Submodular Minimization in the Context of Modern LP and MILP Methods and Solvers

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 matroid-intersection problems formulated as SM problems.

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