Distributed Computing

, Volume 8, Issue 4, pp 191–201 | Cite as

Optimal coteries for rings and related networks

  • Toshihide Ibaraki
  • Hiroshi Nagamochi
  • Tsunehiko Kameda
Article

Summary

Let a distributed system be represented by a graphG=(V, E), whereV is the set of nodes andE is the set of communication links. A coterie is defined as a family,C, of subsets ofV such that any pair of subsets inC has at least one node in common and no subset inC contains any other subset inC. Assuming that each nodev i ∈V (resp. linke j ∈E) is operational with probabilityp i (resp.r j ), the availability of a coterie is defined as the probability that the operational nodes and links ofG connect all nodes in at least one subset in the coterie. Although it is computationally intractable to find an optimal coterie that maximizes availability for general graphG, we show in this paper that, ifG is a ring, either a singleton coterie or a 3-majority coterie is optimal. Therefore, for any ring, an optimal coterie can be computed in polynomial time. This result is extended to the more general graphs, in which each biconnected component is either an edge or a ring.

Key words

Coterie Availability Network Distributed system Mutual exclusion Quorum Ring Fault tolerance 

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References

  1. Ahammad A, Amar MH: Performance characterization of quorumconsensus algorithms for replicated data. Proc 7th IEEE Symp on Reliability in Distributed Software and Database Systems, 1987, pp 161–167Google Scholar
  2. Ball MO: Computational complexity of network reliability analysis: an overview. IEEE Trans Reliab R-35(3): 230–239 (1986)Google Scholar
  3. Barbara D, Garcia-Molina H: The vulnerability of vote assignment. ACM Trans Comput Syst 4: 187–213 (1986)Google Scholar
  4. Barbara D, Garcia-Molina H: The reliability of voting mechanisms. IEEE Trans Comput C-36(10): 1197–1208 (1987)Google Scholar
  5. Berge C: Graphs and Hypergraphs. Amsterdam: North-Holland 1973Google Scholar
  6. Garcia-Molina H, Barbara D: How to assign votes in a distributed system. J ACM 32(4): 841–860 (1985)Google Scholar
  7. Harary F: Graph Theory. Reading, Mass.: Addison-Wesley 1969Google Scholar
  8. Ibaraki T, Kameda T: A boolean theory of coteries. Proc 3rd IEEE Symp on Parallel and Distributed Processing, Dec 1991, pp 150–157Google Scholar
  9. Ibaraki T, Kameda T: A theory of coteries: mutual exclusion in distributed systems. IEEE Trans on Parallel and Distributed Systems, July 1993, pp 779–794Google Scholar
  10. Maekawa M: A N algorithm for mutual exclusion in decentralized systems. ACM Trans Comput Syst 3: 145–159 (1985)Google Scholar
  11. Obradovic M, Berman P: Voting as the optimal static pessimistic scheme for managing replicated data. Proc 9th Symp on Reliable Distributed Systems, Oct 1990, pp 126–135Google Scholar
  12. Papadimitriou CH, Sideri M: Optimal coteries. Proc 10th ACM Symp on Principles of Distributed Computing, Aug 1991, pp 75–80Google Scholar
  13. Spasojevic M: Optimal replica control protocols for ring networks. Proc 11th Symp on Reliable Distributed Systems, Oct 1992, pp 57–65Google Scholar
  14. Ibaraki T, Nagamochi H, Kameda T: Optimal coteries for rings and related networks: Proc 12th International Conference on Distributed Computing Systems, June 1982, pp 650–656Google Scholar
  15. Tong Z, Kain RY: Vote assignments in weighted voting mechanisms. Proc 7th Symp on Reliable Distributed Systems, Oct 1988, pp 138–143Google Scholar
  16. Valiant LG: The complexity of enumeration and reliability problems. SIAM J Comput 8: 410–421 (1979)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Toshihide Ibaraki
    • 1
  • Hiroshi Nagamochi
    • 1
  • Tsunehiko Kameda
    • 2
  1. 1.Department of Applied Mathematics & PhysicsKyoto UniversityKyotoJapan
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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