Bit catastrophes for the Burrows-Wheeler Transform

Sara Giuliani; Shunsuke Inenaga; Zsuzsanna Lipták; Giuseppe Romana; Marinella Sciortino; Cristian Urbina

doi:10.1007/s00224-024-10212-9

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arXiv · 2404.10426

Bit catastrophes for the Burrows-Wheeler Transform

Sara Giuliani·Shunsuke Inenaga·Zsuzsanna Lipták·Giuseppe Romana·Marinella Sciortino·Cristian Urbina

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Abstract

A bit catastrophe, loosely defined, is when a change in just one character of a string causes a significant change in the size of the compressed string. We study this phenomenon for the Burrows-Wheeler Transform (BWT), a string transform at the heart of several of the most popular compressors and aligners today. The parameter determining the size of the compressed data is the number of equal-letter runs of the BWT, commonly denoted $r$. We exhibit infinite families of strings in which insertion, deletion, resp. substitution of one character increases $r$ from constant to $\Theta(\log n)$, where $n$ is the length of the string. These strings can be interpreted both as examples for an increase by a multiplicative or an additive $\Theta(\log n)$-factor. As regards multiplicative factor, they attain the upper bound given by Akagi, Funakoshi, and Inenaga [Inf & Comput. 2023] of $O(\log n \log r)$, since here $r=O(1)$. We then give examples of strings in which insertion, deletion, resp. substitution of a character increases $r$ by a $\Theta(\sqrt{n})$ additive factor. These strings significantly improve the best known lower bound for an additive factor of $\Omega(\log n)$ [Giuliani et al., SOFSEM 2021].

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Sara Giuliani, Shunsuke Inenaga, Zsuzsanna Lipták, Giuseppe Romana, Marinella Sciortino, Cristian Urbina. 2024-04-16. Bit catastrophes for the Burrows-Wheeler Transform. https://doi.org/10.1007/s00224-024-10212-9

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