Algorithms to Find the Girth and Cogirth of a Linear Matroid

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dc.contributor.advisorHicks, Illya Ven_US
dc.contributor.committeeMemberTapia, Richard Aen_US
dc.contributor.committeeMemberYin, Wotaoen_US
dc.contributor.committeeMemberBaraniuk, Richard Gen_US
dc.creatorArellano, John Daviden_US
dc.date.accessioned2016-01-06T20:08:18Zen_US
dc.date.available2016-01-06T20:08:18Zen_US
dc.date.created2014-12en_US
dc.date.issued2014-09-18en_US
dc.date.submittedDecember 2014en_US
dc.date.updated2016-01-06T20:08:18Zen_US
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.en_US
dc.format.mimetypeapplication/pdfen_US
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>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/87699en_US
dc.language.isoengen_US
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.en_US
dc.subjectset coveringen_US
dc.subjectlinear matroiden_US
dc.subjectcogirthen_US
dc.subjectgirthen_US
dc.titleAlgorithms to Find the Girth and Cogirth of a Linear Matroiden_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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