Iterative approximate byzantine consensus in arbitrary directed graphs

This paper proves a necessary and sufficient condition for the existence of iterative algorithms that achieve approximate Byzantine consensus in arbitrary directed graphs, where each directed edge represents a communication channel between a pair of nodes. The class of iterative algorithms considered in this paper ensures that, after each iteration of the algorithm, the state of each fault-free node remains in the convex hull of the states of the fault-free nodes at the end of the previous iteration. The following convergence requirement is imposed: for any > 0, after a sufficiently large number of iterations, the states of the fault-free nodes are guaranteed to be within of each other. To the best of our knowledge, tight necessary and sufficient conditions for the existence of such iterative consensus algorithms in synchronous arbitrary point-to-point networks in presence of Byzantine faults have not been developed previously. The methodology and results presented in this paper ca...

• Type: Journal
• Year: 2012
• Where: PODC
• Authors: Nitin H. Vaidya, Lewis Tseng, Guanfeng Liang
• Keywords: Consensus Algorithms, Distributed And Parallel Computing, National Science Foundation Award, PODC 2012, Science Foundation Award