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
Nondominated coteries on graphs. / Harada, Takashi; Yamashita, Masafumi.
In: IEEE Transactions on Parallel and Distributed Systems, Vol. 8, No. 6, 01.12.1997, p. 667-672.Research output: Contribution to journal › Article
}
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 -