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

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dc.contributor.advisorHicks, Illya V.
dc.contributor.committeeMemberBixby, Robert E.
dc.contributor.committeeMemberCooper, Keith D.
dc.contributor.committeeMemberTapia, Richard A.
dc.creatorFast, Caleb
dc.date.accessioned2014-08-26T21:08:37Z
dc.date.available2014-08-26T21:08:37Z
dc.date.created2014-05
dc.date.issued2014-04-11
dc.date.submittedMay 2014
dc.date.updated2014-08-26T21:08:37Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.urihttps://hdl.handle.net/1911/76721
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.subjectTraveling salesman problem (TSP)
dc.subjectFractional 2-matching instance
dc.subjectSubtour elimination
dc.subject4/3 conjecture
dc.subjectIntegrality gap
dc.subjectApplied mathematics
dc.titleOn the Integrality Gap of the Subtour Relaxation of the Traveling Salesman Problem for Certain Fractional 2-matching Costs
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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