Combinatorial Algorithms for Submodular Function Minimization and Related Problems
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Date
2015-05-19
Authors
Price, Christopher
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Journal ISSN
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Publisher
University of Waterloo
Abstract
Submodular 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.
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Keywords
algorithms, combinatorial optimization, submodular function minimization