Award Date

1-1-2008

Degree Type

Thesis

Degree Name

Master of Electrical Engineering (MEE)

Department

Electrical and Computer Engineering

First Committee Member

Shahram Latifi

Number of Pages

60

Abstract

Hypercube networks have received much attention from both parallel processing and communications areas over the years since they offer a rich interconnection structure with high bandwidth, logarithmic diameter, and high degree of fault tolerance. They are easily partitionable and exhibit a high degree of fault tolerance. Fault-tolerance in hypercube and hypercube-based networks received the attention of several researchers in recent years; The primary idea of this study is to address and analyze the reliability issues in hypercube networks. It is well known that the hypercube can be augmented with one dimension to replace any of the existing dimensions should any dimension fail. In this research, it is shown that it is possible to add i dimensions to the standard hypercube, Qn to tolerate (i - 1) dimension failures, where 0 < i ≤ n. An augmented hypercube, Qn +(n) with n additional dimensions is introduced and compared with two other hypercube networks with the same amount of redundancy. Reliability analysis for the three hypercube networks is done using the combinatorial and Markov modeling. The MTTF values are calculated and compared for all three networks. Comparison between similar size hypercube networks show that the augmented hypercube is more robust than the standard hypercube; As a related problem, we also look at the subcube embeddability. 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 sizes 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

Augmented; Embeddability; Fault; Hypercubes; Subcube; Tolerance

Controlled Subject

Electrical engineering; Computer science

File Format

pdf

File Size

931.84 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

Permissions

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Identifier

https://doi.org/10.25669/gvyf-47lz


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