Abstract
Given a set T of n points in ℝ2, 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 (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(n 2), which improves the 2-approximation algorithm with time complexity Ω(n 8), proposed by Chepoi, Nouioua et al.. To the best of our knowledge, this is the best result on this problem.
This work is supported by Shanghai Leading Academic Discipline Project(Project Number:B412) and National Natural Science Fund (grant #60496321 and #60703091). Correspondence author: He Sun
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Guo, Z., Sun, H., Zhu, H. (2008). A Fast 2-Approximation Algorithm for the Minimum Manhattan Network Problem. In: Fleischer, R., Xu, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2008. Lecture Notes in Computer Science, vol 5034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68880-8_21
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DOI: https://doi.org/10.1007/978-3-540-68880-8_21
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