A New Efficient Algorithm for the All Sorting Reversals Problem with No Bad Components

The problem of finding all reversals that take a permutation one step closer to a target permutation is called the all sorting reversals problem (the ASR problem). For this problem, Siepel had an O(n
³
)-time algorithm. Most complications of his algorithm stem from some peculiar structures called bad components. Since bad components are very rare in both real and simulated data, it is practical to study the ASR problem with no bad components. For the ASR problem with no bad components, Swenson et al. gave an O (n
²
)-time algorithm. Very recently, Swenson found that their algorithm does not always work. In this paper, a new algorithm is presented for the ASR problem with no bad components. The time complexity is O(n
²
) in the worst case and is linear in the size of input and output in practice.