A Fast and Small Subsampled R-index

TL;DR

The paper introduces the sr-index, a space-efficient variant of the r-index for repetitive texts that maintains fast pattern matching while reducing space usage, outperforming most existing compressed indexes.

Contribution

It proposes the sr-index, a novel subsampled r-index that reduces space complexity with a controlled increase in query time, supported by theoretical guarantees and empirical validation.

Findings

The sr-index uses 1.5-3.0 times less space than the r-index.

It outperforms most compressed indexes in time and space on repetitive texts.

Lempel-Ziv indexes achieve better compression but are significantly slower.

Abstract

The $r$-index (Gagie et al., JACM 2020) represented a breakthrough in compressed indexing of repetitive text collections, outperforming its alternatives by orders of magnitude. Its space usage, $\mathcal{O}(r)$ where $r$ is the number of runs in the Burrows-Wheeler Transform of the text, is however larger than Lempel-Ziv and grammar-based indexes, and makes it uninteresting in various real-life scenarios of milder repetitiveness. In this paper we introduce the $sr$-index, a variant that limits the space to $\mathcal{O}(\min(r,n/s))$ for a text of length $n$ and a given parameter $s$, at the expense of multiplying by $s$ the time per occurrence reported. The $sr$-index is obtained by carefully subsampling the text positions indexed by the $r$-index, in a way that we prove is still able to support pattern matching with guaranteed performance. Our experiments demonstrate that the $sr$-index sharply outperforms virtually every other compressed index on repetitive texts, both in time and space, even matching the performance of the $r$-index while using 1.5--3.0 times less space. Only some Lempel-Ziv-based indexes achieve better compression than the $sr$-index, using about half the space, but they are an order of magnitude slower.