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Fault Diameter of k-ary n-cube Networks
September 1997 (vol. 8 no. 9)
pp. 903-907

Abstract—We obtain the fault diameter of k-ary n-cube interconnection networks (also known as n-dimensional k-torus networks). We start by constructing a complete set of node-disjoint paths (i.e., as many paths as the degree) between any two nodes of a k-ary n-cube. Each of the obtained paths is of length zero, two, or four plus the minimum length except for one path in a special case (when the Hamming distance between the two nodes is one) where the increase over the minimum length may attain eight. These results improve those obtained in [8] where the length of some of the paths has a variable increase (which can be arbitrarily large) over the minimum length. These results are then used to derive the fault diameter of the k-ary n-cube, which is shown to be Δ + 1 where Δ is the fault free diameter.

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Index Terms:
Fault diameter, interconnection networks, k-ary n-cube, node-disjoint paths, torus.
Khaled Day, Abdel Elah Al-Ayyoub, "Fault Diameter of k-ary n-cube Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 9, pp. 903-907, Sept. 1997, doi:10.1109/71.615436
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