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A Survey of the Bijective Burrows-Wheeler Transform

Authors Hideo Bannai , Dominik Köppl , Zsuzsanna Lipták

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Mathematics of computing → Combinatorics on words
Keywords
  • Burrows-Wheeler Transform
  • compression
  • text indexing
  • repetitiveness measure
  • Lyndon words
  • index construction algorithms
  • bijective string transformation

Metrics

Abstract

The Bijective BWT (BBWT), conceived by Scott in 2007, later summarized in a preprint by Gil and Scott in 2009 (arXiv 2012), is a variant of the Burrows-Wheeler Transform which is bijective: every string is the BBWT of some string. Indeed, the BBWT of a string is the extended BWT [Mantaci et al., 2007] of the factors of its Lyndon factorization. The BBWT has been receiving increasing interest in recent years. In this paper, we survey existing research on the BBWT, starting with its history and motivation. We then present algorithmic topics including construction algorithms with various complexities and an index on top of the BBWT for pattern matching. We subsequently address some properties of the BBWT as a compressor, discussing robustness to operations such as reversal, edits, rotation, as well as compression power. We close with listing other bijective variants of the BWT and open problems concerning the BBWT.

Cite As Get BibTex

Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták. A Survey of the Bijective Burrows-Wheeler Transform. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 2:1-2:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Manzini.2

Author Details

Hideo Bannai
  • M&D Data Science Center, Institute of Integrated Research, Institute of Science Tokyo, Japan
Dominik Köppl
  • Department of Computer Science and Engineering, University of Yamanashi, Japan
Zsuzsanna Lipták
  • Department of Computer Science, University of Verona, Italy

Funding

  • Bannai, Hideo: JSPS KAKENHI Grant Number JP24K02899
  • Köppl, Dominik: JSPS KAKENHI Grant Numbers JP23H04378 and JP25K21150
  • Lipták, Zsuzsanna: Partially funded by the Italian Ministry of University and Research (MUR) PRIN Project PINC, Pangenome INformatiCs: from Theory to Applications (Grant No. 2022YRB97K), and by the INdAM - GNCS Project CUP_E53C24001950001.

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