Reaching approximate agreement in the presence of faults
Journal of the ACM (JACM)
Asymptotically optimal algorithms for approximate agreement
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Easy impossibility proofs for distributed consensus problems
Proceedings of the fourth annual ACM symposium on Principles of distributed computing
Distributed Algorithms
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
Algorithms
Consensus in networked multi-agent systems with adversaries
Proceedings of the 14th international conference on Hybrid systems: computation and control
Consensus of multi-agent networks in the presence of adversaries using only local information
Proceedings of the 1st international conference on High Confidence Networked Systems
Low complexity resilient consensus in networked multi-agent systems with adversaries
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Brief announcement: reaching approximate byzantine consensus in partially-connected mobile networks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Resilient synchronization in robust networked multi-agent systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
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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 ε 0, after a sufficiently large number of iterations, the states of the fault-free nodes are guaranteed to be within ε 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 can also be extended to asynchronous systems.