Iterative approximate consensus in the presence of Byzantine link failures

Abstract

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free. Recent work has addressed the problem of reaching approximate consensus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [12, 21, 23, 24]. This paper addresses approximate consensus in the presence of Byzantine links. We extend our past work [21, 23] that provided exact characterization of graphs in which the iterative approximate consensus problem in the presence of Byzantine node failures is solvable. In particular, we prove a tight necessary and sufficient condition on the underlying communication graph for the existence of iterative approximate consensus algorithms under transient Byzantine link model [15, 16]. © 2014 Springer International Publishing.