On approximate string matching

Abstract

An algorithm is given for computing the edit distance as well as the corresponding sequence of editing steps (insertions, deletions, changes, transpositions of adjacent symbols) between two strings a₁a₂...a_m and b₁b₂...b_n. The algorithm needs time 0(s·min(m,n)) and space 0(s²) where s is the edit distance, that is, the minimum number of editing steps needed to transform a₁a₂...a_m to b₁b₂...b_n. For small s this is a considerable improvement over the best previously known algorithm that needs time and space 0(mn). If the editing sequence is not required, the space complexity of our algorithm reduces to 0(s). Given a threshold value t, the algorithm can also be modified to test in time 0(t·min(m,n)) and space 0(t) whether the edit distance of the two strings is at most t.