Easy impossibility proofs for distributed consensus problems
Distributed Computing
Distributed agreement in the presence of processor and communication faults
IEEE Transactions on Software Engineering
Fault tolerance in networks of bounded degree
SIAM Journal on Computing
Broadcasting in a hypercube when some calls fail
Information Processing Letters
Atomic broadcast: from simple message diffusion to Byzantine agreement
Information and Computation
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Agreement in the presence of faults, on networks of bounded degree
Information Processing Letters
Fully Polynomial Byzantine Agreement for Processors in Rounds
SIAM Journal on Computing
A tight lower bound for randomized synchronous consensus
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Broadcasting with linearly bounded transmission faults
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
Broadcasting in hypercubes and star graphs with dynamic faults
Information Processing Letters
Optimal broadcasting in hypercubes with dynamic faults
Information Processing Letters
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Layered Analysis of Consensus
SIAM Journal on Computing
Distributed Function Evaluation in the Presence of Transmission Faults
SIGAL '90 Proceedings of the International Symposium on Algorithms
STACS '89 Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science
Computing Input Multiplicity in Anonymous Synchronous Networks with Dynamic Faults
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Polynomial algorithms for multiple processor agreement
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Formally Verified Byzantine Agreement in Presence of Link Faults
ICDCS '02 Proceedings of the 22 nd International Conference on Distributed Computing Systems (ICDCS'02)
Robust Emulations of Shared Memory in a Crash-Recovery Model
ICDCS '04 Proceedings of the 24th International Conference on Distributed Computing Systems (ICDCS'04)
Failure detection and consensus in the crash-recovery model
Distributed Computing
On the probabilistic omission adversary
SSS'07 Proceedings of the 9h international conference on Stabilization, safety, and security of distributed systems
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In this paper we are interested in synchronous distributed systems subject to transient and ubiquitous failures. This includes systems where failures will occur on any communication link, systems where every processor will fail at one time or another, etc., and, following a failure, normal functioning can resume after a finite (although unpredictable) amount of time. Notice that these cases cannot be handled by the traditional component failure models. The model we use is the transmission failure model, known also as the dynamic faults model. Using this model, we study the fundamental problem of agreement in synchronous systems of arbitrary topology.We establish bounds on the number of dynamic faults that make any non-trivial form of agreement (even strong majority) impossible; in turn, these bounds express connectivity requirements which must be met to achieve any meaningful form of agreement. We also provide, constructively, bounds on the number of dynamic faults in spite of which any non-trivial form of agreement (even unanimity) is possible. These bounds are shown to be tight for a large class of networks, that includes hypercubes, toruses, rings, and complete graphs; incidentally, we close the existing gap between possibility and impossibility of non-trivial agreement in complete graphs in presence of dynamic Byzantine faults. None of these results is derivable in the component failure models; in particular, all our possibility results hold in situations for which those models indicate impossibility.