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Erschienen in:
06.01.2022
A unified approach to reliability and edge fault tolerance of cube-based interconnection networks under three hypotheses
Erschienen in: The Journal of Supercomputing | Ausgabe 6/2022
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Abstract
The topological structures of the interconnection networks of some parallel and distributed systems are designed as n-dimensional hypercube \(Q_n\) or n-dimensional folded hypercube \(FQ_n\) with \(N=2^n\) processors. For integers \(0\le k\le {n-1}\), let \(\mathcal {P}_1^k\), \(\mathcal {P}_2^k\) and \(\mathcal {P}_3^k\) be the property of having at least k neighbors for each processor, containing at least \(2^k\) processors and admitting average neighbors at least k, respectively. \(\mathcal {P}\)-conditional edge-connectivity of G, \(\lambda (\mathcal {P},G)\), is the minimum cardinality of faulty edge-cut, whose malfunction divides this network into several components, with each component satisfying the property of \(\mathcal {P}\). For each integer \(0\le k\le {n-1}\), and \(1\le i\le 3\), this paper offers a unified method to investigate the \(\mathcal {P}_i^k\)-conditional edge-connectivity of \(Q_n\) and \(FQ_n\). Exact value of \(\mathcal {P}_i^k\)-conditional edge-connectivity of \(Q_n\), \(\lambda (\mathcal {P}_i^k,Q_n)\), is \((n-k)2^k\), and that of \(\mathcal {P}_i^k\)-conditional edge-connectivity of \(FQ_n\), \(\lambda (\mathcal {P}_i^k,FQ_n)\), is \((n-k+1)2^k\). Our method generalizes the result of Guo and Guo in [The Journal of Supercomputing, 2014, 68:1235-1240] and the previous other results.