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A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs

  • Mamadou Moustapha KantéEmail author
  • Vincent Limouzy
  • Arnaud Mary
  • Lhouari Nourine
  • Takeaki Uno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing the set of minimal transversals in hypergraphs. We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and well-studied graph class where such an algorithm was not known. The algorithm uses a new decomposition method of chordal graphs based on clique trees.

Keywords

Maximal Clique Chordal Graph Extension Problem Graph Class Polynomial Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Mamadou Moustapha Kanté
    • 1
    Email author
  • Vincent Limouzy
    • 1
  • Arnaud Mary
    • 2
  • Lhouari Nourine
    • 1
  • Takeaki Uno
    • 3
  1. 1.Clermont-Université, Université Blaise Pascal, LIMOS, CNRSClermont-FerrandFrance
  2. 2.Université Claude Bernard Lyon 1, LBBE, CNRSVilleurbanneFrance
  3. 3.National Institute of InformaticsTokyoJapan

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