Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.


Durham Research Online
You are in:

Augmented k-ary n-cubes.

Xiang, Y. and Stewart, I. A. (2011) 'Augmented k-ary n-cubes.', Information sciences., 181 (1). pp. 239-256.

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.

Item Type:Article
Keywords:Interconnection networks. Parallel computing. k-ary n-cubes. Augmented cubes.
Full text:PDF - Accepted Version (269Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.ins.2010.09.005
Record Created:25 Aug 2009 11:20
Last Modified:02 Nov 2010 12:19

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Usage statisticsLook up in GoogleScholar | Find in a UK Library