Optimal subcube embeddability in hypercubes with additional dimensions

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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.


Embedded computer systems; Hypercube networks (Computer networks); Parallel Computer Architecture; Parallel processing (Electronic computers)


Computer and Systems Architecture | Digital Communications and Networking | Electrical and Computer Engineering | Systems and Communications | Systems Architecture | Theory and Algorithms


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