Transposition Rearrangement: Linear Algorithm for Length-Cost Model

Abstract

The contemporary computational biology gives motivation to study dependencies between finite sequences. Primary structures of DNA or proteins are represented by such sequences (also called words or strings). In the paper a linear algorithm, computing the distance between two words, is presented. The model operates with transpositions of single letters. The cost of a single transposition is equal to the distance which transposed letter has to cover. Other papers concerning the model give, as the best known, algorithms of time complexity O(n log n). The complexity of our algorithm is O(nk), where k is the size of the alphabet, and O(n) when the size is fixed.