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Issue No. 06 - June (1997 vol. 8)
ISSN: 1045-9219
pp: 667-672
<p><b>Abstract</b>—Let <it>C</it> and <it>D</it> be two distinct coteries under the vertex set <it>V</it> of a graph <it>G</it> = (<it>V</it>, <it>E</it>) that models a distributed system. Coterie <it>C</it> is said to <it>G</it>-dominate <it>D</it> (with respect to <it>G</it>) if the following condition holds: For any connected subgraph <it>H</it> of <it>G</it> that contains a quorum in <it>D</it> (as a subset of its vertex set), there exists a connected subgraph <it>H</it>′ of <it>H</it> that contains a quorum in <it>C</it>. A coterie <it>C</it> on a graph <it>G</it> is said to be <it>G</it>-nondominated (<it>G</it>-ND) (with respect to <it>G</it>) if no coterie <it>D</it> (≠<it>C</it>) on <it>G G</it>-dominates <it>C</it>. Intuitively, a <it>G</it>-ND coterie consists of irreducible quorums.</p><p>This paper characterizes <it>G</it>-ND coteries in graph theoretical terms, and presents a procedure for deciding whether or not a given coterie <it>C</it> is <it>G</it>-ND with respect to a given graph <it>G</it>, based on this characterization. We then improve the time complexity of the decision procedure, provided that the given coterie <it>C</it> is nondominated in the sense of Garcia-Molina and Barbara. Finally, we characterize the class of graphs <it>G</it> on which the majority coterie is <it>G</it>-ND.</p>
Availability, coteries on graphs, distributed mutual exclusion problem, G-nondominatedness, majority consensus.

M. Yamashita and T. Harada, "Nondominated Coteries on Graphs," in IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 667-672, 1997.
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