## Abstract

An exact run in a string T is a non-empty substring of T that is a repetition of a smaller substring possibly followed by a prefix of it. Finding maximal exact runs in strings is an important problem and therefore a well-studied one in the area of stringology. For a given string T of length n, finding all maximal exact runs in the string can be done in O(nlogn) time on general ordered alphabets or O(n) time on integer alphabets. In this paper, we investigate the maximal approximate runs problem: for a given string T and a number k, find non-empty substrings T^{′} of T such that changing at most k letters in T^{′} transforms them into a maximal exact run. We present an O(nk^{2}log^{2}k+occ) algorithm to solve this problem, where occ is the number of substrings found.

Original language | English |
---|---|

Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Theoretical Computer Science |

Volume | 700 |

DOIs | |

State | Published - 14 Nov 2017 |

### Bibliographical note

Funding Information:The first and the third authors are partially supported by the Israel Science Foundation grant 571/14 , DFG and Grant No. 2014028 from the United States–Israel Binational Science Foundation ( BSF ).

Publisher Copyright:

© 2017 Elsevier B.V.

## Keywords

- Algorithms on strings
- Pattern matching
- Repetitions
- Runs
- Tandem repeats

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)