Skip to main content

Fixed-Parameter Algorithm for General Pedigrees with a Single Pair of Sites

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 6053))

Abstract

The problem of computing the minimum number of recombination events for general pedigrees with two sites for all members is investigated. We show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem and therefore can be solved by an O(2k ·n 2) exact algorithm, where n is the number of members and k is the number of recombination events.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chan, B.M.-Y., Chan, J.W.-T., Chin, F.Y.-L., Fung, S.P.-Y., Kao, M.-Y.: Linear-time haplotype inference on pedigrees without recombinations. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS, vol. 4175, pp. 56–67. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Doan, D.D., Evans, P.A., Horton, J.D.: A Near-Linear Time Algorithm for Haplotype Determination on General Pedigrees. Submitted to Journal of Computational Biology (2009) Submission ID: JCB-2009-0133

    Google Scholar 

  3. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  4. Guo, J., Gramm, J., Hüffner, F., Niedermeier, R., Wernicke, S.: Compression-Based Fixed-Parameter Algorithms for Feedback Vertex Set and Edge Bipartization. Journal of Computer and System Sciences 72(8), 1386–1396 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. 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)

    Google Scholar 

  6. Karp, R.M.: Reducibility Among Combinatorial Problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum, New York (1972)

    Google Scholar 

  7. Li, J., Jiang, T.: Efficient inference of haplotypes from genotypes on a pedigree. Jornal of Bioinformatics and Computational Biology 1(1), 41–70 (2003)

    Article  Google Scholar 

  8. Li, J., Jiang, T.: Efficient rule-based haplotyping algorithms for pedigree data. In: Proceedings of Research in Computational Molecular Biology (RECOMB 2003), pp. 197–206. ACM Press, New York (2003)

    Google Scholar 

  9. Li, J., Jiang, T.: An exact solution for finding minimum recombinant haplotype configurations on pedigrees with missing data by integer linear programming. In: Proceedings of Research in Computational Molecular Biology (RECOMB 2004), pp. 20–29. ACM Press, New York (2004)

    Google Scholar 

  10. Liu, L., Chen, X., Xiao, J., Jiang, T.: Complexity and approximation of the minimum recombinant haplotype configuration problem. Theoretical Computer Science 378, 316–330 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)

    Book  MATH  Google Scholar 

  12. Qian, D., Beckmann, L.: Minimum-recombinant haplotyping in pedigrees. American Journal of Human Genetics 70(6), 1434–1445 (2002)

    Article  Google Scholar 

  13. Reed, B., Smith, K., Vetta, A.: Finding odd cycle transversals. Operations Research Letters 32, 299–301 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wernicke, S.: On the algorithmic tractability of single nucleotide polymorphism (SNP) analysis and related problems. Diplomarbeit, Wilhelm-Schickard-Institut für Informatik, Universität Tübingen (2003)

    Google Scholar 

  15. Xiao, J., Liu, L., Xia, L., Jiang, T.: Fast elimination of redundant linear equations and reconstruction of recombination-free mendelian inheritance on a pedigree. In: Proceedings of the eighteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 655–664 (2007)

    Google Scholar 

  16. Xu, S.: The line index and minimum cut of weighted graphs. European Journal of Operational Research 109, 672–682 (1998)

    Article  MATH  Google Scholar 

  17. Zhang, K., Sun, F., Zhao, H.: HAPLORE: a program for haplotype reconstruction in general pedigrees without recombination. Bioinformatics 21(1), 90–103 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Doan, D.D., Evans, P.A. (2010). Fixed-Parameter Algorithm for General Pedigrees with a Single Pair of Sites. In: Borodovsky, M., Gogarten, J.P., Przytycka, T.M., Rajasekaran, S. (eds) Bioinformatics Research and Applications. ISBRA 2010. Lecture Notes in Computer Science(), vol 6053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13078-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13078-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13077-9

  • Online ISBN: 978-3-642-13078-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics