Bisubmodular Function Minimization

This paper presents the first combinatorial, polynomial-time algorithm for minimizing bisubmodular functions, extending the scaling algorithm for submodular function minimization due to Iwata, Fleischer, and Fujishige. A bisubmodular function arises as a rank function of a delta-matroid. The scaling algorithm naturally leads to the first combinatorial polynomial-time algorithm for testing membership in delta-matroid polyhedra. Unlike the case of matroid polyhedra, it remains open to develop a combinatorial strongly polynomial algorithm for this problem.

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