Diagnosis of parallel computers arbitrary connectivity

Recently, D. Fussell and S. Rangarajan (1989) considered performing multiple tests to achieve correct diagnosis of constant degree connection structures. They showed that the probability of correctly identifying every processor approaches one as n→∞, where n is the number of processors in the system. In this paper, we give the performance analysis for the probabilistic diagnosis algorithm defined previously. In comparison with previous results, we first derive a different and formal proof for the analytic expression of the probability processor is correctly identified. We then show an exact analytic expression for the probability of the event that a faulty processor is correctly identified. Our result improves the previous results. Based on our new results, we finally give the asymptotic analysis for the algorithm. We demonstrate that the probability of correctly identifying every processor approaches one as n→∞