Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Hols, Eva-Maria C.; Kratsch, Stefan; Pieterse, Astrid 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-129261
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Approximate Turing Kernelization for Problems Parameterized by Treewidth

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Abstract

We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An α-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm that, when given access to an oracle that outputs c-approximate solutions in 𝒪(1) time, obtains an α ⋅ c-approximate solution to the considered problem, using calls to the oracle of size at most f(k) for some function f that only depends on the parameter. Using this definition, we show that Independent Set parameterized by treewidth 𝓁 has a (1+ε)-approximate Turing kernel with 𝒪(𝓁²/ε) vertices, answering an open question posed by Lokshtanov et al. [STOC 2017]. Furthermore, we give (1+ε)-approximate Turing kernels for the following graph problems parameterized by treewidth: Vertex Cover, Edge Clique Cover, Edge-Disjoint Triangle Packing and Connected Vertex Cover. We generalize the result for Independent Set and Vertex Cover, by showing that all graph problems that we will call friendly admit (1+ε)-approximate Turing kernels of polynomial size when parameterized by treewidth. We use this to obtain approximate Turing kernels for Vertex-Disjoint H-packing for connected graphs H, Clique Cover, Feedback Vertex Set and Edge Dominating Set.

BibTeX - Entry

@InProceedings{hols_et_al:LIPIcs:2020:12926,
  author =	{Eva-Maria C. Hols and Stefan Kratsch and Astrid Pieterse},
  title =	{{Approximate Turing Kernelization for Problems Parameterized by Treewidth}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{60:1--60:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12926},
  URN =		{urn:nbn:de:0030-drops-129261},
  doi =		{10.4230/LIPIcs.ESA.2020.60},
  annote =	{Keywords: Approximation, Turing kernelization, Graph problems, Treewidth}
}

Keywords: Approximation, Turing kernelization, Graph problems, Treewidth
Seminar: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue date: 2020
Date of publication: 26.08.2020


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