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A Polynomial Algebra Method for Computing Exemplar Breakpoint Distance

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Bioinformatics Research and Applications (ISBRA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 6674))

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Abstract

The exemplar breakpoint distance problem is NP-hard. Assume two genomes have at most n genes from m gene families. We develop an O(2m n O(1)) time algorithm to compute the exemplar breakpoint distance if one of them has no repetition. We develop an O(2m m!n O(1)) time algorithm to compute the exemplar breakpoint distance between two arbitrary genomes. If one of the given genomes has at most d repetitions for each gene, the computation time of the second algorithm is only O((2d)m n O(1)). Our algorithms are based on a polynomial algebra approach which uses a multilinear monomial to represent a solution for the exemplar breakpoint distance problem.

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References

  1. Angibaud, S., Fertin, G., Rusu, I., Thévenin, A., Vialette, S.: A pseudo-Boolean programming approach for computing the breakpoint distance between two genomes with duplicate genes. In: Tesler, G., Durand, D. (eds.) RECMOB-CG 2007. LNCS (LNBI), vol. 4751, pp. 16–29. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Angibaud, S., Fertin, G., Rusu, I., Thévenin, A., Vialette, S.: On the ap-proximability of comparing genomes with duplicates. J. Graph Algor. Appli. (accepted)

    Google Scholar 

  3. Blin, G., Chauve, C., Fertin, G., Rizzi, R., Vialette, S.: Comparing genomes with duplications: A computational complexity point of view. IEEE/ACM IEEE Trans. Comput. Biol. Bioinform. 4, 523–534 (2007)

    Article  Google Scholar 

  4. Blin, G., Fertin, G., Sikora, F., Vialette, S.: The exemplar breakpoint distance for non-trivial genomes cannot be approximated. In: Das, S., Uehara, R. (eds.) WALCOM 2009. LNCS, vol. 5431, pp. 357–368. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Bryant, D.: The complexity of calculating exemplar distance. In: Sankoff, D., Nadeau, J. (eds.) Comparative Genomics: Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment, and the Evolution of Gene Families, pp. 207–212 (2000)

    Google Scholar 

  6. Chen, Z., Fu, B., Zhu, B.: Approximations for the exemplar breakpoint distance problem. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 291–302. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Chen, Z., Fu, B.: Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials, Electronic Colloquium on Computational Complexity (ECCC-TR10-124)

    Google Scholar 

  8. Chen, Z., Fu, B.: The Complexity of Testing Monomials in Multivariate Polynomials, Electronic Colloquium on Computational Complexity (ECCC-TR10-114)

    Google Scholar 

  9. Eichler, E.E., Sankoff, D.: Structural dynamics of eukaryotic chromosome evolution. Science 301, 793–797 (2003)

    Article  Google Scholar 

  10. Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. J. Assoc. Comput. Mach. 46, 1–27 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jiang, M.: The zero exemplar distance problem. In: Tannier, E. (ed.) RECOMB-CG 2010. LNCS, vol. 6398, pp. 74–82. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Koutis, I.: Faster algebraic algorithms for path and packing problems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 575–586. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Nadeau, J.H., Taylor, B.A.: Lengths of chromosomal segments conserved since divergence of man and mouse. Proc. Natl. Acad. Sci. USA 81, 814–818 (1984)

    Article  Google Scholar 

  14. Nguyen, C.T.: Algorithms for calculating exemplar distances. Honors Thesis, Department of Computer Science, National University of Singapore (2005)

    Google Scholar 

  15. Nguyen, C.T., Tay, Y.C., Zhang, L.X.: Divide-and-conquer approach for the examplar breakpoint problem. Bioinformatics 21, 2171–2176 (2005)

    Article  Google Scholar 

  16. Sankoff, D.: Mechanisms of genome evolution: models and inference. Bull. Int. Stat. Institut. 47, 461–475 (1989)

    MathSciNet  Google Scholar 

  17. Sankoff, D.: Genome rearrangement with gene families. Bioinformatics 15, 909–917 (2009)

    Article  Google Scholar 

  18. Williams, R.: Finding paths of length k in o *(2k) time. Information Processing Letters 109, 315–318 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Watterson, G.A., Ewens, W.J., Hall, T.E., Morgan, A.: The chromosome inversion problem. J. Theor. Biol. 99, 1–7 (1982)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, Edinburg, TX, 78539, USA

    Bin Fu

  2. Department of Mathematics, National University of Singapore, 119076, Singapore

    Louxin Zhang

Authors
  1. Bin Fu
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  2. Louxin Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, 77843-3112, College Station, TX, USA

    Jianer Chen

  2. School of Information Science and Engineering, Central South University, 410083, Changsha, China

    Jianxin Wang

  3. Department of Computer Science, Georgia State University, 30303, Atlanta, GA, USA

    Alexander Zelikovsky

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Fu, B., Zhang, L. (2011). A Polynomial Algebra Method for Computing Exemplar Breakpoint Distance. In: Chen, J., Wang, J., Zelikovsky, A. (eds) Bioinformatics Research and Applications. ISBRA 2011. Lecture Notes in Computer Science(), vol 6674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21260-4_29

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  • DOI: https://doi.org/10.1007/978-3-642-21260-4_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21259-8

  • Online ISBN: 978-3-642-21260-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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