### Abstract

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

Pages (from-to) | 55-64 |

Number of pages | 10 |

Journal | IEICE technical report. Theoretical foundations of Computing |

Volume | 95 |

Issue number | 344 |

Publication status | Published - Oct 27 1995 |

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*IEICE technical report. Theoretical foundations of Computing*,

*95*(344), 55-64.

**Extracting Best Consensus Motifs from Positive and Negative Examples.** / Tateishi, Erika; Maruyama, Osamu; Miyano, Satoru.

Research output: Contribution to journal › Article

*IEICE technical report. Theoretical foundations of Computing*, vol. 95, no. 344, pp. 55-64.

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TY - JOUR

T1 - Extracting Best Consensus Motifs from Positive and Negative Examples

AU - Tateishi, Erika

AU - Maruyama, Osamu

AU - Miyano, Satoru

PY - 1995/10/27

Y1 - 1995/10/27

N2 - We define the best consensus motif (BCM) problem motivated by the problem of extracting motifs from nucleic acid and amino acid sequences. A type over an alphabetΣ is a familyΩ of subsets of Σ. A motif π of type Ω is a stringπ=π_1…π_n of motif components, each of which stands for an element in Ω. The BCM problem for Ω is, given a yes-no sample S={(α^<(1)>, β^<(1)>),...,(α^<(m)>, β^<(m)>)} of pairs of strings inΣ with α^<(i)>≠β^<(i)> for 1≤i≤m, to find a motif π of type Ω that maximizes the number of good pairs in S, where (α^<(i)>,β^<(i)>) is good forπ if π accepts α^<(i)> and rejects β^<(i)>. We prove that the BCM problem is NP-complete even for a very simple type Ω_1={z|φ≠z⊆Σ}, which is used, in practice, for describing protein motifs in the PROSITE database. We also show that the NP-completeness of the problem does not change for the type Ω_∞=Ω_1∪{Σ+}∪{Σ^<(i, j)>|1≤i≤j}, whereΣ^<(i, j)> is the set of strings over Σ of length between i and j. Furthermore, for the BCM problem forΩ_1, we provide a polynomial-time greedy algorithm based on the probabilistic method. Its performance analysis shows an explicit approximation ratio of the algorithm.

AB - We define the best consensus motif (BCM) problem motivated by the problem of extracting motifs from nucleic acid and amino acid sequences. A type over an alphabetΣ is a familyΩ of subsets of Σ. A motif π of type Ω is a stringπ=π_1…π_n of motif components, each of which stands for an element in Ω. The BCM problem for Ω is, given a yes-no sample S={(α^<(1)>, β^<(1)>),...,(α^<(m)>, β^<(m)>)} of pairs of strings inΣ with α^<(i)>≠β^<(i)> for 1≤i≤m, to find a motif π of type Ω that maximizes the number of good pairs in S, where (α^<(i)>,β^<(i)>) is good forπ if π accepts α^<(i)> and rejects β^<(i)>. We prove that the BCM problem is NP-complete even for a very simple type Ω_1={z|φ≠z⊆Σ}, which is used, in practice, for describing protein motifs in the PROSITE database. We also show that the NP-completeness of the problem does not change for the type Ω_∞=Ω_1∪{Σ+}∪{Σ^<(i, j)>|1≤i≤j}, whereΣ^<(i, j)> is the set of strings over Σ of length between i and j. Furthermore, for the BCM problem forΩ_1, we provide a polynomial-time greedy algorithm based on the probabilistic method. Its performance analysis shows an explicit approximation ratio of the algorithm.

UR - http://ci.nii.ac.jp/naid/110003191466

M3 - Article

VL - 95

SP - 55

EP - 64

JO - IEICE technical report. Theoretical foundations of Computing

JF - IEICE technical report. Theoretical foundations of Computing

IS - 344

ER -