Fault tolerance in networks of bounded degree
SIAM Journal on Computing
Tolerating linear number of faults in networks of bounded degree
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Modular construction of a Byzantine agreement protocol with optimal message bit complexity
Information and Computation
Bit optimal distributed consensus
Computer science
Bounds on information exchange for Byzantine agreement
Journal of the ACM (JACM)
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
Asymptotically Optimal Distributed Consensus (Extended Abstract)
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Polynomial algorithms for multiple processor agreement
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Computational Aspects of VLSI
The round complexity of verifiable secret sharing and secure multicast
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Secure message transmission by public discussion: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Public discussion must be back and forth in secure message transmission
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
Towards robust and efficient computation in dynamic peer-to-peer networks
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Secure message transmission with small public discussion
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Fast byzantine agreement in dynamic networks
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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The Distributed Consensus problem involves n processors each of which holds an initial binary value. At most t of the processors may be faulty and ignore any protocol (even behaving maliciously), yet it is required that the non-faulty processors eventually agree on a value that was initially held by one of them. In this paper we focus on consensus in networks whose degree is bounded, following the work of Dwork, Peleg, Pippenger and Upfal [8]. In such a context, complete consensus among all the correct processors is not possible and some exceptions must be allowed. We first show how to achieve consensus in the butterfly network using O(t + log n loglog n) one-bit parallel transmission steps, while tolerating the asymptotically optimal number of faulty processors (O(n/log n)) and having the asymptotically minimal number of exceptions (O(t log t)). This result considerably improves on the running time of existing butterfly consensus protocols [2, 8]. In particular, it replaces the running time of O(n log n loglog n) of [2] with an asymptotically optimal one. As in [8], we can then decrease the number of exceptions to O(t) by using additional links, while maintaining the same running time. The protocol is derived from a consensus protocol for completely connected networks that is interesting in its own right: it achieves Distributed Consensus with optimal number of processors, asymptotically optimal total bit transfer and nearly optimal number of rounds.