Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems

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dc.contributor.advisorHicks, Illya V
dc.creatorFast, Caleb C
dc.date.accessioned2017-08-01T17:50:49Z
dc.date.available2017-08-01T17:50:49Z
dc.date.created2017-05
dc.date.issued2017-03-31
dc.date.submittedMay 2017
dc.date.updated2017-08-01T17:50:50Z
dc.description.abstractThis thesis presents new methods for solving two graph location problems, the p-Median problem and the zero-forcing problem. For the p-median problem, I present a branch decomposition based method that finds the best p-median solution that is limited to some input support graph. The algorithm can be used to either find an integral solution from a fractional linear programming solution, or it can be used to improve on the solutions given by a pool of heuristics. In either use, the algorithm compares favorably in running time or solution quality to state-of-the-art heuristics. For the zero-forcing problem, this thesis gives both theoretical and computational results. In the theoretical section, I show that the branchwidth of a graph is a lower bound on its zero-forcing number, and I introduce new bounds on the zero-forcing iteration index for cubic graphs. This thesis also introduces a special type of graph structure, a zero-forcing fort, that provides a powerful tool for the analysis and modeling of zero-forcing problems. In the computational section, I introduce multiple integer programming models for finding minimum zero-forcing sets and integer programming and combinatorial branch and bound methods for finding minimum connected zero-forcing sets. While the integer programming methods do not perform better than the best combinatorial method for the basic zero-forcing problem, they are easily adapted to the connected zero-forcing problem, and they are the best methods for the connected zero-forcing problem.
dc.format.mimetypeapplication/pdf
dc.identifier.citationFast, Caleb C. "Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems." (2017) Diss., Rice University. <a href="https://hdl.handle.net/1911/96074">https://hdl.handle.net/1911/96074</a>.
dc.identifier.urihttps://hdl.handle.net/1911/96074
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.subjectp-median
dc.subjectzero forcing
dc.subjectinteger programming
dc.subjectbranch decomposition
dc.subjectbranchwidth
dc.subjectfacility location
dc.subjectpropagation time
dc.titleNovel Techniques for the Zero-Forcing and p-Median Graph Location Problems
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
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