Capacity of Agreement with Finite Link Capacity

In this paper, we consider the problem of maximizing the throughput of Byzantine agreement, when communication links have finite capacity. Byzantine agreement is a classical problem in distributed computing, with initial solutions presented in the seminal work of Pease, Shostak and Lamport. In existing literature, the communication links are implicitly assumed to have infinite capacity. The problem changes significantly when the capacity of links is finite. The notion of throughput here is similar to that used in the networking/communications literature on unicast or multicast traffic. We identify necessary conditions of achievable agreement throughputs. We propose an algorithm structure for achieving agreement capacity in general networks. We also introduce capacity achieving algorithms for two classes of networks: (i) symmetric networks with n ≥ 4 nodes and up to t < n/3 failures; (ii) arbitrary four-node networks with at most 1 failure.