Strong diagnosability and conditional diagnosability of optical multi-mesh hypercube networks under the PMC model

Abstract

The strong diagnosability and conditional diagnosability are both novel concepts for measuring the reliability and fault tolerance of multicomputers. The optical multi-mesh hypercube (OMMH) networks, which integrate satisfactory features of both hypercubes and meshes and circumvent the lack of scalability of hypercubes and the large diameter of meshes, are promising optical interconnection topologies. For $(l,m,n)$-OMMH networks $(l,m\ge 4)$, this study shows that the strong diagnosability is $n+4$, and the conditional diagnosability is $4n+9$ if either (a) $n\ge 1$, or (b) $n=0$ and $(l,m)\ne (4,4),(4,5),(5,4)$.

Keywords:

• strong diagnosability
• conditional diagnosability
• PMC model
• optical multi-mesh hypercube network
• optical interconnect network

2010 AMS Subject Classifications:

• 68M15
• 94C15

Acknowledgments

The authors wish to express sincere gratitude to the anonymous reviewers and the Editor-in-Chief for their valuable comments and helpful suggestions, which have improved the quality of this paper greatly.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by the Scientific Research Fund of Sichuan Provincial Education Department [Grant No: 15ZA0130], the Key Scientific Research Fund of Xihua University [Grant No: z1422615] and the Fund of Lab of Security Insurance of Cyberspace, Sichuan Province [Grant No: szjj2015-057].