Filter data structures are widely used in various areas of computer science to answer approximate set-membership queries. In many applications, the data grows dynamically, requiring their filters to expand along with the data that they represent. However, existing methods for expanding filters cannot maintain stable performance, memory footprint, and false positive rate at the same time. We address this problem with Aleph Filter, which makes the following contributions. (1) It supports all operations (insertions, queries, deletes, etc.) in constant time, no matter how much the data grows. (2) Given any rough estimate of how much the data will ultimately grow, Aleph Filter provides far superior memory vs. false positive rate trade-offs, even if the estimate is off by orders of magnitude.

中文翻译：

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Aleph 滤波器：在恒定时间内达到无穷大

过滤数据结构广泛应用于计算机科学的各个领域，以回答近似的集合成员资格查询。在许多应用程序中，数据动态增长，要求其过滤器随其表示的数据一起扩展。然而，现有的扩展过滤器的方法无法同时保持稳定的性能、内存占用和误报率。我们使用 Aleph Filter 解决了这个问题，它做出了以下贡献。 （1）它支持恒定时间内的所有操作（插入、查询、删除等），无论数据增长多少。 (2) 给定对数据最终增长量的任何粗略估计，Aleph Filter 提供了远远优越的内存与误报率权衡，即使估计值有几个数量级的偏差。