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- W3111983428 abstract "Abstract The diagnosability is one of the most important measures of the reliability of networks. Consider the setting where there are large-scale failures that disconnect the network and result in many components. Then, the diagnosability is closely related to the number of components. In this paper, we define and study the $boldsymbol{g}$-component diagnosability of network $boldsymbol{G}$, which is denoted by $boldsymbol{ct_g(G)}$ and has not been addressed before. $boldsymbol{ct_g(G)}$ is the maximum number of nodes in the faulty node set $boldsymbol{F}$ of $boldsymbol{G}$ such that $boldsymbol{G-F}$ has at least $boldsymbol{g}$ components and diagnosis model can identify all nodes in $boldsymbol{F}$. Under PMC and MM$^*$ diagnosis models, we show that, in the hypercube $boldsymbol{Q_n (ngeq 7)}$, $boldsymbol{ct_{g+1}(Q_n)=-(1/2)g^2+(n-3/2)g+n}$ when $boldsymbol{gleq n-1}$. Moreover, we determine the $boldsymbol{(n+1)}$-component diagnosability $boldsymbol{ct_{n+1}(Q_n)=n^2/2+n/2-2}$ for $boldsymbol{ngeq 7}$." @default.
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- W3111983428 date "2020-12-14" @default.
- W3111983428 modified "2023-10-16" @default.
- W3111983428 title "The Component Diagnosability of Hypercubes with Large-Scale Faulty Nodes" @default.
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- W3111983428 doi "https://doi.org/10.1093/comjnl/bxaa155" @default.
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