An algorithm for conditional-fault local diagnosis of multiprocessor systems under the MM∗ model

Diagnosis is a crucial subject for maintaining the reliability of multiprocessor systems. Under the MM* diagnosis model, Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity O(N5) to diagnose a system with N processors. In this paper, we propose a (a, fl)-trees combination S(u, X, a, fl) and give an algorithm to identify the fault or fault-free status of each processor for conditional local diagnosis under the MM* model. According to our results, a connected network with a (a, fl)-trees combination S(u, X, a, fl) for a node u is conditionally locally (a + 2fl - 3)-diagnosable at node u and the time complexity of our algorithm to diagnose u is O(a2fl + afl2). As an application, we show that our algorithm can identify the status of each node of n-dimensional star graph Sn if the faulty node number does not exceed 3n - 8. Compared with existing algorithms, our algorithm allows more faulty nodes in a multiprocessor system.