Component-Composition Graphs: (t,k)-Diagnosability and Its Application

(t,k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors be identified and replaced in each iteration provided there are at most t faulty processors, where t ≥ k. Let \kappa (G) and n(G) be, respectively, the node connectivity and the number of nodes in a graph G. In this paper, we compute the (t,k)-diagnosability for a class of component-composition graphs under the comparison diagnosis model. We show that the m-dimensional component-composition graph G (m ≥ 4) is (Ω (h), κ (G))-diagnosable, where h= {(2m-2
^m-1
)/2m<;sup>-1<;/sup>×lg(m-1)} if|V(G)|≥m! if 2<;sup>m-1<;/sup>≤|V(G|<;m! and κ(G) and |V(G)|denote the node connectivity and the number of nodes in G, respectively. Based on this result, the (t,k)-diagnosability of several multiprocessor systems can be computed efficiently.