Hicks, Illya V2019-05-172019-05-172018-122018-11-29December 2Bell, Nick. "A Branch and Cut Approach to the Feedback Vertex Set Problem." (2018) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/105909">https://hdl.handle.net/1911/105909</a>.https://hdl.handle.net/1911/105909In this thesis, I use a branch and cut implementation to solve the feedback vertex set problem and add new facet defining inequalities to the literature. Feedback in a system arises when repeated traversal over some cycle causes unwanted growth or decay in the data. This can cause problems in many systems such as excess noise at a concert or deadlock forming cyclical dependence on processes in a group. To eliminate the feedback, I implement a branch and cut algorithm to make the calculations, selecting inequalities based on results from the literature. I report improvements upon previous branch and cut work in a collection of random cases. Along with this implementation, I show that the clique inequalities, which are known to be valid for the feedback vertex problem, are in fact facet inducing for all maximal clique subgraphs of the original network.application/pdfengCopyright 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.Branch and CutFeedback Vertex SetGraph TheoryCombinatorial OptimizationFacetThesis2019-05-17