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Link to original content: https://doi.org/10.1007/978-3-642-13562-0_16
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Revisiting the Minimum Breakpoint Linearization Problem

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6108))

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Abstract

The gene order on a chromosome is a necessary data for most comparative genomics studies, but in many cases only partial orders can be obtained by current genetic mapping techniques. The Minimum Breakpoint Linearization Problem aims at constructing a total order from this partial knowledge, such that the breakpoint distance to a reference genome is minimized. In this paper, we first expose a flaw in two algorithms formerly known for this problem [4,2]. We then present a new modeling for this problem, and use it to design three approximation algorithms, with ratios resp. O(log(k)loglog(k)), O(log2(|X|)) and m 2 + 4m − 4, where k is the optimal breakpoint distance we look for, |X| is upper bounded by the number of pair of genes for which the partial order is in contradiction with the reference genome, and m is the number of genetic maps used to create the input partial order.

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References

  1. Blin, G., Blais, E., Hermelin, D., Guillon, P., Blanchette, M., El-Mabrouk, N.: Gene maps linearization using genomic rearrangement distances. Journal of Computational Biology 14(4), 394–407 (2007)

    Article  MathSciNet  Google Scholar 

  2. Chen, X., Cui, Y.: An approximation algorithm for the minimum breakpoint linearization problem. IEEE/ACM Trans. Comput. Biology Bioinform. 6(3), 401–409 (2009)

    Article  MathSciNet  Google Scholar 

  3. Even, G., Naor, J., Schieber, B., Sudan, M.: Approximating minimum feedback sets and multi-cuts in directed graphs. In: Balas, E., Clausen, J. (eds.) IPCO 1995. LNCS, vol. 920, pp. 14–28. Springer, Heidelberg (1995)

    Google Scholar 

  4. Fu, Z., Jiang, T.: Computing the breakpoint distance between partially ordered genomes. J. Bioinformatics and Computational Biology 5(5), 1087–1101 (2007)

    Article  Google Scholar 

  5. Yap, I.V., Schneider, D., Kleinberg, J., Matthews, D., Cartinhourb, S., McCouch, S.R.: A graph-theoretic approach to comparing and integrating genetic, physical and sequence-based maps. Genetics 165(4), 2235–2247 (2003)

    Google Scholar 

  6. Zheng, C., Lenert, A., Sankoff, D.: Reversal distance for partially ordered genomes. In: ISMB (Supplement of Bioinformatics), pp. 502–508 (2005)

    Google Scholar 

  7. Zheng, C., Sankoff, D.: Genome rearrangements with partially ordered chromosomes. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 52–62. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Bulteau, L., Fertin, G., Rusu, I. (2010). Revisiting the Minimum Breakpoint Linearization Problem. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-13562-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13561-3

  • Online ISBN: 978-3-642-13562-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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