### 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 |
---|---|

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

**Nondominated coteries on graphs.** / Harada, Takashi; Yamashita, Masafumi.

Research output: Contribution to journal › Article

*IEEE Transactions on Parallel and Distributed Systems*, vol. 8, no. 6, pp. 667-672. https://doi.org/10.1109/71.595585

}

TY - JOUR

T1 - Nondominated coteries on graphs

AU - Harada, Takashi

AU - Yamashita, Masafumi

PY - 1997/12/1

Y1 - 1997/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031163623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031163623&partnerID=8YFLogxK

U2 - 10.1109/71.595585

DO - 10.1109/71.595585

M3 - Article

AN - SCOPUS:0031163623

VL - 8

SP - 667

EP - 672

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

SN - 1045-9219

IS - 6

ER -