ZOR filters: fast and smaller than fuse filters

TL;DR

ZOR filters are a deterministic variant of XOR and fuse filters that guarantee construction success, maintain fast query performance, and operate with minimal overhead close to the theoretical lower bound.

Contribution

We introduce ZOR filters, a deterministic construction method for probabilistic membership filters that ensures termination while preserving fast query performance.

Findings

Achieve overhead within 1% of the information-theoretic lower bound.

Abandoned keys fraction drops below 1% for moderate arity.

Prototype builds slower than optimized fuse filters due to explicit incidence maintenance.

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.