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Faster approximation algorithms for the rectilinear steiner tree problem

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Book cover Algorithms and Computation (ISAAC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

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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 parameterized algorithms which reach a performance ratio of 11/8+ε for any ε>0 in time O(n · log2 n), and a ratio of 11/8+log log n log n in time O(n · log3 n).

Parts of this work have been done at Max-Planck-Institut für Informatik, Saarbrücken and at the Fakultät für Mathematik und Informatik, Universität Passau, Passau

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Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Ulrich Fößmeier & Michael Kaufmann

  2. Institute of Mathematics, Academiei 5, 277028, Kishinev, Moldova

    Alexander Zelikovsky

Authors
  1. Ulrich Fößmeier
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  2. Michael Kaufmann
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  3. Alexander Zelikovsky
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Editor information

K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

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© 1993 Springer-Verlag Berlin Heidelberg

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Fößmeier, U., Kaufmann, M., Zelikovsky, A. (1993). Faster approximation algorithms for the rectilinear steiner tree problem. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_285

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  • DOI: https://doi.org/10.1007/3-540-57568-5_285

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57568-9

  • Online ISBN: 978-3-540-48233-8

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