Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

Abstract

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 ≥ 4, which is about four times its ordinary diagnosability under the PMC model.

Conditional diagnosability of bubble-sort star graphs

“…The diagnosability of many interconnection networks has been explored. For example, see [5,[8][9][10]14,[16][17][18][19][20][21][22][23][24].…”

“…In the PMC model, every processor can test the processor that is adjacent to it and only the fault-free processor can guarantee reliable outcome. The PMC model was adopted in [2,14,22].…”

Subnetwork preclusion for bubble-sort networks

“…The bubble-sort graph B n is an attractive interconnection network with many good properties such as nodesymmetric, (n − 1)-regular and bipartite [1,2,7,8,[11][12][13]16].…”