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.ITCS.2022.63
URN: urn:nbn:de:0030-drops-156592
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15659/
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Eiben, Eduard ; Ganian, Robert ; Hamm, Thekla ; Jaffke, Lars ; Kwon, O-joung

A Unifying Framework for Characterizing and Computing Width Measures

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LIPIcs-ITCS-2022-63.pdf (0.9 MB)

Abstract

Algorithms for computing or approximating optimal decompositions for decompositional parameters such as treewidth or clique-width have so far traditionally been tailored to specific width parameters. Moreover, for mim-width, no efficient algorithms for computing good decompositions were known, even under highly restrictive parameterizations. In this work we identify ℱ-branchwidth as a class of generic decompositional parameters that can capture mim-width, treewidth, clique-width as well as other measures. We show that while there is an infinite number of ℱ-branchwidth parameters, only a handful of these are asymptotically distinct. We then develop fixed-parameter and kernelization algorithms (under several structural parameterizations) that can approximate every possible ℱ-branchwidth, providing a unifying parameterized framework that can efficiently obtain near-optimal tree-decompositions, k-expressions, as well as optimal mim-width decompositions.

BibTeX - Entry

@InProceedings{eiben_et_al:LIPIcs.ITCS.2022.63,
  author =	{Eiben, Eduard and Ganian, Robert and Hamm, Thekla and Jaffke, Lars and Kwon, O-joung},
  title =	{{A Unifying Framework for Characterizing and Computing Width Measures}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{63:1--63:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15659},
  URN =		{urn:nbn:de:0030-drops-156592},
  doi =		{10.4230/LIPIcs.ITCS.2022.63},
  annote =	{Keywords: branchwidth, parameterized algorithms, mim-width, treewidth, clique-width}
}

Keywords: branchwidth, parameterized algorithms, mim-width, treewidth, clique-width
Collection: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue Date: 2022
Date of publication: 25.01.2022

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