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International Conference on Algorithmic Applications in Management

AAIM 2016: Algorithmic Aspects in Information and Management pp 113–124Cite as

Algorithmic Aspects of Upper Domination: A Parameterised Perspective

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9778))

Abstract

This paper studies Upper Domination, i.e., the problem of computing the maximum cardinality of a minimal dominating set in a graph, with a focus on parameterised complexity. Our main results include W[1]-hardness for Upper Domination, contrasting FPT membership for the parameterised dual Co-Upper Domination. The study of structural properties also yields some insight into Upper Total Domination. We further consider graphs of bounded degree and derive upper and lower bounds for kernelisation.

C. Bazgan—Institut Universitaire de France.

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Acknowledgements

We thank our colleagues Serge Gaspers, David Manlove and Daniel Meister for some discussions on (total) upper domination. Part of this research was supported by Deutsche Forschungsgemeinschaft, grant FE 560/6-1.

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Authors and Affiliations

  1. PSL, University of Paris-Dauphine, CNRS, LAMSADE UMR 7243, 75775, Paris Cedex 16, France

    Cristina Bazgan, Michael Lampis, Jérôme Monnot & Vangelis Th. Paschos

  2. School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, NSW, 2308, Australia

    Ljiljana Brankovic

  3. Fachbereich 4, Informatikwissenschaften, Universität Trier, 54286, Trier, Germany

    Ljiljana Brankovic, Katrin Casel & Henning Fernau

  4. Institut für Informatik, Universität Kiel, 24098, Kiel, Germany

    Klaus Jansen & Kim-Manuel Klein

  5. University Orléans, INSA Centre Val de Loire, LIFO EA 4022, 45067, Orléans, France

    Mathieu Liedloff

Authors
  1. Cristina Bazgan
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  2. Ljiljana Brankovic
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  3. Katrin Casel
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  4. Henning Fernau
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  5. Klaus Jansen
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  6. Kim-Manuel Klein
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  7. Michael Lampis
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  8. Mathieu Liedloff
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  9. Jérôme Monnot
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  10. Vangelis Th. Paschos
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Corresponding author

Correspondence to Katrin Casel .

Editor information

Editors and Affiliations

  1. Università degli Studi di Bergamo , Bergamo, Italy

    Riccardo Dondi

  2. Université de Nantes , Nantes, France

    Guillaume Fertin

  3. Università degli Studi di Milano-Bicocca , Milano, Italy

    Giancarlo Mauri

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Bazgan, C. et al. (2016). Algorithmic Aspects of Upper Domination: A Parameterised Perspective. In: Dondi, R., Fertin, G., Mauri, G. (eds) Algorithmic Aspects in Information and Management. AAIM 2016. Lecture Notes in Computer Science(), vol 9778. Springer, Cham. https://doi.org/10.1007/978-3-319-41168-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-41168-2_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41167-5

  • Online ISBN: 978-3-319-41168-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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