The cluster-sending problem is the problem of sending a message between two clusters of potentially-unreliable replicas (e.g., clusters managed via a Byzantine fault-tolerant consensus protocol). Recently, it has been shown that the cluster-sending problem is a distinct problem than consensus that can be solved with lower worst-case complexity. For example, in the setting of two clusters with n replicas each of which at-most f, 2f < n are faulty, one can perform cluster sending in O(n) messages.
Using probabilistic techniques one can do significantly better, however: a probabilistic approach can perform cluster-sending under the same circumstances with an expected-case of only four communication phases.