Klim Efremenko

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∈+∈mlogm)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.