Abstract.
The classical Steiner tree problem requires a shortest tree spanning a given vertex subset within a graph G=(V,E). An important variant is the Steiner tree problem in rectilinear metric. Only recently two algorithms were found which achieve better approximations than the ``traditional'' one with a factor of 3/2. These algorithms with an approximation ratio of 11/8 are quite slow and run in time \(O(n^3)\) and \(O(n^{5/2})\) . A new simple implementation reduces the time to \(O(n^{3/2})\) . As our main result we present efficient parametrized algorithms which reach a performance ratio of 11/8 + ɛ for any ɛ > 0 in time \(O(n \cdot \log^2 n)\) , and a ratio of \(11/8 + \log\log n /\log n\) in time \(O(n \cdot \log^3 n)\) .
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Received December 2, 1993, and in revised form July 24, 1996.
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Fößmeier, U., Kaufmann, M. & Zelikovsky, A. Faster Approximation Algorithms for the Rectilinear Steiner Tree Problem . Discrete Comput Geom 18, 93–109 (1997). https://doi.org/10.1007/PL00009310
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DOI: https://doi.org/10.1007/PL00009310