Abstract
In the literature on genome rearrangement, several approaches use different structures to improve the results of genome rearrangement problems. In particular, graphs are structures widely used for the purpose of representing information retrieved from genomes. The breakpoint graph is a useful tool in this area because it allows representing in the same structure the gene orders of two genomes being compared. The maximum cycle decomposition of this graph brings immediate gain for deriving lower bounds for various genome rearrangement problems. This paper introduces a generalization of the Maximum Alternating Cycle Decomposition problem (MAX-ACD), called the Maximum Alternating Balanced Cycle Decomposition problem (MAX-ABCD). The MAX-ACD problem is closely related to the Sorting by Reversals problem and is a relevant topic of investigation in mathematics. The MAX-ABCD problem has applications in the Sorting by Intergenic Reversals problem, which is a problem that takes into account both the gene order and the information present in the intergenic regions. We present an algorithm with a constant approximation factor for the MAX-ABCD problem. Furthermore, we design an improved algorithm for the Sorting by Intergenic Operations of Reversal and Indel problem that guarantees an approximation factor of \(\frac{3}{2}\) considering a scenario where the orientation of the genes is known. For the scenario where the orientation of the genes is unknown and based on an algorithm for the MAX-ABCD problem, we develop approximation algorithms for the Sorting by Intergenic Reversals and Sorting by Intergenic Operations of Reversal and Indel problems with an approximation factor of 2k, where \(k=\frac{31}{21}+\epsilon \).
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Acknowledgments
This work was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and the São Paulo Research Foundation, FAPESP (grants 2013/08293-7 and 2021/13824-8).
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Brito, K.L., Alexandrino, A.O., Siqueira, G., Oliveira, A.R., Dias, U., Dias, Z. (2024). Maximum Alternating Balanced Cycle Decomposition and Applications in Sorting by Intergenic Operations Problems. In: Scornavacca, C., Hernández-Rosales, M. (eds) Comparative Genomics. RECOMB-CG 2024. Lecture Notes in Computer Science(), vol 14616. Springer, Cham. https://doi.org/10.1007/978-3-031-58072-7_8
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