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.
Original language | English |
---|---|
Pages (from-to) | 903-907 |
Number of pages | 5 |
Journal | IEEE Transactions on Parallel and Distributed Systems |
Volume | 8 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1997 |
Keywords
- Fault diameter
- Interconnection networks
- K-ary n-cube
- Node-disjoint paths
- Torus
ASJC Scopus subject areas
- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics