Heuristics for the run-length encoded Burrows–Wheeler transform alphabet ordering problem

Lily Major*, Amanda Clare, Jacqueline Daykin, Benjamin Mora, Christine Zarges

*Corresponding author for this work

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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 alphabet orderings 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 informed search 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.
Original languageEnglish
Article number11
Number of pages29
JournalJournal of Heuristics
Volume31
Issue number1
Early online date28 Jan 2025
DOIs
Publication statusE-pub ahead of print - 28 Jan 2025

Keywords

  • Alphabet ordering
  • Burrows–Wheeler transform
  • Compression
  • Local search
  • Random sampling
  • Run-length encoding

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