Relaxed Paxos: Quorum Intersection Revisited (Again)

TL;DR

This paper revisits quorum intersection in Paxos, showing it can be weakened further by leveraging previous round information, and introduces a new abstraction using write-once registers for better reasoning about consensus protocols.

Contribution

It demonstrates that quorum intersection requirements in Paxos can be relaxed further than previously thought, based on previous round knowledge, and proposes a new abstraction for reasoning about Paxos.

Findings

Quorum intersection can be safely weakened further in Paxos.

Learning previous proposals removes the need for certain quorum intersections.

Introduces a novel abstraction using write-once registers for Paxos reasoning.

Abstract

Distributed consensus, the ability to reach agreement in the face of failures, is a fundamental primitive for constructing reliable distributed systems. The Paxos algorithm is synonymous with consensus and widely utilized in production. Paxos uses two phases: phase one and phase two, each requiring a quorum of acceptors, to reach consensus during a round of the protocol. Traditionally, Paxos requires that all quorums, regardless of phase or round, intersect and majorities are often used for this purpose. Flexible Paxos proved that it is only necessary for phase one quorum of a given round to intersect with the phase two quorums of all previous rounds. In this paper, we re-examine how Paxos approaches the problem of consensus. We look again at quorum intersection in Flexible Paxos and observe that quorum intersection can be safely weakened further. Most notably, we observe that if a proposer learns that a value was proposed in some previous round then its phase one no longer needs to intersect with the phase two quorums from that round or from any previous rounds. Furthermore, in order to provide an intuitive explanation of our results, we propose a novel abstraction for reasoning about Paxos which utilizes write-once registers.