Matching Numeric Strings under Noise

Abstra t. Numeri string is a sequen e of symbols from an alphabet U, where U is some numeri al universe losed under addition and subtra tion. Given two numeri strings A = a 1 a m and B = b 1 b n and a distan e fun tion d(A;B) that gives the s ore of the best (partial) mat hing of A and B, the transposition invariant distan e is min t2U fd(A + t; B)g, where A + t = (a 1 + t)(a 2 + t) : : : (a m + t). The orresponding mat hing problem is to nd o urren es j ofA inB where d(A+t; B j 0 :::j ) is smaller than some given threshold and B j 0 :::j is a substring of B. In this paper, we give e ient algorithms for mat hing numeri strings with and without transposition invarian e under noise; we onsider distan e fun tions d(A;B) su h that symbols a 2 A and b 2 B an be mat hed if jb aj Æ, or the largest di eren es jb aj an be dis arded.