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DOI: 10.4230/LIPIcs.CPM.2020.21

In-Place Bijective Burrows-Wheeler Transforms

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

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract

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.

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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)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2020.21,
  author =	{K\"{o}ppl, Dominik and Hashimoto, Daiki and Hendrian, Diptarama and Shinohara, Ayumi},
  title =	{{In-Place Bijective Burrows-Wheeler Transforms}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.21},
  URN =		{urn:nbn:de:0030-drops-121463},
  doi =		{10.4230/LIPIcs.CPM.2020.21},
  annote =	{Keywords: In-Place Algorithms, Burrows-Wheeler transform, Lyndon words}
}

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In-Place Bijective Burrows-Wheeler Transforms

Abstract

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