Abstract
Given a matrix with real-valued entries, the maximum 2D subarray problem consists in finding a rectangular submatrix with consecutive rows and columns maximizing the sum of its entries. In this work we start a polyhedral study of an integer programming formulation for this problem. We thus define the 2D subarray polytope , explore conditions ensuring the validity of linear inequalities, and provide several families of facet-inducing inequalities. We also report computational experiments assessing the reduction of the dual bound for the linear relaxation achieved by these families of inequalities.
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