Iterative Approximate Consensus in the Presence of Byzantine Link Failures

Abstract

AbstractThis 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].KeywordsIterative AlgorithmMalicious NodeLink FailureNode FailureOutgoing EdgeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.