Linear vertex kernel for Subset-FAST

Establish a linear vertex kernel for Subset-FAST, matching the known linear-kernel bound for Feedback Arc Set in Tournaments, or prove a lower bound based on an established conjecture.

Background

The paper establishes a quadratic vertex kernel for Subset-FAST, improving substantially over the previously available bounds for this subset problem. The conclusion highlights the gap between this result and the non-subset Feedback Arc Set in Tournaments problem, which admits a non-trivial linear vertex kernel. It also identifies the analogous kernel-size question for Subset-FVST as unresolved.

References

A non-trivial linear vertex kernel has been established for {\sc FAST}. It would be interesting to design a linear vertex kernel for that aligns with the bound of {\sc FAST} or to provide a lower bound based on some established conjectures. The same question is also open for {\sc Subset-FVST}.

— A Quadratic Vertex Kernel and a Subexponential Algorithm for Subset-FAST  (2503.07208 - Jana et al., 10 Mar 2025) in Section 6, Conclusion