Multi-break rearrangements and chromosomal evolution

Most genome rearrangements (e.g., reversals and translocations) can be represented as 2-breaks that break a genome at 2 points and glue the resulting fragments in a new order. Multi-break rearrangements break a genome into multiple fragments and further glue them together in a new order. While multi-break rearrangements were studied in depth for k=2 breaks, the k-break distance problem for arbitrary k remains unsolved. We prove a duality theorem for multi-break distance problem and give a polynomial algorithm for computing this distance.