A Simple 3-Approximation of Minimum Manhattan Networks

Given a set P of n points in the plane, a Manhattan network of P is a network that contains a rectilinear shortest path between every pair of points of P. A minimum Manhattan network of P is a Manhattan network of minimum total length. It is unknown whether it is NP-hard to construct a minimum Manhattan network. The best approximations published so far are a combinatorial 3-approximation algorithm in time O(n log n), and an LP-based 2-approximation algorithm. We present a new combinatorial 3-approximation for this problem in time O(n log n). Both our algorithm and its analysis are considerably simpler than the prior 3-approximation.

• Type: Conference
• Year: 2008
• Where: COLOGNETWENTE
• Authors: Bernhard Fuchs, Anna Schulze
• Keywords: COLOGNETWENTE 2008, Log N, Manhattan Network, Minimum Manhattan Network, Optimization