Reference Work Entry

Encyclopedia of Algorithms

pp 265-267

# Edit Distance Under Block Operations

2000; Cormode, Paterson, Sahinalp, Vishkin 2000; Muthukrishnan, Sahinalp
• S. Cenk SahinalpAffiliated withLab for Computational Biology, Simon Fraser University

## 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 ...

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