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The boom of genomic sequencing makes compression of set of sequencesinescapable. This underlies the need for multi-string indexing data structuresthat helps compressing the data. The most prominent example of such datastructures is the Burrows-Wheeler Transform (BWT), a reversible permutation ofa text that improves its compressibility. A similar data structure, theeXtended Burrows-Wheeler Transform (XBW), is able to index a tree labelled withalphabet symbols. A link between a multi-string BWT and the Aho-Corasickautomaton has already been found and led to a way to build a XBW from amulti-string BWT. We exhibit a stronger link between a multi-string BWT and aXBW by using the order of the concatenation in the multi-string. This bijectivelink has several applications: first, it allows to build one data structurefrom the other; second, it enables one to compute an ordering of the inputstrings that optimises a Run-Length measure (i.e., the compressibility) of theBWT or of the XBW.

Strong link between BWT and XBW via Aho-Corasick automaton and applications to Run-Length Encoding