Abstract
Rearrangements are mutations that affect large portions of a genome. When comparing two genomes, one wants to find a sequence of rearrangements that transforms one into another. When we use permutations to represent the genomes, this reduces to the problem of sorting a permutation using some sequence of rearrangements. The traditional approach is to find a sequence of minimum length. However, some studies show that some rearrangements are more likely to disturb an individual, and so a weighted approach is closer to the real evolutionary process. Most weighted approaches consider that the cost of a rearrangement can be related to its type or to the number of elements affected by it. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for 5 versions of the fragmentation-weighted problem involving reversals and transpositions events.
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Acknowledgments
This work was partially supported by the São Paulo Research Foundation, FAPESP (grants 2013/08293-7, 2015/11937-9, 2016/14132-4, 2017/12646-3, and 2017/16871-1), the National Counsel of Technological and Scientific Development, CNPq (grants 400487/2016-0, 425340/2016-3, and 131182/2017-0), and the program between the Brazilian Federal Agency for the Support and Evaluation of Graduate Education, CAPES, and the French Committee for the Evaluation of Academic and Scientific Cooperation with Brazil, COFECUB (grant 831/15).
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Alexandrino, A.O., Lintzmayer, C.N., Dias, Z. (2018). Approximation Algorithms for Sorting Permutations by Fragmentation-Weighted Operations. In: Jansson, J., Martín-Vide, C., Vega-Rodríguez, M. (eds) Algorithms for Computational Biology. AlCoB 2018. Lecture Notes in Computer Science(), vol 10849. Springer, Cham. https://doi.org/10.1007/978-3-319-91938-6_5
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DOI: https://doi.org/10.1007/978-3-319-91938-6_5
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