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A Novel Conditional Diagnostic Scheme for Hypercube-Based Multiprocessor Systems
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DOI：10.1109/TON.2025.3638453.png)
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Abstract
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With the scale of multiprocessor systems constantly increasing, the large number of interconnected processors (or nodes) makes faulty nodes inevitable. The fault diagnosis of multiprocessor systems therefore is a key technique for the system’s robustness. In this paper, we first propose a novel diagnostic metric, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula>-extra <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-component diagnosability, denoted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ECD^{h}_{r}(G)$ </tex-math></inline-formula>, which characterizes one special pattern of faults. We derive some theoretical results for the ECD of hypercube, denoted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ECD^{h}_{r}(Q_{n})$ </tex-math></inline-formula>, under the PMC model. Diagnostic algorithms is proposed and implemented to detect faulty nodes that will disconnect hypercube <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{n}$ </tex-math></inline-formula> into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> components each containing at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h+1$ </tex-math></inline-formula> nodes. We also test the ECD-PMC algorithm to the hypercube network with different number of faulty processors satisfying the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula>-extra <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-component condition. Extensive simulation results show that our proposed method achieves very good performance in terms of ACCR, TPR, FPR, and TNR.
Keywords:
Interconnection networks
$h$ -extra $r$ -component diagnosability
hypercube
network reliability
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