An optimal algorithm for one-separation of a set of isothetic polygons

We consider the problem of separating a collection of isothetic polygons in the plane by translating one polygon at a time to infinity. The directions of translation are the four isothetic (parallel to the axes) directions, but a particular polygon can be translated only in one of these four directions. Our algorithm detects whether a scene is separable in this sense and computes a translational ordering of the polygons. The time and space complexities of our algorithm are O(n log n) and O(n) respectively, where n is the total number of vertices of the polygons in the scene. The best previous algorithm in the plane for this problem has complexities of O(n log(2) n) time and O(n log n) space. (C) 2003 Elsevier Inc. All rights reserved.