Rearrangement Models and Single-Cut Operations

There have been many widely used genome rearrangement models, such as reversals, Hannenhalli- Pevzner, and double-cut and join. Though each one can be precisely defined, the general notion of a model remains undefined. In this paper, we give a formal set-theoretic definition, which allows us to investigate and prove relationships between distances under various existing and new models. We also initiate the formal study of single-cut operations by giving a linear time algorithm for the distance problem under a new single-cut and join model.