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Primal-Dual Approaches to the Steiner Problem

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Approximation Algorithms for Combinatorial Optimization (APPROX 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1913))

Abstract

We study several old and new algorithms for computing lower and upper bounds for the Steiner problem in networks using dualascent and primal-dual strategies. We show that none of the known algorithms can both generate tight lower bounds empirically and guarantee their quality theoretically; and we present a new algorithm which combines both features. The new algorithm has running time O(re logn) and guarantees a ratio of at most two between the generated upper and lower bounds, whereas the fastest previous algorithm with comparably tight empirical bounds has running time O(e 2) without a constant approximation ratio. Furthermore, we show that the approximation ratio two between the bounds can even be achieved in time O(e + n log n), improving the previous time bound of O(n 2 log n).

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Mannheim, 68131, Mannheim, Germany

    Tobias Polzin & Siavash Vahdati

Authors
  1. Tobias Polzin
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  2. Siavash Vahdati
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Editor information

Editors and Affiliations

  1. Christian-Albrechts-Universität zu Kiel Institut für Informatik und praktische Mathematik Olshausenstr, 40, 24098, Kiel, Germany

    Klaus Jansen

  2. Computer Science Department, University of Maryland, A.V. Williams Bldg College Park, MD 20742, USA

    Samir Khuller

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© 2000 Springer-Verlag Berlin Heidelberg

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Polzin, T., Vahdati, S. (2000). Primal-Dual Approaches to the Steiner Problem. In: Jansen, K., Khuller, S. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2000. Lecture Notes in Computer Science, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44436-X_22

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  • DOI: https://doi.org/10.1007/3-540-44436-X_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67996-7

  • Online ISBN: 978-3-540-44436-7

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