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In this paper we study Lyndon structures related to the Burrows-Wheeler Transform with potential application to bioinformatics. Next-Generation Sequencing techniques require the alignment of a large set of short reads (between dozens to hundreds of letters) on a reference sequence (millions of letters). The Burrows-Wheeler Transform has been used in various alignment programs which generally compute the Lyndon factorization of the reference sequence as a preprocessing step. We compute the quadratic factorization of all rotations of an input string and the Burrows-Wheeler Transform of a Lyndon substring. From the factored rotations we introduce the Lyndon fountain.

Motivation: The constant advances in sequencing technology are turning whole-genome sequencing into a routine procedure, resulting in massive amounts of data that need to be processed. Tens of gigabytes of data in the form of short reads need to be mapped back to reference sequences, a few gigabases long. A first generation of short read alignment software successfully employed hash tables, and the current second generation uses Burrows-Wheeler Transform, further improving mapping speed. However, there is still demand for faster and more accurate mapping.Results: In this paper, we present REad ALigner, an efficient, accurate and consistent tool for aligning short reads obtained from next generation sequencing. It is based on a new, simple, yet efficient mapping algorithm that can match and outperform current BWT-based software.