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
Early stopping in Byzantine agreement
Journal of the ACM (JACM)
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Fully Polynomial Byzantine Agreement for Processors in Rounds
SIAM Journal on Computing
Muteness detectors for consensus with Byzantine processes
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Distributed Algorithms
Convex Optimization
Algorithms for center and Tverberg points
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Solving Vector Consensus with a Wormhole
IEEE Transactions on Parallel and Distributed Systems
Approximate centerpoints with proofs
Computational Geometry: Theory and Applications
Optimal resilience asynchronous approximate agreement
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Approximating Tverberg points in linear time for any fixed dimension
Proceedings of the twenty-eighth annual symposium on Computational geometry
Multidimensional approximate agreement in Byzantine asynchronous systems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Consider a network of n processes, each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system; thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). We prove that in a synchronous system, n≥ max(3f+1, (d+1)f+1) is necessary and sufficient for achieving Byzantine vector consensus. In an asynchronous system, it is known that exact consensus is impossible in presence of faulty processes. For an asynchronous system, we prove that n≥ (d+2)f+1 is necessary and sufficient to achieve approximate Byzantine vector consensus. Our sufficiency proofs are constructive. We prove sufficiency by providing explicit algorithms that solve exact BVC in synchronous systems, and approximate BVC in asynchronous systems.