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Improved Steiner Tree Algorithms for Bounded Treewidth

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Combinatorial Algorithms (IWOCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7056))

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Abstract

We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V to optimality in \(\ensuremath{\mathcal{O}(B_{\ensuremath{\textit{tw}}+2}^2 \cdot \ensuremath{\textit{tw}}\ \cdot |V|)}\) time, where \(\ensuremath{\textit{tw}}\) is the graph’s treewidth and the Bell number B k is the number of partitions of a k-element set. This is a linear time algorithm for graphs with fixed treewidth and a polynomial algorithm for \(\ensuremath{\textit{tw}} = \ensuremath{\mathcal{O}(\log|V|/\log\log|V|)}\).

While being faster than the previously known algorithms, our thereby used coloring scheme can be extended to give new, improved algorithms for the prize-collecting Steiner tree as well as the k-cardinality tree problems.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Friedrich-Schiller-University of Jena, Germany

    Markus Chimani

  2. Department of Computer Science, TU, Dortmund, Germany

    Petra Mutzel & Bernd Zey

Authors
  1. Markus Chimani
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  2. Petra Mutzel
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  3. Bernd Zey
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Editor information

Editors and Affiliations

  1. Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, Australia

    Costas S. Iliopoulos

  2. Department of Computing and Software Information Technology Building, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    William F. Smyth

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© 2011 Springer-Verlag Berlin Heidelberg

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Chimani, M., Mutzel, P., Zey, B. (2011). Improved Steiner Tree Algorithms for Bounded Treewidth. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_30

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  • DOI: https://doi.org/10.1007/978-3-642-25011-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25010-1

  • Online ISBN: 978-3-642-25011-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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