Skip to main content

A Linear-Time Algorithm for the Perfect Phylogeny Haplotyping (PPH) Problem

  • Conference paper
Research in Computational Molecular Biology (RECOMB 2005)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 3500))

Abstract

Since the introduction of the Perfect Phylogeny Haplotyping (PPH) Problem in Recomb 2002 [15], the problem of finding a linear-time (deterministic, worst-case) solution for it has remained open, despite broad interest in the PPH problem and a series of papers on various aspects of it. In this paper we solve the open problem, giving a practical, deterministic linear-time algorithm based on a simple data-structure and simple operations on it. The method is straightforward to program and has been fully implemented. Simulations show that it is much faster in practice than prior methods. The value of a linear-time solution to the PPH problem is partly conceptual and partly for use in the inner-loop of algorithms for more complex problems, where the PPH problem must be solved repeatedly.

Research partially supported by grant EIA-0220154 from the National Science Foundation. Thanks to Chuck Langley for helpful discussions

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bafna, V., Gusfield, D., Hannenhalli, S., Yooseph, S.: A note on efficient computation of haplotypes via perfect phylogeny. J. Comp. Bio. 11(5), 858–866 (2004)

    Article  Google Scholar 

  2. Bafna, V., Gusfield, D., Lancia, G., Yooseph, S.: Haplotyping as perfect phylogeny: A direct approach. J. Computational Biology 10, 323–340 (2003)

    Article  Google Scholar 

  3. Barzuza, T., Beckmann, J.S., Shamir, R., Pe’er, I.: Computational Problems in Perfect Phylogeny Haplotyping: Xor-Genotypes and Tag SNP’s. In: Proc. of CPM 2004 (2004)

    Google Scholar 

  4. Bixby, R.E., Wagner, D.K.: An almost linear-time algorithm for graph realization. Mathematics of Operations Research 13, 99–123 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bonizzoni, P., Vedova, G.D., Dondi, R., Li, J.: The haplotyping problem: Models and solutions. J. Computer Science and Technology 18, 675–688 (2003)

    Article  MATH  Google Scholar 

  6. Chung, R.H., Gusfield, D.: Perfect phylogeny haplotyper: Haplotye inferral using a tree model. Bioinformatics 19(6), 780–781 (2003)

    Article  Google Scholar 

  7. Chung, R.H., Gusfield, D.: Empirical Exploration of Perfect Phylogeny Haplotyping and Haplotypers. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 5–9. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Damaschke, P.: Fast perfect phylogeny haplotype inference. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol. 2751, pp. 183–194. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Damaschke, P.: Incremental haplotype inference, phylogeny and almost bipartite graphs. In: 2nd RECOMB Satellite Workshop on Computational Methods for SNPs and Haplotypes, pre-proceedings, pp. 1–11 (2004)

    Google Scholar 

  10. Eskin, E., Halperin, E., Karp, R.M.: Efficient Reconstruction of Haplotype Structure via Perfect Phylogeny. J. Bioinformatics and Computational Biology 1(1), 1–20 (2003)

    Article  Google Scholar 

  11. Eskin, E., Halperin, E., Sharan, R.: Optimally Phasing Long Genomic Regions using Local Haplotype Predictions. In: Proc. of the Second RECOMB Satellite Workshop on Computational Methods for SNPs and Haplotypes, Pittsburg, USA, Feburary 20–21 (2004)

    Google Scholar 

  12. Gramm, J., Nierhoff, T., Tantau, T., Sharan, R.: On the Complexity of Haplotyping Via Perfect Phylogeny. Presented at the Second RECOMB Satellite Workshop on Computational Methods for SNPs and Haplotypes, Pittsburgh, USA, February 20–21. Proceedings to appear in LNBI. Springer, Heidelberg (2004)

    Google Scholar 

  13. Gramm, J., Nierhoff, T., Tantau, T.: Perfect Path Phylogeny Haplotyping with Missing Data is Fixed-Parameter Tractable. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 174–186. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Gusfield, D.: http://wwwcsif.cs.ucdavis.edu/~gusfield/lpph/

  15. Gusfield, D.: Haplotyping as perfect phylogeny: Conceptual framework and efficient solutions (extended abstract). In: Proc. of RECOMB 2002, pp. 166–175 (2002)

    Google Scholar 

  16. Gusfield, D.: An overview of combinatorial methods for haplotype inference. In: Istrail, S., Waterman, M.S., Clark, A. (eds.) DIMACS/RECOMB Satellite Workshop 2002. LNCS (LNBI), vol. 2983, pp. 9–25. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  17. Halldórsson, B.V., Bafna, V., Edwards, N., Lippert, R., Yooseph, S., Istrail, S.: A survey of computational methods for determining haplotypes. In: Istrail, S., Waterman, M.S., Clark, A. (eds.) DIMACS/RECOMB Satellite Workshop 2002. LNCS (LNBI), vol. 2983, pp. 26–47. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Halldórsson, B., Bafna, V., Edwards, N., Lipert, R., Yooseph, S., Istrail, S.: Combinatorial problems arising in SNP and haplotype analysis. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds.) DMTCS 2003. LNCS, vol. 2731. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Halperin, E., Eskin, E.: Haplotype reconstruction from genotype data using Imperfect Phylogeny. Bioinformatics 20, 1842–1849 (2004)

    Article  Google Scholar 

  20. Halperin, E., Karp, R.M.: Perfect Phylogeny and Haplotype Assignment. In: Proc. of RECOMB 2004, pp. 10–19 (2004)

    Google Scholar 

  21. Helmuth, L.: Genome research: Map of the human genome 3.0. Science 293(5530), 583–585 (2001)

    Article  Google Scholar 

  22. Hudson, R.: Gene genealogies and the coalescent process. Oxford Survey of Evolutionary Biology 7, 1–44 (1990)

    Google Scholar 

  23. Hudson, R.: Generating samples under the Wright-Fisher neutral model of genetic variation. Bioinformatics 18(2), 337–338 (2002)

    Article  Google Scholar 

  24. Kimmel, G., Shamir, R.: The Incomplete Perfect Phylogeny Haplotype Problem. Presented at the Second RECOMB Satellite Workshop on Computational Methods for SNPs and Haplotypes, Pittsburgh, USA, February 20–21 (2004); To appear in J. Bioinformatics and Computational Biology

    Google Scholar 

  25. Tavare, S.: Calibrating the clock: Using stochastic processes to measure the rate of evolution. In: Lander, E., Waterman, M. (eds.) Calculating the Secretes of Life. National Academy Press, Washington (1995)

    Google Scholar 

  26. Wiuf, C.: Inference on Recombination and Block Structure Using Unphased Data. Genetics 166(1), 537–545 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ding, Z., Filkov, V., Gusfield, D. (2005). A Linear-Time Algorithm for the Perfect Phylogeny Haplotyping (PPH) Problem. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds) Research in Computational Molecular Biology. RECOMB 2005. Lecture Notes in Computer Science(), vol 3500. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11415770_44

Download citation

  • DOI: https://doi.org/10.1007/11415770_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25866-7

  • Online ISBN: 978-3-540-31950-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics