Fast Succinct Retrieval and Approximate Membership using Ribbon

TL;DR

This paper introduces BuRR, a practical succinct retrieval data structure that achieves near-optimal space efficiency and high speed, outperforming traditional Bloom filters and previous retrieval methods in both space and time.

Contribution

The paper presents the first practical succinct retrieval data structure, BuRR, with extremely low space overhead and superior speed, improving upon prior theoretical and practical solutions.

Findings

BuRR achieves space overheads below 1% in experiments.

BuRR outperforms traditional Bloom filters in speed and space efficiency.

Homogeneous ribbon filter AMQs are simpler and faster with slightly larger space overhead.

Abstract

A retrieval data structure for a static function $f:S\rightarrow \{0,1\}^r$ supports queries that return $f(x)$ for any $x \in S$. Retrieval data structures can be used to implement a static approximate membership query data structure (AMQ), i.e., a Bloom filter alternative, with false positive rate $2^{-r}$. The information-theoretic lower bound for both tasks is $r|S|$ bits. While succinct theoretical constructions using $(1+o(1))r|S|$ bits were known, these could not achieve very small overheads in practice because they have an unfavorable space--time tradeoff hidden in the asymptotic costs or because small overheads would only be reached for physically impossible input sizes. With bumped ribbon retrieval (BuRR), we present the first practical succinct retrieval data structure. In an extensive experimental evaluation BuRR achieves space overheads well below 1\,\% while being faster than most previously used retrieval data structures (typically with space overheads at least an order of magnitude larger) and faster than classical Bloom filters (with space overhead $\geq 44\,\%$). This efficiency, including favorable constants, stems from a combination of simplicity, word parallelism, and high locality. We additionally describe homogeneous ribbon filter AMQs, which are even simpler and faster at the price of slightly larger space overhead.