K-mismatch with don't cares

  • Authors:
  • Raphaël Clifford;Klim Efremenko;Ely Porat;Amir Rothschild

  • Affiliations:
  • University of Bristol, Dept. of Computer Science, Bristol, UK;Bar-Ilan University, Dept. of Computer Science, Ramat-Gan, Israel and Weizman institute, Dept. of Computer Science and Applied Mathematics, Rehovot, Israel;Bar-Ilan University, Dept. of Computer Science, Ramat-Gan, Israel;Tel-Aviv University, Dept. of computer science, Tel-Aviv, Israel and Bar-Ilan University, Dept. of Computer Science, Ramat-Gan, Israel

  • Venue:
  • ESA'07 Proceedings of the 15th annual European conference on Algorithms
  • Year:
  • 2007

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Abstract

We give the first non-trivial algorithms 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 O(n(k + log n log log n) logm) time randomised solution which finds the correct answer with high probability. We then present a new deterministic O(nk2 log3 m) time solution that uses tools developed for group testing and finally an approach based on k-selectors that runs in O(nk polylog m) time but requires O(poly m) time preprocessing. In each case, the location of the mismatches at each alignment is also given at no extra cost.