The Strong Local Diagnosability of a Hypercube Network with Missing Edges

Abstract

In the research on the reliability of a connection network, diagnosability is an important problem that should be considered. In this article, a new concept regarding diagnosability, called strong local diagnosability (SLD), which describes the local status of the strong diagnosability (SD) of a system, is presented. In addition, a few important results related to the SLD of a node of a system are presented. Based on these results, we conclude that in a hypercube network of n dimensions, denoted by Q n , the SLD of a node is equal to its degree when n ⩾ 4. Moreover, we explore the SLD of a node of an incomplete hypercube network. We determine that the SLD of a node is equal to its remaining degree (RD) in an incomplete hypercube network, which is true provided that the number of faulty edges in this hypercube network does not exceed n − 3 . Finally, we discuss the SLD of a node for an incomplete hypercube network and obtain the following results: if the minimum RD of nodes in an incomplete hypercube network of n-dimensions is greater than 3, then the SLD of any node is still equal to its RD provided that the number of faulty edges does not exceed 7 n − 3 − 1. If the RD of each node is greater than 4, then the SLD of each node is also equal to its RD, no matter how many faulty edges exist in Q n .

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

“…In [21], Hsu et al proposed the concept of local diagnosability and proved several related theorems. The researchers believed that a t-diagnosable system might correctly diagnose all faulty nodes in the system if the number of faulty nodes exceeded t. Xie et al [22] proposed a definition of strong local diagnosability that could more directly determine the local diagnosability of nodes in a system. In the cited article, the researchers also determined that a hypercube and an incomplete hypercube had strong local diagnosability at each node under certain conditions.…”

Two-Round Diagnosability Measures for Multiprocessor Systems

“…For a system having at most t faulty nodes, if it can determine a set with the size s (s ≤ t) that contains all its faulty nodes, then it is t/s-diagnosable. Numerous studies have been reported on a t/s-diagnosable system, such as [6][7][8][9][10][11][12].…”