Beaches of Islands of Tractability: Algorithms for Parsimony and Minimum Perfect Phylogeny Haplotyping Problems

  • Leo van Iersel
  • Judith Keijsper
  • Steven Kelk
  • Leen Stougie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4175)


The problem Parsimony Haplotyping (PH) asks for the smallest set of haplotypes which can explain a given set of genotypes, and the problem Minimum Perfect Phylogeny Haplotyping (MPPH) asks for the smallest such set which also allows the haplotypes to be embedded in a perfect phylogeny evolutionary tree, a well-known biologically-motivated data structure. For PH we extend recent work of [17] by further mapping the interface between “easy” and “hard” instances, within the framework of (k,l)-bounded instances. By exploring, in the same way, the tractability frontier of MPPH we provide the first concrete, positive results for this problem, and the algorithms underpinning these results offer new insights about how MPPH might be further tackled in the future. In both PH and MPPH intriguing open problems remain.


Vertex Cover Chordal Graph Haplotype Inference Identical Column Simplicial Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alimonti, P., Kann, V.: Hardness of approximating problems on cubic graphs. In: Proc. of the 3rd Italian Conf. on Algorithms and Complexity, pp. 288–298 (1997)Google Scholar
  2. 2.
    Bafna, V., Gusfield, D., Hannenhalli, S., Yooseph, S.: A Note on Efficient Computation of Haplotypes via Perfect Phylogeny. J. of Computational Biology 11(5), 858–866 (2004)CrossRefGoogle Scholar
  3. 3.
    Blair, J.R.S., Peyton, B.: An introduction to chordal graphs and clique trees. In: Graph theory and sparse matrix computation, pp. 1–29. Springer, Heidelberg (1993)Google Scholar
  4. 4.
    Bonizzoni, P., Vedova, G.D., Dondi, R., Li, J.: The haplotyping problem: an overview of computational models and solutions. J. of Computer Science and Technology 18(6), 675–688 (2003)MATHCrossRefGoogle Scholar
  5. 5.
    Brown, D., Harrower, I.: Integer programming approaches to haplotype inference by pure parsimony. IEEE/ACM Transactions on Computational Biology and Informatics 3(2) (2006)Google Scholar
  6. 6.
    Cilibrasi, R., Iersel, L.J.J., van Kelk, S.M., Tromp, J.: On the Complexity of Several Haplotyping Problems. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 128–139. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Ding, Z., Filkov, V., Gusfield, D.: A linear-time algorithm for the perfect phylogeny haplotyping (PPH) problem. J. of Computational Biology 13(2), 522–533 (2006)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)MATHCrossRefGoogle Scholar
  9. 9.
    Gusfield, D.: Efficient algorithms for inferring evolutionary history. Networks 21, 19–28 (1991)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gusfield, D.: Haplotype inference 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
  11. 11.
    Halldórsson, B.V., Bafna, V., Edwards, N., Lippert, R., Yooseph, S., Istrail, S.: A survey of computational methods for determining haplotypes. In: Proc. DIMACS/RECOMB Satellite Workshop: Computational Methods for SNPs and Haplotype Inference, pp. 26–47 (2004)Google Scholar
  12. 12.
    Iersel, L.J.J., van Keijsper, J.C.M., Kelk, S.M., Stougie, L.: Beaches of islands of tractability: Algorithms for parsimony and minimum perfect phylogeny haplotyping problems, technical report (2006),
  13. 13.
    Lancia, G., Pinotti, M., Rizzi, R.: Haplotyping populations by pure parsimony: complexity of exact and approximation algorithms. INFORMS J. 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(3), 289–295 (2006)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. System Sci. 43, 425–440 (1991)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5, 266–283 (1976)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Sharan, R., Halldórsson, B.V., Istrail, S.: Islands of tractability for parsimony haplotyping. IEEE/ACM Transactions on Computational Biology and Bioinformatics (to appear)Google Scholar
  18. 18.
    Song, Y.S., Wu, Y., Gusfield, D.: Algorithms for imperfect phylogeny haplotyping (IPPH) with single haploplasy or recombination event. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 152–164. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    VijayaSatya, R., Mukherjee, A.: An optimal algorithm for perfect phylogeny haplotyping. J. of Computational Biology (to appear)Google Scholar
  20. 20.
    Zhang, X.-S., Wang, R.-S., Wu, L.-Y., Chen, L.: Models and Algorithms for Haplotyping Problem. Current Bioinformatics 1, 105–114 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Leo van Iersel
    • 1
  • Judith Keijsper
    • 1
  • Steven Kelk
    • 2
  • Leen Stougie
    • 1
    • 2
  1. 1.Technische Universiteit Eindhoven (TU/e)AX EindhovenNetherlands
  2. 2.Centrum voor Wiskunde en Informatica (CWI)SJ AmsterdamNetherlands

Personalised recommendations