The local diagnosability of directed interconnection networks

The diagnosability is a vital parameter to measure the self-fault diagnosis ability of interconnection networks of computer systems. The local diagnosability is a generalization of diagnosability, which focuses on the fault diagnosability at a given processor. In this paper, we discuss the local diagnosability and the good in-neighbor conditional local diagnosability of directed networks, and present some necessary and sufficient conditions for a directed network to be locally ζ-diagnosable or good in-neighbor conditional locally ζ-diagnosable at a processor. We also present an algorithm under the PMC model to determine the fault or fault-free state of a given processor in a directed network. As an empirical testing, we demonstrate that our algorithm can ascertain the state of each vertex of unidirectional hypercube $U{Q}_n$ if the number of faulty vertices is not more than $n-1$.