Typical Sequences Revisited - Computing Width Parameters of Graphs

Authors Hans L. Bodlaender , Lars Jaffke , Jan Arne Telle

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Author Details

Hans L. Bodlaender
  • Department of Computer Science, Utrecht University, The Netherlands
Lars Jaffke
  • Department of Informatics, University of Bergen, Norway
Jan Arne Telle
  • Department of Informatics, University of Bergen, Norway


This work was started when the third author was visiting Universitat Politecnica de Valencia, and part of it was done while the second author was visiting Utrecht University.

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Hans L. Bodlaender, Lars Jaffke, and Jan Arne Telle. Typical Sequences Revisited - Computing Width Parameters of Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In this work, we give a structural lemma on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP 1991] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth. The lemma addresses a runtime bottleneck in those algorithms but so far it does not lead to asymptotically faster algorithms. However, we apply the lemma to show that the cutwidth and the modified cutwidth of series parallel digraphs can be computed in ?(n²) time.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Graph algorithms
  • typical sequences
  • treewidth
  • series parallel digraphs
  • cutwidth
  • modified cutwidth


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