### Abstract

In the motif finding problem one seeks a set of mutually similar subsequences within a collection of biological sequences. This is an important and widely-studied problem, as such shared motifs in DNA often correspond to regulatory elements. We study a combinatorial framework where the goal is to find subsequences of a given length such that the sum of their pairwise distances is minimized. We describe a novel integer linear program for the problem, which uses the fact that; distances between subsequences come from a limited set of possibilities. We show how to tighten its linear programming relaxation by adding an exponential set of constraints and give an efficient separation algorithm that can find violated constraints, thereby showing that the tightened linear program can still be solved in polynomial time. We apply our approach to find optimal solutions for the motif finding problem and show that it is effective in practice in uncovering known transcription factor binding sites.

Original language | English (US) |
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Title of host publication | Combinatorial Pattern Matching - 17th Annual Symposium, CPM 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 233-245 |

Number of pages | 13 |

ISBN (Print) | 3540354557, 9783540354550 |

DOIs | |

State | Published - Jan 1 2006 |

Event | 17th Annual Symposium on Combinatorial Pattern Matching, CPM 2006 - Barcelona, Spain Duration: Jul 5 2006 → Jul 7 2006 |

### 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 | 4009 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th Annual Symposium on Combinatorial Pattern Matching, CPM 2006 |
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Country | Spain |

City | Barcelona |

Period | 7/5/06 → 7/7/06 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 17th Annual Symposium, CPM 2006, Proceedings*(pp. 233-245). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4009 LNCS). Springer Verlag. https://doi.org/10.1007/11780441_22