On the Integrality Gap of the Subtour Relaxation of the Traveling Salesman Problem for Certain Fractional 2-matching Costs

dc.contributor.advisorHicks, Illya V.en_US
dc.contributor.committeeMemberBixby, Robert E.en_US
dc.contributor.committeeMemberCooper, Keith D.en_US
dc.contributor.committeeMemberTapia, Richard A.en_US
dc.creatorFast, Caleben_US
dc.date.accessioned2014-08-26T21:08:37Zen_US
dc.date.available2014-08-26T21:08:37Zen_US
dc.date.created2014-05en_US
dc.date.issued2014-04-11en_US
dc.date.submittedMay 2014en_US
dc.date.updated2014-08-26T21:08:37Zen_US
dc.description.abstractThis thesis provides new bounds on the strength of the subtour relaxation of the Traveling Salesman Problem (TSP) for fractional 2-matching cost instances whose support graphs have no fractional cycles larger than five vertices. This work provides insight for improving approximation heuristics for the TSP and into the structure of solutions produced by the subtour relaxation. Guided by a T-join derived from the subtour relaxation, I form a tour by adding edges to the subtour relaxation. By this constructive process, I prove that the optimal solution of the TSP is within 4/3, 17/12, or strictly less than 3/2 of the optimal solution of the subtour relaxation. Thus, this thesis takes a step towards proving the 4/3 conjecture for the TSP and the development of a 4/3 approximation algorithm for the TSP. These developments would provide improved approximations for applications such as DNA sequencing, route planning, and circuit board testing.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationFast, Caleb. "On the Integrality Gap of the Subtour Relaxation of the Traveling Salesman Problem for Certain Fractional 2-matching Costs." (2014) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/76721">https://hdl.handle.net/1911/76721</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/76721en_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.subjectTraveling salesman problem (TSP)en_US
dc.subjectFractional 2-matching instanceen_US
dc.subjectSubtour eliminationen_US
dc.subject4/3 conjectureen_US
dc.subjectIntegrality gapen_US
dc.subjectApplied mathematicsen_US
dc.titleOn the Integrality Gap of the Subtour Relaxation of the Traveling Salesman Problem for Certain Fractional 2-matching Costsen_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.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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