Distributive lattices, stable matchings, and robust solutions
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The stable matching problem, first presented by mathematical economists Gale and Shapley, has been studied extensively since its introduction. As a result, a remarkably rich literature on the problem has accumulated in both theory and practice. In this thesis we further extend our understanding on several algorithmic and structural aspects of stable matching. We summarize the main contributions of the thesis as follows: generalizing stable matching to maximum weight stable matching; finding stable matchings that are robust to shifts; generalizing Birkhoff's Theorem, and providing an application to robust stable matching.