[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

Scalable and dynamic quorum systems

  • Published:
Distributed Computing Aims and scope Submit manuscript

Abstract.

We investigate issues related to the probe complexity of quorum systems and their implementation in a dynamic environment. Our contribution is twofold. The first regards the algorithmic complexity of finding a quorum in case of random failures. We show a tradeoff between the load of a quorum system and its probe complexity for non adaptive algorithms. We analyze the algorithmic probe complexity of the Paths quorum system suggested by Naor and Wool in [29], and present two optimal algorithms. The first is a non adaptive algorithm that matches our lower bound. The second is an adaptive algorithm with a probe complexity that is linear in the cardinality of the smallest quorum set. We supply a constant degree network in which these algorithms could be executed efficiently. Thus the Paths quorum system is shown to have good balance between many measures of quality. Our second contribution is presenting Dynamic Paths - a suggestion for a dynamic and scalable quorum system, which can operate in an environment where elements join and leave the system. The quorum system could be viewed as a dynamic adaptation of the Paths system, and therefore has low load high availability and good probe complexity. We show that it scales gracefully as the number of elements grows.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. El Abbadi A, Skeen D, Cristian F: An efficient, fault-tolerant protocal for replicated data management. In: Proceedings of the 5th ACM SIGACT/SIGMOD Conference on Principles of Database Systems, 1985, pp 215-229

  2. Abraham I, Awerbuch B, Azar Y, Bartal Y, Malkhi D, Pavlov E: A generic scheme for building overlay networks in adversarial scenarios. In: Proceedings of the International Parallel and Distributed Processing Symposium (IPDPS), 2003, p 40

  3. Abraham I, Malkhi D: Probabilistic quorums for dynamic systmes. In: Proceedings of the 17th International Symposium on Distributed Computing (DISC), 2003, pp 60-74

  4. Adler M, Halperin E, Karp RM, Vazirani VV: A stochastic process on the hypercube with applications to peer-to-peer networks. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (STOC), 2003, pp 575-584

  5. Agrawal D, Egecioglu O, El Abbadi A: Billiard quorums on the grid. Information Processing Letters 64(1):9-16 (1997)

    Google Scholar 

  6. Aizenman M, Chayes J, Chayes L, Frohlich J, Russo L: On a sharp transition from area low to perimeter low in a system of random surfaces. Commun Math Phys 92:19-69, 1983.

    Google Scholar 

  7. Bazzi RA: Planar quorums. In: Distributed Algorithms, 10th International Workshop, WDAG ‘96, pp 251-268

  8. Bearden M, Bianchini RP Jr: A fault-tolerant algorithm for decentralized on-line quorum adaptation. In: Symposium on Fault-Tolerant Computing, 1998, pp 262-271

  9. Bollobas B, Riordan O: The critical probability for random voronoi percolation in the plane is 1/2. In: Front for the Mathematics ArXiv, math.PR/0410336, 14 October 2004

  10. Garcia-Molina H, Barbara D: How to assign votes in a distributed system. J Assoc Comput Mach 32(4):841-855 (1985)

    Google Scholar 

  11. Goldreich O: Randomized Methods in Computation - Lecture Notes. http://www.wisdom.weizmann.ac.il/~oded/rnd.html, 2001

  12. Grimmett G: Percolation, 2nd ed. Springer-Verlag, 1999

  13. Haas ZJ, Liang B: Ad hoc mobility management with uniform quorum systems. IEEE/ACM Trans Network 7(2):228-240 (1999)

    Google Scholar 

  14. Hassin Y, Peleg D: Average probe complexity in quorum systems. In: 20th ACM Symposium on Principles of Distributed Computing (PODC), 2001, pp 180-189

  15. Herlihy M: Dynamic quorum adjustment for partitioned data. ACM Trans Database Syst (TODS) 12:170-194 (1987)

    Google Scholar 

  16. Jajodia S. Mutchler D: Dynamic voting algorithms for maintaining the consistency of a replicated database. ACM Trans Database Syst 15(2):230-280 (1990)

    Google Scholar 

  17. Karumanchi G, Muralidharan S, Prakash R: Information dissemination in partitionable mobile ad hoc networks. In: Proceedings of IEEE Symposium on Reliable Distributed Systems, 1999, pp 4-13

  18. Liggett TL, Schonmann RH, Stacey AM: Domination by product measures. The Annals of Probability 25(1):71-95 (1997)

    Google Scholar 

  19. Lotem EY, Keidar I, Dolev D: Dynamic voting for consistent primary components. In: Symposium on Principles of Distributed Computing (PODC), 1997, pp 63-71

  20. Lynch N, Shvartsman A: Robust emulation of shared memory using dynamic quorum-acknowledged broadcasts. In: Symposium on Fault-Tolerant Computing, 1997, pp 272-281

  21. Lynch N, Shvartsman A: Rambo: A reconfigurable atomic memory service for dynamic networks. In: Proceedings of the 16th International Symposium on Distributed Computing, 2002, pp 173-190

  22. Maekawa M: A \(\sqrt{N}\) algorithm for mutual exclusion in decentralized systems. ACM Trans Comput Syst 3(2):145-159 (1985)

    Google Scholar 

  23. Malkhi D, Naor M, Ratajczak D: Viceroy: A scalable and dynamic emulation of the butterfly. In: ACM Conf. on Principles of Distributed Computing (PODC), 2002, pp 183-192

  24. Menshikov MV: Coincidence of critical points in percolation problems. Soviet Mathematics Doklady 33:856-859 (1986)

    Google Scholar 

  25. Motwani R, Raghavan P: Randomized Algorithms. Cambridge University Press, 1997

  26. Nadav U, Naor M: Fault-tolerant storage in a dynamic environment. In: Proceedings of the 18th Annual Conference on Distributed Computing (DISC). Lecture Notes in Computer Science 3274, Springer, 2004, pp 390-404

  27. Naor M, Wieder U: Novel architectures for p2p applications: the continuous-discrete approach. In: Fifteenth ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2003, pp 50-59

  28. Naor M, Wool A: Access control and signatures via quorum secret sharing. IEEE Trans Parallel Distrib Syst 9(9):909-922 (1998)

    Google Scholar 

  29. Naor M, Wool A: The load, capacity, and availability of quorum systems. SIAM J Comput 27(2):423-447 (1998)

    Google Scholar 

  30. Okabe A, Boots B, Sugihara K, Chiu SN: Spatial Tessellations -- Concepts and Applications of Voronoi Diagrams. Wiley, Chichester, 2nd ed., 2000

  31. Peleg D, Wool A: How to be an efficient snoop, or the probe complexity of quorum systems. SIAM J Discrete Math 15(3):416-433 (2002)

    Google Scholar 

  32. De Prisco R, Fekete A, Lynch N, Shvartsman A: A dynamic view-oriented group communication service. In: Symposium on Principles of Distributed Computing (PODC), 1998, pp 227-236

  33. Ratnasamy S, Francis P, Handley M, Karp R, Shenker S: A scalable content addressable network. In: Proc ACM SIGCOMM, 2001, pp 161-172

  34. Sanders BA: The information structure of distributed mutual exclusion algorithms. ACM Trans Comput Syst 5(3):284-299 (1987)

    Google Scholar 

  35. Stoica I, Morris R, Karger D, Kaashoek F, Balakrishnan H: Chord: A scalable Peer-To-Peer lookup service for internet applications. In: Proceedings of the 2001 ACM SIGCOMM Conference, 2001, pp 149-160

  36. Stojmenović I, Pena PEV: A scalable quorum based location update scheme for routing in ad hoc wireless networks. Technical Report TR-99-09, SITE, University of Ottawa, September 1999

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Moni Naor.

Additional information

Published online: 10 December 2004

Moni Naor: Incumbent of the Judith Kleeman ProfessorialChair.

Research supported in part by the RAND/APX grant from the EU Program IST

Rights and permissions

Reprints and permissions

About this article

Cite this article

Naor, M., Wieder, U. Scalable and dynamic quorum systems. Distrib. Comput. 17, 311–322 (2005). https://doi.org/10.1007/s00446-004-0114-3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00446-004-0114-3

Keywords

Navigation