Paxos is a protocol where, during phase-1, a Proposer must generate an integer value n as the rnd number. However, this definition can be expanded beyond integers. By using any value from a partially ordered set, the essential ordering property of rnd in Paxos is still preserved, which is critical for the protocol's correctness.
In a generalized Paxos, the rnd can employ a partial order, allowing for a choice between mandatory conflict exclusion, akin to the Two-Phase Commit Protocol (2PC), and non-mandatory conflict exclusion, reminiscent of the potential for livelock in Paxos, to uphold the safety of the consensus process.
Consider the divisibility as a partial ordering criterion in Paxos, where rnd is a positive integer, and the order is determined by divisibility: if a divides b, then a is less than b. For example, we have 1 < 2 < 6, and 1 < 3 < 6, but 2 is not comparable to 3. In a scenario where Proposer P2 has finished phase-1, P3 cannot proceed because 3 ≯ 2 on Acceptor A2. Therefore, P3 quits and P6 can initiate phase-1 and proceed to phase-2, ultimately commit a value.
In practical applications, the concept of a partial order rnd greatly expands the possibilities for consistency algorithms like Paxos by introducing multi-dimensional ordering, which can be thought of as an analogy to multi-dimensional time.
For instance, in a distributed storage system, one could establish two separate rnd groups:
- One group of Proposers might use powers of 2 for
rnd, targeting transaction A; - The other group may use powers of 3 for
rnd, targeting transaction B.
These two groups operate independently, ensuring that only one transaction can be committed at a time, thus avoiding Paxos’s livelock issues. Additionally, multiple Proposers within the same group can provide redundancy and high availability, without the single point of failure risk inherent in 2PC's Coordinator.
In conclusion, partial order Paxos cleverly combines the transaction exclusivity of 2PC with the robustness of Paxos. This fusion simplifies the complex two-layer framework found in distributed databases, such as Spanner, into a more streamlined single-layer architecture.