Linking BWT and XBW via Aho-Corasick Automaton: Applications to Run-Length Encoding ; Lien entre Transformée de Burrows-Wheeler (BWT) et BWT étendue (XBW) via l'automate d'Aho-Corasick : applications en compression par encodage des longueurs

URN: urn:nbn:de:0030-drops-104955URL: http://drops.dagstuhl.de/opus/volltexte/2019/10495/ISBN ={978-3-95977-103-0},ISSN ={1868-8969}, ; International audience ; 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.