### 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. A well known dynamic programming algorithm takes time O(nm) to solve this problem, and it is an important open problem in Combinatorial Pattern Matching to significantly improve this bound. We relax the problem so that (a) we allow an additional operation, namely, substring moves, and (b) we approximate the string edit distance upto a factor of O(log n log∗ n).1 Our result is a near linear time deterministic algorithm for this version of the problem. 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 Li vector space using a simplified parsing technique we call Edit Sensitive Parsing (ESP). This embedding is approximately distance preserving, and we show many applications of this embedding to string proximity problems including nearest neighbors, oudiers, and streaming computations with strings.

Original language | English (US) |
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Title of host publication | Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 |

Publisher | Association for Computing Machinery |

Pages | 667-676 |

Number of pages | 10 |

ISBN (Electronic) | 089871513X |

State | Published - 2002 |

Event | 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States Duration: Jan 6 2002 → Jan 8 2002 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 06-08-January-2002 |

### Other

Other | 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 |
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Country | United States |

City | San Francisco |

Period | 1/6/02 → 1/8/02 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002*(pp. 667-676). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 06-08-January-2002). Association for Computing Machinery.