Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems
| dc.contributor.author | Fast, Caleb C. | |
| dc.date.accessioned | 2018-06-19T17:51:22Z | |
| dc.date.available | 2018-06-19T17:51:22Z | |
| dc.date.issued | 2017-05 | |
| dc.date.note | May 2017 | |
| dc.description | This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/96074 | |
| 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. | |
| dc.format.extent | 193 pp | |
| dc.identifier.citation | Fast, Caleb C.. "Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems." (2017) <a href="https://hdl.handle.net/1911/102254">https://hdl.handle.net/1911/102254</a>. | |
| dc.identifier.digital | TR17-08 | |
| dc.identifier.uri | https://hdl.handle.net/1911/102254 | |
| dc.language.iso | eng | |
| dc.title | Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems | |
| dc.type | Technical report | |
| dc.type.dcmi | Text |
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