The g-extra diagnosability of the balanced hypercube under the PMC and MM* model

Abstract

Fault diagnosis plays an important role in the measuring of the fault tolerance of an interconnection network, which is of great value in the design and maintenance of large-scale multiprocessor systems. As a classical variant of the hypercube, the Balanced Hypercube, denoted by BH_n(n $\ge$ 1), has drawn a lot of research attention, and its $g$-extra diagnosability has been studied to improve the network diagnostic ability. However, the current literatures on $g$-extra diagnosability of BH_n under the PMC model only cover the cases of $g < 6$, and what’s more, seldom involve its $g$-extra diagnosability under the MM* model, which is a great limitation on the research of BH_n diagnosability. In this paper, the upper and lower bounds of the $g$-extra diagnosability of the balanced hypercube are proved, respectively, based on the $g$-extra connectivity by the contradiction method, and finally, the $g$-extra diagnosability of BH_n for $2 \le g \le 2n - 1$ under the PMC and MM* model is obtained, i.e., $2\left[ {\left( {n - 2} \right)\lceil\frac{g - 1}{2}\rceil + n} \right] + g$. In addition, as a special case, the $g$-extra diagnosability of the balanced hypercube for $g = 2n$ is proved to be $2^{2n - 1} - 1$ under the PMC and MM* model. In the end, simulation experiments are conducted to verify the effectiveness of our proposed theories. The conclusion of this paper has certain theory and application value for the research of BH_n fault diagnosis.