Improved Steiner Tree Algorithms for Bounded Treewidth

  • Markus Chimani
  • Petra Mutzel
  • Bernd Zey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)


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.


Planar Graph Steiner Tree Tree Decomposition Steiner Tree Problem Secondary Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Markus Chimani
    • 1
  • Petra Mutzel
    • 2
  • Bernd Zey
    • 2
  1. 1.Institute of Computer ScienceFriedrich-Schiller-University of JenaGermany
  2. 2.Department of Computer ScienceTUDortmundGermany

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