FFNLFD: Fault Diagnosis of Multiprocessor Systems at Local Node with Fault-Free Neighbors under PMC Model and MM∗ Model

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 mm-fault-free-neighbor local fault diagnosability (for short, mm-FFNLFD) is a novel indicator, which describes the diagnosability of a system at a local node with mm fault-free neighbors. In this paper, we propose the mm-FFNLFD of general networks at local node under the Preparata Metze Chien model. Moreover, we also characterize some important properties of mm-FFNLFD of a multiprocessor system under the comparison model. Furthermore, we apply our proposed conclusions to directly obtain the mm-FFNLFD of 11 well-known networks under PMC-M and MM*-M, including hypercubes, locally twisted cubes, kk-ary nn-cubes, crossed cubes, twisted hypercubes, exchanged hypercubes, star graphs, (n,k)(n,k)-star graphs, (n,k)(n,k)-arrangement graphs, data center network DCells and BCDCs. Finally, we compare the mm-FFNLFD with both diagnosability and conditional diagnosability, and it is shown that the mm-FFNLFD is greater than all the other fault diagnosabilities.