Pure Parsimony Xor Haplotyping

  • Paola Bonizzoni
  • Gianluca Della Vedova
  • Riccardo Dondi
  • Yuri Pirola
  • Romeo Rizzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5542)

Abstract

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies [1]. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a formulation based on a well known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial-time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Moreover we propose a heuristic and produce an experimental analysis showing that it scales to real-world instances taken from the HapMap project.

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References

  1. 1.
    Barzuza, T., Beckmann, J.S., Shamir, R., Pe’er, I.: Computational problems in perfect phylogeny haplotyping: Xor-genotypes and tag SNPs. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 14–31. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Barzuza, T., Beckmann, J.S., Shamir, R., Pe’er, I.: Computational problems in perfect phylogeny haplotyping: Typing without calling the allele. IEEE/ACM Trans. on Comput. Biol. and Bioinform. 5(1), 101–109 (2008)CrossRefGoogle Scholar
  3. 3.
    Bitner, J.R., Ehrlich, G., Reingold, E.M.: Efficient generation of the binary reflected Gray code and its applications. Comm. of the ACM 19(9), 517–521 (1976)CrossRefGoogle Scholar
  4. 4.
    Bixby, R.E., Wagner, D.K.: An almost linear-time algorithm for graph realization. Mathematics of Operations Research 13, 99–123 (1988)CrossRefGoogle Scholar
  5. 5.
    Brown, D.G., Harrower, I.M.: Integer programming approaches to haplotype inference by pure parsimony. IEEE/ACM Trans. on Comput. Biol. and Bioinform. 3(2), 141–154 (2006)CrossRefGoogle Scholar
  6. 6.
    Diestel, R.: Graph Theory, 3rd edn. Graduate Texts in Mathematics, vol. 173. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Fredkin, E.: Trie memory. Comm. of the ACM 3(9), 490–499 (1960)CrossRefGoogle Scholar
  9. 9.
    Fujishige, S.: An efficient PQ-graph algorithm for solving the graph realization problem. J. of Computer and System Science 21, 63–86 (1980)CrossRefGoogle Scholar
  10. 10.
    Gusfield, D.: Haplotyping as perfect phylogeny: Conceptual framework and efficient solutions. In: Proc. 6th RECOMB, pp. 166–175 (2002)Google Scholar
  11. 11.
    Gusfield, D.: Haplotyping by pure parsimony. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 144–155. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Lancia, G., Pinotti, M.C., Rizzi, R.: Haplotyping populations by pure parsimony: Complexity of exact and approximation algorithms. INFORMS J. Comp. 16(4), 348–359 (2004)CrossRefGoogle Scholar
  13. 13.
    Savage, C.: A survey of combinatorial Gray codes. SIAM Rev. 39(4), 605–629 (1997)CrossRefGoogle Scholar
  14. 14.
    The International HapMap Consortium. A haplotype map of the human genome. Nature 437(7063), 1299–1320 (2005)Google Scholar
  15. 15.
    Tutte, W.T.: An algorithm for determining whether a given binary matroid is graphic. Proc. of the American Mathematical Society 11(6), 905–917 (1960)Google Scholar
  16. 16.
    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. on Comput. Biol. and Bioinform. 5(2), 301–312 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paola Bonizzoni
    • 1
  • Gianluca Della Vedova
    • 2
  • Riccardo Dondi
    • 3
  • Yuri Pirola
    • 1
  • Romeo Rizzi
    • 4
  1. 1.DISCoUniv. Milano-BicoccaItaly
  2. 2.Dip. StatisticaUniv. Milano-BicoccaItaly
  3. 3.Dip. Scienze dei Linguaggi, della Comunicazione e degli Studi CulturaliUniv. BergamoItaly
  4. 4.DIMIUniv. UdineItaly

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