Consensus in the presence of partial synchrony
Journal of the ACM (JACM)
On the minimum size of tight hypergraphs
Journal of Graph Theory
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Asynchronous consensus and broadcast protocols
Journal of the ACM (JACM)
Secure hypergraphs: privacy from partial broadcast
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
From partial consistency to global broadcast
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
About the upper chromatic number of a co-hypergraph
Discrete Mathematics
A Continuum of Failure Models for Distributed Computing
WDAG '92 Proceedings of the 6th International Workshop on Distributed Algorithms
Efficient Byzantine Agreement Secure Against General Adversaries
DISC '98 Proceedings of the 12th International Symposium on Distributed Computing
A proof of alon's second eigenvalue conjecture
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An asynchronous [(n - 1)/3]-resilient consensus protocol
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
Distributed consensus in the presence of sectional faults
Proceedings of the twenty-second annual symposium on Principles of distributed computing
BAR fault tolerance for cooperative services
Proceedings of the twentieth ACM symposium on Operating systems principles
Zyzzyva: speculative byzantine fault tolerance
Proceedings of twenty-first ACM SIGOPS symposium on Operating systems principles
PeerReview: practical accountability for distributed systems
Proceedings of twenty-first ACM SIGOPS symposium on Operating systems principles
Attested append-only memory: making adversaries stick to their word
Proceedings of twenty-first ACM SIGOPS symposium on Operating systems principles
HQ replication: a hybrid quorum protocol for byzantine fault tolerance
OSDI '06 Proceedings of the 7th symposium on Operating systems design and implementation
Journal of Graph Theory
Making Byzantine fault tolerant systems tolerate Byzantine faults
NSDI'09 Proceedings of the 6th USENIX symposium on Networked systems design and implementation
Smallest Set-Transversals of k-Partitions
Graphs and Combinatorics
Fast asynchronous consensus with optimal resilience
DISC'10 Proceedings of the 24th international conference on Distributed computing
CheapBFT: resource-efficient byzantine fault tolerance
Proceedings of the 7th ACM european conference on Computer Systems
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In the Byzantine agreement problem, a set of n processors, any f of whom may be arbitrarily faulty, must reach agreement on a value proposed by one of the correct processors. It is a celebrated result that unless n 3f, Byzantine agreement is impossible in a variety of computation and communication models. This is due to the fact that faulty processors can equivocate, that is, say different things to different processors. If this ability is mitigated, for example by assuming a global broadcast channel, then n 2f is sufficient. With very few exceptions, the literature on Byzantine agreement has been confined to the n 2f and n 3f paradigms. We bridge the gap between these two paradigms by assuming partial broadcast channels among sets of three processors, observing that equivocation is fundamentally an act involving three parties: a faulty processor that lies (inconsistently) to two correct processors. We characterize the conditions under which Byzantine agreement is possible for all n = 2f + h, h an integer in [1..f], by giving asymptotically tight bounds on the number of necessary and sufficient partial broadcast channels. We prove these bounds by a reduction to a problem in extremal combinatorics, which itself is a natural generalization of a well-studied hypergraph coloring problem. Algorithmically, we show that deciding whether a given set of broadcast channels enables Byzantine agreement is co-NP-complete. Although partial broadcast channels have been studied in prior work, the bounds obtained on the number of required channels were sub-optimal by up to a factor of Θ(n2). Moreover, this work has been confined to the synchronous model. In contrast, we apply our results to several distinct models and provide stronger motivation for using partial broadcast channels in practice, drawing from recent work in the systems community.