Abstract
In this paper we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set and Triangle Hitting. We focus on the class of pseudo-disk graphs, which forms a common generalization of several graph classes where such results exist, like disk graphs and square graphs. In these graphs we show that given a geometric representation FVS can be solved in time \(2^{\mathcal {O}(k^{9/10}\log k)}n^{\mathcal {O}(1)}\) and TH in time \(2^{\mathcal {O}(k^{3/4}\log k)}n^{\mathcal {O}(1)}\).
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Notes
- 1.
Informally: yes-instances are minor-closed and a solution on the (r, r)-grid has size \(\varOmega (r^2)\).
- 2.
We have been told in a private communication that it might be possible to extend the arguments of [12] for FVS in pseudo-disk graphs without a geometrical representation, and that the time complexity would be worse than the one we obtain.
- 3.
The ply is the maximum number of pseudo-disks sharing a common point.
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Berthe, G., Bougeret, M., Gonçalves, D., Raymond, JF. (2025). Feedback Vertex Set for Pseudo-disk Graphs in Subexponential FPT Time. In: Kráľ, D., Milanič, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2024. Lecture Notes in Computer Science, vol 14760. Springer, Cham. https://doi.org/10.1007/978-3-031-75409-8_5
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