### Abstract

Consider the following problem: Find the shortest pattern that does not occur in a given text. To make the problem non-trivial, the pattern is required to consist only of characters that occur in the text. This problem can be solved easily in linear time using the suffix tree of the text. In this paper, we study an extension of this problem, namely the missing patterns problem: Find the shortest pair of patterns that do not occur close to each other in a given text, i.e., the distance between their occurrences is always greater than a given threshold a. We show that the missing patterns problem can be solved in O(min(αn log n, n^{2})) time, where n is the size of the text. For the special case where both pairs are required to have the same length, we give an algorithm with time complexity O(αn log log n). The problem is motivated by optimization of multiplexed nested-PCR.

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

Pages (from-to) | 463-474 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3240 |

Publication status | Published - Dec 1 2004 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*3240*, 463-474.

**Finding missing patterns.** / Inenaga, Shunsuke; Kivioja, Teemu; Mäkinen, Veli.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 3240, pp. 463-474.

}

TY - JOUR

T1 - Finding missing patterns

AU - Inenaga, Shunsuke

AU - Kivioja, Teemu

AU - Mäkinen, Veli

PY - 2004/12/1

Y1 - 2004/12/1

N2 - Consider the following problem: Find the shortest pattern that does not occur in a given text. To make the problem non-trivial, the pattern is required to consist only of characters that occur in the text. This problem can be solved easily in linear time using the suffix tree of the text. In this paper, we study an extension of this problem, namely the missing patterns problem: Find the shortest pair of patterns that do not occur close to each other in a given text, i.e., the distance between their occurrences is always greater than a given threshold a. We show that the missing patterns problem can be solved in O(min(αn log n, n2)) time, where n is the size of the text. For the special case where both pairs are required to have the same length, we give an algorithm with time complexity O(αn log log n). The problem is motivated by optimization of multiplexed nested-PCR.

AB - Consider the following problem: Find the shortest pattern that does not occur in a given text. To make the problem non-trivial, the pattern is required to consist only of characters that occur in the text. This problem can be solved easily in linear time using the suffix tree of the text. In this paper, we study an extension of this problem, namely the missing patterns problem: Find the shortest pair of patterns that do not occur close to each other in a given text, i.e., the distance between their occurrences is always greater than a given threshold a. We show that the missing patterns problem can be solved in O(min(αn log n, n2)) time, where n is the size of the text. For the special case where both pairs are required to have the same length, we give an algorithm with time complexity O(αn log log n). The problem is motivated by optimization of multiplexed nested-PCR.

UR - http://www.scopus.com/inward/record.url?scp=33646730028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646730028&partnerID=8YFLogxK

M3 - Article

VL - 3240

SP - 463

EP - 474

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -