Aleph Filter: To Infinity in Constant Time

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.