Computing Smallest Suffixient Arrays in Sublinear Time

Abstract

A suffixient array is a novel data structure that, when combined with an index providing direct access on a text $T$, allows us to answer a variety of pattern matching queries. In this work, we show how to compute a smallest suffixient array for $T[1\dots n]$ in $O(\frac{n\log \sigma}{\sqrt{\log n}}+\min(r,\bar{r})\log^\epsilon n)$ time for any $\epsilon > 0$, where $\sigma$ is the alphabet size of $T$ and $r$ and $\bar{r}$ are the numbers of equal-letter runs of the Burrows-Wheeler transforms of $T$ and its reverse $\overline{T}$, respectively. This time complexity becomes sublinear when $\sigma$ is small enough and $\min(r,\bar{r})=o(\frac{n}{\log^\epsilon n})$, yielding an asymptotic improvement over state-of-the-art algorithms. We also present a series of connected algorithmic results.