Vector clock causality comparison

Two replicas each tag a write with a vector clock: a map from node id to a non-negative integer counter. Given two vector clocks a and b (as dicts; a missing node means 0), determine their causal relationship. Return 'before' if a happens-before b (a <= b componentwise and a != b), 'after' if b happens-before a, 'equal' if they are identical, and 'concurrent' otherwise. This is the comparison a Dynamo-style store uses to decide whether one version dominates another or whether the two versions conflict.