Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

As the size of a multiprocessor system increases, processor failure is inevitable, and fault identification in such a system is crucial for reliable computing. The fault diagnosis is the process of identifying faulty processors in a multiprocessor system through testing. For the practical fault diagnosis systems, the probability that all neighboring processors of a processor are faulty simultaneously is very small, and the conditional diagnosability, which is a new metric for evaluating fault tolerance of such systems, assumes that every faulty set does not contain all neighbors of any processor in the systems. This paper shows that the conditional diagnosability of bubble sort graphs $B_n$ under the PMC model is $4n-11$ for $n \geq 4$, which is about four times its ordinary diagnosability under the PMC model.