Measuring the clustering effect of BWT via RLE

Sabrina Mantaci, Marinella Sciortino, Luca Versari, Giovanna Rosone

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The BurrowsâWheeler Transform (BWT) is a reversible transformation on which are based several text compressors and many other tools used in Bioinformatics and Computational Biology. The BWT is not actually a compressor, but a transformation that performs a context-dependent permutation of the letters of the input text that often create runs of equal letters (clusters) longer than the ones in the original text, usually referred to as the âclustering effectâ of BWT. In particular, from a combinatorial point of view, great attention has been given to the case in which the BWT produces the fewest number of clusters (cf. [5,16,21,23],). In this paper we are concerned about the cases when the clustering effect of the BWT is not achieved. For this purpose we introduce a complexity measure that counts the number of equal-letter runs of a word. This measure highlights that there exist many words for which BWT gives an âun-clustering effectâ, that is BWT produce a great number of short clusters. More in general we show that the application of BWT to any word at worst doubles the number of equal-letter runs. Moreover, we prove that this bound is tight by exhibiting some families of words where such upper bound is always reached. We also prove that for binary words the case in which the BWT produces the maximal number of clusters is related to the very well known Artin's conjecture on primitive roots. The study of some combinatorial properties underlying this transformation could be useful for improving indexing and compression strategies.
Original languageEnglish
Pages (from-to)79-87
Number of pages9
JournalTheoretical Computer Science
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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