Covering Orthogonal Polygons with Non-Piercing Rectangles

Abstract

Given a simply connected orthogonal polygon P, a polynomial time algorithm is presented to cover the polygon with the minimum number of rectangles, under the restriction that if A and B are two overlapping rectangles in the cover then either A - B or B - A is connected. The algorithm runs in O(n log n + nm) time, where n is the number of vertices of P and m is the number of edges in the visibility graph of P that are either horizontal, vertical or form the diagonal of an empty rectangle.