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CHAPTER 3. KNOWN REVISIONS 73 and need not be exposed externally as values can be re-assigned consequence (virtual) indexes. Batching is used extensively in consensus, examples include Chubby [CGR07], Mencius [MJM08], VRR [LC12, §6.2] and Raft [OO14]. This abstraction means that a sequence of length zero is a nil value which can be decided. We see no-ops like this utilised in various algorithms such as Simple Paxos [Lam01a, §3] and Mencius [MJM08]. Fast Paxos Fast Paxos [Lam05a] is a variant of Classic Paxos whereby for a subset of epochs, if an acceptor receives no proposals within its phase one (and thus could propose its own value) then it can notify all other acceptors and any acceptor can propose their own value in phase two directly, without executing phase one again. The literature refers to these epochs as fast and all other epochs as classic. In addition to requiring that all quorums intersect, to preserve safety, Fast Paxos requires that any two fast and a classic quorum must intersect. Fast Paxos uses counting quorum of size kf for fast epochs and kc for classic epochs such that16 : na < 2kc 2na <2kf +kc 3.13 Summary Classic Paxos has been the subject of extensive study and this chapter only begins to discuss the wide range of consensus algorithms within the Classic Paxos family. All algorithms in this family share three key characteristics: epochs, two phases and majority (or intersecting quorum) agreement. Over the next three chapters, we will revise each of these aspects, beginning with quorum intersection. 16These expressions are re-arranged from §3.4.1 of [Lam05a]PDF Image | Distributed consensus
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