On the approximability of orthogonal order preserving layout adjustment

Abstract

Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the orthogonal order i.e. maintains the sorted ordering of the rectangle centers along both x-axis and y-axis with respect to the initial placement. This problem is known as Layout Adjustment for Disjoint Rectangles (LADR). It was known that LADR is ℕℙ-hard, but only heuristics were known for it. We show that a certain decision version of LADR is (image found)ℙ(image found)-hard, and give a constant factor approximation for LADR.