Nondominated Coteries on Graphs

  • Authors:
  • Takashi Harada;Masafumi Yamashita

  • Affiliations:
  • -;-

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1997

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Abstract

Let C and D be two distinct coteries under the vertex set V of a graph G = (V, E) that models a distributed system. Coterie C is said to G-dominate D (with respect to G) if the following condition holds: For any connected subgraph H of G that contains a quorum in D (as a subset of its vertex set), there exists a connected subgraph H驴 of H that contains a quorum in C. A coterie C on a graph G is said to be G-nondominated (G-ND) (with respect to G) if no coterie D (驴C) on G G-dominates C. Intuitively, a G-ND coterie consists of irreducible quorums.This paper characterizes G-ND coteries in graph theoretical terms, and presents a procedure for deciding whether or not a given coterie C is G-ND with respect to a given graph G, based on this characterization. We then improve the time complexity of the decision procedure, provided that the given coterie C is nondominated in the sense of Garcia-Molina and Barbara. Finally, we characterize the class of graphs G on which the majority coterie is G-ND.