Title

Optimal Subcube Embeddability in Hypercubes with Additional Dimension

Document Type

Conference Proceeding

Publication Date

2008

Publication Title

Proceedings of the 2008 International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA 2008

Publisher

CSREA Press

First page number:

183

Last page number:

187

Abstract

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.

Keywords

Covering; Hamming Distance; Job Allocation; Link; Node-identical

Disciplines

Controls and Control Theory | Electrical and Computer Engineering | Power and Energy | Signal Processing | Systems and Communications

Language

English

Permissions

Use Find in Your Library, contact the author, or interlibrary loan to garner a copy of the item. Publisher policy does not allow archiving the final published version. If a post-print (author's peer-reviewed manuscript) is allowed and available, or publisher policy changes, the item will be deposited.

Identifier

DOI: http://dx.doi.org/10.1142/S0129626410000077

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