Prove the conjectured top-m query complexity bound for BlitzRank in the transitive case

Prove that the BlitzRank algorithm (Algorithm 1), applied to top-m selection from n items using a k-wise comparison oracle under a transitive tournament on V, terminates in O((n−1)/(k−1) + ((m−1)/(k−1))·log_k m) oracle queries for any m > 1.

Background

The paper establishes a tight bound for top-1 selection and empirically validates a general form for top-m, proposing a specific asymptotic bound for the number of k-wise oracle calls when the underlying tournament is transitive.

Although extensive experiments show observed query counts within 1.25× of the conjectured bound, a formal proof remains missing, motivating a theoretical confirmation of the claimed complexity.

References

For general $m$, we conjecture a bound of $O((n-1)/(k-1) + (m-1)/(k-1)\cdot\log_k m)$, decomposing into a candidate reduction term and a frontier refinement term (Conjecture~\ref{conj:query-complexity}). A formal proof for $m>1$ remains open; see Appendix~\ref{sec:query-complexity} for details.

— BLITZRANK: Principled Zero-shot Ranking Agents with Tournament Graphs  (2602.05448 - Agrawal et al., 5 Feb 2026) in Section Guarantees (Query Complexity)