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Set Agreement

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 199 Accesses

Years and Authors of Summarized Original Work

  • 1993; Chaudhuri

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...

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Recommended Reading

  1. Borowsky E, Gafni E (1993) Generalized FLP impossibility results for t-resilient asynchronous computations. In: Proceedings of the 25th ACM symposium on theory of computation, California, pp 91–100

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  2. Chaudhuri S (1993) More choices allow more faults: set consensus problems in totally asynchronous systems. Inf Comput 105:132–158

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  3. Chaudhuri S, Herlihy M, Lynch N, Tuttle M (2000) Tight bounds for k set agreement. J ACM 47(5):912–943

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  4. Gafni E, Guerraoui R, Pochon B (2005) From a static impossibility to an adaptive lower bound: the complexity of early deciding set agreement. In: Proceedings of the 37th ACM symposium on theory of computing (STOC 2005). ACM, New York, pp 714–722

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  5. Gafni E, Rajsbaum S, Herlihy M (2006) Subconsensus tasks: renaming is weaker than set agreement. In: Proceedings of the 20th international symposium on distributed computing (DISC'06). LNCS, vol 4167. Springer, Berlin, pp 329–338

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  8. Mostefaoui A, Rajsbaum S, Raynal M (2005) The combined power of conditions and failure detectors to solve asynchronous set agreement. In: Proceedings of the 24th ACM symposium on principles of distributed computing (PODC'05). ACM, New York, pp 179–188

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  9. Mostefaoui A, Raynal M (2000) k set agreement with limited scope accuracy failure detectors. In: Proceedings of the 19th ACM symposium on principles of distributed computing. ACM, New York, pp 143–152

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  10. Mostefaoui A, Raynal M (2001) Randomized set agreement. In: Proceedings of the 13th ACM symposium on parallel algorithms and architectures (SPAA'01), Hersonissos (Crete). ACM, New York, pp 291–297

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  11. Perry KJ, Toueg S (1986) Distributed agreement in the presence of processor and communication faults. IEEE Trans Softw Eng SE-12(3):477–482

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  12. Raipin Parvedy P, Raynal M, Travers C (2005) Early-stopping k-set agreement in synchronous systems prone to any number of process crashes. In: Proceedings of the 8th international conference on parallel computing technologies (PaCT'05). LNCS, vol 3606. Springer, Berlin, pp 49–58

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  13. Raipin Parvedy P, Raynal M, Travers C (2006) Strongly-terminating early-stopping k-set agreement in synchronous systems with general omission failures. In: Proceedings of the 13th colloquium on structural information and communication complexity (SIROCCO'06). LNCS, vol 4056. Springer, Berlin, pp 182–196

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  14. Raynal M, Travers C (2006) Synchronous set agreement: a concise guided tour (including a new algorithm and a list of open problems). In: Proceedings of the 12th international IEEE pacific rim dependable computing symposium (PRDC'2006). IEEE Computer Society, Los Alamitos, pp 267–274

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  15. Saks M, Zaharoglou F (2000) Wait-free k-set agreement is impossible: the topology of public knowledge. SIAM J Comput 29(5):1449–1483

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Author information

Authors and Affiliations

  1. Institut Universitaire de France and IRISA, Université de Rennes, Rennes, France

    Michel Raynal

Authors
  1. Michel Raynal
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Raynal, M. (2016). Set Agreement. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_367

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