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DOI: 10.4230/LIPIcs.FSTTCS.2013.79
URN: urn:nbn:de:0030-drops-43636
URL: http://drops.dagstuhl.de/opus/volltexte/2013/4363/
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Chitnis, Rajesh ; Fomin, Fedor V. ; Golovach, Petr A.

Parameterized Complexity of the Anchored k-Core Problem for Directed Graphs

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Abstract

We consider the Directed Anchored k-Core problem, where the task is for a given directed graph G and integers b, k and p, to find an induced subgraph H with at least p vertices (the core) such that all but at most b vertices (the anchors) of H have in-degree at least k. For undirected graphs, this problem was introduced by Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012]. We undertake a systematic analysis of the computational complexity of Directed Anchored k-Core and show that: - The decision version of the problem is NP-complete for every k>=1 even if the input graph is restricted to be a planar directed acyclic graph of maximum degree at most k+2. - The problem is fixed parameter tractable (FPT) parameterized by the size of the core p for k=1, and W[1]-hard for k>=2. - When the maximum degree of the graph is at most Delta, the problem is FPT parameterized by p+Delta if k>=Delta/2.

BibTeX - Entry

@InProceedings{chitnis_et_al:LIPIcs:2013:4363,
  author =	{Rajesh Chitnis and Fedor V. Fomin and Petr A. Golovach},
  title =	{{Parameterized Complexity of the Anchored k-Core Problem for Directed Graphs}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{79--90},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Anil Seth and Nisheeth K. Vishnoi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4363},
  URN =		{urn:nbn:de:0030-drops-43636},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.79},
  annote =	{Keywords: Parameterized complexity, directed graphs, anchored $k$-core}
}

Keywords: Parameterized complexity, directed graphs, anchored $k$-core
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Issue Date: 2013
Date of publication: 09.12.2013


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