### 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′ 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 (≠ 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.

Original language | English |
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Pages (from-to) | 667-672 |

Number of pages | 6 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 8 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 1997 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*8*(6), 667-672. https://doi.org/10.1109/71.595585