election (test-and-set) and renaming are two fundamental distributed tasks. We prove that both tasks can be solved using expected O(n²) messages -- the same asymptotic complexity as a single all-to-all broadcast -- and that this message complexity is in fact optimal.