A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
On the complexity of submodular function minimisation on diamonds
Discrete Optimization
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This paper discusses an extension of the Dulmage--Mendelsohn decomposition for a certain class of matrices whose row-set and column-set are divided into couples or singletons. A genericity assumption is imposed and an admissible transformation is defined in respect of this partition structure. Extensions of the Konig--Egervary theorem and the Hall--Ore theorem are established. The latter states that the rank of such a matrix is characterized by the minimum value of a submodular function, of which the set of minimizers yields a canonical block-triangularization under the admissible transformations.