The Component Diagnosability of General Networks

TL;DR

This paper investigates the maximum number of faulty nodes that can be accurately diagnosed in general networks under specific models, with applications to various well-known network structures and comparisons to other diagnosability measures.

Contribution

It determines the $(h+1)$-component diagnosability of general networks under the PMC and MM* models, extending fault diagnosis theory to multiple network types.

Findings

Derived the $(h+1)$-component diagnosability for general networks.

Analyzed diagnosability for several specific network topologies.

Compared component diagnosability with other fault diagnosability measures.

Abstract

The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The $h$-component diagnosability of $G$, denoted by $ct_{h}(G)$, is the maximum number of nodes of the faulty set $F$ that is correctly identified in a system, and the number of components in $G-F$ is at least $h$. In this paper, we determine the $(h+1)$-component diagnosability of general networks under the PMC model and MM$^{*}$ model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.