Minimum Manhattan network is NP-complete
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximating minimum manhattan networks in higher dimensions
ESA'11 Proceedings of the 19th European conference on Algorithms
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Given a set T of n points inℝ2, a Manhattan Network G is anetwork with all its edges horizontal or vertical segments, suchthat for all p,q ε T, inG there exists a path (named a Manhattan path) of thelength exactly the Manhattan distance between p andq. The Minimum Manhattan Network problem is to find aManhattan network of the minimum length, i.e., the totallength of the segments of the network is to be minimized. In thispaper we present a 2-approximation algorithm with time complexityO(nlogn), which improves the2-approximation algorithm with time complexityO(n2). Moreover, compared with other2-approximation algorithms employing linear programming or dynamicprogramming technique, it was first discovered that only greedystrategy suffices to get 2-approximation network.