# A Faster Implementation of Online Run-Length Burrows-Wheeler Transform

## TL;DR

This paper introduces a faster online run-length Burrows-Wheeler transform algorithm that improves empirical construction time, especially for highly repetitive strings, by using dynamic lists instead of wavelet trees.

## Contribution

The paper presents a novel online RLBWT algorithm that operates in run-compressed space and replaces wavelet tree rank queries with direct list comparisons, enhancing speed.

## Key findings

- Significantly faster empirical construction time for highly repetitive strings.
- Efficient in run-compressed space with $O(n\\lg r)$ time complexity.
- Outperforms previous algorithms on various benchmarks.

## Abstract

Run-length encoding Burrows-Wheeler Transformed strings, resulting in Run-Length BWT (RLBWT), is a powerful tool for processing highly repetitive strings. We propose a new algorithm for online RLBWT working in run-compressed space, which runs in $O(n\lg r)$ time and $O(r\lg n)$ bits of space, where $n$ is the length of input string $S$ received so far and $r$ is the number of runs in the BWT of the reversed $S$. We improve the state-of-the-art algorithm for online RLBWT in terms of empirical construction time. Adopting the dynamic list for maintaining a total order, we can replace rank queries in a dynamic wavelet tree on a run-length compressed string by the direct comparison of labels in a dynamic list. The empirical result for various benchmarks show the efficiency of our algorithm, especially for highly repetitive strings.