The G-Good-Neighbor Local Diagnosability of a Hypercube Network Under the PMC Model

Abstract

A significant indicator used in evaluating the reliability of a multiprocessor system is fault diagnosability. Researchers concentrate on the diagnosability of the entire system while ignoring important local information about the system. In our paper, an innovative concept of fault diagnosability, called $g$ -good-neighbor local diagnosability, is put forward to study the diagnosability of a system at a node under the $g$ -good-neighbor condition. Moreover, we obtain the relationship between the local diagnosability of a system at each node and the whole system’s diagnosability under the $g$ -good-neighbor condition. Under the PMC model, we prove that the $g$ -good-neighbor local diagnosability of an $n$ -dimensional hypercube network $Q_{n}$ at each node is at least $2^{g} (n-g+1)-1$ for $0 \leq g \leq n-3$ and that when $n-2 \leq g \leq n-1$ , the $g$ -good-neighbor local diagnosability of $Q_{n}$ at each node is $2^{n-1}-1$ . Further, we easily derive the diagnosability of hypercube $Q_{n}$ under the $g$ -good-neighbor condition.