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Linking BWT and XBW via Aho-Corasick Automaton: Applications to Run-Length Encoding

Bastien Cazaux 1, 2 Eric Rivals 2, 1
1 MAB - Méthodes et Algorithmes pour la Bioinformatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The boom of genomic sequencing makes compression of sets of sequences inescapable. This underlies the need for multi-string indexing data structures that helps compressing the data. The most prominent example of such data structures is the Burrows-Wheeler Transform (BWT), a reversible permutation of a text that improves its compressibility. A similar data structure, the eXtended Burrows-Wheeler Transform (XBW), is able to index a tree labelled with alphabet symbols. A link between a multi-string BWT and the Aho-Corasick automaton has already been found and led to a way to build a XBW from a multi-string BWT. We exhibit a stronger link between a multi-string BWT and a XBW by using the order of the concatenation in the multi-string. This bijective link has several applications: first, it allows one to build one data structure from the other; second, it enables one to compute an ordering of the input strings that optimises a Run-Length measure (i.e., the compressibility) of the BWT or of the XBW.
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Bastien Cazaux, Eric Rivals. Linking BWT and XBW via Aho-Corasick Automaton: Applications to Run-Length Encoding. 30th Annual Symposium on Combinatorial Pattern Matching (CPM), University of Pisa, Jun 2019, Pise, Italy. pp.24:1--24:20, ⟨10.4230/LIPIcs.CPM.2019.24⟩. ⟨lirmm-02382066⟩

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