Abstract
Given a d-dimensional array, the maximum subarray problem consists in finding an axis-parallel slice of the array maximizing the sum of its entries. In this work we start a polyhedral study of a natural integer programming formulation for this problem when d = 2. Such an exploration is motivated by the need of solving large-scale instances of the rectilinear picture compression problem (RPC), a problem which arises in different scenarios. The obtained results can be useful to solve the column generation phase of a branch and price approach for RPC, a technique that applies naturally to 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.
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