A cactus is a connected graph that does not contain $K_4 - e$ as a minor. Given a graph $G = (V, E)$ and integer $k \ge 0$, Cactus Vertex Deletion (also known as Diamond Hitting Set) is the problem of deciding whether $G$ has a vertex set of size at most $k$ whose removal leaves a forest of cacti. The current best deterministic parameterized algorithm for this problem was due to Bonnet et al. [WG 2016], which runs in time $26^kn^{O(1)}$, where $n$ is the number of vertices of $G$. In this paper, we design a deterministic algorithm for Cactus Vertex Deletion, which runs in time $17.64^kn^{O(1)}$. As a straightforward application of our algorithm, we give a $17.64^kn^{O(1)}$-time algorithm for Even Cycle Transversal. The idea behind this improvement is to apply the measure and conquer analysis with a slightly elaborate measure of instances.
翻译：仙人掌是一个连接的图表,它并不包含4-e美元作为未成年人。根据一个图形$G = (V, E)$和整数 $g = (G) 0 $,Cactus Vertex Deletion (又称钻石击落区) 是决定$G 是否有一个顶点大小为$k$的顶点数组的问题,因为清除离开仙人林的最多美元。目前这一问题的最佳确定性参数化算法是波恩特等人[WG 的[2016],它运行的时间是26 kn ⁇ O(1) $,其中美元是G$的顶点数。在本文中,我们为Cact Vertex Deletion设计了一种确定性算法,它运行的时间是17.64 kn ⁇ O(1) 。作为我们算法的简单应用,我们给出了17.64 kn ⁇ O (1) $-时间算法,用于“甚至循环转基因” 。改进的构想是应用测量和征服分析方法,并略细细地测量实例。
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