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Exponential Time Algorithms for the Minimum Dominating Set Problem on Some Graph Classes

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Algorithm Theory – SWAT 2006 (SWAT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

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Abstract

The Minimum Dominating Set problem remains NP-hard when restricted to chordal graphs, circle graphs and c-dense graphs (i.e. |E| ≥cn 2 for a constant c, 0<c<1/2). For each of these three graph classes we present an exponential time algorithm solving the Minimum Dominating Set problem. The running times of those algorithms are O(1.4173n) for chordal graphs, O(1.4956n) for circle graphs, and \(O(1.2303^{(1+\sqrt{1-2c})n})\) for c-dense graphs.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Serge Gaspers

  2. LITA, Université de Paul Verlaine – Metz, 57045 Cedex 01, Metz, France

    Dieter Kratsch & Mathieu Liedloff

Authors
  1. Serge Gaspers
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  2. Dieter Kratsch
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  3. Mathieu Liedloff
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Editor information

Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

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© 2006 Springer-Verlag Berlin Heidelberg

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Gaspers, S., Kratsch, D., Liedloff, M. (2006). Exponential Time Algorithms for the Minimum Dominating Set Problem on Some Graph Classes. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_16

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  • DOI: https://doi.org/10.1007/11785293_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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