Maximizing a submodular function by integer programming: Polyhedral results for the quadratic case

We give a new mixed integer programming (MIP) formulation for the quadratic cost partition problem that is derived from a MIP formulation for maximizing a submodular function. Several classes of valid inequalities for the convex hull of the feasible solutions are derived using the valid inequalities for the node packing polyhedron. Facet defining conditions and separation algorithms are discussed and computational results are reported.