### Abstract

We consider the problem of identifying motifs that abstracts the task of finding short conserved sites in genomic DNA. The planted (l, d)-motif problem, PMP, is the mathematical abstraction of this problem, which consists of finding a substring of length l that occurs in each s _{i} in a set of input sequences S = {s _{1}, s _{2}, . . ., s _{t}} with at most d substitutions. Our propose algorithm combines the voting algorithm and pattern matching algorithm to find exact motifs. The combined algorithm is achieved by running the voting algorithm on t′ sequences, t′ < t. After that we use the pattern matching on the output of the voting algorithm and the reminder sequences, t - t′. Two values of t′ are calculated. The first value of t′ makes the running time of our proposed algorithm less than the running time of voting algorithm. The second value of t′ makes the running time of our proposed algorithm is minimal. We show that our proposed algorithm is faster than the voting algorithm by testing both algorithms on simulated data from (9, d ≤ 2) to (19, d ≤ 7). Finally, we test the performance of the combined algorithm on realistic biological data.

Original language | English |
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Pages (from-to) | 387-399 |

Number of pages | 13 |

Journal | Mathematics in Computer Science |

Volume | 7 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Dec 2013 |

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### Keywords

- DNA motifs
- Exact algorithms
- Pattern matching
- Planted (l, d)-motif
- Transcription factor binding sites

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics in Computer Science*,

*7*(4), 387-399. https://doi.org/10.1007/s11786-013-0165-6