Tightening the Zhang–Yeung entropic bound

Determine whether the entropic bound for the Zhang–Yeung conjunctive query with the stated cardinality constraints and functional dependencies is strictly smaller than the established upper bound of \(\frac{43}{11}\log(N)\).

Background

The paper uses the Zhang–Yeung query as a base instance for separating the polymatroid and entropic bounds. Combining a non-Shannon information inequality with the query’s cardinality and functional-dependency constraints yields an entropic upper bound of $\frac{43}{11}\log(N)$. The authors explicitly note that this bound might not be optimal, because additional consequences of the laws of Shannon entropy could potentially produce a smaller value.