Iterative Approximate Byzantine Consensus under a Generalized Fault Model

In this work, we consider a generalized fault model that can be used to represent awide range of failure scenarios, including correlated failures and non-uniform node reliabilities. This fault model is general in the sense that fault models studied in prior relatedwork, such as f -total and f -local models, are special cases of the generalized fault model. Under the generalized fault model, we explore iterative approximate Byzantine consensus (IABC) algorithms in arbitrary directed networks. We prove a necessary and sufficient condition for the existence of IABC algorithms. The use of the generalized fault model helps to gain a better understanding of IABC algorithms. ∗This research is supported in part by National Science Foundation award CNS 1059540 and Army Research Office grant W-911-NF-0710287. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the funding agencies or the U.S. government.