Faster run-length compressed suffix arrays

TL;DR

This paper introduces a faster method for computing suffix array intervals in run-length compressed suffix arrays, significantly improving query times without increasing space, with potential applications in indexing and pattern matching.

Contribution

The authors develop a novel modification of RLCSA that reduces SA interval query time to O(log r_a) while maintaining the same space complexity, by leveraging select queries on sparse bitvectors.

Findings

Achieved faster SA interval computation in RLCSA

Maintained asymptotic space bounds despite speed improvements

Potential enhancements for indexing and pattern matching algorithms

Abstract

We first review how we can store a run-length compressed suffix array (RLCSA) for a text $T$ of length $n$ over an alphabet of size $\sigma$ whose Burrows-Wheeler Transform (BWT) consists of $r$ runs in $O \left( \rule{0ex}{2ex} r \log (n / r) + r \log \sigma + \sigma \right)$ bits such that later, given character $a$ and the suffix array interval for $P$, we can find the suffix-array (SA) interval for $a P$ in $O (\log r_a + \log \log n)$ time, where $r_a$ is the number of runs of copies of $a$ in the BWT. We then show how to modify the RLCSA such that we find the SA interval for $a P$ in only $O (\log r_a)$ time, without increasing its asymptotic space bound. Our key idea is applying a result by Nishimoto and Tabei (ICALP 2021) and then replacing rank queries on sparse bitvectors by a constant number of select queries. We also review two-level indexing and discuss how our faster RLCSA may be useful in improving it. Finally, we briefly discuss how two-level indexing may speed up a recent heuristic for finding maximal exact matches of a pattern with respect to an indexed text.