Abstract
Given a set Tof npoints in ?2, a Manhattan Network Gis a network with all its edges horizontal or vertical segments, such that for all p,q? T, in Gthere exists a path (named a Manhattan path) of the length exactly the Manhattan distance between pand q. The Minimum Manhattan Network (MMN) problem is to find a Manhattan network of the minimum length, i.e., the total length of the segments of the network is to be minimized. In this paper we present a 2-approximation algorithm with time complexity O(n2), which improves the 2-approximation algorithm with time complexity ?(n8), proposed by Chepoi, Nouioua et al.. To the best of our knowledge, this is the best result on this problem.
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