Losing Treewidth In The Presence Of Weights
<|reference_start|>Losing Treewidth In The Presence Of Weights: In the Weighted Treewidth-$\eta$ 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 $\eta$. We show that Weighted Treewidth-$\eta$ Deletion admits a randomized polynomial-time constant-factor approximation algorithm for every fixed $\eta$. 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.<|reference_end|>
@article{włodarczyk2024losing,
    title={Losing Treewidth In The Presence Of Weights},
    author={Micha{l} W{l}odarczyk},
    journal={arXiv preprint arXiv:2410.06343},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.06343},
    primaryClass={cs.DS}
}