Title

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.

Identifier

DOI: 10.1142/S0129626410000077

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