Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915128463589376 |
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| author | Wlodarczyk, Michal |
| author_facet | Wlodarczyk, Michal |
| contents | In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth $tw$ of the input graph $G$. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time $2^{O(tw)} \cdot |V(G)|$, improving upon the running time $2^{O(tw^2)} \cdot |V(G)|^{O(1)}$ by Jansen, de Kroon, and Wlodarczyk (STOC'21). When a tree decomposition of width $tw$ is given, then the base of the exponent equals $2^{ω-1}\cdot 3 + 1$. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known $2^{O(tw \log tw)} \cdot |V(G)|$-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03440 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth Wlodarczyk, Michal Data Structures and Algorithms In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth $tw$ of the input graph $G$. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time $2^{O(tw)} \cdot |V(G)|$, improving upon the running time $2^{O(tw^2)} \cdot |V(G)|^{O(1)}$ by Jansen, de Kroon, and Wlodarczyk (STOC'21). When a tree decomposition of width $tw$ is given, then the base of the exponent equals $2^{ω-1}\cdot 3 + 1$. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known $2^{O(tw \log tw)} \cdot |V(G)|$-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis. |
| title | Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2305.03440 |