Prefix Block-Interchanges on Binary Strings

Abstract

A block-interchange acting on a string s exchanges two non-overlapping but not necessary adjacent substrings in s. A prefix block-interchange is a special block-interchange in which one of the two exchanged substrings is restricted to a prefix of s. In this study, we study the problem of sorting by prefix block-interchanges on binary strings, which is to find the minimum number of prefix block-interchanges to sort a given binary string. In addition, we study the problem of computing the prefix block-interchange distance between two binary strings, which is to compute the minimum number of prefix block-interchanges to transform a given binary string into another given binary string. Consequently, we design a linear-time algorithm to solve the problem of sorting by prefix block-interchange on binary strings and also show that the problem of computing the prefix block-interchange distance between two binary strings is NP-hard.