Agreement is harder than consensus: set consensus problems in totally asynchronous systems
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Unreliable failure detectors for reliable distributed systems
Journal of the ACM (JACM)
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
Unifying synchronous and asynchronous message-passing models
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Structured derivations of consensus algorithms for failure detectors
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
The topological structure of asynchronous computability
Journal of the ACM (JACM)
k-set agreement with limited accuracy failure detectors
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
SIAM Journal on Computing
Tight bounds for k-set agreement
Journal of the ACM (JACM)
A New Synchronous Lower Bound for Set Agreement
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Condition-Based Protocols for Set Agreement Problems
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
Wait-Free n-Set Consensus When Inputs Are Restricted
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
Mathematical Structures in Computer Science
Irreducibility and additivity of set agreement-oriented failure detector classes
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Failure detectors are schedulers
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
The Iterated Restricted Immediate Snapshot Model
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
From adaptive renaming to set agreement
Theoretical Computer Science
Brief announcement: weakest failure detectors via an egg-laying simulation
Proceedings of the 28th ACM symposium on Principles of distributed computing
Narrowing power vs efficiency in synchronous set agreement: Relationship, algorithms and lower bound
Theoretical Computer Science
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
From renaming to set agreement
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Narrowing power vs. efficiency in synchronous set agreement
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
(anti-Ωx × Σz)-based k-set agreement algorithms
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
In search of the holy grail: looking for the weakest failure detector for wait-free set agreement
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Simulations and reductions for colorless tasks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Weakening failure detectors for k-set agreement via the partition approach
DISC'07 Proceedings of the 21st international conference on Distributed Computing
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In a system with limited-scope failure detectors, there are q disjoint clusters of processes such that some correct process in each cluster is never suspected by any process in that cluster. The failure detector class Sx,q satisfies this property all the time, while ♦Sx,q satisfies it eventually. This paper gives the first tight bounds for the k-set agreement task in asynchronous message-passing models augmented with failure detectors from either the Sx,q or ♦Sx,q classes. For Sx,q, we show that any k-set agreement protocol that tolerates f failures must satisfy f k+x-q if q k and f x otherwise, where x is the combined size of the q disjoint clusters if q k (or the k largest, otherwise). This result establishes for the first time that the protocol of Mostéfaoui and Raynal for the Sx = Sx,1 failure detector is optimal.For ♦Sx,q, we show that any k-set agreement protocol that tolerates f failures must satisfy f n+1/2, k+x-q) if q and f n+1/2,x) otherwise, where n + 1 is the total number of processes. We give a novel protocol that matches our lower bound, disproving a conjecture of Mostéfaoui and Raynal for the ♦Sx = ♦Sx,1 failure detector.Our lower bounds exploit techniques borrowed from Combinatorial Topology, demonstrating for the first time that this approach is applicable to models that encompass failure detectors.