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International Conference on Algorithmic Applications in Management

AAIM 2019: Algorithmic Aspects in Information and Management pp 108–120Cite as

Profit Parameterizations of Dominating Set

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11640))

Abstract

Dominating Set is one of the most classical NP-complete combinatorial graph problems. Unfortunately, the natural parameterization (by solution size) does not make this problem feasible in the sense of Parameterized Complexity. We propose two new views to consider Dominating Set, and a new parameterization of this problem (by the profit parameter) and give algorithms for these parameterizations that show the problems to be in FPT. More precisely, we give a linear-size kernel and a search-tree procedure.

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Notes

  1. 1.

    Note that below we also discuss the possibility replacing term \(\omega |N|\) by some function \(\omega :N\rightarrow [0,1]\) that assigns weights to vertices from N.

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Acknowledgements

Part of this work resulted from the \(16^{\mathrm{th}}\) Bellairs Workshop on Comp. Geometry (Feb. 2017). The \(1^{\mathrm{st}}\)-author’s research visit at the \(2^{\mathrm{nd}}\)-author’s institution in late 2018 was financed by DFG project overhead money. The \(2^{\mathrm{nd}}\)-author is supported by an NSERC DG. We are grateful for discussions with Iris van Rooij.

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Authors and Affiliations

  1. Fachbereich 4 – Abteilung Informatikwissenschaften, CIRT, Universität Trier, 54286, Trier, Germany

    Henning Fernau

  2. Department of Computer Science, University of Victoria, Victoria, Canada

    Ulrike Stege

Authors
  1. Henning Fernau
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  2. Ulrike Stege
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Corresponding author

Correspondence to Ulrike Stege .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Hefei University of Technology, Hefei, China

    Lian Li

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

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Fernau, H., Stege, U. (2019). Profit Parameterizations of Dominating Set. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_10

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  • DOI: https://doi.org/10.1007/978-3-030-27195-4_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27194-7

  • Online ISBN: 978-3-030-27195-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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