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A Class Representative Model for Pure Parsimony Haplotyping under Uncertain Data

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  • Daniele Catanzaro
  • Martine Labbé
  • Luciano Porretta

Abstract

The Pure Parsimony Haplotyping (PPH) problem is a NP-hard combinatorial optimization problem that consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. PPH has attracted more and more attention in recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from mapping complex disease genes to inferring population histories, passing through designing drugs, functional genomics and pharmacogenetics. In this article we investigate, for the first time, a recent version of PPH called the Pure Parsimony Haplotype problem under Uncertain Data (PPH-UD). This version mainly arises when the input genotypes are not accurate, i.e., when some single nucleotide polymorphisms are missing or affected by errors. We propose an exact approach to solution of PPH-UD based on an extended version of Catanzaro et al. [1] class representative model for PPH, currently the state-of-the-art integer programming model for PPH. The model is efficient, accurate, compact, polynomial-sized, easy to implement, solvable with any solver for mixed integer programming, and usable in all those cases for which the parsimony criterion is well suited for haplotype estimation.

Suggested Citation

  • Daniele Catanzaro & Martine Labbé & Luciano Porretta, 2011. "A Class Representative Model for Pure Parsimony Haplotyping under Uncertain Data," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-10, March.
    • Handle: RePEc:plo:pone00:0017937
    DOI: 10.1371/journal.pone.0017937
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    References listed on IDEAS

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    1. Yasunori Ogura & Denise K. Bonen & Naohiro Inohara & Dan L. Nicolae & Felicia F. Chen & Richard Ramos & Heidi Britton & Thomas Moran & Reda Karaliuskas & Richard H. Duerr & Jean-Paul Achkar & Steven R, 2001. "A frameshift mutation in NOD2 associated with susceptibility to Crohn's disease," Nature, Nature, vol. 411(6837), pages 603-606, May.
    2. Paul Van Eerdewegh & Randall D. Little & Josée Dupuis & Richard G. Del Mastro & Kathy Falls & Jason Simon & Dana Torrey & Sunil Pandit & Joyce McKenny & Karen Braunschweiger & Alison Walsh & Ziying Li, 2002. "Association of the ADAM33 gene with asthma and bronchial hyperresponsiveness," Nature, Nature, vol. 418(6896), pages 426-430, July.
    3. Jean-Pierre Hugot & Mathias Chamaillard & Habib Zouali & Suzanne Lesage & Jean-Pierre Cézard & Jacques Belaiche & Sven Almer & Curt Tysk & Colm A. O'Morain & Miquel Gassull & Vibeke Binder & Yigael Fi, 2001. "Association of NOD2 leucine-rich repeat variants with susceptibility to Crohn's disease," Nature, Nature, vol. 411(6837), pages 599-603, May.
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