Canonical-DAG scaffold for repairing inconsistent constraints

Determine whether the canonical DAG G_R associated with a relation satisfying X1 can be used to find a largest realizable subset of R, identify minimal conflicts in R, or define a useful measure of the distance from R to realizability.

Background

Even when a relation R is not realizable, its plus-closure R+ may be realizable, and the canonical DAG G_R realizes R+. This motivates using G_R as a structural scaffold for diagnosing or repairing the original constraints. The authors explicitly leave unresolved whether this scaffold can support maximum-subset selection, conflict identification, or a practical distance-to-realizability measure.

References

This raises the question of whether the canonical DAG $G_R$ that realizes $R+$ could serve as a scaffold for determining a largest realizable subset, or for identifying minimal conflicts within relations satisfying {X1}.

— 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”