On Exponential Lower Bound for Protocols for Reliable Communication in Networks

This work deals with the problem of fault-tolerant communication over networks, some of whose nodes are corrupted by a centralized byzantine adversary. The extant literature’s perspective of the problem of reliable communication, especially in networks whose topology is known, is that of a simple problem to which even some naive solutions (like message-flooding etc.) turn out to be reasonably efficient. In this paper, we give an example of a directed graph and a non threshold adversary structure, which will require every protocol for perfect reliable unicast to transmit exponential number of bits in order to reliably transmit a single bit.