Sorting by prefix block-interchanges

We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation using as few such operations as possible. We give a 2-approximation algorithm for this problem, as well as a 4/3-approximation for simple permutations; we prove tight lower and upper bounds on the corresponding distance; and we bound the largest value that the distance can reach. (c) 2023 Elsevier B.V. All rights reserved.