The string edit distance matching problem with moves

Graham Cormode, S. Muthukrishnan

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119 Scopus citations


The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes, and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smallest edit distance between p and substrings of t.We relax the problem so that: (a) we allow an additional operation, namely, substring moves; and (b) we allow approximation of this string edit distance. Our result is a near-linear time deterministic algorithm to produce a factor of O(log n log* n) approximation to the string edit distance with moves. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into L1 vector space using a simplified parsing technique, which we call edit-sensitive parsing (ESP).

Original languageEnglish (US)
Article number1219947
JournalACM Transactions on Algorithms
Issue number1
StatePublished - Feb 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


  • Approximate pattern matching
  • Data streams
  • Edit distance
  • Embedding
  • Similarity search
  • String matching


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