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Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem

Lily Major Orcid Logo, Amanda Clare Orcid Logo, Jacqueline Daykin Orcid Logo, Benjamin Mora Orcid Logo, Christine Zarges Orcid Logo

Journal of Heuristics

Swansea University Author: Benjamin Mora Orcid Logo

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Abstract

The Burrows-Wheeler Transform (BWT) is a string transformation technique widely used in areas such as bioinformatics and file compression. Many applications combine a run-length encoding (RLE) with the BWT in a way which preserves the ability to query the compressed data efficiently. However, these...

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Published in: Journal of Heuristics
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URI: https://cronfa.swan.ac.uk/Record/cronfa67539
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Abstract: The Burrows-Wheeler Transform (BWT) is a string transformation technique widely used in areas such as bioinformatics and file compression. Many applications combine a run-length encoding (RLE) with the BWT in a way which preserves the ability to query the compressed data efficiently. However, these methods may not take full advantage of the compressibility of the BWT as they do not modify the alphabet ordering for the sorting step embedded in computing the BWT. Indeed, any such alteration of the alphabet ordering can have a considerable impact on the output of the BWT, in particular on the number of runs. For an alphabet Σ containing σ characters, the space of all alphabetorderings is of size σ!. While for small alphabets an exhaustive investigation is possible, finding the optimal ordering for larger alphabets is not feasible. Therefore, there is a need for a more informedsearch strategy than brute-force sampling the entire space, which motivates a new heuristic approach. In this paper, we explore the non-trivial cases for the problem of minimizing the size of a run-length encoded BWT (RLBWT) via selecting a new ordering for the alphabet. We show that random sampling of the space of alphabet orderings usually gives sub-optimal orderings for compression and that a local search strategy can provide a large improvement in relatively few steps. We also inspect a selection of initial alphabet orderings, including ASCII, letter appearance, and letter frequency. While this alphabet ordering problem is computationally hard we demonstrate gain in compressibility.
Keywords: Alphabet ordering; Burrows-Wheeler Transform; Compression; Local search; Random sampling; Run-Length Encoding
College: Faculty of Science and Engineering
Funders: Engineering and Physical Sciences Research Council (EP/S023992/1); European Regional Development Fund (80761-AU-137)

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