A Rounding Algorithm for Approximating Minimum Manhattan Networks

A rounding algorithm for approximating minimum Manhattan networks1

For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T ) = (V, E) with the property that its edges are horizontal or vertical segments connecting points in V ⊇ T and for every pair of terminals, the network N(T ) contains a shortest l1-path between them. A minimum Manhattan network on T is a Manhattan network of minimum possible length. The problem of findin...

Approximating Minimum Manhattan Networks

Given a set S of n points in the plane, we deene a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G = (V; E), where the vertex set V corresp...

Approximating a Minimum Manhattan Network

The Minimum Manhattan Network Problem: A Fast Factor-3 Approximation

Given a set of nodes in the plane and a constant t ≥ 1, a Euclidean t-spanner is a network in which, for any pair of nodes, the ratio of the network distance and the Euclidean distance of the two nodes is at most t. Such networks have applications in transportation or communication network design and have been studied extensively. In this paper we study 1-spanners under the Manhattan (or L1-) m...

Bidirected minimum Manhattan network problem

In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, we need to construct a network N (T) of minimum total length with the property that the edges of N (T) are axis-parallel and oriented in a such a way that every ordered pair of terminals is connected in N (T) by a directed Manhattan path. In this paper, we present a polynomial factor 2 approximation ...