Abstract
Given a set T of n points in 
, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p,q ∈ T, in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network 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(nlogn), which improves the 2-approximation algorithm with time complexity O(n2). Moreover, compared with other 2-approximation algorithms employing linear programming or dynamic programming technique, it was first discovered that only greedy strategy suffices to get 2-approximation network.
This work is supported by Shanghai Leading Academic Discipline Project(Project Number:B412), National Natural Science Fund (grant #60496321), and the ChunTsung Undergraduate Research Endowment.
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Guo, Z., Sun, H., Zhu, H. (2008). Greedy Construction of 2-Approximation Minimum Manhattan Network. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_4
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DOI: https://doi.org/10.1007/978-3-540-92182-0_4
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