Attainment of entropic width as a query-evaluation exponent

Determine whether the entropic width introduced with PANDA is attained as an exponent for query evaluation.

Background

The paper places entropic and almost-entropic width parameters within a hierarchy of polymatroid-based width measures. Although almost-entropic optimization provides the entropic width used with PANDA, the paper states that it is unresolved whether this width is actually attained as a query-evaluation exponent.

References

Almost-entropic optimisation also gives the entropic width introduced with PANDA, whose attainment as a query-evaluation exponent remains open.

— FPT=PTIME for Homomorphism Problems on Sparse-Incidence and Bounded-Independence Patterns  (2609.21840 - Lanzinger, 18 Sep 2026) in Section 5, paragraph beginning "The intermediate cones are not merely formal interpolations"