ON THE COMBINATORIAL PROPERTIES OF k-ARY n-CUBES-Reference-Cited by-同舟云学术

ON THE COMBINATORIAL PROPERTIES OF k-ARY n-CUBES

Published:2004-03 Issue:01 Volume:05 Page:79-91
ISSN:0219-2659
Container-title:Journal of Interconnection Networks
language:en
Short-container-title:J. Inter. Net.

Author:

SARBAZI-AZAD H.¹,OULD-KHAOUA M.²,MACKENZIE L. M.²,AKL S. G.³

Affiliation:

1. Sharif University of Technology Computer Engineering Department & IPM School of Computer Science, Tehran, Iran

2. Department of Computing Science, University of Glasgow, Glasgow, G12 8QQ, U.K.

3. School of Computing, Queen's University, Kingston, Ontario, Canada

Abstract

The k-ary n-cube has been used as the underlying topology for most practical multicomputers, and has been extensively studied in the past. In this paper, we investigate some properties of this network. In particular, we study the problem of finding the number of nodes located i hops away from a given node (surface area) and the number of nodes located within i hops away from a given node (volume) in both the unidirectional and bidirectional k-ary n-cube, and have derived exact expressions calculating these numbers. These results are very useful when studying, for example, the spanning tree structure of the k-ary n-cube and the problem of resource placement in this network.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Networks and Communications

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219265904001039

Reference16 articles.

1. On Embedding Cycles in k-Ary n-Cubes

2. Communication algorithms in k-ary n-cube interconnection networks

3. On the k-ary hypercube

4. Rotator graphs: an efficient topology for point-to-point multiprocessor networks

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