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Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time

Authors Hideo Bannai , Juha Kärkkäinen, Dominik Köppl , Marcin Piątkowski



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Author Details

Hideo Bannai
  • M&D Data Science Center, Tokyo Medical and Dental University, Tokyo, Japan
Juha Kärkkäinen
  • Helsinki Institute of Information Technology (HIIT), Finland
Dominik Köppl
  • M&D Data Science Center, Tokyo Medical and Dental University, Tokyo, Japan
Marcin Piątkowski
  • Nicolaus Copernicus University, Toruń, Poland

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Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piątkowski. Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 7:1-7:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CPM.2021.7

Abstract

The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in linear time for integer alphabets by using a linear time suffix array construction algorithm, it was up to now only conjectured that the BBWT can also be constructed in linear time. We confirm this conjecture in the word RAM model by proposing a construction algorithm that is based on SAIS, improving the best known result of O(n lg n / lg lg n) time to linear. Since we can reduce the problem of constructing the extended BWT to constructing the BBWT in linear time, we obtain a linear-time algorithm computing the extended BWT at the same time.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Mathematics of computing → Combinatorics on words
Keywords
  • Burrows-Wheeler Transform
  • Lyndon words
  • Circular Suffix Array
  • Suffix Array Construction Algorithm

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References

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