Distributed Computing

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

Optimal coteries for rings and related networks

  • Toshihide Ibaraki
  • Hiroshi Nagamochi
  • Tsunehiko Kameda


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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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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