Optimal subcube embeddability in hypercubes with additional dimension
Subcube embeddability of the hypercube can be enhanced by introducing an additional dimension. A set of new dimensions, characterized by the Hamming distance between the pairs of nodes it connects, is introduced using a measure defined as the magnitude of a dimension. An enumeration of subcubes of various size is presented for a dimension parameterized by its magnitude. It is shown that the maximum number of subcubes for a Qn can only be attained when the magnitude of dimension is n-1 or n. It is further shown that the latter two dimensions can optimally increase the number of subcubes among all possible choices.
Covering; Hamming Distance; Job Allocation; Link; Node-identical
Controls and Control Theory | Electrical and Computer Engineering | Power and Energy | Signal Processing | Systems and Communications
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Optimal subcube embeddability in hypercubes with additional dimension.
Proceedings of the 2008 International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA 2008