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. However, existing methods for expanding filters cannot maintain stable performance, memory footprint, and false positive rate (FPR) simultaneously. 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 an estimate of how much the data will ultimately grow, Aleph Filter provides a memory vs. FPR trade-offs on par with static filters.

翻译：过滤器数据结构在计算机科学的多个领域中被广泛用于回答近似集合成员查询。在许多应用中，数据动态增长，要求其过滤器能够随数据一同扩展。然而，现有的过滤器扩展方法无法同时维持稳定的性能、内存占用和误判率。我们通过Aleph Filter解决了这一问题，其主要贡献如下：(1) 无论数据增长到何种规模，它都支持所有操作（插入、查询、删除等）在恒定时间内完成。(2) 在给定数据最终增长规模的预估条件下，Aleph Filter能提供与静态过滤器相当的内存与误判率权衡。