Skip to main content
SpringerLink
Log in

Planar quorums

  • Regular Papers
  • Conference paper
  • First Online:
Distributed Algorithms (WDAG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1151))

Included in the following conference series:

Abstract

Quorum systems are used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. This paper presents a new class of quorum systems based on connected regions in planar graphs. This class has an intuitive geometric nature and is easy to visualize and map to the system topology. We show that for triangulated graphs, the resulting quorum systems are non-dominated, which is a desirable property. We study the performance of these systems in terms of their availability, load, and cost of failures. We formally introduce the concept of cost of failures and argue that it is needed to analyze the message complexity of quorum-based protocols. We show that quorums of triangulated graphs with bounded degree have optimal cost of failure. We study a particular member of this class, the triangle lattice. The triangle lattice has small quorum size, optimal load for its size, high availability, and optimal cost of failures. Its parameters are not matched by any other proposed system in the literature. We use percolation theory to study the availability of this system.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Agrawal and A. El-Abbadi. An efficient and fault-tolerant solution for distributed mutual exclusion. ACM Transactions on Computer Systems, 9(1):1–20, 1991.

    Article  Google Scholar 

  2. B. Bollobás. Graph Theory, An Introductory Course Graduate Texts in Mathematics, Springer Verlag, 1979.

    Google Scholar 

  3. B. Bollobás. Combinatorics. Cambridge, 1983.

    Google Scholar 

  4. N. Condorcet. Essai sur l'application de l'analyse a la probabilité des decision rendues à la pluralité des voix. Paris, 1785.

    Google Scholar 

  5. H. Garcia-Molina and D. Barbara. How to assign votes in a distributed system. Journal of the ACM, 32(4):481–860, 1985.

    Article  Google Scholar 

  6. D. K. Gifford. Weighted Voting for Replicated Data Proceeding of 7th ACM Symposium on Operating Systems Principles, pages 150–162, December 1979.

    Google Scholar 

  7. G. R. Grimmett. Percolation. Springer Verlag, 1989.

    Google Scholar 

  8. M. P. Herlihy. Replication Methods for Abstract Data Types. Ph.D. Thesis, Massachusetts Institute of Technology, 1984.

    Google Scholar 

  9. J. G. Hocking and G. S. Young Topology. Dover, 1988

    Google Scholar 

  10. T. Ibaraki and T. Kameda. A theory of Coteries: Mutual Exclusion in Distributed Systems. IEEE Transactions on Parallel and Distributed Systems, 4(7):779–749, 1993.

    Article  Google Scholar 

  11. H. Kesten. Percolation Theorey for Mathematicians. Progress in Probability and Statistics, Birkhäuser, 1982.

    Google Scholar 

  12. A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Transactions of Computers, 40(9):996–1004, 1991.

    Article  Google Scholar 

  13. A. Kumar., M. Rabinovich, and R. Sinha. A performance study of general grid structures for replicated data. In Proceedings of International Conference on Distributed Computing Systems, pages 178–185, May, 1993.

    Google Scholar 

  14. L. Lovász. Covering and colorings of hypergraphs. In Proceedings of 4th Southeastern Conference on Combinatorics, Graph Theory and Computing, pages 3–12, 1973.

    Google Scholar 

  15. M. Maekawa. A √n algorithm for mutual exclusion in decentralized systems. ACM Transactions on Computer Systems, 3(2):145–159, 1985.

    Article  Google Scholar 

  16. C. R. F. Maunder Algebraic Topology Van Nostrand, 1970

    Google Scholar 

  17. S. J. Mullender and P. M. B. Vitanyi. Distributed Match Making. Algorithmica, 3:367–391, 1992.

    Article  Google Scholar 

  18. M. L. Neilsen Quorum Structures in Distributed Systems. Ph.D. Thesis, Department of Computer and Information Sciences, Kansas State University, 1992.

    Google Scholar 

  19. M. L. Neilsen and M. Mizuno. Decentralized Consensus Porotocols In Proceedings of 10th International Phoenix Conference on Computing and Communications, pages 257–262, 1991.

    Google Scholar 

  20. M. Naor and A. Wool The Load, capacity and availability of quorum systems. In Proceedings of the 35th IEEE Symposium on Foundations of Computer Science, pages 214–225. 1994.

    Google Scholar 

  21. D. Peleg and A. Wool. The availability of quorum systems. Information and Computation, 123(2):210–223, 1995.

    Article  Google Scholar 

  22. D. Peleg and A. Wool. Crumbling Walls: A class of high availability quorum systems. In Processedings 14th ACM Symposium on Principles of Distributed Computing, pages 120–129, 1995.

    Google Scholar 

  23. D. Skeen. A quorum-based commit protocol. In Proceedings of 6th Berkeley Workshop on Distributed Data Management and Computer Networks, pages 69–80, 1982.

    Google Scholar 

  24. A majority consensus approach to concurrency control for multiple copy database. ACM Transactions on Database Systems, 4(2):180–209, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, Florida International University, 33199, Miami, Florida, USA

    Rida A. Bazzi

Authors
  1. Rida A. Bazzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Özalp Babaoğlu Keith Marzullo

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bazzi, R.A. (1996). Planar quorums. In: Babaoğlu, Ö., Marzullo, K. (eds) Distributed Algorithms. WDAG 1996. Lecture Notes in Computer Science, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61769-8_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-61769-8_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61769-3

  • Online ISBN: 978-3-540-70679-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation