Typical Sequences Revisited - Computing Width Parameters of Graphs
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.
typical sequences
treewidth
series parallel digraphs
cutwidth
modified cutwidth
Mathematics of computing~Combinatorial algorithms
Mathematics of computing~Graph algorithms
57:1-57:16
Regular Paper
A full version of the paper is available at https://arxiv.org/abs/1905.03643.
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.
Hans L.
Bodlaender
Hans L. Bodlaender
Department of Computer Science, Utrecht University, The Netherlands
https://orcid.org/0000-0002-9297-3330
Partially supported by the Networks project, funded by the Netherlands Organization for Scientific Research (NWO).
Lars
Jaffke
Lars Jaffke
Department of Informatics, University of Bergen, Norway
https://orcid.org/0000-0003-4856-5863
Supported by the Bergen Research Foundation (BFS).
Jan Arne
Telle
Jan Arne Telle
Department of Informatics, University of Bergen, Norway
10.4230/LIPIcs.STACS.2020.57
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Hans L. Bodlaender, Lars Jaffke, and Jan Arne Telle
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