Computing the (t,k)-diagnosability of component-composition graphs and its application

Abstract

(t,k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors should be identified and repaired in each iteration provided there are at most t faulty processors, where t ≥ k. Let κ(G) and n(G) be the node connectivity and the number of nodes in G, respectively. We show that the class of m-dimensional component-composition graphs G for m ≥ 4 is (Ω(h),κ(G))-diagnosable, where h = 2 m-2 x lg (m-1)/m-1 if 2m-1 ≤ n(G) < m!; and h = 2m-2 if n(G) ≥ m!. Based on this result, the (t,k)-diagnosability of numerous multiprocessor systems can be computed efficiently. © 2010 Springer-Verlag.