Constructing Suffixient Arrays Revisited

TL;DR

This paper introduces a new one-pass linear-time algorithm for constructing suffixient arrays, improving efficiency over previous methods that required multiple scans or more complex time bounds.

Contribution

It presents a novel one-pass linear-time construction algorithm for suffixient arrays under the standard RAM model.

Findings

The new algorithm constructs suffixient arrays in linear time.

It improves over previous algorithms requiring multiple scans or higher complexity.

The approach is efficient for large texts and practical applications.

Abstract

Recently, Cenzato et al.\ proposed a new text index, called the \emph{suffixient array}, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random access to the input text $T[1..n]$ is available. They show that, given the suffix array, the longest common prefix array, and the Burrows--Wheeler transform (BWT) of the reverse of $T[1..n]$ over an alphabet $\{1,\ldots,\sigma\}$, a suffixient array can be constructed in linear time. However, their construction algorithms require multiple scans of these arrays. When restricted to a single pass over the arrays, they present an alternative construction algorithm running in $O(n + \overline{r} \log \sigma)$ time, where $\overline{r}$ is the number of runs in the BWT of the reversed text. In this paper, we present a new one-pass algorithm that constructs a suffixient array in linear time under the standard RAM model.