On some properties of k-ary n-cubes

Author

Azad, H. Sarbazi ; Khaoua, M. Odd ; Mackenzie, L.M. ; Akl, S.G.

Author_Institution

Dept. of Comput. Sci., Glasgow Univ., UK

fYear

2001

fDate

2001

Firstpage

517

Lastpage

524

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. 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

Keywords

multiprocessor interconnection networks; parallel architectures; resource allocation; trees (mathematics); bidirectional k-ary n-cube; hops; multicomputers; multiprocessor interconnection; nodes; resource placement; spanning tree structure; topology; unidirectional k-ary n-cube; Broadcasting; Delay; Hamming distance; Hypercubes; Load management; Multiprocessor interconnection networks; Network topology; Routing; Tree data structures;

fLanguage

English

Publisher

ieee

Conference_Titel

Parallel and Distributed Systems, 2001. ICPADS 2001. Proceedings. Eighth International Conference on

Conference_Location

Kyongju City

ISSN

1521-9097

Print_ISBN

0-7695-1153-8

Type

conf

DOI

10.1109/ICPADS.2001.934861

Filename

934861