Submodular function minimization and related topics

It had been a long-standing open problem to devise a combinatorial polynomial algorithm for minimizing submodular functions. Iwata-Fleischer-Fujishige (IFF) and Schrijver resolved the problem independently and simultaneously. The present article is basically a survey, though not comprehensive, on submodular function minimization algorithms and also describes additional results and research subjects. In this article we first give an outline of the IFF algorithm and then show two modifications of the original IFF algorithm, which seem to be promising in practical implementation. We also describe a brief history of developments in submodular function minimization. Finally, we furnish some possible future research subjects in submodular function minimization.

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