Polynomial time algorithms for three-label point labeling

Abstract

In this paper, we present an O(n(2) log n) time solution for the following multi-label map labeling problem: given a set S of n distinct sites in the plane, place at each site a triple of uniform squares of maximum possible size such that all the squares are axis-parallel and a site is on the boundaries of its three labeling squares. We also study the problem under the discrete model, i.e., a site must be at the corners of its three label squares. We obtain an optimal O(n log n) time algorithm for the latter problem. (C) 2002 Elsevier Science B.V. All rights reserved