De novo repeat classification and fragment assembly

Repetitive sequences make up a significant fraction of almost any genome and an important and still open question in bioinformatics is how to represent all repeats in DNA sequences. We propose a radically new approach to repeat classification that is motivated by the fundamental topological notion of quotient spaces. A torus or Klein bottle are examples of quotient spaces that can be obtained from a square by gluing some points. Our new repeat classification algorithm is based on the observation that the alignment-induced quotient space of a DNA sequence compactly represents all sequence repeats. This observation leads to a simple and efficient solution of the repeat classification problem as well as new approaches to fragment assembly and multiple alignment.