On the minimal synchronism needed for distributed consensus
Journal of the ACM (JACM)
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The asynchronous computability theorem for t-resilient tasks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Failure detectors and the wait-free hierarchy (extended abstract)
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
Unreliable failure detectors for reliable distributed systems
Journal of the ACM (JACM)
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
SIAM Journal on Computing
Distributed Algorithms
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Uniform consensus is harder than consensus
Journal of Algorithms
Weak Synchrony Models and Failure Detectors for Message Passing (k-)Set Agreement
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Tight failure detection bounds on atomic object implementations
Journal of the ACM (JACM)
Brief announcement: new bounds for partially synchronous set agreement
DISC'10 Proceedings of the 24th international conference on Distributed computing
(anti-Ωx × Σz)-based k-set agreement algorithms
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
A non-topological proof for the impossibility of k-set agreement
Theoretical Computer Science
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Despite of being quite similar (agreement) problems, 1-set agreement (consensus) and general k-set agreement require surprisingly different techniques for proving the impossibility in asynchronous systems with crash failures: Rather than the relatively simple bivalence arguments as in the impossibility proof for consensus in the presence of a single crash failure, known proofs for the impossibility of k-set agreement in shared memory systems with f≥k1 crash failures use algebraic topology or a variant of Sperner's Lemma. In this paper, we present a generic theorem for proving the impossibility of k-set agreement in various message passing settings, which is based on a reduction to the consensus impossibility in a certain subsystem resulting from a partitioning argument. We demonstrate the broad applicability of our result by exploring the possibility/impossibility border of k-set agreement in several message-passing system models: (i) asynchronous systems with crash failures, (ii) partially synchronous processes with (initial) crash failures, and, most importantly, (iii) asynchronous systems augmented with failure detectors. In (i), (ii), and (iii), the impossibility part is an instantiation of our main theorem, whereas the possibility of achieving k-set agreement in (ii) follows by generalizing the consensus algorithm for initial crashes by Fisher, Lynch and Patterson. In (iii), applying our technique reveals the exact border for the parameter k where k-set agreement is solvable with the failure detector class ($#931;k ,Ωk )1≤k≤n−1 of Bonnet and Raynal. As $#931;k was shown to be necessary for solving k-set agreement, this result yields new insights on the quest for the weakest failure detector.