Computability of the entropic bound

Determine whether the entropic bound for conjunctive queries under functional dependencies is computable.

Background

The paper contrasts the entropic bound, which is asymptotically tight for query-result sizes under functional dependencies, with the polymatroid bound, a computable linear-programming relaxation that may be non-tight. The computability of the entropic bound depends on understanding the entropic cone, whose structure is not currently fully characterized. Consequently, the absence of an effective procedure for computing the entropic bound prevents it from directly yielding a general query-evaluation algorithm.

References

While this sounds promising, this result comes with a catch: it is not known if the entropic bound is even computable!

— Size Bounds for CQs Under Acyclic Constraints  (2608.26775 - Mengel et al., 27 Aug 2026) in Section 1, Introduction

This has been investigated in and , but the problem has not been fully resolved yet.

— Size bounds and query plans for relational joins  (1711.03860 - Atserias et al., 2017) in Section Conclusions