In-Place Bijective Burrows-Wheeler Transforms

Authors Dominik Köppl , Daiki Hashimoto, Diptarama Hendrian , Ayumi Shinohara

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Author Details

Dominik Köppl
  • Department of Informatics, Kyushu University, Fukuoka, Japan
  • Japan Society for Promotion of Science (JSPS), Tokyo, Japan
Daiki Hashimoto
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Diptarama Hendrian
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Ayumi Shinohara
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan


We thank the anonymous reviewers for attracting our attention to the related work of Mantaci et al. [Sabrina Mantaci et al., 2014].

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Dominik Köppl, Daiki Hashimoto, Diptarama Hendrian, and Ayumi Shinohara. In-Place Bijective Burrows-Wheeler Transforms. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


One of the most well-known variants of the Burrows-Wheeler transform (BWT) [Burrows and Wheeler, 1994] is the bijective BWT (BBWT) [Gil and Scott, arXiv 2012], which applies the extended BWT (EBWT) [Mantaci et al., TCS 2007] to the multiset of Lyndon factors of a given text. Since the EBWT is invertible, the BBWT is a bijective transform in the sense that the inverse image of the EBWT restores this multiset of Lyndon factors such that the original text can be obtained by sorting these factors in non-increasing order. In this paper, we present algorithms constructing or inverting the BBWT in-place using quadratic time. We also present conversions from the BBWT to the BWT, or vice versa, either (a) in-place using quadratic time, or (b) in the run-length compressed setting using 𝒪(n lg r / lg lg r) time with 𝒪(r lg n) bits of words, where r is the sum of character runs in the BWT and the BBWT.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Mathematics of computing → Combinatorics on words
  • In-Place Algorithms
  • Burrows-Wheeler transform
  • Lyndon words


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