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.
- 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.
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.
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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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