LP-based constant approximation for Treewidth Deletion

Develop LP-based approximation algorithms for the Treewidth Deletion problem, preferably improving the known constant factor and establishing a deterministic constant-factor approximation.

Background

Treewidth Deletion asks for a minimum-cost vertex set whose removal leaves a graph of treewidth at most a fixed parameter eta. The paper notes that randomized constant-factor approximations are known for every fixed eta, while LP-based approaches remain undeveloped. The stated direction is to transfer the LP-based methodology used for Feedback Vertex Set to Treewidth Deletion, with the goals of improving the approximation factor and obtaining a deterministic constant-factor algorithm.

References

Designing LP-based approximations for this problem remains open.

— An iterative rounding $2$-approximation for Feedback Vertex Set via AI-assisted proof of an extreme point property  (2609.04414 - Chandrasekaran et al., 3 Sep 2026) in Section 1, paragraph “Motivations for the Extreme Point Conjecture” and Section 8, Conclusion