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

Date
2017-05
Journal Title
Journal ISSN
Volume Title
Publisher
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.

Description
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/96074
Advisor
Degree
Type
Technical report
Keywords
Citation

Fast, Caleb C.. "Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems." (2017) https://hdl.handle.net/1911/102254.

Has part(s)
Forms part of
Published Version
Rights
Link to license
Citable link to this page