Abstract
Reliability measure of multiprocessor systems is of great significant importance to the design and maintenance of multiprocessor systems. As a generalization of traditional edge-connectivity, extra edge-connectivity is one important parameter to evaluate the fault-tolerant capability of multiprocessor systems. Fast identifying the extra edge-connectivity of high order remains a scientific problem for many useful multiprocessor systems. In this paper, we determine the h-extra edge-connectivity of the n-dimensional augmented cube \(AQ_n\) for \(h \in [1, 2^{n-1}]\). Specifically, we divide the interval \([1, 2^{n-1}]\) into some subintervals and obtain the monotonicity of \(\lambda _h(AQ_n)\) in these subintervals, and then deduce a recursive formula of \(\lambda _h(AQ_n)\). Based on this formula, an efficient algorithm with complexity \(O(\log _2 N)\) is designed to determine the exact values of h-extra edge-connectivity of \(AQ_n\) for \(h \in [1, 2^{n-1}]\) completely. Some previous results in Ma et al. (Inf Process Lett 106: 59-63, 2008) and Zhang et al. (J Parall Distrib Comput 147: 124-131, 2021) are extended.
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This work is supported by Natural Science Foundation of Fujian Province, China (No.2021J01860), National Natural Science Foundation of China (Nos.11301217, 61572010), New Century Excellent Talents in Fujian Province University (No.JA14168).
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Xu, L., Zhou, S. An O(log2 N) algorithm for reliability assessment of augmented cubes based on h-extra edge-connectivity. J Supercomput 78, 6739–6751 (2022). https://doi.org/10.1007/s11227-021-04129-0
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DOI: https://doi.org/10.1007/s11227-021-04129-0