R-enum: Enumeration of Characteristic Substrings in BWT-runs Bounded Space

TL;DR

This paper introduces r-enum, a space-efficient algorithm for enumerating characteristic substrings in strings using run-length encoded Burrows-Wheeler transform, optimized for highly repetitive strings and large datasets.

Contribution

The paper presents the first RLBWT-based enumeration algorithm for characteristic substrings, achieving improved space efficiency for highly repetitive strings.

Findings

Runs in $O(n \, \log \log (n/r))$ time

Uses $O(r \log n)$ bits of space, with $r$ being the number of RLBWT runs

More space-efficient than previous methods on benchmark datasets

Abstract

Enumerating characteristic substrings (e.g., maximal repeats, minimal unique substrings, and minimal absent words) in a given string has been an important research topic because there are a wide variety of applications in various areas such as string processing and computational biology. Although several enumeration algorithms for characteristic substrings have been proposed, they are not space-efficient in that their space-usage is proportional to the length of an input string. Recently, the run-length encoded Burrows-Wheeler transform (RLBWT) has attracted increased attention in string processing, and various algorithms for the RLBWT have been developed. Developing enumeration algorithms for characteristic substrings with the RLBWT, however, remains a challenge. In this paper, we present r-enum (RLBWT-based enumeration), the first enumeration algorithm for characteristic substrings based on RLBWT. R-enum runs in $O(n \log \log (n/r))$ time and with $O(r \log n)$ bits of working space for string length $n$ and number $r$ of runs in RLBWT, where $r$ is expected to be significantly smaller than $n$ for highly repetitive strings (i.e., strings with many repetitions). Experiments using a benchmark dataset of highly repetitive strings show that the results of r-enum are more space-efficient than the previous results. In addition, we demonstrate the applicability of r-enum to a huge string by performing experiments on a 300-gigabyte string of 100 human genomes.