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Target Set Selection Parameterized by Clique-Width and Maximum Threshold

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SOFSEM 2018: Theory and Practice of Computer Science (SOFSEM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10706))

Abstract

The Target Set Selection problem takes as an input a graph G and a non-negative integer threshold \( \mathsf {thr}(v) \) for every vertex v. A vertex v can get active as soon as at least \( \mathsf {thr}(v) \) of its neighbors have been activated. The objective is to select a smallest possible initial set of vertices, the target set, whose activation eventually leads to the activation of all vertices in the graph.

We show that Target Set Selection is in FPT when parameterized with the combined parameters clique-width of the graph and the maximum threshold value. This generalizes all previous FPT-membership results for the parameterization by maximum threshold, and thereby solves an open question from the literature. We stress that the time complexity of our algorithm is surprisingly well-behaved and grows only single-exponentially in the parameters.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik 1, RWTH Aachen University, Aachen, Germany

    Tim A. Hartmann

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  1. Tim A. Hartmann
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Correspondence to Tim A. Hartmann .

Editor information

Editors and Affiliations

  1. Vienna University of Technology , Vienna, Austria

    A Min Tjoa

  2. ISAE-ENSMA, Chasseneuil-du-Poitou, France

    Ladjel Bellatreche

  3. Vienna University of Technology, Vienna, Austria

    Stefan Biffl

  4. Utrecht University, Utrecht, The Netherlands

    Jan van Leeuwen

  5. Academy of Sciences, Prague, Czech Republic

    Jiří Wiedermann

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Hartmann, T.A. (2018). Target Set Selection Parameterized by Clique-Width and Maximum Threshold. In: Tjoa, A., Bellatreche, L., Biffl, S., van Leeuwen, J., Wiedermann, J. (eds) SOFSEM 2018: Theory and Practice of Computer Science. SOFSEM 2018. Lecture Notes in Computer Science(), vol 10706. Edizioni della Normale, Cham. https://doi.org/10.1007/978-3-319-73117-9_10

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  • DOI: https://doi.org/10.1007/978-3-319-73117-9_10

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  • Publisher Name: Edizioni della Normale, Cham

  • Print ISBN: 978-3-319-73116-2

  • Online ISBN: 978-3-319-73117-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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