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ZOR filters: fast and smaller than fuse filters
Antoine Limasset
https://arxiv.org/abs/2602.03525 https://arxiv.org/pdf/2602.03525 https://arxiv.org/html/2602.03525
arXiv:2602.03525v1 Announce Type: new
Abstract: Probabilistic membership filters support fast approximate membership queries with a controlled false-positive probability $\varepsilon$ and are widely used across storage, analytics, networking, and bioinformatics \cite{chang2008bigtable,dayan2018optimalbloom,broder2004network,harris2020improved,marchet2023scalable,chikhi2025logan,hernandez2025reindeer2}. In the static setting, state-of-the-art designs such as XOR and fuse filters achieve low overhead and very fast queries, but their peeling-based construction succeeds only with high probability, which complicates deterministic builds \cite{graf2020xor,graf2022binary,ulrich2023taxor}.
We introduce \emph{ZOR filters}, a deterministic continuation of XOR/fuse filters that guarantees construction termination while preserving the same XOR-based query mechanism. ZOR replaces restart-on-failure with deterministic peeling that abandons a small fraction of keys, and restores false-positive-only semantics by storing the remainder in a compact auxiliary structure. In our experiments, the abandoned fraction drops below $1\%$ for moderate arity (e.g., $N\ge 5$), so the auxiliary handles a negligible fraction of keys. As a result, ZOR filters can achieve overhead within $1\%$ of the information-theoretic lower bound $\log_2(1/\varepsilon)$ while retaining fuse-like query performance; the additional cost is concentrated on negative queries due to the auxiliary check. Our current prototype builds several-fold slower than highly optimized fuse builders because it maintains explicit incidence information during deterministic peeling; closing this optimisation gap is an engineering target.
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