Abstract
A pairwise sequence alignment is a structure describing a set of editing operations that transforms one given sequence into another given sequence. We consider insertion, deletion, and substitution of symbols as editing operations. Given a fixed function assigning a weight for each editing operation, the weight of an alignment A is the sum of the editing operations described by A. Needleman and Wunsch proposed an algorithm for finding a pairwise sequence alignment of minimum editing weight. However, a sequence of editing operations that transforms one sequence into another cannot always be represented by an alignment. We present a more general structure that allows us to represent any sequence of editing operations that transforms one sequence into another. We also show how to find a minimum weight sequence of editing operations to transform one sequence into another in quadratic time, even if they cannot be represented by an alignment. Additionally, we show that there exists no algorithm to solve the problem with subquadratic running time, unless SETH is false. This approach may be used to explain non-trivial evolutionary models in Molecular Biology, where the triangle inequality does not hold for the distance between the sequences, such as those involving adaptive and back mutations.
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Acknowledgments
The authors thank José Augusto Ramos Soares, Said Sadique Adi, and Vagner Pedrotti for valuable discussions on this topic.
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Araujo, E., Martinez, F.V., Rozante, L.C., Almeida, N.F. (2023). Extended Pairwise Sequence Alignment. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023. ICCSA 2023. Lecture Notes in Computer Science, vol 13956 . Springer, Cham. https://doi.org/10.1007/978-3-031-36805-9_15
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DOI: https://doi.org/10.1007/978-3-031-36805-9_15
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