Abstract
We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane, called terminals, find a Steiner tree with at most k Steiner points such that the length of the longest edge in the tree is minimized. This problem is known to be NP-hard even to approximate within ratio \(\sqrt{2}\). We focus on finding exact solutions to the problem for a small constant k. Based on geometric properties of optimal location of Steiner points, we present an O(n logn) time exact algorithm for k = 1 and an O(n 2) time algorithm for k = 2. Also, we present an O(n logn) time exact algorithm to the problem for a special case where there is no edge between Steiner points.
Work by S.W. Bae was supported by the Brain Korea 21 Project. Work by C. Lee and S. Choi was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R01-2007-000-20865-0).
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Bae, S.W., Lee, C., Choi, S. (2009). On Exact Solutions to the Euclidean Bottleneck Steiner Tree Problem . In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_10
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DOI: https://doi.org/10.1007/978-3-642-00202-1_10
Publisher Name: Springer, Berlin, Heidelberg
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