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answers:

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Are there any algorithms that are commonly used for achieving eventual consistency in distributed systems?

There are algorithms that have been developed for ACID transactions in distributed systems, Paxos in particular, but is there a similar body of theory that has been developed for BASE scenarios, with weaker consistency guarantees?

Edit: This appears to be an area of academic research that is only beginning to be developed. Mcdowella's answer shows that there has been at least some work in this area.

+1  A: 

BASE and weaker consistency boils down to the convergence of copies in a replication scenario. There is a large literature on replication in distributed system, with eiter eager or lazy replication, with group or master copy, etc.

Consensus is one problem that can be precisely formulated. Several solutions/algorithms can be proposed. Lazy replication with convergence of copies isn't. I feel like it's more an architectural issue. But as I just said, there is a large body of work on replication or distributed storage, which might be what you are looking for.

Here are nevertheless a few links which I found interesting:

ewernli
I'm not sure if I agree that the problem of how to handle lazy replication can't be precisely stated. I expect that a body of theory will arise surrounding what integrity constraints are compatible with this kind of architecture, and which aren't, how to handle colliding updates, etc.
Rob Lachlan
Maybe you are right. Models will probably be proposed in the coming years to reason about elasticity, eventual consistency, etc. Whether they can be called theories will be another question. But I would love to see that!
ewernli
+2  A: 

If "Anti-entropy protocols for repairing replicated data, which operate by comparing replicas and reconciling differences." fits your definition look at http://en.wikipedia.org/wiki/Gossip_protocol

mcdowella
+1. That's pretty good.
Rob Lachlan