On Directed Feedback Vertex Set parameterized by treewidth

  title={On Directed Feedback Vertex Set parameterized by treewidth},
  author={Marthe Bonamy and Lukasz Kowalik and Jesper Nederlof and Michal Pilipczuk and Arkadiusz Socala and Marcin Wrochna},
We study the Directed Feedback Vertex Set problem parameterized by the treewidth of the input graph. We prove that unless the Exponential Time Hypothesis fails, the problem cannot be solved in time $2^{o(t\log t)}\cdot n^{\mathcal{O}(1)}$ on general directed graphs, where $t$ is the treewidth of the underlying undirected graph. This is matched by a dynamic programming algorithm with running time $2^{\mathcal{O}(t\log t)}\cdot n^{\mathcal{O}(1)}$. On the other hand, we show that if the input… 

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