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Burrows-Wheeler Transform and Run-Length Enconding

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10432)


In this paper we study the clustering effect of the Burrows-Wheeler Transform (BWT) from a combinatorial viewpoint. In particular, given a word w we define the BWT-clustering ratio of w as the ratio between the number of clusters produced by BWT and the number of the clusters of w. The number of clusters of a word is measured by its Run-Length Encoding. We show that the BWT-clustering ratio ranges in ]0, 2]. Moreover, given a rational number \(r\,\in \,]0,2]\), it is possible to find infinitely many words having BWT-clustering ratio equal to r. Finally, we show how the words can be classified according to their BWT-clustering ratio. The behavior of such a parameter is studied for very well-known families of binary words.


  • Burrows-Wheeler transform
  • Run-length encoding
  • Clustering effect

Partially supported by the project MIUR-SIR CMACBioSeq (“Combinatorial methods for analysis and compression of biological sequences”) grant no. RBSI146R5 and by the Gruppo Nazionale per il Calcolo Scientifico (GNCS-INDAM).

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  • DOI: 10.1007/978-3-319-66396-8_21
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  1. Adjeroh, D., Bell, T., Mukherjee, A.: The Burrows-Wheeler Transform: Data Compression, Suffix Arrays, and Pattern Matching. Springer, New York (2008)

    CrossRef  Google Scholar 

  2. Berstel, J., Lauve, A., Reutenauer, C., Saliola, F.: Combinatorics on Words: Christoffel Words and Repetitions in Words. CRM Monograph Series, vol. 27. American Mathematical Soc., Providence (2008)

    Google Scholar 

  3. Burrows, M., Wheeler, D.J.: A block sorting data compression algorithm. Tech. report, DIGITAL System Research Center (1994)

    Google Scholar 

  4. Fredricksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Rev. 24(2), 195–221 (1982)

    MathSciNet  CrossRef  MATH  Google Scholar 

  5. Higgins, P.M.: Burrows-Wheeler transformations and de Bruijn words. Theoret. Comput. Sci. 457, 128–136 (2012)

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. Lothaire, M.: Applied Combinatorics on Words. Encyclopedia of Mathematics and its Applications. Cambridge University Press, New York (2005)

    CrossRef  MATH  Google Scholar 

  7. Mantaci, S., Restivo, A., Rosone, G., Russo, F., Sciortino, M.: On fixed points of the Burrows-Wheeler Transform. Fundamenta Informaticae 154, 277–288 (2017)

    CrossRef  Google Scholar 

  8. Mantaci, S., Restivo, A., Rosone, G., Sciortino, M., Versari, L.: Measuring the clustering effect of BWT via RLE. Theor. Comput. Sci. (in press)

    Google Scholar 

  9. Mantaci, S., Restivo, A., Sciortino, M.: Burrows-Wheeler transform and Sturmian words. Inf. Process. Lett. 86, 241–246 (2003)

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. Perrin, D., Restivo, A.: Words. In: Bona, M. (ed.) Handbook of Enumerative Combinatorics. CRC Press (2015)

    Google Scholar 

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We thank the anonymous reviewers for providing us with many helpful comments and suggestions.

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Correspondence to Sabrina Mantaci , Antonio Restivo , Giovanna Rosone or Marinella Sciortino .

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Mantaci, S., Restivo, A., Rosone, G., Sciortino, M. (2017). Burrows-Wheeler Transform and Run-Length Enconding. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham.

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