License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.ESA.2023.66
URN: urn:nbn:de:0030-drops-187195
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Jansen, Bart M. P. ; de Kroon, Jari J. H. ; Włodarczyk, Michał

5-Approximation for ℋ-Treewidth Essentially as Fast as ℋ-Deletion Parameterized by Solution Size

LIPIcs-ESA-2023-66.pdf (0.9 MB)


The notion of ℋ-treewidth, where ℋ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of ℋ-treewidth at most k can be decomposed into (arbitrarily large) ℋ-subgraphs which interact only through vertex sets of size ?(k) which can be organized in a tree-like fashion. ℋ-treewidth can be used as a hybrid parameterization to develop fixed-parameter tractable algorithms for ℋ-deletion problems, which ask to find a minimum vertex set whose removal from a given graph G turns it into a member of ℋ. The bottleneck in the current parameterized algorithms lies in the computation of suitable tree ℋ-decompositions.
We present FPT-approximation algorithms to compute tree ℋ-decompositions for hereditary and union-closed graph classes ℋ. Given a graph of ℋ-treewidth k, we can compute a 5-approximate tree ℋ-decomposition in time f(?(k)) ⋅ n^?(1) whenever ℋ-deletion parameterized by solution size can be solved in time f(k) ⋅ n^?(1) for some function f(k) ≥ 2^k. The current-best algorithms either achieve an approximation factor of k^?(1) or construct optimal decompositions while suffering from non-uniformity with unknown parameter dependence. Using these decompositions, we obtain algorithms solving Odd Cycle Transversal in time 2^?(k) ⋅ n^?(1) parameterized by bipartite-treewidth and Vertex Planarization in time 2^?(k log k) ⋅ n^?(1) parameterized by planar-treewidth, showing that these can be as fast as the solution-size parameterizations and giving the first ETH-tight algorithms for parameterizations by hybrid width measures.

BibTeX - Entry

  author =	{Jansen, Bart M. P. and de Kroon, Jari J. H. and W{\l}odarczyk, Micha{\l}},
  title =	{{5-Approximation for ℋ-Treewidth Essentially as Fast as ℋ-Deletion Parameterized by Solution Size}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{66:1--66:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-187195},
  doi =		{10.4230/LIPIcs.ESA.2023.66},
  annote =	{Keywords: fixed-parameter tractability, treewidth, graph decompositions}

Keywords: fixed-parameter tractability, treewidth, graph decompositions
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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