Keywords and Synonyms
Distributed coordination
Problem Definition
Short History
The k-set agreement problem is a paradigm of coordination problems. Defined in the setting of systems made up of processes prone to failures, it is a simple generalization of the consensus problem (that corresponds to the case \( { k=1 } \)). That problem was introduced in 1993 by Chaudhuri [2] to investigate how the number of choices (k) allowed for the processes is related to the maximum number of processes that can crash. (After it has crashed, a process executes no more steps: a crash is a premature halting.)
Definition
Let S be a system made up of n processes where up to t can crash and where each process has an input value (called a proposed value). The problem is defined by the three following properties (i. e., any algorithm that solves that problem has to satisfy these properties):
- 1.
Termination. Every nonfaulty process decides a value.
- 2.
Validity. A decided value is a proposed value.
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Borowsky, E., Gafni, E.: Generalized FLP Impossibility Results for t-Resilient Asynchronous Computations. In: Proc. 25th ACM Symposium on Theory of Computation, California, 1993, pp. 91–100
Chaudhuri, S.: More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems. Inf. Comput. 105, 132–158 (1993)
Chaudhuri, S., Herlihy, M., Lynch, N., Tuttle, M.: Tight Bounds for k-Set Agreement. J. ACM 47(5), 912–943 (2000)
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Mostefaoui, A., Raynal, M.: k-Set Agreement with Limited Accuracy Failure Detectors. In: Proc. 19th ACM Symposium on Principles of Distributed Computing, pp. 143–152. ACM Press, New York (2000)
Mostefaoui, A., Raynal, M.: Randomized Set Agreement. In: Proc. 13th ACM Symposium on Parallel Algorithms and Architectures (SPAA'01), Hersonissos (Crete) pp. 291–297. ACM Press, New York (2001)
Perry, K.J., Toueg, S.: Distributed Agreement in the Presence of Processor and Communication Faults. IEEE Trans. Softw. Eng. SE-12(3), 477–482 (1986)
Raipin Parvedy, P., Raynal, M., Travers, C.: Early-stopping k‑set agreement in synchronous systems prone to any number of process crashes. In: Proc. 8th Int'l Conference on Parallel Computing Technologies (PaCT'05). LNCS, vol. 3606, pp. 49–58. Springer, Berlin (2005)
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Raynal, M., Travers, C.: Synchronous set agreement: a concise guided tour (including a new algorithm and a list of open problems). In: Proc. 12th Int'l IEEE Pacific Rim Dependable Computing Symposium (PRDC'2006), pp. 267–274. IEEE Society Computer Press, Los Alamitos (2006)
Saks, M., Zaharoglou, F.: Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge. SIAM J. Comput. 29(5), 1449–1483 (2000)
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Raynal, M. (2008). Set Agreement. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_367
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DOI: https://doi.org/10.1007/978-0-387-30162-4_367
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