Issue No. 09 - September (1997 vol. 8)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.615436
<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>
Fault diameter, interconnection networks, k-ary n-cube, node-disjoint paths, torus.
K. Day and A. E. Al-Ayyoub, "Fault Diameter of k-ary n-cube Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 903-907, 1997.