Reference Work Entry

Encyclopedia of Algorithms

pp 1-99

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 substrin ...

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