Efficient string matching with k mismatches
Theoretical Computer Science
SIAM Journal on Computing
Introduction to algorithms
Fast algorithms for approximately counting mismatches
Information Processing Letters
Faster Algorithms for String Matching Problems: Matching the Convolution Bound
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
Approximating general metric distances between a pattern and a text
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
From coding theory to efficient pattern matching
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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We reconsider 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 to 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 up to c mismatches 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.