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Treewidth, Kernels, and Algorithms pp 173–188Cite as

Surprising Applications of Treewidth Bounds for Planar Graphs

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

Abstract

In this chapter we continue a story told from in Dániel Marx’s Chapter and present three examples of surprising use of treewidth. In all cases, we present a state-of-the-art and provably optimal (assuming the Exponential Time Hypothesis) algorithm exploiting a sublinear bound on the treewidth of an auxiliary graph taken out of the blue.

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Notes

  1. 1.

    Both Figs. 1 and 2 are due to Dániel Marx and Michał Pilipczuk, from their slides on the work [8], reproduced with authors’ permission.

  2. 2.

    Technically speaking, the largest of the sets \(Y^1 \cup Y^2 \cup X_\gamma \) among all guesses of which element of \(\mathcal {W}\) is the pair \((X_\gamma ,W_\gamma )\), and a negative answer if no found set is of size at most k.

  3. 3.

    Again, since in fact the algorithm guesses \(X_\gamma \) and \(\mathcal {B}_\gamma \) by iterating over all options, we return the best solution found for all cases.

References

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Author information

Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Marcin Pilipczuk

Authors
  1. Marcin Pilipczuk
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Correspondence to Marcin Pilipczuk .

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Editors and Affiliations

  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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Pilipczuk, M. (2020). Surprising Applications of Treewidth Bounds for Planar Graphs. 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_13

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  • DOI: https://doi.org/10.1007/978-3-030-42071-0_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-42070-3

  • Online ISBN: 978-3-030-42071-0

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