Skip to main content

Research Repository

Advanced Search

Embedding long paths in k-ary n-cubes with faulty nodes and links

Stewart, I.A.; Xiang, Y.

Embedding long paths in k-ary n-cubes with faulty nodes and links Thumbnail


Authors

Y. Xiang



Abstract

Let $k \geq 4$ be even and let $n \geq 2$. Consider a faulty k-ary n-cube $Q_n^k$ in which the number of node faults $f_n$ and the number of link faults $f_e$ are such that $f_n + f_e \leq 2n-2$. We prove that given any two healthy nodes s and e of $Q_n^k$, there is a path from s to e of length at least $k^n - 2f_n - 1$ (resp. $k^n - 2f_n - 2$) if the nodes s and e have different (resp. the same) parities (the parity of a node in $Q_n^k$ is the sum modulo 2 of the elements in the n-tuple over {0, 1, ..., k-1} representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.

Citation

Stewart, I., & Xiang, Y. (2008). Embedding long paths in k-ary n-cubes with faulty nodes and links. IEEE Transactions on Parallel and Distributed Systems, 19(8), 1071-1085. https://doi.org/10.1109/tpds.2007.70787

Journal Article Type Article
Publication Date Aug 1, 2008
Deposit Date Jun 29, 2009
Publicly Available Date Mar 28, 2024
Journal IEEE Transactions on Parallel and Distributed Systems
Print ISSN 1045-9219
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 19
Issue 8
Pages 1071-1085
DOI https://doi.org/10.1109/tpds.2007.70787
Publisher URL http://www.dur.ac.uk/i.a.stewart/Papers/embedding.pdf

Files





You might also like



Downloadable Citations