A 1.5-Approximation of the Minimal Manhattan Network Problem
Given a set of points in the plane, the Minimal Manhattan Network Problem asks for an axis-parallel network that connects every pair of points by a shortest path under L 1-norm (Manhattan metric). The goal is to minimize the overall length of the network.
We present an approximation algorithm that provides a solution of length at most 1.5 times the optimum. Previously, the best known algorithm has given only a 2-approximation.
KeywordsShort Path Line Segment Grid Line Admissible Solution Vertical Line Segment
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- 2.Benkert, M., Shirabe, T., Wolff, A.: The Minimum Manhattan Network Problem—Approximations and Exact Solution. In: Proc. 20th European Workshop on Computational Geometry (EWCG 2004), pp. 209–212 (2004)Google Scholar