Submodular minimization in the context of modern LP and MILP methods and solvers

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Abstract

We consider the application of mixed-integer linear programming (MILP) solvers to the minimization of submodular functions. We evaluate common large-scale linear-programming (LP) techniques (e.g., column generation, row generation, dual stabilization) for solving a LP reformulation of the submodular minimization (SM) problem. We present heuristics based on the LP framework and a MILP solver. We evaluated the performance of our methods on a test bed of min-cut and matroidintersection problems formulated as SM problems.

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Orso, A., Lee, J., & Shen, S. (2015). Submodular minimization in the context of modern LP and MILP methods and solvers. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9125, pp. 193–204). Springer Verlag. https://doi.org/10.1007/978-3-319-20086-6_15

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