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On Inverting the Burrows-Wheeler Transform

Author Nicola Cotumaccio

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Models of computation
Keywords
  • Burrows-Wheeler transform
  • sorting
  • suffix array
  • element distinctness

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Abstract

We study the relationship between four fundamental problems: sorting, suffix sorting, element distinctness and BWT inversion. Our main contribution is an Ω(n log n) lower bound for BWT inversion in the comparison model. As a corollary, we obtain a new proof of the classical Ω(n log n) lower bound for sorting, which we believe to be of didactic interest for those who are not familiar with the Burrows-Wheeler transform.

Cite As Get BibTex

Nicola Cotumaccio. On Inverting the Burrows-Wheeler Transform. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 17:1-17:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.17

Author Details

Nicola Cotumaccio
  • University of Helsinki, Finland

Funding

Funded by the Helsinki Institute for Information Technology (HIIT).

References

  1. Michael Ben-Or. Lower bounds for algebraic computation trees. In Proceedings of the fifteenth Annual ACM Symposium on Theory of Computing, pages 80-86, 1983. Google Scholar
  2. Michael Burrows and David J. Wheeler. A block-sorting lossless data compression algorithm. Technical report, Systems Research Center, 1994. Google Scholar
  3. Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, and Clifford Stein. Introduction to algorithms. MIT press, 2022. Google Scholar
  4. David P Dobkin and Richard J Lipton. On the complexity of computations under varying sets of primitives. Journal of Computer and System Sciences, 18(1):86-91, 1979. URL: https://doi.org/10.1016/0022-0000(79)90054-0.
  5. Martin Farach. Optimal suffix tree construction with large alphabets. In Proceedings 38th Annual Symposium on Foundations of Computer Science, pages 137-143. IEEE, 1997. URL: https://doi.org/10.1109/SFCS.1997.646102.
  6. Paolo Ferragina and Giovanni Manzini. Opportunistic data structures with applications. In Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 390-398. IEEE, 2000. URL: https://doi.org/10.1109/SFCS.2000.892127.
  7. Roberto Grossi and Jeffrey Scott Vitter. Compressed suffix arrays and suffix trees with applications to text indexing and string matching. In Proceedings of the thirty-second Annual ACM Symposium on Theory of Computing, pages 397-406, 2000. Google Scholar
  8. Torben Hagerup. Sorting and searching on the word RAM. In STACS 98: 15th Annual Symposium on Theoretical Aspects of Computer Science Paris, France, February 25-27, 1998 Proceedings 15, pages 366-398. Springer, 1998. URL: https://doi.org/10.1007/BFB0028575.
  9. Yijie Han. Deterministic sorting in O (n log log n) time and linear space. Journal of Algorithms, 50(1):96-105, 2004. URL: https://doi.org/10.1016/J.JALGOR.2003.09.001.
  10. John E Hopcroft, Jeffrey D Ullman, and Alfred Vaino Aho. Data structures and algorithms, volume 175. Addison-wesley Boston, MA, USA:, 1983. Google Scholar
  11. Juha Kärkkäinen, Peter Sanders, and Stefan Burkhardt. Linear work suffix array construction. Journal of the ACM (JACM), 53(6):918-936, 2006. URL: https://doi.org/10.1145/1217856.1217858.
  12. Donald E Knuth. The Art of Computer Programming: Sorting and Searching, volume 3. Addison-Wesley Professional, 1998. Google Scholar
  13. Giovanni Manzini. An analysis of the Burrows-Wheeler transform. Journal of the ACM (JACM), 48(3):407-430, 2001. URL: https://doi.org/10.1145/382780.382782.
  14. Gonzalo Navarro. Compact data structures: A practical approach. Cambridge University Press, 2016. Google Scholar
  15. Simon J Puglisi, William F Smyth, and Andrew H Turpin. A taxonomy of suffix array construction algorithms. ACM Computing Surveys (CSUR), 39(2):4-es, 2007. Google Scholar
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