Edit Distance Under Block Operations

Keywords and Synonyms

Block edit distance        

Problem Definition

Given two strings $S=s_1s_2\,\ldots\,s_n$ and $R=r_1r_2\,\ldots\,r_m$ (wlog let $n \geq m$) over an alphabet $\sigma=\{\sigma_1,\,\sigma_2,\,\ldots\,\sigma_{\ell}\}$, the standard edit distance between S and R, denoted ED(S, R) is the minimum number of single character edits, specifically insertions, deletions and replacements, to transform S into R (equivalently R into S).

If the input strings S and R are permutations of the alphabet σ (so that $|S| = |R| = |\sigma|$) then an analogous permutation edit distance between S and R, denoted PED(S, R) can be defined as the minimum number of single character moves, to transform S into R (or vice versa).

A generalization of the standard edit distance is edit distance with moves, which, for input strings S and R is denoted EDM(S, R), and is defined as the minimum number of character edits and substring (block) movesto transform one of the strings into the other....