Distributed consensus

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Distributed consensus ( distributed-consensus )

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CHAPTER 5. PROMISES REVISED 93 Algorithm 15: Proposer algorithm for Paxos revision C. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 v,emax←nil QP,QA←∅ e ← min(E ) E←E\{e} /* Start Phase 1 for epoch e */ send prepare( e) to acceptors while ∃z∈E,∃Q∈Qz2 :(emax =nil∨emax emax) then emax ← f, v ← w case timeout goto line 1 if v=nilthen v←γ /* Start Phase 2 for proposal (e,v) */ send propose( e,v) to acceptors while∀Q∈Qe2 :QA ̸⊇Qdo switch do case accept( e) received from acceptor a QA ← QA ∪ {a} case timeout goto line 1 return v Lemma 18 (Weakened quorum intersection for Paxos revision C). If a value v is decided in epoch e then in all subsequent epochs either: • at least one acceptor which accepted proposal (e,v) will promise, or • an acceptor will promise with the proposal (e,v) or a proposal from a subsequent epoch. Proof of lemma 18. Assume the value v is decided in epoch e, thus some phase two quorum of acceptors Q ∈ Qe2 would have accepted the proposal (e, v). Consider a proposal in epoch f where f > e. Before a value could be proposed in f, a phase one quorum of acceptors for proposal in epoch f must promise to the proposer of f (Property 15).

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