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

Acknowledgements

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

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.CPM.2020.21

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.

Subject Classification

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

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References

  1. Donald Adjeroh, Timothy Bell, and Amar Mukherjee. The Burrows-Wheeler Transform:: Data Compression, Suffix Arrays, and Pattern Matching. Springer, 2008. Google Scholar
  2. Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piatkowski. Constructing the bijective BWT. ArXiv 1911.06985, 2019. Google Scholar
  3. Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piatkowski. Indexing the bijective BWT. In Proc. CPM, volume 128 of LIPIcs, pages 17:1-17:14, 2019. Google Scholar
  4. Philip Bille, Anders Roy Christiansen, Patrick Hagge Cording, Inge Li Gørtz, Frederik Rye Skjoldjensen, Hjalte Wedel Vildhøj, and Søren Vind. Dynamic relative compression, dynamic partial sums, and substring concatenation. Algorithmica, 80(11):3207-3224, 2018. Google Scholar
  5. Silvia Bonomo, Sabrina Mantaci, Antonio Restivo, Giovanna Rosone, and Marinella Sciortino. Sorting conjugates and suffixes of words in a multiset. Int. J. Found. Comput. Sci., 25(8):1161, 2014. Google Scholar
  6. Michael Burrows and David J. Wheeler. A block sorting lossless data compression algorithm. Technical Report 124, Digital Equipment Corporation, Palo Alto, California, 1994. Google Scholar
  7. Timothy M. Chan, J. Ian Munro, and Venkatesh Raman. Selection and sorting in the "restore" model. ACM Trans. Algorithms, 14(2):11:1-11:18, 2018. Google Scholar
  8. Kuo Tsai Chen, Ralph H. Fox, and Roger C. Lyndon. Free differential calculus, IV. The quotient groups of the lower central series. Annals of Mathematics, pages 81-95, 1958. Google Scholar
  9. Maxime Crochemore, Roberto Grossi, Juha Kärkkäinen, and Gad M. Landau. Computing the Burrows-Wheeler transform in place and in small space. J. Discrete Algorithms, 32:44-52, 2015. Google Scholar
  10. Jean-Pierre Duval. Factorizing words over an ordered alphabet. J. Algorithms, 4(4):363-381, 1983. Google Scholar
  11. Paolo Ferragina and Giovanni Manzini. Opportunistic data structures with applications. In Proc. FOCS, pages 390-398, 2000. Google Scholar
  12. Paolo Ferragina, Giovanni Manzini, and S. Muthu Muthukrishnan. The Burrows-Wheeler Transform: Ten Years Later. DIMACS, 2004. Google Scholar
  13. Michael L. Fredman and Dan E. Willard. Surpassing the information theoretic bound with fusion trees. J. Comput. Syst. Sci., 47(3):424-436, 1993. Google Scholar
  14. Travis Gagie, Giovanni Manzini, Gonzalo Navarro, and Jens Stoye. 25 Years of the Burrows-Wheeler Transform (Dagstuhl Seminar 19241). Dagstuhl Reports, 9(6):55-68, 2019. Google Scholar
  15. Raffaele Giancarlo, Antonio Restivo, and Marinella Sciortino. From first principles to the Burrows and Wheeler transform and beyond, via combinatorial optimization. Theor. Comput. Sci., 387(3):236-248, 2007. Google Scholar
  16. Joseph Yossi Gil and David Allen Scott. A bijective string sorting transform. ArXiv 1201.3077, 2012. Google Scholar
  17. Roberto Grossi, Ankur Gupta, and Jeffrey Scott Vitter. High-order entropy-compressed text indexes. In Proc. SODA, pages 841-850, 2003. Google Scholar
  18. Torben Hagerup. Fast deterministic construction of static dictionaries. In Proc. SODA, pages 414-418, 1999. Google Scholar
  19. Wing-Kai Hon, Tsung-Han Ku, Chen-Hua Lu, Rahul Shah, and Sharma V. Thankachan. Efficient algorithm for circular Burrows-Wheeler transform. In Proc. CPM, volume 7354 of LNCS, pages 257-268, 2012. Google Scholar
  20. R. C. Lyndon. On Burnside’s problem. Transactions of the American Mathematical Society, 77(2):202-215, 1954. Google Scholar
  21. Veli Mäkinen and Gonzalo Navarro. Succinct suffix arrays based on run-length encoding. Nord. J. Comput., 12(1):40-66, 2005. Google Scholar
  22. Udi Manber and Eugene W. Myers. Suffix arrays: A new method for on-line string searches. SIAM J. Comput., 22(5):935-948, 1993. Google Scholar
  23. Sabrina Mantaci, Antonio Restivo, Giovanna Rosone, and Marinella Sciortino. An extension of the Burrows-Wheeler transform. Theor. Comput. Sci., 387(3):298-312, 2007. Google Scholar
  24. Sabrina Mantaci, Antonio Restivo, Giovanna Rosone, and Marinella Sciortino. Suffix array and Lyndon factorization of a text. J. Discrete Algorithms, 28:2-8, 2014. Google Scholar
  25. Sabrina Mantaci, Antonio Restivo, and Marinella Sciortino. Burrows-Wheeler transform and Sturmian words. Inf. Process. Lett., 86(5):241-246, 2003. Google Scholar
  26. J. Ian Munro and Venkatesh Raman. Selection from read-only memory and sorting with minimum data movement. Theor. Comput. Sci., 165(2):311-323, 1996. Google Scholar
  27. Gonzalo Navarro and Yakov Nekrich. Optimal dynamic sequence representations. SIAM J. Comput., 43(5):1781-1806, 2014. Google Scholar
  28. Ge Nong, Sen Zhang, and Wai Hong Chan. Two efficient algorithms for linear time suffix array construction. IEEE Trans. Computers, 60(10):1471-1484, 2011. Google Scholar
  29. Tatsuya Ohno, Yoshimasa Takabatake, Tomohiro I, and Hiroshi Sakamoto. A faster implementation of online run-length Burrows-Wheeler transform. In Proc. IWOCA, volume 10765 of LNCS, pages 409-419, 2017. Google Scholar
  30. Alberto Policriti and Nicola Prezza. LZ77 computation based on the run-length encoded BWT. Algorithmica, 80(7):1986-2011, 2018. Google Scholar
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