Integer Linear Programming Models for the Problem of Covering a Polygonal Region by Rectangles

Abstract

The aim of the paper is to develop integer linear programming (ILP) models for the problem of covering a polygonal region by rectangles. We formulate a Beasley-type model in which the number of variables depends on the size parameters. Another ILP model is proposed which has O(n2 max{m, n}) variables where m is the number of edges of the target set and n is the number of given rectangles. In particular we consider the case where the polygonal region is convex. Extensions are also discussed where we allow the polygonal region to be a union of a finite number of convex subsets.