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.ISAAC.2018.18
URN: urn:nbn:de:0030-drops-99666
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9966/
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Dvorák, Pavel ; Knop, Dusan ; Toufar, Tomás

Target Set Selection in Dense Graph Classes

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LIPIcs-ISAAC-2018-18.pdf (0.5 MB)

Abstract

In this paper we study the Target Set Selection problem from a parameterized complexity perspective. Here for a given graph and a threshold for each vertex the task is to find a set of vertices (called a target set) to activate at the beginning which activates the whole graph during the following iterative process. A vertex outside the active set becomes active if the number of so far activated vertices in its neighborhood is at least its threshold.
We give two parameterized algorithms for a special case where each vertex has the threshold set to the half of its neighbors (the so called Majority Target Set Selection problem) for parameterizations by the neighborhood diversity and the twin cover number of the input graph.
We complement these results from the negative side. We give a hardness proof for the Majority Target Set Selection problem when parameterized by (a restriction of) the modular-width - a natural generalization of both previous structural parameters. We show that the Target Set Selection problem parameterized by the neighborhood diversity when there is no restriction on the thresholds is W[1]-hard.

BibTeX - Entry

@InProceedings{dvork_et_al:LIPIcs:2018:9966,
  author =	{Pavel Dvor{\'a}k and Dusan Knop and Tom{\'a}s Toufar},
  title =	{{Target Set Selection in Dense Graph Classes}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9966},
  URN =		{urn:nbn:de:0030-drops-99666},
  doi =		{10.4230/LIPIcs.ISAAC.2018.18},
  annote =	{Keywords: parameterized complexity, target set selection, dense graphs}
}

Keywords: parameterized complexity, target set selection, dense graphs
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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