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Nondominated Coteries on Graphs
June 1997 (vol. 8 no. 6)
pp. 667-672

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.

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Index Terms:
Availability, coteries on graphs, distributed mutual exclusion problem, G-nondominatedness, majority consensus.
Takashi Harada, Masafumi Yamashita, "Nondominated Coteries on Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 6, pp. 667-672, June 1997, doi:10.1109/71.595585
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