Algorithms to Find the Girth and Cogirth of a Linear Matroid

Simple item page
dc.contributor.advisorHicks, Illya V
dc.contributor.committeeMemberTapia, Richard A
dc.contributor.committeeMemberYin, Wotao
dc.contributor.committeeMemberBaraniuk, Richard G
dc.creatorArellano, John David
dc.date.accessioned2016-01-06T20:08:18Z
dc.date.available2016-01-06T20:08:18Z
dc.date.created2014-12
dc.date.issued2014-09-18
dc.date.submittedDecember 2014
dc.date.updated2016-01-06T20:08:18Z
dc.description.abstractIn this thesis, I present algorithms to find the cogirth and girth, the cardinality of the smallest cocircuit and circuit respectively, of a linear matroid. A set covering problem (SCP) formulation of the problems is presented. The solution to the linear matroid cogirth problem provides the degree of redundancy of the corresponding sensor network, and allows for the evaluation of the quality of the network. Hence, addressing the linear matroid cogirth problem can lead to significantly enhancing the design process of sensor networks. The linear matroid girth problem is related to reconstructing a signal in compressive sensing. I provide an introduction to matroids and their relation to the degree of redundancy problem as well as compressive sensing. I also provide an overview of the methods used to address linear matroid cogirth/girth problems, the SCP, and reconstructing a signal in compressive sensing. Computational results are provided to validate a branch-and-cut algorithm that addresses the SCP formulation as well as an algorithm which uses branch decompositions and dynamic programming to find the girth of a linear matroid.
dc.format.mimetypeapplication/pdf
dc.identifier.citationArellano, John David. "Algorithms to Find the Girth and Cogirth of a Linear Matroid." (2014) Diss., Rice University. <a href="https://hdl.handle.net/1911/87699">https://hdl.handle.net/1911/87699</a>.
dc.identifier.urihttps://hdl.handle.net/1911/87699
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectset covering
dc.subjectlinear matroid
dc.subjectcogirth
dc.subjectgirth
dc.titleAlgorithms to Find the Girth and Cogirth of a Linear Matroid
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
ARELLANO-DOCUMENT-2014.pdf
Size:
3.95 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.84 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.61 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Electronic Theses and Dissertations