System-level testing assignment for hypercubes with lower fault bounds

The maximum allowed number of faulty processors in an n-dimensional hypercube system is n under PMC model for diagnosis. When the n fault bound is adopted, all links will be used to perform diagnosis. However, if the fault bound is lower than n, many links can be freed from the task of performing diagnosis. In this paper, we show that each drop of the fault bound by 1 can free 2^n-1 links from diagnosis. We present an algorithm that selects, in a systematic way, the to-be-freed links. For a fault-bound-drop by k, the proposed algorithm will produce an (n-k)-diagnosable system that remains connected and symmetrically structured. The freed links will never be used for the purpose of diagnosis, so that the diagnosis and some normal computation can be carried out simultaneously, improving the performance of the system as a whole.