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.ICALP.2023.106
URN: urn:nbn:de:0030-drops-181585
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18158/
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Włodarczyk, Michał

Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth

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LIPIcs-ICALP-2023-106.pdf (1 MB)

Abstract

In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth tw of the input graph G. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time 2^?(tw)⋅|V(G)|, improving upon the running time 2^?(tw²)⋅|V(G)|^?(1) by Jansen, de Kroon, and Włodarczyk (STOC'21). When a tree decomposition of width tw is given, then the base of the exponent equals 2^{ω-1}⋅3 + 1. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known 2^?(tw log tw)⋅|V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.

BibTeX - Entry

@InProceedings{wlodarczyk:LIPIcs.ICALP.2023.106,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{106:1--106:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18158},
  URN =		{urn:nbn:de:0030-drops-181585},
  doi =		{10.4230/LIPIcs.ICALP.2023.106},
  annote =	{Keywords: fixed-parameter tractability, treewidth, chordal graphs, interval graphs, matroids, representative families}
}

Keywords: fixed-parameter tractability, treewidth, chordal graphs, interval graphs, matroids, representative families
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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