Genome rearrangements distance by fusion, fission, and transposition is easy

Given two genomes represented as circularly ordered sequences of genes, we show a polynomial time algorithm for the minimum weight series of fusion, jissions, and transpositions (with transpositions weighing twice as much as fusions and$ssions) that transforms one genome into the other. The algorithm is based on classical results ofpermutation group theory and is the jirst polynomial result for a genome rearrangement problem involving transpositions. It has been observed in real biological instances that transpositions occur with about ha&- the frequency of reversals. Although we are not using reversals in this study, this observation motivated the double weight assigned to transpositions.