## Abstract

Finding an approximate period in a given string S of length n is defined as follows. Let S′ be a periodic string closest to S under some distance metric, find the smallest period of S′. This period is called an approximate period of S under the given metric. Let the distance between the input string S and a closest periodic string under the Hamming distance S′ be k. We develop algorithms that construct an approximate period of S under the Hamming distance in time O(nk loglogn) and under the swap distance in time O(n^{2}). Finally, we show an O(n logn) algorithm for finite alphabets, and an O(n log^{3}n) algorithm for infinite alphabets, that approximate the minimum number of mismatches between the input string and a closest periodic string under the Hamming distance.

Original language | English |
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Pages (from-to) | 215-226 |

Number of pages | 12 |

Journal | Information and Computation |

Volume | 241 |

DOIs | |

State | Published - 1 Apr 2015 |

### Bibliographical note

Publisher Copyright:© 2015 Elsevier Inc. All rights reserved.

## Keywords

- Approximate matching
- Approximate periodicity
- Hamming distance
- Periodicity
- String algorithms
- Swap distance