## Abstract

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 Θ (n(k + log m log k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deterministic Θ ^{`}nk^{2} log^{2} m´ time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we develop an approach based on k-selectors that runs in Θ (nk polylogm) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.

Original language | English |
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Journal | Dagstuhl Seminar Proceedings |

Volume | 9281 |

State | Published - 2009 |

Event | Search Methodologies 2009 - Wadern, Germany Duration: 5 Jul 2009 → 10 Jul 2009 |

### Bibliographical note

Publisher Copyright:© 2009 Dagstuhl Seminar Proceedings. All rights reserved.

### Funding

∗Research supported in part by the Binational Science Foundation (BSF)

Funders | Funder number |
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British Skin Foundation | |

United States-Israel Binational Science Foundation |