Early stopping in Byzantine agreement
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
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
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
On the Impact of Fast Failure Detectors on Real-Time Fault-Tolerant Systems
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
Conditions on input vectors for consensus solvability in asynchronous distributed systems
Journal of the ACM (JACM)
Mathematical Structures in Computer Science
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The combined power of conditions and failure detectors to solve asynchronous set agreement
Proceedings of the twenty-fourth 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
From adaptive renaming to set agreement
Theoretical Computer Science
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The k-set agreement problem is a generalization of the uniform consensus problem: each process proposes a value, and each non-faulty process has to decide a value such that a decided value is a proposed value, and at most k different values are decided. It has been shown that any algorithm that solves the k-set agreement problem in synchronous systems that can suffer up to t crash failures requires ⌊t/k⌋ + 1 rounds in the worst case. It has also been shown that it is possible to design early deciding algorithms where no process decides and halts after min (⌊f/k⌋ + 2, ⌊t/k⌋ + 1) rounds, where f is the number of actual crashes in a run (0 ≤ f ≤ t). This paper explores a new direction to solve the k-set agreement problem in a synchronous system. It considers that the system is enriched with base objects (denoted [m, l]-SA objects) that allow solving the l-set agreement problem in a set of mprocesses (m n). The paper has several contributions. It first proposes a synchronous k-set agreement algorithm that benefits from such underlying base objects. This algorithm requires O(tl/mk ) rounds, more precisely, Rt = ⌊t/Δ⌋ + 1 rounds, where Δ = m⌊k/l⌋ + (k mod l). The paper then shows that this bound, that involves all the parameters that characterize both the problem (k) and its environment (t, m and l), is a lower bound. The proof of this lower bound sheds additional light on the deep connection between synchronous efficiency and asynchronous computability. Finally, the paper extends its investigation to the early deciding case. It presents a k-set agreement algorithm that directs the processes to decide and stop by round Rf = min ⌊f/Δ⌋ + 2, ⌊t/Δ⌋ + 1). These bounds generalize the bounds previously established for solving the k-set problem in pure synchronous systems.