Extracting best consensus motifs from positive and negative examples

  • Erika TateishiEmail author
  • Osamu Maruyama
  • Satoru Miyano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


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 alphabet Σ is a family Ω of subsets of Σ*. A motif π of type Ω is a string π=π1πn 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)(1),..., (α(m)(m))} of pairs of strings in Σ* 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 for π if π accepts α(i) and rejects β(i) We prove that the BCM problem is NP-complete even for a very simple type Ω1=2 −{θ}, 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 Ω1∪ {Σ+}∪{Σ[i,j]¦1≤i≤ j}, where Σ[i,j] is the set of strings over Σ of length between i and j Furthermore, for the BCM problem for Ω1 we provide a polynomial-time greedy algorithm based on the probabilistic method. Its performance analysis shows an explicit approximation ratio of the algorithm.


algorithms and computational complexity genome informatics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Department of Information SystemsKyushu University 39KasugaJapan
  2. 2.Research Institute of Fundamental Information ScienceKyushu University 33FukuokaJapan

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