Subset Feedback Vertex Set on Graphs of Bounded Independent Set Size
Charis Papadopoulos, Spyridon Tzimas

TL;DR
This paper investigates the complexity of the Subset Feedback Vertex Set problem on graphs with bounded independent set size, providing polynomial algorithms for small sizes and NP-hardness results for larger sizes, and extends these findings to related terminal set problems.
Contribution
It establishes a complexity dichotomy for the problem based on the maximum independent set size, solving it efficiently for size at most three and proving NP-hardness for size four.
Findings
Polynomial-time algorithm for graphs with independent set size at most three
NP-hardness of the problem for graphs with independent set size four
Extension of techniques to other terminal set problems on bounded independent set graphs
Abstract
The (\textsc{Weighted}) \textsc{Subset Feedback Vertex Set} problem is a generalization of the classical \textsc{Feedback Vertex Set} problem and asks for a vertex set of minimum (weighted) size that intersects all cycles containing a vertex of a predescribed set of vertices. Although the two problems exhibit different computational complexity on split graphs, no similar characterization is known on other classes of graphs. Towards the understanding of the complexity difference between the two problems, it is natural to study the importance of a structural graph parameter. Here we consider graphs of bounded independent set number for which it is known that \textsc{Weighted Feedback Vertex Set} is solved in polynomial time. We provide a dichotomy result with respect to the size of a maximum independent set. In particular we show that \textsc{Weighted Subset Feedback Vertex Set} can be…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
