Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Kobayashi, Yasuaki; Otachi, Yota https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-133241
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Parameterized Complexity of Graph Burning

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Abstract

Graph Burning asks, given a graph G = (V,E) and an integer k, whether there exists (b₀,… ,b_{k-1}) ∈ V^{k} such that every vertex in G has distance at most i from some b_i. This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions arose by Kare and Reddy [IWOCA 2019] about parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP ⊆ coNP/poly. We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Although the parameterization by distance to split graphs cannot be handled with the clique-width argument, we show that this is also tractable by a reduction to a generalized problem with a smaller solution size.

BibTeX - Entry

@InProceedings{kobayashi_et_al:LIPIcs:2020:13324,
  author =	{Yasuaki Kobayashi and Yota Otachi},
  title =	{{Parameterized Complexity of Graph Burning}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{21:1--21:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13324},
  URN =		{urn:nbn:de:0030-drops-133241},
  doi =		{10.4230/LIPIcs.IPEC.2020.21},
  annote =	{Keywords: Graph burning, parameterized complexity, fixed-parameter tractability}
}

Keywords: Graph burning, parameterized complexity, fixed-parameter tractability
Seminar: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue date: 2020
Date of publication: 04.12.2020


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