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.ESA.2021.78
URN: urn:nbn:de:0030-drops-146590
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14659/
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Ramanujan, M. S.

On Approximate Compressions for Connected Minor-Hitting Sets

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LIPIcs-ESA-2021-78.pdf (0.8 MB)

Abstract

In the Connected ℱ-Deletion problem, ℱ is a fixed finite family of graphs and the objective is to compute a minimum set of vertices (or a vertex set of size at most k for some given k) such that (a) this set induces a connected subgraph of the given graph and (b) deleting this set results in a graph which excludes every F ∈ ℱ as a minor. In the area of kernelization, this problem is well known to exclude a polynomial kernel subject to standard complexity hypotheses even in very special cases such as ℱ = K₂, i.e., Connected Vertex Cover.
In this work, we give a (2+ε)-approximate polynomial compression for the Connected ℱ-Deletion problem when ℱ contains at least one planar graph. This is the first approximate polynomial compression result for this generic problem. As a corollary, we obtain the first approximate polynomial compression result for the special case of Connected η-Treewidth Deletion.

BibTeX - Entry

@InProceedings{ramanujan:LIPIcs.ESA.2021.78,
  author =	{Ramanujan, M. S.},
  title =	{{On Approximate Compressions for Connected Minor-Hitting Sets}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{78:1--78:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14659},
  URN =		{urn:nbn:de:0030-drops-146590},
  doi =		{10.4230/LIPIcs.ESA.2021.78},
  annote =	{Keywords: Parameterized Complexity, Kernelization, Approximation Algorithms}
}

Keywords: Parameterized Complexity, Kernelization, Approximation Algorithms
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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