Why multi-paxos is called multi-paxos? I can't see how it is "multi".
Paxos Definition Paxos is a family of protocols for solving the problem of consensus in distributed networks. First submitted in 1989, the Paxos protocol is named after a fictional legislative consensus system on the island of Paxos in Greece.
Multi-Paxos does not assume a unique leader. Instead, it allows multiple leaders to propose requests concurrently without affecting safety. In extreme cases, it degrades to Basic Paxos. The difference between multi-Paxos and Basic Paxos does not lie in multiplicity, because Basic Paxos also supports multiplicity.
The Paxos algorithm was developed by Leslie Lamport, published in his 1998 paper The Part-Time Parliament. Paxos works in three phases to make sure multiple nodes agree on the same value in spite of partial network or node failures.
Paxos can be used to select a leader Notice that a Proposer in Paxos could propose "I am the leader," (or, for example, "Proposer X is the leader"). Because of the agreement and validity guarantees of Paxos, if accepted by a Quorum, then the Proposer is now known to be the leader to all other nodes.
It's about multiple rounds of the algorithm to agree sequential requests from a stable leader with minimal messaging. Initially with no recognised leader you must run at least one round of basic Paxos where a candidate leader sends a prepare request (using the terminology of the paper Paxos Made Simple). Positive responses from a majority confirm it as leader. It then sends accept messages for that round which terminates successfully if you get a majority of accept acknowledgements. Rather than start again with prepare requests it can move immediately to a galloping mode where it sends successive accept messages when it hears a majority of acknowledgments for the previous accept request. This is highly efficient as it needs the minimal number of messages but it only occurs for multiple rounds from a stable leader. This may be interrupted by the leader crashing else a network failure which causes a follower to timeout on an otherwise healthy leader. It will then issue its own prepare request as a leadership challenge which is resolved via basic Paxos rules. As soon as you get a stable leader it can upgrade to multi-Paxos galloping mode.
See also this answer which talks about why it is safe to do this https://stackoverflow.com/a/64759874/329496
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