Optimal early stopping uniform consensus in synchronous systems with process omission failures

• Authors: Philippe Raïpin Parvédy;Michel Raynal
• Venue: Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
• Year: 2004

Consensus is a central problem of fault-tolerant distributed computing that, in the context of synchronous distributed systems, has received a lot of attention in the crash failure model and in the Byzantine failure model. This paper considers synchronous distributed systems made up of n processes, where up to t can commit failures by crashing or omitting to send or receive messages when they should ("process omission" failure model). It presents a protocol solving uniform consensus in such a context. This protocol has several noteworthy features. First, it is particularly simple. Then, it is optimal both in (1) the number of communication steps needed for processes to decide and stop, namely, min(f+2,t+1) where f is the actual number of faulty processes, and (2) the number of processes that can be faulty, namely tn/2. Moreover, (3) it ensures that no process (be it correct or faulty) executes more than min(f+2,t+1) rounds, thereby extending the decision lower bound to the full completion time. The design of a uniform consensus protocol with such optimality requirements was an open problem. Interestingly, as min(f+2,t+1) is a lower bound to solve uniform consensus in the synchronous crash failure model, the proposed protocol shows that uniform consensus is not "harder'' in the omission failure model than in the crash failure model. The protocol is also message size efficient as, in addition to values, a message has to piggyback only n bits of control information.