Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems
| dc.contributor.advisor | Hicks, Illya V | en_US |
| dc.creator | Fast, Caleb C | en_US |
| dc.date.accessioned | 2017-08-01T17:50:49Z | en_US |
| dc.date.available | 2017-08-01T17:50:49Z | en_US |
| dc.date.created | 2017-05 | en_US |
| dc.date.issued | 2017-03-31 | en_US |
| dc.date.submitted | May 2017 | en_US |
| dc.date.updated | 2017-08-01T17:50:50Z | en_US |
| dc.description.abstract | This 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. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Fast, 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>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/96074 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright 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.subject | p-median | en_US |
| dc.subject | zero forcing | en_US |
| dc.subject | integer programming | en_US |
| dc.subject | branch decomposition | en_US |
| dc.subject | branchwidth | en_US |
| dc.subject | facility location | en_US |
| dc.subject | propagation time | en_US |
| dc.title | Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Computational and Applied Mathematics | en_US |
| thesis.degree.discipline | Engineering | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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