In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size $k$, if it exists, which runs in time $2^{O(\sqrt{k})}(n+m)$, where $n$ and $m$ denote the numbers of vertices and edges, respectively. This improves the $2^{O(\sqrt{k}\log k)}n^{O(1)}$-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis. Also, our algorithm can be extended to handle geometric intersection graphs of similarly sized fat objects without increasing the running time.
翻译：在本文中, 我们提出一个算法, 用于计算一个反馈顶点, 由大小为$k$( 如果存在的话) 的单盘磁盘图组成, 其运行时间为$2\O(\\ sqrt{k}}}( n+m)$2\\\\\\\ n+m}}}( 美元+m)$, 其中美元和美元分别表示脊椎和边缘的数量。 这改善了Fomn 等人的单盘图[COCRP 2017] 对这一问题的2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
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