Computing Smallest Suffixient Arrays in Sublinear Time

2026-06-30

AI Summary

This work addresses the problem of efficiently constructing the minimal suffix-covering array to support a variety of pattern matching queries. We propose the first sublinear-time construction algorithm, running in $O(n \log \sigma / \sqrt{\log n} + \min(r, \bar{r}) \log^\varepsilon n)$ time, where $r$ and $\bar{r}$ denote the number of equal-letter runs in the Burrows–Wheeler Transform (BWT) of the text and its reverse, respectively. By integrating run-length analysis of the BWT with sublinear indexing techniques, our approach significantly outperforms existing methods on small alphabets with sparse BWT runs. This result marks the first sublinear-time construction of the minimal suffix-covering array, establishing a new benchmark for space-efficient pattern matching data structures.

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 $O(\frac{n\log σ}{\sqrt{\log n}}+\min(r,\bar{r})\log^εn)$ time for any $ε> 0$, where $σ$ 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 $σ$ is small enough and $\min(r,\bar{r})=o(\frac{n}{\log^εn})$, yielding an asymptotic improvement over state-of-the-art algorithms. We also present a series of connected algorithmic results.

Problem

• suffixient array
• sublinear time
• pattern matching
• Burrows-Wheeler transform
• data structure

Innovation

• suffixient array
• sublinear time
• Burrows-Wheeler transform
• pattern matching
• run-length encoding