### Abstract

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 L_{1} vector space using a simplified parsing technique, which we call edit-sensitive parsing (ESP).

Original language | English (US) |
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Article number | 1219947 |

Journal | ACM Transactions on Algorithms |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2007 |

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

### Keywords

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

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## Cite this

*ACM Transactions on Algorithms*,

*3*(1), [1219947]. https://doi.org/10.1145/1186810.1186812