On some properties of k-ary n-cubes

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...

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Bibliographic Details
Published in:Proceedings. Eighth International Conference on Parallel and Distributed Systems. ICPADS 2001 pp. 517 - 524
Main Authors: Sarbazi-Azad, H., Ould-Khaoua, M., Mackenzie, L.M., Akl, S.G.
Format: Conference Proceeding
Language:English
Published: IEEE 2001
Subjects:
Broadcasting
Delay
Hamming distance
Hypercubes
Load management
Multiprocessor interconnection networks
Network topology
Routing
Tree data structures
ISBN:0769511538, 9780769511535
ISSN:1521-9097
Online Access:Get full text
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Summary: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.
ISBN:0769511538
9780769511535
ISSN:1521-9097
DOI:10.1109/ICPADS.2001.934861