Extended Islands of Tractability for Parsimony Haplotyping

  • Rudolf Fleischer
  • Jiong Guo
  • Rolf Niedermeier
  • Johannes Uhlmann
  • Yihui Wang
  • Mathias Weller
  • Xi Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6129)

Abstract

Parsimony haplotyping is the problem of finding a smallest size set of haplotypes that can explain a given set of genotypes. The problem is NP-hard, and many heuristic and approximation algorithms as well as polynomial-time solvable special cases have been discovered. We propose improved fixed-parameter tractability results with respect to the parameter “size of the target haplotype set” k by presenting an O*(k4k)-time algorithm. This also applies to the practically important constrained case, where we can only use haplotypes from a given set. Furthermore, we show that the problem becomes polynomial-time solvable if the given set of genotypes is complete, i.e., contains all possible genotypes that can be explained by the set of haplotypes.

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References

  1. 1.
    Bodlaender, H.L., Downey, R.G., Fellows, M.R., Hermelin, D.: On problems without polynomial kernels. J. Comput. System Sci. 75(8), 423–434 (2009)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Catanzaro, D., Labbé, M.: The pure parsimony haplotyping problem: Overview and computational advances. International Transactions in Operational Research 16(5), 561–584 (2009)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cicalese, F., Milanič, M.: On parsimony haplotyping. Technical Report 2008-04, Universität Bielefeld (2008)Google Scholar
  4. 4.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Fellows, M.R., Hartman, T., Hermelin, D., Landau, G.M., Rosamond, F.A., Rozenberg, L.: Haplotype inference constrained by plausible haplotype data. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 339–352. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  7. 7.
    Fortnow, L., Santhanam, R.: Infeasibility of instance compression and succinct PCPs for NP. In: Proc. 40th STOC, pp. 133–142. ACM Press, New York (2008)Google Scholar
  8. 8.
    Guo, J., Hüffner, F., Niedermeier, R.: A structural view on parameterizing problems: Distance from triviality. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 162–173. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. ACM SIGACT News 38(1), 31–45 (2007)CrossRefGoogle Scholar
  10. 10.
    Gusfield, D., Orzack, S.H.: Haplotype inference. CRC Handbook on Bioinformatics, ch. 1, pp. 1–25. CRC Press, Boca Raton (2005)Google Scholar
  11. 11.
    van Iersel, L., Keijsper, J., Kelk, S., Stougie, L.: Shorelines of islands of tractability: Algorithms for parsimony and minimum perfect phylogeny haplotyping problems. IEEE/ACM Trans. Comput. Biology Bioinform. 5(2), 301–312 (2008)CrossRefGoogle Scholar
  12. 12.
    Jäger, G., Climer, S., Zhang, W.: Complete parsimony haplotype inference problem and algorithms. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 337–348. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Lancia, G., Pinotti, M.C., Rizzi, R.: Haplotyping populations by pure parsimony: Complexity of exact and approximation algorithms. INFORMS Journal on Computing 16(4), 348–359 (2004)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Lancia, G., Rizzi, R.: A polynomial case of the parsimony haplotyping problem. Operations Research Letters 34, 289–295 (2006)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)MATHCrossRefGoogle Scholar
  16. 16.
    Sharan, R., Halldórsson, B.V., Istrail, S.: Islands of tractability for parsimony haplotyping. IEEE/ACM Trans. Comput. Biology Bioinform. 3(3), 303–311 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  • Jiong Guo
    • 2
  • Rolf Niedermeier
    • 3
  • Johannes Uhlmann
    • 3
  • Yihui Wang
    • 1
  • Mathias Weller
    • 3
  • Xi Wu
    • 1
  1. 1.School of Computer Science, IIPLFudan UniversityShanghaiChina
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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