License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2022.15
URN: urn:nbn:de:0030-drops-173714
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17371/
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Ganian, Robert ; Korchemna, Viktoriia

Slim Tree-Cut Width

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LIPIcs-IPEC-2022-15.pdf (1 MB)

Abstract

Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it turned out that tree-cut width falls short as an edge-cut based alternative to treewidth in algorithmic aspects. This has led to the very recent introduction of a simple edge-based parameter called edge-cut width [WG 2022], which has precisely the algorithmic applications one would expect from an analogue of treewidth for edge cuts, but does not have the desired structural properties.
In this paper, we study a variant of tree-cut width obtained by changing the threshold for so-called thin nodes in tree-cut decompositions from 2 to 1. We show that this "slim tree-cut width" satisfies all the requirements of an edge-cut based analogue of treewidth, both structural and algorithmic, while being less restrictive than edge-cut width. Our results also include an alternative characterization of slim tree-cut width via an easy-to-use spanning-tree decomposition akin to the one used for edge-cut width, a characterization of slim tree-cut width in terms of forbidden immersions as well as an approximation algorithm for computing the parameter.

BibTeX - Entry

@InProceedings{ganian_et_al:LIPIcs.IPEC.2022.15,
  author =	{Ganian, Robert and Korchemna, Viktoriia},
  title =	{{Slim Tree-Cut Width}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17371},
  URN =		{urn:nbn:de:0030-drops-173714},
  doi =		{10.4230/LIPIcs.IPEC.2022.15},
  annote =	{Keywords: tree-cut width, structural parameters, graph immersions}
}

Keywords: tree-cut width, structural parameters, graph immersions
Collection: 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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