The g-good-neighbour conditional diagnosability of enhanced hypercube under PMC model

Abstract

The significant increase in the number of processors of multiprocessor system increases its vulnerability to component failures. Diagnosability is an important indicator for the reliability of interconnection networks. The g-good-neighbour conditional diagnosability is the maximum number of faulty vertices a network can guarantee to identify, under the condition that every fault-free vertex has at least g fault-free neighbours (i.e. good neighbours). In this paper, we establish that the 1-good-neighbour conditional diagnosability of $(n,k)$-enhanced hypercube network $Q_{n,k}$ under PMC model is 2n−1 for n = k + 1 and $k\ge 3$, or 2n + 1 for n>k + 1 and $k\ge 3$, respectively. Moreover, the 2-good-neighbour conditional diagnosability of $Q_{n,k}$ is 3n−3 for n = k + 1 and $k\ge 4$, or 4n−5 for n = k + 2 and $k\ge 3$, or 4n−1 for n>k + 2 and $k\ge 3$, respectively.

Keywords:

• Enhanced hypercube
• PMC model
• g-good-neighbour conditional diagnosability
• system-level diagnosis

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 61702100, 61702103, 61771140), the China Postdoctoral Science Foundation (Nos. 2018T110636, 2017M612107); and the Foundation of Digital Fujian Institute of Big Data for Agriculture and Forestry (No. 117-KJG18019A); Fujian University of Technology (No. GY-Z17008). Education Department of Fujian Province (No. JAT170397). Limei Lin and Riqing Chen are the corresponding authors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 61702100, No. 61702103, No. 61771140), the China Postdoctoral Science Foundation (No. 2018T110636, No. 2017M612107); and the Foundation of Digital Fujian Institute of Big Data for Agriculture and Forestry (No. 117-KJG18019A); Fujian University of Technology (No. GY-Z17008). Education Department of Fujian Province (No. JAT170397). Limei Lin and Riqing Chen are the corresponding authors.