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New formulations of the multiple sequence alignment problem

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Abstract

A well known formulation of the multiple sequence alignment (MSA) problem is the maximum weight trace (MWT), a 0–1 linear programming problem. In this paper, we propose a new integer quadratic programming formulation of the MSA. The number of constraints and variables in the problem are only of the order of kL 2, where, k is the number of sequences and L is the total length of the sequences, that is, \({L= \sum_{i=1}^{k}l_{i}}\) , where l i is the length of sequence i. Based on this formulation we introduce an equivalent linear constrained 0–1 quadratic programming problem. We also propose a 0–1 linear programming formulation of the MWT problem, with polynomially many constraints. Our formulation provides the first direct compact formulation that ensures that the critical circuit inequalities (which are exponentially many) are all met.

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Authors and Affiliations

  1. Department of ISOM, University of Auckland, Auckland, New Zealand

    Thiru S. Arthanari

  2. Laboratory of Theoretical and Applied Computer Science, UFR MIM, Paul Verlaine University-Metz, Ile du Saulcy, 57045, Metz, France

    Hoai An Le Thi

Authors
  1. Thiru S. Arthanari
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  2. Hoai An Le Thi
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Correspondence to Hoai An Le Thi.

Additional information

Part of this work was completed during the visit of T. S. Arthanari at the Laboratory of Theoretical and Applied Computer Science, UFR MIM, Paul Verlaine University-Metz, France.

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Arthanari, T.S., Le Thi, H.A. New formulations of the multiple sequence alignment problem. Optim Lett 5, 27–40 (2011). https://doi.org/10.1007/s11590-010-0188-8

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  • DOI: https://doi.org/10.1007/s11590-010-0188-8

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