FFNLFD: Fault Diagnosis of Multiprocessor Systems at Local Node With Fault-Free Neighbors Under PMC Model and MM* Model

Limei Lin, Yanze Huang, Yuhang Lin, Sun-Yuan Hsieh, Li Xu

Abstract: Fault diagnosability is utilized as a significant measure that reflects the reliability of a multiprocessor system. However, people frequently pay close attention to the entire system’s diagnosability while ignoring the system’s important local information. The <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -fault-free-neighbor local fault diagnosability (for short, <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -FFNLFD) is a novel indicator, which describes the diagnosability of a system at a local node with <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fault-free neighbors. In this paper, we propose the <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -FFNLFD of general networks at local node under the Preparata Metze Chien model. Moreover, we also characterize some important properties of <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -FFNLFD of a multiprocessor system under the comparison model. Furthermore, we apply our proposed conclusions to directly obtain the <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -FFNLFD of 11 well-known networks under PMC-M and MM*-M, including hypercubes, locally twisted cubes, <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -ary <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -cubes, crossed cubes, twisted hypercubes, exchanged hypercubes, star graphs, <inline-formula><tex-math notation="LaTeX">$(n,k)$</tex-math></inline-formula> -star graphs, <inline-formula><tex-math notation="LaTeX">$(n,k)$</tex-math></inline-formula> -arrangement graphs, data center network DCells and BCDCs. Finally, we compare the <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -FFNLFD with both diagnosability and conditional diagnosability, and it is shown that the <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -FFNLFD is greater than all the other fault diagnosabilities.