Efficiently recognize the exactness class

Determine how to efficiently detect whether a given multiple sequence alignment with gaps belongs to the class for which the gaps-as-symbols approach yields an optimal height-optimization solution.

Background

The paper proposes that a class of multiple sequence alignments may exist in which treating gaps as alphabet symbols produces an exact optimum rather than merely an upper bound. Beyond characterizing this class, the authors leave unresolved the algorithmic problem of deciding efficiently whether an input alignment belongs to it.

References

This raises several natural questions: What is the exact form of the characterization? How to efficiently detect if a given MSA is part of this class?

— Pangenome Optimization via Elastic Degenerate Strings  (2609.26542 - Rizzo et al., 22 Sep 2026) in Section Discussion, subsection “Gaps as symbols yield exact solutions?”

Do all optimal alignments under some column-wise scoring function belong to this class?

— Pangenome Optimization via Elastic Degenerate Strings  (2609.26542 - Rizzo et al., 22 Sep 2026) in Section Discussion, subsection “Gaps as symbols yield exact solutions?”