Fault Diagnosability of Arrangement Graphs

The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all remaining vertices in the $(n,k)$-arrangement graph $A_{n,k}$ when the number of moved faulty vertices is up to twice or three times the traditional connectivity. Based on this fault resiliency, we establishes that the conditional diagnosability of $A_{n,k}$ under the comparison model. We prove that for $k\geq 4$, $n\geq k+2$, the conditional diagnosability of $A_{n,k}$ is $(3k-2)(n-k)-3$; the conditional diagnosability of $A_{n,n-1}$ is $3n-7$ for $n\geq 5$.

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