Swift Algorithms for Repeated Consensus

We introduce the notion of a swift algorithm. Informally, an algorithm that solves the repeated consensus is swift if, in a partial synchronous run of this algorithm, eventually no timeout expires, i.e., the algorithm execution proceeds with the actual speed of the system. This definition differs from other efficiency criteria for partial synchronous systems. Furthermore, we show that the notion of swiftness explains why failure detector based algorithms are typically more efficient than round-based algorithms, since the former are naturally swift while the latter are naturally non-swift. We show that this is not an inherent difference between the models, and provide a round implementation that is swift, therefore performing similarly to failure detector algorithms while maintaining the advantages of the round model.