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arXiv · 2311.03665

Faster Algorithms for Cycle Hitting Problems on Disk Graphs

Shinwoo An·Kyungjin Cho·Eunjin Oh
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Abstract

In this paper, we consider three hitting problems on a disk intersection graph: Triangle Hitting Set, Feedback Vertex Set, and Odd Cycle Transversal. Given a disk intersection graph $G$, our goal is to compute a set of vertices hitting all triangles, all cycles, or all odd cycles, respectively. Our algorithms run in time $2^{\tilde O(k^{4/5})}n^{O(1)}$, $2^{\tilde O(k^{9/10})}n^{O(1)}$, and $2^{\tilde O(k^{19/20})}n^{O(1)}$, respectively, where $n$ denotes the number of vertices of $G$. These do not require a geometric representation of a disk graph. If a geometric representation of a disk graph is given as input, we can solve these problems more efficiently. In this way, we improve the algorithms for those three problem by Lokshtanov et al. [SODA 2022].

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Shinwoo An, Kyungjin Cho, Eunjin Oh. 2023-11-07. Faster Algorithms for Cycle Hitting Problems on Disk Graphs. https://arxiv.org/abs/2311.03665

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