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Chapter 4 Quorum intersection revised In this chapter, we prove that the usual description of Classic Paxos (as given in Chapter 2) is more conservative than is necessary. More specifically, we will demonstrate that the quorum intersection requirement for Classic Paxos, which requires all quorums to intersect (formally stated by eq. 3.1 in §3.11), can be substantially weakened. This result has wide- ranging implications, which will be explored throughout this thesis. In particular, we will demonstrate that it provides much greater flexibility in how we reach distributed consensus. This chapter progressively refines the quorum intersection requirements in two distinct stages: revision A (§4.1) & revision B (§4.2). We begin with the Classic Paxos generalisation to quorums (§3.11). Each stage generalises over the previous revision by further weakening the quorum intersection requirements. 4.1 Quorum intersection across phases We begin by differentiating between the quorums used by phase one of Classic Paxos, which we will refer to as Q1 and the quorums for phase two, referred to as Q2. We could use different quorum sets of each of the two phases of Classic Paxos. As before, we begin by revising our definition of decided: Definition 9. A proposal (e,v) is decided if the proposal (e,v) has been accepted by a phase two quorum of acceptors. Since Classic Paxos requires that all quorums intersect, regardless of the phase of the algorithm, the quorum sets Q1, Q2 must satisfy all the following three intersection require- ments: ∀Q,Q′ ∈Q1 :Q∩Q′ ̸=∅ ∀Q,Q′ ∈Q2 :Q∩Q′ ̸=∅ ∀Q1 ∈Q1,∀Q2 ∈Q2 :Q1 ∩Q2 ̸=∅ (4.1) (4.2) (4.3) 75PDF Image | Distributed consensus
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