ZOR过滤器：比融合过滤器更快且更小
ZOR filters: fast and smaller than fuse filters
AI总结：
ZOR过滤器通过确定性剥离技术在保持异或查询性能的同时，实现了比融合过滤器更小的开销和更快的构建速度。
摘要：
概率成员过滤器支持通过控制误报概率ε来实现快速的近似成员查询，并被广泛应用于存储、分析、网络和生物信息学等领域。在静态设置中，最先进的设计如异或和融合过滤器实现了低开销和非常快的查询，但其基于剥离的构造仅在高概率下成功，这使得确定性构建变得复杂。我们引入了ZOR过滤器，这是一种确定性的异或/融合过滤器延续，保证了构造终止的同时保持相同的异或查询机制。ZOR用确定性的剥离替代了失败重试，放弃少量的键，并通过在紧凑的辅助结构中存储剩余部分来恢复仅误报的语义。在我们的实验中，丢弃的比率在适度的 arity（例如N≥5）下低于1%，因此辅助结构处理的键比例可以忽略不计。因此，ZOR过滤器可以在接近信息论下界log₂(1/ε)的开销内实现，同时保留融合式查询性能；额外的成本集中在负查询上，因为有辅助检查。我们的当前原型构建速度比高度优化的融合构建器慢几倍，因为它在确定性剥离过程中维护了显式的关联信息；缩小这个优化差距是一个工程目标。
英文摘要：
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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