On Tamaki’s Algorithm to Compute Treewidths

Authors Ernst Althaus , Daniela Schnurbusch, Julian Wüschner, Sarah Ziegler

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Ernst Althaus
  • Johannes Gutenberg-Universität Mainz, Germany
Daniela Schnurbusch
  • Johannes Gutenberg-Universität Mainz, Germany
Julian Wüschner
  • Johannes Gutenberg-Universität Mainz, Germany
Sarah Ziegler
  • Johannes Gutenberg-Universität Mainz, Germany

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Ernst Althaus, Daniela Schnurbusch, Julian Wüschner, and Sarah Ziegler. On Tamaki’s Algorithm to Compute Treewidths. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Tree Decomposition
  • Exact Algorithm
  • Algorithms Engineering


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