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- W3163454130 abstract "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." @default.
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- W3163454130 date "2020-12-09" @default.
- W3163454130 modified "2023-10-16" @default.
- W3163454130 title "An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion" @default.
- W3163454130 doi "https://doi.org/10.48550/arxiv.2012.04910" @default.
- W3163454130 hasPublicationYear "2020" @default.
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