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68 3.11. GENERALISATION TO QUORUMS p1 a1 a2 a3 p2 epro:5 eacc :5 vacc :B epro:5 eacc :5 vacc :B epro:5 eacc :5 vacc :B e : 0, E : {2, . . . } prepare(0) no-promise(0,5,5,B) e:5,v:5,E:{6,...},QA :{a1} propose(5,B) accept(5) accept(5) QA :{a1,a2} 3.11 Figure 3.5: Classic Paxos with proposal copying from NACKs (Alg. 4,11) Generalisation to quorums Recall that we assume a finite set of acceptors A = {a1,a2,...,ana}, with |A| = na. Definition 6. A quorum Q is defined as a non-empty subset of acceptors, Q ∈ P(A) \ ∅. Definition 7. A quorum set Q is a non-empty set of quorums, Q ⊆ P(A) \ ∅. Classic Paxos as described thus far uses strict majority quorums. Formally we define the quorum set as follows: Q = {Q ∈ P(A)| |Q| ≥ ⌊na/2⌋ + 1} Classic Paxos cannot make progress without majority participation, thus it is able to handle up to a minority ⌈na/2⌉ − 1 of acceptors failing. This approach tightly couples the total number of acceptors, the number of acceptors needed to participate in consensus and the number of failures tolerated. Ideally, we would like to minimise the number of acceptors in the system and the number required to participate in consensus, as the proposer must wait upon the acceptors to reply and send more messages. Conversely, we would like toPDF Image | Distributed consensus
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