Evolutionary Search Techniques for the Lyndon Factorization of Biosequences

A non-empty string x over an ordered alphabet is said to be a Lyndon word if it is alphabetically smaller than all of its cyclic rotations. Any string can be uniquely factored into Lyndon words and efficient algorithms exist to perform the factorization process in linear time and constant space. Lyndon words find wide-ranging applications including string matching and pattern inference in bioinformatics. Here we investigate the impact of permuting the alphabet ordering on the resulting factorization and demonstrate significant variations in the numbers of factors obtained. We also propose an evolutionary algorithm to find optimal orderings of the alphabet to enhance this factorization process and illustrate the impact of different operators. The flexibility of such an approach is illustrated by our use of five fitness functions which produce different factorizations suitable for different downstream tasks.