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Issue No.09 - September (1997 vol.8)

pp: 903-907

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.615436

ABSTRACT

<p><b>Abstract</b>—We obtain the fault diameter of <it>k</it>-ary <it>n</it>-cube interconnection networks (also known as <it>n</it>-dimensional <it>k</it>-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 <it>k</it>-ary <it>n</it>-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 [<ref rid="bibl09038" type="bib">8</ref>] 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 <it>k</it>-ary <it>n</it>-cube, which is shown to be Δ + 1 where Δ is the fault free diameter.</p>

INDEX TERMS

Fault diameter, interconnection networks, k-ary n-cube, node-disjoint paths, torus.

CITATION

Khaled Day, Abdel Elah Al-Ayyoub, "Fault Diameter of k-ary n-cube Networks",

*IEEE Transactions on Parallel & Distributed Systems*, vol.8, no. 9, pp. 903-907, September 1997, doi:10.1109/71.615436