Optimal Subcube Embeddability in Hypercubes with Additional Dimensions
Document Type
Article
Publication Date
2010
Publication Title
Parallel Processing Letters
Volume
20
Issue
1
First page number:
91
Last page number:
99
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
Embedded computer systems; Hypercube networks (Computer networks); Parallel Computer Architecture; Parallel processing (Electronic computers)
Disciplines
Computer and Systems Architecture | Digital Communications and Networking | Electrical and Computer Engineering | Systems and Communications | Systems Architecture | Theory and Algorithms
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.
(2010).
Optimal Subcube Embeddability in Hypercubes with Additional Dimensions.
Parallel Processing Letters, 20(1),
91-99.
