Abstract
Processor fault diagnosis plays an important role for measuring the reliability of multiprocessor systems, and the diagnosability of many well-known interconnection networks has been investigated widely. Conditional diagnosability is a novel measure of diagnosability, which is introduced by Lai et al., by adding an additional condition that any faulty set cannot contain all the neighbors of any vertex in a system. The class of k-ary n-cubes contains as special cases many topologies important to parallel processing, such as rings, hypercubes, and tori. In this paper, we study some topological properties of the k-ary n-cube, denoted by \(Q^k_n\). Then we apply them to show that the conditional diagnosability of \(Q^k_n\) under the comparison diagnosis model is \(t_c(Q^k_n)=6n-5\) for k ≥ 4 and n ≥ 4.
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Hsieh, SY., Kao, CY. (2011). Determining the Conditional Diagnosability of k-Ary n-Cubes Under the MM* Model. In: Kosowski, A., Yamashita, M. (eds) Structural Information and Communication Complexity. SIROCCO 2011. Lecture Notes in Computer Science, vol 6796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22212-2_8
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DOI: https://doi.org/10.1007/978-3-642-22212-2_8
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