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.
Repository Citation
Yasim, S.,
Latifi, S.
(2008).
Optimal Subcube Embeddability in Hypercubes with Additional Dimension.
Proceedings of the 2008 International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA 2008
183-187.
CSREA Press.