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Fort Neighborhoods: A Set Cover Formulation for Power Domination
This thesis introduces a novel separation algorithm for calculating power domination numbers and minimum power dominating sets in graphs. Additionally, it shows how the existence of solutions of special forms can be exploited ...
A Branch and Cut Approach to the Feedback Vertex Set Problem
In 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 ...
A Branch-and-Cut Method for Solving the Bilevel Clique Interdiction Problem
I introduce an algorithm to solve the current formulation of the bilevel clique interdiction problem. Interdiction, a military term, describes the removal of enemy resources. The single level clique interdiction problem ...
Bilevel Clique Interdiction and Related Problems
I introduce a formulation of the bilevel clique interdiction problem. Interdiction, a military term, describes the removal of enemy resources. The single level clique interdiction problem describes the attempt of an attacker ...
A Spectral Decomposition Heuristic for Near Optimal Capture Sets In Consensus Models
Given a network G=(V,E), consider the problem of selecting a subset of nodes, A, of a fixed size, k, such that the sum expected walk length from V to A, or hitting time, is minimized. This study is motivated by modeling ...