# Approximating the DCJ distance of balanced genomes in linear time

Rubert DP, Feijão P, Dias Vieira Braga M, Stoye J, Martinez FHV (2017) *Algorithms for Molecular Biology* 12: 3.

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*Original Article*|

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Author

Rubert, Diego P.
;
Feijão, Pedro
;
Dias Vieira Braga, Marília

^{UniBi}; Stoye, Jens^{UniBi}^{}; Martinez, Fábio Henrique ViduaniDepartment

Abstract / Notes

Background
Rearrangements are large-scale mutations in genomes, responsible for complex changes and structural variations. Most rearrangements that modify the organization of a genome can be represented by the double cut and join (DCJ) operation. Given two balanced genomes, i.e., two genomes that have exactly the same number of occurrences of each gene in each genome, we are interested in the problem of computing the rearrangement distance between them, i.e., finding the minimum number of DCJ operations that transform one genome into the other. This problem is known to be NP-hard.
Results
We propose a linear time approximation algorithm with approximation factor O(k) for the DCJ distance problem, where k is the maximum number of occurrences of any gene in the input genomes. Our algorithm works for linear and circular unichromosomal balanced genomes and uses as an intermediate step an O(k)-approximation for the minimum common string partition problem, which is closely related to the DCJ distance problem.
Conclusions
Experiments on simulated data sets show that our approximation algorithm is very competitive both in efficiency and in quality of the solutions.

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Financial disclosure

Article Processing Charge funded by the Deutsche Forschungsgemeinschaft and the Open Access Publication Fund of Bielefeld University.

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### Cite this

Rubert DP, Feijão P, Dias Vieira Braga M, Stoye J, Martinez FHV. Approximating the DCJ distance of balanced genomes in linear time.

*Algorithms for Molecular Biology*. 2017;12: 3.Rubert, D. P., Feijão, P., Dias Vieira Braga, M., Stoye, J., & Martinez, F. H. V. (2017). Approximating the DCJ distance of balanced genomes in linear time.

*Algorithms for Molecular Biology*,*12*, 3. doi:10.1186/s13015-017-0095-yRubert, D. P., Feijão, P., Dias Vieira Braga, M., Stoye, J., and Martinez, F. H. V. (2017). Approximating the DCJ distance of balanced genomes in linear time.

*Algorithms for Molecular Biology*12:3.Rubert, D.P., et al., 2017. Approximating the DCJ distance of balanced genomes in linear time.

*Algorithms for Molecular Biology*, 12: 3. D.P. Rubert, et al., “Approximating the DCJ distance of balanced genomes in linear time”,

*Algorithms for Molecular Biology*, vol. 12, 2017, : 3. Rubert, D.P., Feijão, P., Dias Vieira Braga, M., Stoye, J., Martinez, F.H.V.: Approximating the DCJ distance of balanced genomes in linear time. Algorithms for Molecular Biology. 12, : 3 (2017).

Rubert, Diego P., Feijão, Pedro, Dias Vieira Braga, Marília, Stoye, Jens, and Martinez, Fábio Henrique Viduani. “Approximating the DCJ distance of balanced genomes in linear time”.

*Algorithms for Molecular Biology*12 (2017): 3.**All files available under the following license(s):**

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