Tightness of Deletion Bound I under the cover and swap conditions

Let $\mathcal{J}$ be a set satisfying the cover condition and the swap condition. Let $MVSS(\mathcal{J})$ denote the relevant minimum-variable stopping set associated with $\mathcal{J}$, and let Algorithm~ be the procedure called Deletion Bound I.

Deletion Bound I tightness conjecture. If set $\mathcal{J}$ satisfies both cover condition and swap condition, then Algorithm~ (Deletion Bound I) can find the exact value of $|MVSS(\mathcal{J})|$.

The conjecture asserts that Deletion Bound I is tight for sets satisfying both conditions. A practical method for computing $|MVSS(\mathcal{J})|$ remains an open problem, and the paper identifies proving NP-hardness as a possible direction for future work.