Covering a set of points in a plane using two parallel rectangles

In this paper we consider the problem of finding two parallel rectangles in arbitrary orientation for covering a given set of n points in a plane, such that the area of the larger rectangle is minimized. We propose an algorithm that solves the problem in O(n3) time using O(n2) space. Without altering the complexity, our approach can be used to solve another optimization problem namely, minimize the sum of the areas of two arbitrarily oriented parallel rectangles covering a given set of points in a plane.