Abstract
Given n terminals in the plane ℝ2 and a positive integer k, the bottleneck Steiner tree problem is to find k Steiner points in ℝ2 so that the longest edge length of the resulting Steiner tree is minimized. In this paper, we study this problem in any L p metric. We present the first fixed-parameter tractable algorithm running in O(f(k)·n 2logn) time for the L 1 and the L ∞ metrics, and the first exact algorithm for any other L p metric with 1 < p < ∞ whose time complexity is O(f(k)·(n k + n logn)), where f(k) is a function dependent only on k. Note that prior to this paper there was no known exact algorithm even for the L 2 metric, and our algorithms take a polynomial time in n for fixed k.
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 Fouundation (KOSEF) grant funded by the Korea Government (MEST) (No.R01-2007-000-20865-0). Work by S.Tanigawa was supported by Grant-in-Aid for JSPS Research Fellowship for Young Scientists.
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Bae, S.W., Choi, S., Lee, C., Tanigawa, Si. (2009). Exact Algorithms for the Bottleneck Steiner Tree Problem. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_5
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DOI: https://doi.org/10.1007/978-3-642-10631-6_5
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