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Encyclopedia of Algorithms pp 829–831Cite as

Set Agreement

1993; Chaudhuri

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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. 1.

    Termination. Every nonfaulty process decides a value.

  2. 2.

    Validity. A decided value is a proposed value.

    ...

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Recommended Reading

  1. 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

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  2. Chaudhuri, S.: More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems. Inf. Comput. 105, 132–158 (1993)

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  3. 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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  4. Gafni, E., Guerraoui, R., Pochon, B.: From a Static Impossibility to an Adaptive Lower Bound: The Complexity of Early Deciding Set Agreement. In: Proc. 37th ACM Symposium on Theory of Computing (STOC 2005), pp. 714–722. ACM Press, New York (2005)

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  5. Gafni, E., Rajsbaum, S., Herlihy, M.: Subconsensus Tasks: Renaming is Weaker than Set Agreement. In: Proc. 20th Int'l Symposium on Distributed Computing (DISC'06). LNCS, vol. 4167, pp. 329–338. Springer, Berlin (2006)

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  6. Herlihy, M.P., Penso, L.D.: Tight Bounds for k-Set Agreement with Limited Scope Accuracy Failure Detectors. Distrib. Comput. 18(2), 157–166 (2005)

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  7. Herlihy, M.P., Shavit, N.: The Topological Structure of Asynchronous Computability. J. ACM 46(6), 858–923 (1999)

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  8. Mostefaoui, A., Rajsbaum, S., Raynal, M.: The Combined Power of Conditions and Failure Detectors to Solve Asynchronous Set Agreement. In: Proc. 24th ACM Symposium on Principles of Distributed Computing (PODC'05), pp. 179–188. ACM Press, New York (2005)

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  9. 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)

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  10. 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)

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  11. 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)

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  12. 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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  13. Raipin Parvedy, P., Raynal, M., Travers, C.: Strongly‐terminating early-stopping k-set agreement in synchronous systems with general omission failures. In: Proc. 13th Colloquium on Structural Information and Communication Complexity (SIROCCO'06). LNCS, vol. 4056, pp. 182–196. Springer, Berlin (2006)

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  14. 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)

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  15. 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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Author information

Authors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Michel Raynal

Authors
  1. Michel Raynal
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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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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