Losing Treewidth In The Presence Of Weights
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916428643303424 |
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| author | Włodarczyk, Michał |
| author_facet | Włodarczyk, Michał |
| contents | In the Weighted Treewidth-$η$ Deletion problem we are given a node-weighted graph $G$ and we look for a vertex subset $X$ of minimum weight such that the treewidth of $G-X$ is at most $η$. We show that Weighted Treewidth-$η$ Deletion admits a randomized polynomial-time constant-factor approximation algorithm for every fixed $η$. Our algorithm also works for the more general Weighted Planar $F$-M-Deletion problem.
This work extends the results for unweighted graphs by [Fomin, Lokshtanov, Misra, Saurabh; FOCS '12] and answers a question posed by [Agrawal, Lokshtanov, Misra, Saurabh, Zehavi; APPROX/RANDOM '18] and [Kim, Lee, Thilikos; APPROX/RANDOM '21]. The presented algorithm is based on a novel technique of random sampling of so-called protrusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Losing Treewidth In The Presence Of Weights Włodarczyk, Michał Data Structures and Algorithms In the Weighted Treewidth-$η$ Deletion problem we are given a node-weighted graph $G$ and we look for a vertex subset $X$ of minimum weight such that the treewidth of $G-X$ is at most $η$. We show that Weighted Treewidth-$η$ Deletion admits a randomized polynomial-time constant-factor approximation algorithm for every fixed $η$. Our algorithm also works for the more general Weighted Planar $F$-M-Deletion problem. This work extends the results for unweighted graphs by [Fomin, Lokshtanov, Misra, Saurabh; FOCS '12] and answers a question posed by [Agrawal, Lokshtanov, Misra, Saurabh, Zehavi; APPROX/RANDOM '18] and [Kim, Lee, Thilikos; APPROX/RANDOM '21]. The presented algorithm is based on a novel technique of random sampling of so-called protrusions. |
| title | Losing Treewidth In The Presence Of Weights |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2410.06343 |