Skip to main content
SpringerLink
Log in
Book cover

Trends in Contemporary Mathematics pp 73–84Cite as

Mathematical Models and Solutions for the Analysis of Human Genotypes

  • Conference paper
  • First Online:

  • 1251 Accesses

Part of the book series: Springer INdAM Series ((SINDAMS,volume 8))

Abstract

The past few years have seen the birth and the growth of a new reseach area in bioinformatics, called haplotyping. Haplotyping problems are combinatorial and optimization problems concerned with the analysis of human polymorphisms in populations, and with the study of common patterns for such polymorphisms. In this chapter we review the most important haplotyping problems, and describe the mathematical models and algorithmic approaches employed for their solution.

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

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. V. Bafna, D. Gusfield, G. Lancia, S. Yooseph, Haplotyping as perfect phylogeny: a direct approach. J. Comput. Biol. 10, 323–340 (2003)

    Article  Google Scholar 

  2. P. Bertolazzi, A. Godi, M. Labbé, L. Tininini, Solving haplotyping inference parsimony problem using a new basic polynomial formulation. Comput. Math. Appl. 55, 900–911 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Bonizzoni, A linear-time algorithm for the perfect phylogeny haplotype problem. Algorithmica 48, 267–285 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Bonizzoni, G. Della Vedova, R. Dondi, J. Li, The haplotyping problem: an overview of computational models and solutions. J. Comput. Sci. Technol. 19, 1–23 (2004)

    Article  Google Scholar 

  5. P. Bonizzoni, C. Braghin, R. Dondi, G. Trucco, The binary perfect phylogeny with persistent characters. Theor. Comput. Sci. 454, 51–63 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  6. D.G. Brown, I.M. Harrower, A new integer programming formulation for the pure parsimony problem in haplotype analysis, in Annual Workshop on Algorithms in Bioinformatics – WABI, Bergen. LNCS 3240 (Springer, Berlin/Heidelberg, 2004), pp. 254–265

    Google Scholar 

  7. D.G. Brown, I.M. Harrower, A new formulation for haplotype inference by pure parsimony. Technical report CS-2005-03, Department of Computer Science, University of Waterloo, Canada (2005)

    Google Scholar 

  8. D. Catanzaro, A. Godi, M. Labbè, A class representative model for pure parsimony haplotyping. INFORMS J. Comput. 22, 195–209 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Clark, Inference of haplotypes from PCR amplified samples of diploid populations. Mol. Biol. Evol. 7, 111–122 (1990)

    Google Scholar 

  10. L. Di Gaspero, A. Roli, Stochastic local search for large-scale instances of the haplotype inference problem by pure parsimony. J. Algebra 63, 55–69 (2008)

    MATH  Google Scholar 

  11. Z. Ding, V. Filkov, D. Gusfield, A linear-time algorithm for the perfect phylogeny haplotyping problem. J. Comput. Biol. 13, 522–553 (2006)

    Article  MathSciNet  Google Scholar 

  12. E. Eskin, E. Halperin, R. Karp, Efficient reconstruction of haplotype structure via perfect phylogeny. J. Bioinformatics Comput. Biol. 1, 1–20 (2003)

    Article  Google Scholar 

  13. A. Graca, J. Marques-Silva, I. Lynce, A.L. Oliviera, Efficient haplotype inference with pseudo-Boolean optimization, in 2nd International Conference on Algebraic Biology – AB, Castle of Hagenberg. LNCS 4545 (Springer, Berlin/Heidelberg/New York, 2007), pp. 125–139

    Google Scholar 

  14. D. Gusfield, A Practical algorithm for optimal inference of haplotypes from diploid populations, in Annual International Conference on Intelligent Systems for Molecular Biology (ISMB), La Jolla/San Diego (AAAI, Menlo Park, 2000), pp. 183–189

    Google Scholar 

  15. D. Gusfield, Inference of haplotypes from samples of diploid populations: complexity and algorithms. J. Comput. Biol. 8, 305–324 (2001)

    Article  Google Scholar 

  16. D. Gusfield, Haplotyping as perfect phylogeny: conceptual framework and efficient solutions, in International Conference on Computational Molecular Biology – RECOMB, Washington (ACM, New York, 2002), pp. 166–175

    Google Scholar 

  17. D. Gusfield, Haplotype inference by pure parsimony, in Annual Symposium on Combinatorial Pattern Matching – CPM, Morelia, Michocán. LNCS 2676 (Springer, Berlin/Heidelberg/ New York, 2003), pp. 144–155

    Google Scholar 

  18. D. Gusfield, S.H. Orzack, Haplotype inference, in Handbook of Computational Molecular Biology, ed. by S. Aluru. (Champman and Hall/CRC, 2005), pp. 1–28

    Google Scholar 

  19. B. Halldorsson, V. Bafna, N. Edwards, R. Lippert, S. Yooseph, S. Istrail, A survey of computational methods for determining haplotypes, in Computational Methods for SNP and Haplotype Inference: DIMACS/RECOMB Satellite Workshop, Piscataway. LNCS 2983 (Springer, Berlin, 2004), pp. 26–47

    Google Scholar 

  20. Y.T. Huang, K.M. Chao, T. Chen, An approximation algorithm for haplotype inference by maximum parsimony, in ACM Symposium on Applied Computing – SAC, Santa Fe, pp. 146–150 (2005)

    Google Scholar 

  21. K. Kalpakis, P. Namjoshi, Haplotype phasing using semidefinite programming, in 5th IEEE Symposium on Bioinformatics and Bioengineering – BIBE, Minneapolis, pp. 145–152 (2005)

    Google Scholar 

  22. C. Kanz et al., The EMBL nucleotide sequence database. Nucl. Acid Res. 33, D29–D33 (2005)

    Article  Google Scholar 

  23. G. Lancia, Applications to computational molecular biology, in Handbook on Modeling for Discrete Optimization, eds. by G. Appa, P. Williams, P. Leonidas, H. Paul. International Series in Operations Research and Management Science, vol. 88 (Springer, New York, 2006), pp. 270–304

    Google Scholar 

  24. G. Lancia, R. Rizzi, A polynomial case of the parsimony haplotyping problem. Oper. Res. Lett. 34, 289–295 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. G. Lancia, P. Serafini, A set covering approach with column generation for parsimony haplotyping. INFORMS J. Comput. 21, 151–166 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. G. Lancia, C. Pinotti, R. Rizzi, Haplotyping populations by pure parsimony: complexity, exact and approximation algorithms. INFORMS J. Comput. 16, 17–29 (2004)

    Article  MathSciNet  Google Scholar 

  27. I. Lynce, J. Marques-Silva, SAT in bioinformatics: making the case with haplotype inference, in Theory and Applications of Satisfiability Testing – SAT, Seattle, LNCS 4121 (Springer, Berlin/Heidelberg, 2006), pp. 136–141

    Google Scholar 

  28. J. Marques-Silva, I. Lynce, A. Graca, A.L. Oliveira, Efficient and tight upper bounds for haplotype inference by pure parsimony using delayed haplotype selection, in Progress in Artificial Intelligence, ed. by J. Neves, M.F. Santos, J.M. Machado. LNCS 4874 (Springer, Berlin, 2007), pp. 621–632

    Google Scholar 

  29. G.L. Nemhauser, L.A. Wolsey, Integer and Combinatorial Optimization (Wiley, New York, 1988)

    Book  MATH  Google Scholar 

  30. A. Schrijver, Theory of Linear and Integer Programming (Wiley, New York, 1986)

    MATH  Google Scholar 

  31. L. Tininini, P. Bertolazzi, A. Godi, G. Lancia, CollHaps: a heuristic approach to haplotype inference by parsimony. IEEE/ACM Trans. Comput. Biol. Bioinformatics 7, 511–523 (2010)

    Article  Google Scholar 

  32. L. Wang, Y. Xu, Haplotype inference by maximum parsimony. Bioinformatics 19, 1773–1780 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Udine, via delle Scienze 206, 33100, Udine, Italy

    Giuseppe Lancia

Authors
  1. Giuseppe Lancia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giuseppe Lancia .

Editor information

Editors and Affiliations

  1. Istituto Nazionale di Alta Matematica "Francesco Severi", Roma, Italy

    Vincenzo Ancona

  2. Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Roma, Italy

    Elisabetta Strickland

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Lancia, G. (2014). Mathematical Models and Solutions for the Analysis of Human Genotypes. In: Ancona, V., Strickland, E. (eds) Trends in Contemporary Mathematics. Springer INdAM Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05254-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation