Consensus is one of the key problems in fault-tolerant distributed computing. Although the solvability of consensus is now a well-understood problem, comparing different algorithms in terms of efficiency is still an open problem. In this paper, we address this question for round-based consensus algorithms using communication predicates, on top of a partial synchronous system that alternates between good and bad periods (synchronous and nonsynchronous periods). Communication predicates together with the detailed timing information of the underlying partially synchronous system provide a convenient and powerful framework for comparing different consensus algorithms and their implementations. This approach allows us to quantify the required length of a good period to solve a given number of consensus instances. With our results, we can observe several interesting issues, such as the number of rounds of an algorithm is not necessarily a good metric for its performance.

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.

Most papers addressing consensus in wireless ad hoc networks adopt system models similar to those developed for wired networks. These models are focused towards node failures while ignoring link failures, and thus are poorly suited for wireless ad hoc networks. The recently proposed HO model does not have this drawback. The paper shows that an existing algorithm and the HO model can be used for multi-hop wireless ad hoc networks, if extended with an adequate communication layer. The description of the communication layer is augmented with simulation results that validate the feasibility of our approach and provide better understanding of the behavior of wireless environments.