Fast genuine generalized consensus

Consensus (agreeing on a sequence of commands) is central to the operation and performance of distributed systems. A well-known solution to consensus is Fast Paxos. In a recent paper, Lamport enhances Fast Paxos by leveraging the commutativity of concurrent commands. The new primitive, called Generalized Paxos, reduces the collision rate, and thus the latency of Fast Paxos. However if a collision occurs, Generalized Paxos needs four communication steps to recover, which is slower than Fast Paxos. This paper presents FGGC, a novel consensus algorithm that reduces recovery delay when a collision occurs to one. FGGC tolerates f < n/2 replicas crashes, and during failure-free runs, processes learn commands in two steps if all commands commute, and three steps otherwise; this is optimal. Moreover, as long as no fault occurs, FGGC needs only f + 1 replicas to progress.