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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

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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spelling v2 67539 2024-09-03 Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem 557f93dfae240600e5bd4398bf203821 0000-0002-2945-3519 Benjamin Mora Benjamin Mora true false 2024-09-03 MACS 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. Journal Article Journal of Heuristics 0 0 0 0001-01-01 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee 2024-09-03T10:17:59.5871792 2024-09-03T09:07:44.9209564 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Lily Major 0000-0002-5783-8432 1 Amanda Clare https://orcid.org/0000-0001-8315-3659 2 Jacqueline Daykin https://orcid.org/0000-0003-1123-8703 3 Benjamin Mora 0000-0002-2945-3519 4 Christine Zarges https://orcid.org/0000-0002-2829-4296 5
title Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
spellingShingle Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
Benjamin Mora
title_short Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
title_full Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
title_fullStr Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
title_full_unstemmed Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
title_sort Heuristics for the Run-length Encoded Burrows-Wheeler Transform Alphabet Ordering Problem
author_id_str_mv 557f93dfae240600e5bd4398bf203821
author_id_fullname_str_mv 557f93dfae240600e5bd4398bf203821_***_Benjamin Mora
author Benjamin Mora
author2 Lily Major
Amanda Clare
Jacqueline Daykin
Benjamin Mora
Christine Zarges
format Journal article
container_title Journal of Heuristics
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 0
active_str 0
description 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.
published_date 0001-01-01T10:17:58Z
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score 11.028798

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