### Abstract

We consider the problem of finding pairs of short patterns such that, in a given input sequence of length n, the distance between each pair's patterns is at least α. The problem was introduced in [1] and is motivated by the optimization of multiplexed nested PCR. We study algorithms for the following two cases; the special case when the two patterns in the pair are required to have the same length, and the more general case when the patterns can have different lengths. For the first case we present an O(αn log log n) time and O(n) space algorithm, and for the general case we give an O(αn log n) time and O(n) space algorithm. The algorithms work for any alphabet size and use asymptotically less space than the algorithms presented in [1]. For alphabets of constant size we also give an O(n√n log^{2} n) time algorithm for the general case. We demonstrate that the algorithms perform well in practice and present our findings for the human genome. In addition, we study an extended version of the problem where patterns in the pair occur at certain positions at a distance at most α, but do not occur α-close anywhere else, in the input sequence.

Original language | English |
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Title of host publication | String Processing and Information Retrieval - 12th International Conference, SPIRE 2005, Proceedings |

Pages | 167-178 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Dec 1 2005 |

Event | 12th International Conference on String Processing and Information Retrieval, SPIRE 2005 - Buenos Aires, Argentina Duration: Nov 2 2005 → Nov 4 2005 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3772 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Conference on String Processing and Information Retrieval, SPIRE 2005 |
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Country | Argentina |

City | Buenos Aires |

Period | 11/2/05 → 11/4/05 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*String Processing and Information Retrieval - 12th International Conference, SPIRE 2005, Proceedings*(pp. 167-178). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3772 LNCS). https://doi.org/10.1007/11575832_19