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arXiv · 2605.24925

Top-k Approximate Functional Dependency Discovery

Xiaolong Wan·Xixian Han
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Abstract

Approximate functional dependencies (AFDs) relax exact functional dependencies by tolerating a bounded degree of violation, making them suited for data quality auditing. Threshold-based discovery returns all dependencies above a user-specified cutoff, but output size is uncontrollable, the right threshold varies across datasets, and widely used measures are sensitive to LHS dimensionality. We study global top-$k$ AFD discovery, where neither the LHS nor the RHS is fixed and the $k$ strongest dependencies under $\mu^+$ are returned directly. The cross-attribute comparability of $\mu^+$ makes such a global ranking well-defined. We prove a Triangle Incompatibility Theorem showing that minimality, global top-$k$ ranking, and exact-$k$ output cannot simultaneously hold under any non-monotonic scoring function, justifying the removal of the minimality requirement. We present two algorithms: TALE-Base, which returns the exact global top-$k$ result by exhaustive level-wise evaluation, and TALE-Opt, which reduces computation through Apriori-style candidate generation, LHS computation reuse, and two complementary pruning rules exploiting exact FD monotonicity and an optimistic upper bound on $\mu^+$. Experiments on 41 real-world datasets show that TALE-Opt achieves pruning ratios up to 99.81\% and speedups over TALE-Base up to 78.81$\times$.

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Xiaolong Wan, Xixian Han. 2026-05-24. Top-k Approximate Functional Dependency Discovery. https://arxiv.org/abs/2605.24925

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