Minimum closure representatives

Determine how difficult it is to find a minimum-sized subset R' of a realizable relation R such that the classical closure of R' equals the classical closure of R.

Background

The paper relates its plus-closure to the classical closure of realizable LCA relations. In contrast to settings such as rooted-tree triplets, minimum closure representatives need not have equal cardinality and do not generally form the bases of a matroid. The authors consequently leave the computational problem of finding a smallest closure-equivalent subset unresolved.

References

The latter raises the question of how difficult it is to find a minimum-sized subset $R' \subseteq R$ for a realizable relation $R$ such that $(R') = (R)$.

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