Algorithms for Normalized Multiple Sequence Alignments

Authors Eloi Araujo , Luiz C. Rozante , Diego P. Rubert , Fábio V. Martinez

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Author Details

Eloi Araujo
  • Faculdade de Computação, Universidade Federal de Mato Grosso do Sul, Campo Grande, MS, Brasil
Luiz C. Rozante
  • Centro de Matemática Computação e Cognição, Universidade Federal do ABC, Santo André, MS, Brasil
Diego P. Rubert
  • Faculdade de Computação, Universidade Federal de Mato Grosso do Sul, Campo Grande, MS, Brasil
Fábio V. Martinez
  • Faculdade de Computação, Universidade Federal de Mato Grosso do Sul, Campo Grande, MS, Brasil


We thank the three anonymous reviewers for their valuable comments and suggestions on our manuscript.

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Eloi Araujo, Luiz C. Rozante, Diego P. Rubert, and Fábio V. Martinez. Algorithms for Normalized Multiple Sequence Alignments. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Sequence alignment supports numerous tasks in bioinformatics, natural language processing, pattern recognition, social sciences, and other fields. While the alignment of two sequences may be performed swiftly in many applications, the simultaneous alignment of multiple sequences proved to be naturally more intricate. Although most multiple sequence alignment (MSA) formulations are NP-hard, several approaches have been developed, as they can outperform pairwise alignment methods or are necessary for some applications. Taking into account not only similarities but also the lengths of the compared sequences (i.e. normalization) can provide better alignment results than both unnormalized or post-normalized approaches. While some normalized methods have been developed for pairwise sequence alignment, none have been proposed for MSA. This work is a first effort towards the development of normalized methods for MSA. We discuss multiple aspects of normalized multiple sequence alignment (NMSA). We define three new criteria for computing normalized scores when aligning multiple sequences, showing the NP-hardness and exact algorithms for solving the NMSA using those criteria. In addition, we provide approximation algorithms for MSA and NMSA for some classes of scoring matrices.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Approximation algorithms analysis
  • Applied computing → Molecular sequence analysis
  • Multiple sequence alignment
  • Normalized multiple sequence alignment
  • Algorithms and complexity


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