Title :
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
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;
Conference_Titel :
Parallel and Distributed Systems, 2001. ICPADS 2001. Proceedings. Eighth International Conference on
Conference_Location :
Kyongju City
Print_ISBN :
0-7695-1153-8
DOI :
10.1109/ICPADS.2001.934861
