Tight Bounds on Early Local Decisions in Uniform Consensus

Abstract

AbstractWhen devising a uniform consensus algorithm, it is common to minimize the time complexity of global decisions, which is typically measured as the number of communication rounds needed for all correct processes to decide. In practice, what we might want to minimize is the time complexity of local decisions, which we define as the number of communication rounds needed for at least one correct process to decide. We investigate tight bounds on uniform consensus local decisions in crash-stop message-passing models where at most t processes may fail in any given run.In the synchronous model, we show that any uniform consensus algorithm has (1) a run in which at most f ≤ t-1 processes crash such that no correct process decides before round f+1 in that run, and (2) a run in which at most f ≤ t-3 processes crash such that at most one correct process decides before round f+2 in that run. We show that the above lower bounds are tight by pointing out a simple uniform consensus algorithm.In the eventually synchronous model, we show that any uniform consensus algorithm has a synchronous run in which at most f ≤ t-3 processes crash such that no correct process decides before round f+2 in that run. We present a new uniform consensus algorithm that globally decides in f+2 rounds in every synchronous run in which at most f processes crash. Thus the local and the global decision tight bounds are the same for synchronous runs of the eventually synchronous model.KeywordsLocal DecisionCorrect ProcessTight BoundRound NumberInformation Processing LetterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.