A (1+)-approximation algorithm for 2-line-center

We consider the following instance of projective clustering, known as the 2-line-center problem: Given a set S of n points in R2, cover S by two congruent strips of minimum width. Algorithms that find the optimal solution for this problem have near-quadratic running time. In this paper we present an algorithm that, for any ε > 0, computes in time O(n(logn+ ε−2 log(1/ε))+ ε−7/2 log(1/ε)) a cover of S by two strips of width at most (1 + ε)w∗.  2003 Elsevier B.V. All rights reserved.