On some properties of k-ary n-cubes

H. Sarbazi-Azad, M. Ould-Khaoua, L. M. Mackenzie, S. G. Akl

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationProceedings of the Internatoinal Conference on Parallel and Distributed Systems - ICPADS
Pages517-524
Number of pages8
Publication statusPublished - 2001
Event8th International Conference on Parallel and Distributed Systems - Kyongju, Korea, Republic of
Duration: Jun 26 2001Jun 29 2001

Other

Other8th International Conference on Parallel and Distributed Systems
CountryKorea, Republic of
CityKyongju
Period6/26/016/29/01

ASJC Scopus subject areas

  • Engineering(all)

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    Sarbazi-Azad, H., Ould-Khaoua, M., Mackenzie, L. M., & Akl, S. G. (2001). On some properties of k-ary n-cubes. In Proceedings of the Internatoinal Conference on Parallel and Distributed Systems - ICPADS (pp. 517-524)