2012/04/18 by Shuming Zhou, Zhou, Shuming, Jun‐Ming Xu +1
Computer Science · #Combinatorics (math.CO) #Distributed systems and fault tolerance #FOS: Mathematics #Graph Theory and Algorithms #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1204.4018
openalex publication_date 2012/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 An,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 An,k under the comparison model. We prove that for k≥ 4, n≥ k+2, the conditional diagnosability of An,k is (3k-2)(n-k)-3; the conditional diagnosability of An,n-1 is 3n-7 for n≥ 5.