Faster run-length compressed suffix arrays

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 $O\left(r\text{log}\right(n/r)+r\text{log}\sigma +\sigma )$ bits such that later, given character $a$ and the suffix-array (SA) interval for $P$ , we can find the SA interval for $aP$ in $O\left(\text{log}{r}_a+\text{log}\text{log}n\right)$ 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 $aP$ in only $O\left(\text{log}{r}_a\right)$ 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.