In this work, we consider a generalized fault model that can be used to
represent a wide 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 related work, 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.Comment: arXiv admin note: text overlap with arXiv:1203.188