Abstract
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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Fujishige, S., Iwata, S. (2001). Bisubmodular Function Minimization. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_13
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DOI: https://doi.org/10.1007/3-540-45535-3_13
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