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142 8.2. SUMMARY OF CONTRIBUTIONS In practice, when reaching agreement over a sequence with Paxos, the Multi-Paxos opti- misation is used almost exclusively. So much so that the terms Paxos and Multi-Paxos are often used interchangeably. The academic literature has proposed agreeing upon a sequence without Multi-Paxos, for example using Fast Paxos, however, such proposals have seen little practical application. Multi-Paxos allows agreements to be reached in one round trip to the majority of acceptors, ignoring the possible extra round trip to the leader and back. Whats more, the leader in Multi-Paxos acts a point of serialisation, preventing duelling between proposers, however, synchrony is needed to reliably detect and replace failed leaders. The primary limitation of centralised approaches such as Multi-Paxos is that the leader is the performance bottleneck. 8.2 Summary of contributions This thesis proves that Paxos is conservative in its approach by weakening the requirements for quorum intersection, phase completion, value selection and epoch allocation. After outlining the widely known Classic Paxos algorithm in chapter 2, we begin with our systemisation of knowledge study (chapter 3) which surveyed the key refinements to the Classic Paxos algorithm. In chapter 4, we revised the Paxos’s quorum intersection from: ∀Q,Q′ ∈Q:Q∩Q′ ̸=∅ to the following, for each epoch e: ∀ Q ∈ Q e1 , ∀ f ∈ E : f < e = ⇒ ∀ Q ′ ∈ Q f2 : Q ∩ Q ′ ̸ = ∅ In other words, we have shown that it is not necessary to require that phase one quorums intersect, nor that phase two quorums intersect nor that the phase one quorum intersects with phase two quorums of subsequent epochs. In chapter 5, we proved that if a proposer received a promise with the proposal (e,v) then this is sufficient to satisfy the quorum intersection requirements for epochs up to e (inclusive). In chapter 6, we demonstrated that Paxos’s value selection rule of proposing the value associated with the greatest epoch is a conservative approximation of quorum based value selection. If more promises are received than is necessary to satisfy quorum intersection then tracking quorums can allow a proposer to propose their candidate values, instead of being required to propose a previous value.PDF Image | Distributed consensus
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