Skip to main content
SpringerLink
Log in

Simultaneous Consensus vs Set Agreement: A Message-Passing-Sensitive Hierarchy of Agreement Problems

  • Conference paper
Structural Information and Communication Complexity (SIROCCO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8179))

Abstract

This paper investigates the relation linking the s-simultaneous consensus problem and the k-set agreement problem in wait-free message-passing systems. To this end, it first defines the (s,k)-SSA problem which captures jointly both problems: each process proposes a value, executes s simultaneous instances of a k-set agreement algorithm, and has to decide a value so that no more than sk different values are decided. The paper introduces then a new failure detector class denoted Z s,k , which is made up of two components, one focused on the “shared memory object” that allows the processes to cooperate, and the other focused on the liveness of (s,k)-SSA algorithms. A novelty of this failure detector lies in the fact that the definition of its two components are intimately related. Then, the paper presents a Z s,k -based algorithm that solves the (s,k)-SSA problem, and shows that the “shared memory”-oriented part of Z s,k is necessary to solve the (s,k)-SSA problem (this generalizes and refines a previous result that showed that the generalized quorum failure detector Σ k is necessary to solve k-set agreement). Finally, the paper investigates the structure of the family of (s,k)-SSA problems and introduces generalized (asymmetric) simultaneous set agreement problems in which the parameter k can differ in each underlying k-set agreement instance. Among other points, it shows that, for s,k > 1, (a) the (sk,1)-SSA problem is strictly stronger that the (s,k)-SSA problem which is itself strictly stronger than the (1,ks)-SSA problem, and (b) there are pairs (s 1,k 1) and (s 2,k 2) such that s 1 k 1 = s 2 k 2 and (s 1,k 1)-SSA and (s 2,k 2)-SSA are incomparable.

The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-03578-9_29

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Afek, Y., Gafni, E., Rajsbaum, S., Raynal, M., Travers, C.: The k-Simultaneous Consensus Problem. Distributed Computing 22, 185–195 (2010)

    Article  MATH  Google Scholar 

  2. Attiya, H., Bar-Noy, A., Dolev, D.: Sharing Memory Robustly in Message Passing Systems. Journal of the ACM 42(1), 121–132 (1995)

    Article  MATH  Google Scholar 

  3. Bonnet, F., Raynal, M.: On the Road to the Weakest Failure Detector for k-Set Agreement in Message-passing Systems. Theoretical Computer Science 412(33), 4273–4284 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Borowsky, E., Gafni, E.: Generalized FLP Impossibility Impossibility Results for t-Resilient Asynchronous Computations. In: Proc. 25th ACM Symposium on Theory of Computation (STOC 1993), pp. 91–100 (1993)

    Google Scholar 

  5. Bouzid, Z., Travers, C.: (anti −Ωx ×Σ z )-Based k-Set Agreement Algorithms. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 189–204. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Bouzid, Z., Travers, C.: Simultaneous Consensus is Harder than Set Agreement in Message-Passing. In: Proc. 33rd Int’l IEEE Conference on Distributed Computing Systems (ICDCS 2013). IEEE Press (2013)

    Google Scholar 

  7. Chandra, T., Toueg, S.: Unreliable Failure Detectors for Reliable Distributed Systems. Journal of the ACM 43(2), 225–267 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chandra, T., Hadzilacos, V., Toueg, S.: The Weakest Failure Detector for Solving Consensus. Journal of the ACM 43(4), 685–722 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chaudhuri, S.: More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems. Information and Computation 105, 132–158 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, W., Zhang, J., Chen, Y., Liu, X.: Weakening Failure Detectors for k-Set Agreement Via the Partition Approach. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 123–138. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R.: Tight Failure Detection Bounds on Atomic Object Implementations. Journal of the ACM 57(4), Article 22 (2010)

    Google Scholar 

  12. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Tielmann, A.: The Weakest Failure Detector for Message Passing Set-Agreement. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 109–120. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Gafni, E., Kuznetsov, P.: On Set Consensus Numbers. Distributed Computing 24(3-4), 149–163 (2011)

    Article  MATH  Google Scholar 

  14. Guerraoui, R., Raynal, M.: The Alpha of Indulgent Consensus. The Computer Journal 50(1), 53–67 (2007)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Mostéfaoui, A., Raynal, M.: k-Set Agreement with Limited Accuracy Failure Detectors. In: Proc. 19th ACM Symposium on Principles of Distributed Computing (PODC 2000), pp. 143–152. ACM Press (2000)

    Google Scholar 

  17. Mostéfaoui, A., Raynal, M., Stainer, J.: Relations Linking Failure Detectors Associated with k-Set Agreement in Message-Passing Systems. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 341–355. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Mostéfaoui, A., Raynal, M., Stainer, J.: Chasing the Weakest Failure Detector for k-Set Agreement in Message-Passing Systems. In: Proc. 11th IEEE Int’l Symp. on Network Computing and Applications (NCA 2012), pp. 44–51. IEEE Press (2012)

    Google Scholar 

  19. Raynal, M.: K-anti-Omega. In: Rump Session at 26th ACM Symposium on Principles of Distributed Computing, PODC 2007 (2007)

    Google Scholar 

  20. Raynal, M.: Fault-Tolerant Agreement in Synchronous Message-Passing Systems, 165 pages. Morgan & Claypool Publishers (2010) ISBN: 978-1-60845-525-6

    Google Scholar 

  21. Raynal, M.: Failure Detectors to Solve Asynchronous k-Set Agreement: a Glimpse of Recent Results. Bulletin of the EATCS 103, 74–95 (2011)

    MATH  Google Scholar 

  22. Raynal, M.: Concurrent Programming: Algorithms, Principles, and Foundations, 515 pages. Springer (2013) ISBN 978-3-642-32027-9

    Google Scholar 

  23. Raynal, M., Stainer, J.: Simultaneous Consensus vs Set Agreement: a Message-passing Sensitive Hierarchy of Agreement Problems. Tech Report PI 2003, IRISA, University of Rennes (F) (2013), http://hal.inria.fr/hal-00787992

  24. Raynal, M., Travers, C.: In Search of the Holy Grail: Looking for the Weakest Failure Detector for Wait-Free Set Agreement. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 3–19. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. Saks, M., Zaharoglou, F.: Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge. SIAM Journal on Computing 29(5), 1449–1483 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zielinski, P.: Anti-Omega: the Weakest Failure Detector for Set Agreement. In: Proc. 27th ACM Symp. on Principles of Distributed Computing (PODC 2008), pp. 55–64. ACM Press (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Universitaire de France, France

    Michel Raynal & Julien Stainer

  2. IRISA, Campus de Beaulieu, 35042, Rennes Cedex, France

    Michel Raynal

Authors
  1. Michel Raynal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julien Stainer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. System Algorithms Research Group, Microsoft Research Asia, No. 5, Dan Ling Street, 100080, Beijing, China

    Thomas Moscibroda

  2. Dipartimento di Informatica, Università di Salerno, Via Ponte don Melillo, 84084, Fisciano, SA, Italy

    Adele A. Rescigno

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Raynal, M., Stainer, J. (2013). Simultaneous Consensus vs Set Agreement: A Message-Passing-Sensitive Hierarchy of Agreement Problems. In: Moscibroda, T., Rescigno, A.A. (eds) Structural Information and Communication Complexity. SIROCCO 2013. Lecture Notes in Computer Science, vol 8179. Springer, Cham. https://doi.org/10.1007/978-3-319-03578-9_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03578-9_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03577-2

  • Online ISBN: 978-3-319-03578-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation