Iterative Approximate Byzantine Consensus in Arbitrary Directed Graphs
  In this paper, we explore the problem of iterative approximate Byzantine consensus in arbitrary directed graphs. In particular, we prove a necessary and sufficient condition for the existence of iterative byzantine consensus algorithms. Additionally, we use our sufficient condition to examine whether such algorithms exist for some specific graphs. 
Nitin Vaidya and Lewis Tseng and Guanfeng Liang
cs.DC