Price, Christopher2015-05-192015-05-192015-05-192015http://hdl.handle.net/10012/9356Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut problem and also contains a number of other combinatorial optimization problems as special cases. In this thesis, we study submodular function minimization and two related problems: matroid polyhedron membership and matroid intersection. A significant contribution concerns algorithms for the latter problems due to Cunningham. In particular, we identify and correct errors in the original proofs of the running time bounds for these algorithms.enalgorithmscombinatorial optimizationsubmodular function minimizationMaster ThesisCombinatorics and Optimization