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A Retrospective on (Meta) Kernelization

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Treewidth, Kernels, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12160))

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Abstract

In parameterized complexity, a kernelization algorithm can be seen as a reduction of a parameterized problem to itself, so that the produced equivalent instance has size depending exclusively on the parameter. If this size is polynomial, then we say that the parameterized problem in question admits a polynomial kernelization algorithm. Kernelization can be seen as a formalization of the notion of preprocessing and has occupied a big part of the research on Multi-variate Algorithmics. The first algorithmic meta-theorem on kernelization appeared in [14] and unified a large family of previously known kernelization results on problems defined on topologically embeddable graphs. In this exposition we present the central results of this paper. During our presentation we pay attention to the abstractions on which the results where founded and take into account the subsequent advancements on this topic.

«Een mens zijn zin is een mens zijn leven.»

Supported by projects DEMOGRAPH (ANR-16-CE40-0028) and ESIGMA (ANR-17-CE23-0010) and by the Research Council of Norway and the French Ministry of Europe and Foreign Affairs, via the Franco-Norwegian project PHC AURORA 2019.

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Acknowledgements

I wish to whole-heartedly thank Professor Hans L. Bodlaender for being the one who «told me a little but he taught me a lot».

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  1. LIRMM, Univ Montpellier, CNRS, Montpellier, France

    Dimitrios M. Thilikos

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  1. University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Humboldt-University, Berlin, Germany

    Stefan Kratsch

  3. Utrecht University, Utrecht, The Netherlands

    Erik Jan van Leeuwen

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Thilikos, D.M. (2020). A Retrospective on (Meta) Kernelization. In: Fomin, F.V., Kratsch, S., van Leeuwen, E.J. (eds) Treewidth, Kernels, and Algorithms. Lecture Notes in Computer Science(), vol 12160. Springer, Cham. https://doi.org/10.1007/978-3-030-42071-0_16

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