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(/spl ne/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 (1985). Finally, we characterize the class of graphs G on which the majority coterie is G-ND.
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机译:令C和D是在对分布式系统建模的图G =(V,E)的顶点集V下的两个不同的变量。如果满足以下条件,则将Coterie C称为G主导D(相对于G):对于在D中包含仲裁(作为其顶点集的子集)的G的任何连通子图H,存在连通子图H H的C中包含定额。如果G上的C上没有C子集D(/ spl ne / C),则图G上的C子集C被认为是G端接的(G-ND)(相对于G)。直觉上,G-ND coterie由不可约的仲裁组成。本文用图理论术语表征了G-ND坐标,并基于此表征,给出了确定给定图C相对于给定图G是否为G-ND的过程。然后,如果给定的小规模C在Garcia-Molina和Barbara(1985)的意义上不占主导地位,那么我们将改善决策过程的时间复杂度。最后,我们描述了大多数小族是G-ND的图G的类别。
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