Feedback Vertex Set for pseudo-disk graphs in subexponential FPT time

Document detail

ID

oai:arXiv.org:2410.23878

Topic

Computer Science - Data Structures... Computer Science - Discrete Mathem...

Author

Berthe, Gaétan Bougeret, Marin Gonçalves, Daniel Raymond, Jean-Florent

Year

2024

listing date

11/6/2024

Keywords

graphs

Metrics

Abstract

In this paper, we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set (FVS) and Triangle Hitting (TH).

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 TH can be solved in time $2^{O(k^{3/4}\log k)}n^{O(1)}$, and given a geometric representation FVS can be solved in time $2^{O(k^{6/7}\log k)}n^{O(1)}$.

;Comment: Presented at the conference WG 2024

Berthe, Gaétan,Bougeret, Marin,Gonçalves, Daniel,Raymond, Jean-Florent, 2024, Feedback Vertex Set for pseudo-disk graphs in subexponential FPT time