License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2019.27
URN: urn:nbn:de:0030-drops-102660
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10266/
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Fabianski, Grzegorz ; Pilipczuk, Michal ; Siebertz, Sebastian ; Torunczyk, Szymon

Progressive Algorithms for Domination and Independence

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LIPIcs-STACS-2019-27.pdf (0.8 MB)


Abstract

We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive algorithms, namely variants of the Helly property and stability. We demonstrate our approach by giving linear-time fixed-parameter algorithms for the Distance-r Dominating Set problem (parameterized by the solution size) in a wide variety of restricted graph classes, such as powers of nowhere dense classes, map graphs, and (for r=1) biclique-free graphs. Similarly, for the Distance-r Independent Set problem the technique can be used to give a linear-time fixed-parameter algorithm on any nowhere dense class. Despite the simplicity of the method, in several cases our results extend known boundaries of tractability for the considered problems and improve the best known running times.

BibTeX - Entry

@InProceedings{fabianski_et_al:LIPIcs:2019:10266,
  author =	{Grzegorz Fabianski and Michal Pilipczuk and Sebastian Siebertz and Szymon Torunczyk},
  title =	{{Progressive Algorithms for Domination and Independence}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10266},
  doi =		{10.4230/LIPIcs.STACS.2019.27},
  annote =	{Keywords: Dominating Set, Independent Set, nowhere denseness, stability, fixed-parameter tractability}
}

Keywords: Dominating Set, Independent Set, nowhere denseness, stability, fixed-parameter tractability
Collection: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue Date: 2019
Date of publication: 12.03.2019


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