Augmented k-ary n-cubes

Xiang, Y.; Stewart, I.A.

Abstract

We define an interconnection network AQn,k which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQn,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQn,k: is a Cayley graph (and so is vertex-symmetric); has connectivity 4n-2, and is such that we can build a set of 4n-2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{(n-1)k-(n-2), k+7}; has diameter ⌊ k/3 ⌋ + ⌈ (k-1)/3 ⌉, when n = 2; and has diameter at most k(n+1)/4, for n ≥ 3 and k even, and at most k(n+1)/4+n/4, for n ≥ 3 and k odd.

Citation

Xiang, Y., & Stewart, I. (2011). Augmented k-ary n-cubes. Information Sciences, 181(1), 239-256. https://doi.org/10.1016/j.ins.2010.09.005

• Journal Article Type: Article
• Publication Date: Jan 1, 2011
• Deposit Date: Aug 25, 2009
• Publicly Available Date: Oct 25, 2010
• Journal: Information Sciences
• Print ISSN: 0020-0255
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 181
• Issue: 1
• Pages: 239-256
• DOI: https://doi.org/10.1016/j.ins.2010.09.005
• Keywords: Interconnection networks. Parallel computing. k-ary n-cubes. Augmented cubes.
• Public URL: https://durham-repository.worktribe.com/output/1532485
• Publisher URL: http://www.dur.ac.uk/i.a.stewart/Papers/Augkaryncube.pdf