Weak Synchrony Models and Failure Detectors for Message Passing (k-)Set Agreement

  • Martin Biely
  • Peter Robinson
  • Ulrich Schmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5923)

Abstract

The recent discovery of the weakest failure detector \({\mathcal{L}}\) for message passing set agreement has renewed the interest in exploring the border between solvable and unsolvable problems in message passing systems. This paper contributes to this research by introducing two novel system models \({\mathcal{M}^\text{anti}}\) and \({\mathcal{M}^\text{sink}}\) with very weak synchrony requirements, where \({\mathcal{L}}\) can be implemented. To the best of our knowledge, they are the first message passing models where set agreement is solvable but consensus is not. We also generalize \({\mathcal{L}}\) by a novel “(nk)-loneliness” failure detector \({\mathcal{L}}(k)\), which allows to solve k-set agreement but not (k−1)-set agreement. We also present an algorithm that solves k-set agreement with \({\mathcal{L}}(k)\), which is anonymous in that it does not require unique process identifiers. This reveals that \({\mathcal{L}}\) is also the weakest failure detector for anonymous set agreement. Finally, we analyze the relationship between \({\mathcal{L}}(k)\) and other failure detectors, namely the limited scope failure detector \({\mathcal{S}}_{n-k+1}\) and the quorum failure detector Σ.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: On implementing Omega with weak reliability and synchrony assumptions. In: Proceedings of the 22nd ACM Symposium on Principles of Distributed Computing, pp. 306–314 (July 2003)Google Scholar
  2. 2.
    Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: Communication-efficient leader election and consensus with limited link synchrony. In: Proceedings of the 23rd ACM Symposium on Principles of Distributed Computing (PODC 2004), St. John’s, Newfoundland, Canada, pp. 328–337. ACM Press, New York (2004)CrossRefGoogle Scholar
  3. 3.
    Angluin, D.: Local and global properties in networks of processors (extended abstract). In: Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, pp. 82–93. ACM, New York (1980)CrossRefGoogle Scholar
  4. 4.
    Attiya, H., Snir, M., Warmuth, M.K.: Computing on an anonymous ring. J. ACM 35(4), 845–875 (1988)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Biely, M., Hutle, M., Penso, L.D., Widder, J.: Relating stabilizing timing assumptions to stabilizing failure detectors regarding solvability and efficiency. In: Masuzawa, T., Tixeuil, S. (eds.) SSS 2007. LNCS, vol. 4838, pp. 4–20. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Biely, M., Robinson, P., Schmid, U.: Weak synchrony models and failure detectors for message passing k-set agreement. Research Report 51/2009, Technische Universität Wien, Inst. Technische Informatik, 182-2, 1040 Vienna, Austria (2009)Google Scholar
  7. 7.
    Biely, M., Widder, J.: Optimal message-driven implementation of Omega with mute processes. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 110–121. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Bonnet, F., Raynal, M.: Looking for the weakest failure detector for k-set agreement in message-passing systems: Is Πk the end of the road? In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 129–164. Springer, Heidelberg (2009)Google Scholar
  9. 9.
    Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: STOC 1993: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, pp. 91–100. ACM, New York (1993)CrossRefGoogle Scholar
  10. 10.
    Chandra, T.D., Hadzilacos, V., Toueg, S.: The weakest failure detector for solving consensus. Journal of the ACM 43(4), 685–722 (1996)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. Journal of the ACM 43(2), 225–267 (1996)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Charron-Bost, B., Schiper, A.: Uniform consensus is harder than consensus. J. Algorithms 51(1), 15–37 (2004); Also published as Tech. Rep. DSC/2000/028, Ecole Polytechnique Fédérale de LausanneGoogle Scholar
  13. 13.
    Chaudhuri, S.: More choices allow more faults: set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Delporte-Gallet, C., Fauconnier, H., Guerraoui, R.: Shared Memory vs Message Passing. LPD-REPORT 001, Ecole Polytechnique Federale de Lausanne (2003)Google Scholar
  15. 15.
    Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Hadzilacos, V., Kouznetsov, P., Toueg, S.: The weakest failure detectors to solve certain fundamental problems in distributed computing. In: Proceedings of the 23rd ACM Symposium on Principles of Distributed Computing (PODC 2004), pp. 338–346. ACM Press, New York (2004)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Dolev, D., Dwork, C., Stockmeyer, L.: On the minimal synchronism needed for distributed consensus. Journal of the ACM 34(1), 77–97 (1987)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the presence of partial synchrony. Journal of the ACM 35(2), 288–323 (1988)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Fuegger, M., Schmid, U., Fuchs, G., Kempf, G.: Fault-Tolerant Distributed Clock Generation in VLSI Systems-on-Chip. In: Proceedings of the Sixth European Dependable Computing Conference (EDCC-6), pp. 87–96. IEEE Computer Society, Los Alamitos (2006)CrossRefGoogle Scholar
  21. 21.
    Gafni, E., Kuznetsov, P.: The weakest failure detector for solving k-set agreement. In: 28th ACM Symposium on Principles of Distributed Computing (PODC) (2009)Google Scholar
  22. 22.
    Guerraoui, R., Herlihy, M., Kouznetsov, P., Lynch, N., Newport, C.: On the weakest failure detector ever. In: Proceedings of the twenty-sixth annual ACM Symposium on Principles of Distributed Computing (PODC 2007), pp. 235–243. ACM, New York (2007)Google Scholar
  23. 23.
    Guerraoui, R., Schiper, A.: “gamma-accurate” failure detectors. In: Babaoğlu, Ö., Marzullo, K. (eds.) WDAG 1996. LNCS, vol. 1151, pp. 269–286. Springer, Heidelberg (1996)Google Scholar
  24. 24.
    Herlihy, M., Shavit, N.: The asynchronous computability theorem for t-resilient tasks. In: STOC 1993: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, pp. 111–120. ACM, New York (1993)CrossRefGoogle Scholar
  25. 25.
    Hutle, M., Malkhi, D., Schmid, U., Zhou, L.: Chasing the weakest system model for implementing omega and consensus. IEEE Transactions on Dependable and Secure Computing (to appear, 2009)Google Scholar
  26. 26.
    Larrea, M., Fernández, A., Arévalo, S.: Optimal implementation of the weakest failure detector for solving consensus. In: Proceedings of the 19th IEEE Symposium on Reliable Distributed Systems (SRDS), Nürnberg, Germany, pp. 52–59 (October 2000)Google Scholar
  27. 27.
    Malkhi, D., Oprea, F., Zhou, L.: Ω meets paxos: Leader election and stability without eventual timely links. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 199–213. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  28. 28.
    Mostefaoui, A., Mourgaya, E., Raynal, M.: Asynchronous implementation of failure detectors. In: Proceedings of the International Conference on Dependable Systems and Networks (DSN 2003), San Francisco, CA, June 22–25 (2003)Google Scholar
  29. 29.
    Mostéfaoui, A., Raynal, M.: Unreliable failure detectors with limited scope accuracy and an application to consensus. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 329–340. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  30. 30.
    Mostéfaoui, A., Raynal, M.: k-set agreement with limited accuracy failure detectors. In: PODC 2000: Proceedings of the 19th annual ACM symposium on Principles of distributed computing, pp. 143–152. ACM, New York (2000)CrossRefGoogle Scholar
  31. 31.
    Mostefaoui, A., Raynal, M., Travers, C.: Crash-resilient time-free eventual leadership. In: Proceedings of the 23rd IEEE Symposium on Reliable Distributed Systems (SRDS 2004), pp. 208–217. IEEE Computer Society, Los Alamitos (2004)CrossRefGoogle Scholar
  32. 32.
    Raynal, M.: k-anti-Ω. Rump session at PODC 2007 (August 2007)Google Scholar
  33. 33.
    Robinson, P., Schmid, U.: The Asynchronous Bounded-Cycle Model. In: Kulkarni, S., Schiper, A. (eds.) SSS 2008. LNCS, vol. 5340, pp. 246–262. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  34. 34.
    Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. Comput. 29(5), 1449–1483 (2000)MATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    Schneider, F.B.: Implementing fault-tolerant services using the state machine approach: a tutorial. ACM Comput. Surv. 22(4), 299–319 (1990)CrossRefGoogle Scholar
  36. 36.
    Widder, J., Schmid, U.: The Theta-Model: Achieving synchrony without clocks. Distributed Computing 22(1), 29–47 (2009)CrossRefGoogle Scholar
  37. 37.
    Zielinski, P.: Automatic classification of eventual failure detectors. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 465–479. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  38. 38.
    Zielinski, P.: Anti-Ω: the weakest failure detector for set agreement. In: PODC 2008: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing, pp. 55–64. ACM, New York (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Martin Biely
    • 1
    • 2
  • Peter Robinson
    • 1
  • Ulrich Schmid
    • 1
  1. 1.Embedded Computing Systems GroupTechnische Universität WienAustria
  2. 2.LIXEcole polytechniqueFrance

Personalised recommendations