Grafite: Taming Adversarial Queries with Optimal Range Filters

Abstract

Range filters allow checking whether a query range intersects a given set of keys with a chance of returning a false positive answer, thus generalising the functionality of Bloom filters from point to range queries. Existing practical range filters have addressed this problem heuristically, resulting in high false positive rates and query times when dealing with adversarial inputs, such as in the common scenario where queries are correlated with the keys. We introduce Grafite, a novel range filter that solves these issues with a simple design and clear theoretical guarantees that hold regardless of the input data and query distribution: given a fixed space budget of $B$ bits per key, the query time is $O(1)$, and the false positive probability is upper bounded by $\ell/2^{B-2}$, where $\ell$ is the query range size. Our experimental evaluation shows that Grafite is the only range filter to date to achieve robust and predictable false positive rates across all combinations of datasets, query workloads, and range sizes, while providing faster queries and construction times, and dominating all competitors in the case of correlated queries. As a further contribution, we introduce a very simple heuristic range filter whose performance on uncorrelated queries is very close to or better than the one achieved by the best heuristic range filters proposed in the literature so far.