An improved algorithm for the minimum manhattan network problem

Abstract

For a set S of n points in the plane, a Manhattan network on S is a geometric network G(S) such that, for each pair of points in S, G(S) contains a rectilinear path between them of length equal to their distance in the L 1-metric. The minimum Manhattan network problem is a problem of finding a Manhattan network of minimum length. Gudmundsson, Levcopoulos, and Narasimhan proposed a 4-approximation algorithm and conjectured that there is a 2-approximation algorithm for this problem. In this paper, based on a different approach, we improve their bound and present a 2-approximation algorithm. © Springer-Verlag Berlin Heidelberg 2002.