Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
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)
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
k-Arbiter: a safe and general scheme for h-out of-k mutual exclusion
Theoretical Computer Science
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)
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Using Failure Detectors to Solve Consensus in Asynchronous Sharde-Memory Systems (Extended Abstract)
WDAG '94 Proceedings of the 8th International Workshop on Distributed Algorithms
The weakest failure detectors to solve certain fundamental problems in distributed computing
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Tight bounds for k-set agreement with limited-scope failure detectors
Distributed Computing - Special issue: DISC 03
PRDC '06 Proceedings of the 12th Pacific Rim International Symposium on Dependable Computing
Anti-Ω: the weakest failure detector for set agreement
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Sharing is harder than agreeing
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
The Weakest Failure Detector for Message Passing Set-Agreement
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
The weakest failure detector for solving k-set agreement
Proceedings of the 28th ACM symposium on Principles of distributed computing
The disagreement power of an adversary: extended abstract
Proceedings of the 28th ACM symposium on Principles of distributed computing
Brief announcement: weakest failure detectors via an egg-laying simulation
Proceedings of the 28th ACM symposium on Principles of distributed computing
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
Simultaneous consensus tasks: a tighter characterization of set-consensus
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Weakening failure detectors for k-set agreement via the partition approach
DISC'07 Proceedings of the 21st international conference on Distributed Computing
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
Anonymous asynchronous systems: the case of failure detectors
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
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In the k -set agreement problem, each process (in a set of n processes) proposes a value and has to decide a proposed value in such a way that at most k different values are decided. While this problem can easily be solved in asynchronous systems prone to t process crashes when k t , it cannot be solved when k ≤ t . Since several years, the failure detector-based approach has been investigated to circumvent this impossibility. While the weakest failure detector class to solve the k -set agreement problem in read/write shared-memory systems has recently been discovered (PODC 2009), the situation is different in message-passing systems where the weakest failure detector classes are known only for the extreme cases k = 1 (consensus) and k = n *** 1 (set agreement). This paper introduces a candidate for the general case. It presents a new failure detector class, denoted ${\it \Pi}_k$, and shows ${\it \Pi}_1={\it \Sigma}\times {\it \Omega}$ (the weakest class for k = 1), and ${\it \Pi}_{n-1}={\cal L}$ (the weakest class for k = n *** 1). Then, the paper investigates the structure of ${\it \Pi}_k$ and shows it is the combination of two failures detector classes denoted ${\it \Sigma}_k$ and ${\it \Omega}_k$ (that generalize the previous "quorums" and "eventual leaders" failure detectors classes). Finally, the paper proves that ${\it \Sigma}_k$ is a necessary requirement (as far as information on failure is concerned) to solve the k -set agreement problem in message-passing systems. The paper presents also a ${\it \Pi}_{n-1}$-based algorithm that solves the (n *** 1)-set agreement problem. This algorithm provides us with a new algorithmic insight on the way the (n *** 1)-set agreeement problem can be solved in asynchronous message-passing systems (insight from the point of view of the non-partitioning constraint defined by ${\it \Sigma}_{n-1}$).