Largest realizable subset of a non-realizable relation

Determine whether the largest realizable subset of a non-realizable relation R can be found efficiently, or prove that finding such a subset is NP-hard.

Background

The paper characterizes realizability through Conditions X1 and X2, so relations violating these conditions may not be realizable by any DAG. For such relations, one natural repair strategy is to remove constraints until a realizable subset remains. The authors ask whether a largest such subset can be computed efficiently or whether the problem is computationally intractable.

References

Given a non-realizable relation $R$, one may ask whether it is possible to efficiently determine the largest subset $R'\subseteq R$ that is realizable, or whether this problem is NP-hard.

— Inferring DAGs and Phylogenetic Networks from Least Common Ancestors  (2511.07965 - Lindeberg et al., 11 Nov 2025) in Section 8, Discussion and Outlook, paragraph “Underlying Optimization Problems”