A Fixed-Parameter Algorithm for String-to-String Correction

In the String-to-String Correction problem we are given two strings x and y and a positive integer k, and are asked whether it is possible to transform y into x with at most k single character deletions and adjacent character exchanges. We present a first simple fixed-parameter algorithm for Stringto-String Correction that runs in O∗(2k). Moreover, we present a search tree algorithm that exhibits a novel technique of bookkeeping called charging, which leads to an improved algorithm whose running time is in O∗(1.62k).