Establish a matching lower bound for top-m query complexity

Derive a matching lower bound on the number of k-wise oracle queries required to identify the top-m items under a transitive tournament, ideally matching the conjectured upper bound for the BlitzRank algorithm up to constant factors.

Background

Beyond proving the conjectured upper bound, the authors highlight the importance of a complementary lower bound to certify near-optimality of the approach.

A tight lower bound would clarify whether the conjectured complexity is instance-optimal or whether further algorithmic improvements are theoretically possible.

References

(Query complexity.) We showed $\lceil(n-1)/(k-1)\rceil$ complexity for top-1 selection and conjectured a bound for general $m$ (Conjecture~\ref{conj:query-complexity}) from empirical observations. A formal proof -- or matching lower bound -- remains open.

— BLITZRANK: Principled Zero-shot Ranking Agents with Tournament Graphs  (2602.05448 - Agrawal et al., 5 Feb 2026) in Conclusion, Future work