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### The string edit distance matching problem with moves

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UNSPECIFIED
(2002)
*The string edit distance matching problem with moves.*
In: 13th Annual ACM/SIAM Symposium on Discrete Algorithms, SAN FRANCISCO, CA, JAN 06-08, 2002. Published in: PROCEEDINGS OF THE THIRTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS
pp. 667-676.

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## 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 L-1 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, outliers, and streaming computations with strings.

Item Type: | Conference Item (UNSPECIFIED) |
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QA Mathematics |

Series Name: | SIAM PROCEEDINGS SERIES |

Journal or Publication Title: | PROCEEDINGS OF THE THIRTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS |

Publisher: | SIAM |

ISBN: | 0-89871-513-X |

Date: | 2002 |

Number of Pages: | 10 |

Page Range: | pp. 667-676 |

Publication Status: | Published |

Title of Event: | 13th Annual ACM/SIAM Symposium on Discrete Algorithms |

Location of Event: | SAN FRANCISCO, CA |

Date(s) of Event: | JAN 06-08, 2002 |

URI: | http://wrap.warwick.ac.uk/id/eprint/10250 |

Data sourced from Thomson Reuters' Web of Knowledge

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