TY - GEN

T1 - The string edit distance matching problem with moves

AU - Cormode, Graham

AU - Muthukrishnan, S.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:26444481117

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 667

EP - 676

BT - Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002

PB - Association for Computing Machinery

T2 - 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002

Y2 - 6 January 2002 through 8 January 2002

ER -