
We present solutions for the k-mismatch pattern matching problem with don't cares. Given a text t of length n and a pattern p of length m with don't care symbols and a bound k, our algorithms find all the places that the pattern matches the text with at most k mismatches. We first give an \Theta(n(k + logmlog k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deter- ministic \Theta(nk^2 log^m)time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we de- velop an approach based on k-selectors that runs in \Theta(nk polylogm) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.
String algorithms, Computer Networks and Communications, Applied Mathematics, Pattern recognition, speech recognition, Randomized algorithms, string algorithms, Streaming, 004, Theoretical Computer Science, Randomised algorithms, Pattern Matching, pattern matching, randomised algorithms, Computational Theory and Mathematics, Group Testing, Pattern matching, Group testing, group testing, Prime Numbers, ddc: ddc:004
String algorithms, Computer Networks and Communications, Applied Mathematics, Pattern recognition, speech recognition, Randomized algorithms, string algorithms, Streaming, 004, Theoretical Computer Science, Randomised algorithms, Pattern Matching, pattern matching, randomised algorithms, Computational Theory and Mathematics, Group Testing, Pattern matching, Group testing, group testing, Prime Numbers, ddc: ddc:004
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