Abstract
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.
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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Acknowledgements
We thank the anonymous reviewers for providing us with many helpful comments and suggestions.
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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. https://doi.org/10.1007/978-3-319-66396-8_21
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DOI: https://doi.org/10.1007/978-3-319-66396-8_21
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