Mismatch Sampling

Authors:
Raphaël Clifford;Klim Efremenko;Benny Porat;Ely Porat;Amir Rothschild
Affiliations:
Dept. of Computer Science, University of Bristol, Bristol, UK BS8 1UB;Dept. of Computer Science, 52900 Ramat-Gan, Israel and Weizman institute, Dept. of Computer Science and Applied Mathematics, Bar-Ilan University, Rehovot, Israel;Dept. of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900;Dept. of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900;Dept. of computer science, Tel-Aviv, Israel and Bar-Ilan University, Dept. of Computer Science, Tel-Aviv University, Ramat-Gan, Israel 52900
Venue:
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Year:
2008

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Abstract

We consider the well known problem of pattern matching under the Hamming distance. Previous approaches have shown how to count the number of mismatches efficiently, especially when a bound is known for the maximum Hamming distance. Our interest is different in that we wish collect a random sample of mismatches of fixed size at each position in the text. Given a pattern p of length m and a text t of length n , we show how to sample with high probability c mismatches where possible from every alignment of p and t in O ((c + logn )(n + m logm )logm ) time. Further, we guarantee that the mismatches are sampled uniformly and can therefore be seen as representative of the types of mismatches that occur.