Set covering polyhedra graphs, and matroids

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My primary area of interest is combinatorial optimization, in particular the integer programming models known as packing and covering. A wide variety of practical questions can be formulated in this setting and include: scheduling problems, assignment problems, and the problem of shipping one or more commodities across a network. Sometimes, owing to the special structure of the problem, the natural linear programming relaxation yields an optimal solution. When this occurs the problem can be solved efficiently. The focus of my research has been to characterize when this phenomenon occurs. Although these models have their roots in real life, this leads to deep questions of a purely mathematical nature.