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A Practical Exact Algorithm for the Individual Haplotyping Problem MEC/GI

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Haplotypes play an important role in genetic association studies of complex diseases. Recently, computational techniques helping to determine human haplotypes were studied extensively. Given the genotype and the aligned single nucleotide polymorphism (SNP) fragments of an individual, Minimum Error Correction with Genotype Information (MEC/GI) is an important computational model to infer a pair of haplotypes compatible with the genotype by correcting minimum number of SNPs in the given SNP fragments. The MEC/GI problem has been proven NP-hard, for which there is no practical exact algorithm. Despite the rapid advances in molecular biological techniques, modern high-throughput sequencers cannot sequence directly a DNA fragment that contains more than 1200 nucleotide bases. With low SNP density, current available data reveal that the number k of SNP sites that a DNA fragment covers is usually smaller than 10. Based on the above fact, we develop a new dynamic programming algorithm with running time O(mk2k+mlog m+mk), where m is the number of fragments. Since k is small in real biological applications, the algorithm is practical and efficient.

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  1. Wang, D.G., Fan, J.B., Siao, C.J., : Large-scale identification, mapping, and genotyping of single-nucleotide polymorphisms in the human genome. Science 280(5366), 1077–1082 (1998)

    Article  Google Scholar 

  2. Stephens, J.C., Schneider, J.A., Tanguay, D.A., : Haplotype variation and linkage disequilibrium in 313 human genes. Science 293(5529), 489–493 (2001)

    Article  Google Scholar 

  3. Zhang, X.S., Wang, R.S., Wu, L.Y., Chen, L.: Models and algorithms for haplotyping problem. Curr. Bioinform. 1(1), 105–114 (2006)

    Article  Google Scholar 

  4. Lancia, G., Bafna, V., Istrail, S., Lippert, R., Schwartz, R.: SNPs problems, complexity and algorithms. In: Meyer, F. (ed.) Proc. Ann. European Symp. on Algorithms (ESA). Lecture Notes in Computer Science, vol. 2191, pp. 182–193. Springer, Berlin (2001)

    Google Scholar 

  5. Gusfield, D.: An overview of combinatorial methods for haplotype inference. In: Istrail, S., Waterman, M.S., Clark, A.G. (eds.) The 1st RECOMB Satellite Workshop on Computational Methods for SNPs and Haplotype Inference. Lecture Notes in Computer Science, vol. 2983, pp. 9–25. Springer, Berlin (2004)

    Google Scholar 

  6. Xie, M., Chen, J., Wang, J.: Research on parameterized algorithms of the individual haplotyping problem. J. Bioinform. Comput. Biol. 5(3), 795–816 (2007)

    Article  MathSciNet  Google Scholar 

  7. Xie, M., Wang, J.: An improved (and practical) parameterized algorithm for the individual haplotyping problem MFR with mate-pairs. Algorithmica 52(2), 250–266 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lippert, R., Schwartz, R., Lancia, G., Istrail, S.: Algorithmic strategies for the single nucleotide polymorphism haplotype assembly problem. Brief. Bioinform. 3(1), 1–9 (2002)

    Article  Google Scholar 

  9. Wang, R.S., Wu, L.Y., Li, Z.P., Zhang, X.S.: Haplotype reconstruction from SNP fragments by minimum error correction. Bioinformatics 21(10), 2456–2462 (2005)

    Article  Google Scholar 

  10. Zhang, X., Wang, R., Wu, L., Zhang, W.: Minimum conflict individual haplotyping from SNP fragments and related genotype. Evol. Bioinform. 2, 271–280 (2006)

    Google Scholar 

  11. Downey, R., Fellows, M.: Parameterized Complexity. Springer, Berlin (1999)

    Google Scholar 

  12. Chen, J.: Parameterized computation and complexity: a new approach dealing with NP-hardness. J. Comput. Sci. Technol. 20(1), 18–37 (2005)

    Article  Google Scholar 

  13. The International SNP Map Working Group: A map of human genome sequence variation containing 1.42 million single nucleotide polymorphisms. Nature 409(6822), 928–933 (2001)

    Article  Google Scholar 

  14. Sanger, F., Nicklen, S., Coulson, A.R.: DNA sequencing with chain-terminating inhibitors. Proc. Natl. Acad. Sci. 74(12), 5463–5467 (1977)

    Article  Google Scholar 

  15. Gabriel, S.B., Schaffner, S.F., Nguyen, H., : The structure of haplotype blocks in the human genome. Science 296(5576), 2225–2229 (2002)

    Article  Google Scholar 

  16. Hinds, D.A., Stuve, L.L., Nilsen, G.B., : Whole-genome patterns of common DNA variation in three human populations. Science 307(5712), 1072–1079 (2005)

    Article  Google Scholar 

  17. The International HapMap Consortium: A haplotype map of the human genome. Nature 437(7063), 1299–1320 (2005)

    Article  Google Scholar 

  18. Hüffner, F.: Algorithm engineering for optimal graph bipartization. In: Nikoletseas, S.E. (ed.) Proc. WEA. Lecture Notes in Computer Science, vol. 3503, pp. 240–252. Springer, Berlin (2005)

    Google Scholar 

  19. Panconesi, A., Sozio, M.: Fast hare: a fast heuristic for single individual SNP haplotype reconstruction. In: Jonassen, I., Kim, J. (eds.) Proc. WABI. Lecture Notes in Computer Science, vol. 3240, pp. 266–277. Springer, Berlin (2004)

    Google Scholar 

  20. Myers, G.: A dataset generator for whole genome shotgun sequencing. In: Lengauer, T., Schneider, R., Bork, P., (eds.) Proc. ISMB, pp. 202–210. AAAI Press, Menlo Park (1999)

    Google Scholar 

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Correspondence to Minzhu Xie.

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A preliminary version of this paper was presented at The 14th Annual International Computing and Combinatorics Conference (COCOON 2008), June 27–29, 2008, Dalian, China. This research was supported in part by the National Natural Science Foundation of China under Grant No. 60773111, the National Basic Research 973 Program of China No. 2008CB317107, Postdoctoral Science Foundation of Central South University, the Program for New Century Excellent Talents in University No. NCET-05-0683, and the Program for Changjiang Scholars and Innovative Research Team in University No. IRT0661.

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Wang, J., Xie, M. & Chen, J. A Practical Exact Algorithm for the Individual Haplotyping Problem MEC/GI. Algorithmica 56, 283–296 (2010).

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