Exact and Approximation Algorithms for the Inversion Distance Between Two Chromosomes

1 I n t r o d u c t i o n Much research has been devoted to efficient a lgo r i thms for the edi t d i s t ance be tween two s t r ings , t ha t is, the m i n i m u m number of inser t ions, delet ions, and s u b s t i t u t i o n s to t r a n s f o r m one s t r ing into another . Mot iva t ion comes in large pa r t f rom comput a t i o n a l b io logy: a t the level of ind iv idua l characters , genet ic sequences m u t a t e by these ope ra t ions , so edi t d is tance is a useful measure of evo lu t i ona ry d is tance . At the ch romosome level, however, genet ic sequences m u t a t e by more g loba l ope r a t i ons such as the reversal of a subs t r ing ( invers ion) , the de le t ion and subsequen t re inser t ion of a subs t r i ng far f rom its or ig inal s i te (transposition), d u p l i c a t i o n of a subs t r ing , and the exchange of prefixes or suffixes of two sequences in the s a m e o r g a n i s m (translocation). An inversion, which takes takes a subs t r ing of un res t r i c t ed size and replaces i t by its reverse in one opera t ion , has the effect of revers ing the