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.2019.63
URN: urn:nbn:de:0030-drops-115591
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11559/
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Defrain, Oscar ; Nourine, Lhouari

Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7 - Free and P_8 - Free Chordal Graphs

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Abstract

In [M. M. Kanté, V. Limouzy, A. Mary, and L. Nourine. On the enumeration of minimal dominating sets and related notions. SIAM Journal on Discrete Mathematics, 28(4):1916-1929, 2014.] the authors give an O(n+m) delay algorithm based on neighborhood inclusions for the enumeration of minimal dominating sets in split and P_6-free chordal graphs. In this paper, we investigate generalizations of this technique to P_k-free chordal graphs for larger integers k. In particular, we give O(n+m) and O(n^3 * m) delays algorithms in the classes of P_7-free and P_8-free chordal graphs. As for P_k-free chordal graphs for k >= 9, we give evidence that such a technique is inefficient as a key step of the algorithm, namely the irredundant extension problem, becomes NP-complete.

BibTeX - Entry

@InProceedings{defrain_et_al:LIPIcs:2019:11559,
  author =	{Oscar Defrain and Lhouari Nourine},
  title =	{{Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7 - Free and P_8 - Free Chordal Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{63:1--63:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11559},
  URN =		{urn:nbn:de:0030-drops-115591},
  doi =		{10.4230/LIPIcs.ISAAC.2019.63},
  annote =	{Keywords: Minimal dominating sets, enumeration algorithms, linear delay enumeration, chordal graphs, forbidden induced paths}
}

Keywords: Minimal dominating sets, enumeration algorithms, linear delay enumeration, chordal graphs, forbidden induced paths
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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