Exact double DCJ distance between circular genomes

The double cut-and-join (DCJ) operation, or 2-break rearrangement was introduced by Yancopoulos et al. ([1]). Finding DCJ distance between double genomes is NP-hard ([2]). To a pair of regular and all-duplicates genome, having only circular chromosomes, we assign generalized breakpoint graph (introduced by Alekseyev and Pevzner ([3]). We give an algorithm for finding the approximation and exact double DCJ distance. We do this by decomposing GBG into maximum number of alternating, closed trails, using branch-and-bound method.