Minimum stabbing rectangular partitions of rectilinear polygons

We study integer programming (ip) models for the problem of finding a rectangular partition of a rectilinear polygon with minimum stabbing number. Strong valid inequalities are introduced for an existing formulation and a new model is proposed. We compare the dual bounds yielded by the relaxations of the two models and prove that the new one is stronger than the old one. Computational experiments with the problem are reported for the first time in which polygons with thousands of vertices are solved to optimality. The (ip) branch-and-bound algorithm based on the new model is faster and more robust than those relying on the previous formulation.