Sliding Bloom Filters

TL;DR

This paper introduces a Sliding Bloom Filter, a data structure for efficiently maintaining membership information of the last n elements in a stream with low memory and constant update time, balancing error probability.

Contribution

It formally defines the Sliding Bloom Filter, provides a low space construction with O(1) update time, and proves a near-optimal space lower bound, advancing streaming data structure theory.

Findings

Achieves constant time updates with high probability

Uses minimal space close to the theoretical lower bound

Supports membership queries over sliding windows efficiently

Abstract

A Bloom filter is a method for reducing the space (memory) required for representing a set by allowing a small error probability. In this paper we consider a \emph{Sliding Bloom Filter}: a data structure that, given a stream of elements, supports membership queries of the set of the last $n$ elements (a sliding window), while allowing a small error probability. We formally define the data structure and its relevant parameters and analyze the time and memory requirements needed to achieve them. We give a low space construction that runs in O(1) time per update with high probability (that is, for all sequences with high probability all operations take constant time) and provide an almost matching lower bound on the space that shows that our construction has the best possible space consumption up to an additive lower order term.