Analytical modelling of wormhole-routed k-ary n-cubes in the presence of matrix-transpose traffic
Journal of Parallel and Distributed Computing
The necklace-hypercube: a well scalable hypercube-based interconnection network for multiprocessors
Proceedings of the 2005 ACM symposium on Applied computing
Determining the conditional diagnosability of k-ary n-cubes under the MM* model
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
The edge-centered surface area of the arrangement graph
Journal of Combinatorial Optimization
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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.