Sorting by Cuts, Joins, and Whole Chromosome Duplications

Genome rearrangement problems have been extensively studied due to their importance in biology. Most studied models assumed a single copy per gene. However, in reality, duplicated genes are common, most notably in cancer. In this study, we make a step toward handling duplicated genes by considering a model that allows the atomic operations of cut, join, and whole chromosome duplication. Given two linear genomes, [Formula: see text] with one copy per gene and [Formula: see text] with two copies per gene, we give a linear time algorithm for computing a shortest sequence of operations transforming [Formula: see text] into [Formula: see text] such that all intermediate genomes are linear. We also show that computing an optimal sequence with fewest duplications is NP-hard.