A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on pedigrees without mating loops

Lan Liu () and Tao Jiang ()
Additional contact information
Lan Liu: University of California
Tao Jiang: University of California

Journal of Combinatorial Optimization, 2010, vol. 19, issue 2, No 7, 217-240

Abstract: Abstract With the launch of the international HapMap project, the haplotype inference problem has attracted a great deal of attention in the computational biology community recently. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree without mating loops, assuming that the hereditary process was free of mutations (i.e. the Mendelian law of inheritance) and recombinants. We model the haplotype inference problem as a system of linear equations as in (Xiao et al. in Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’07), pp. 655–664, 2007) and present an (optimal) linear-time (i.e. O(mn) time) algorithm to generate a particular solution to the haplotype inference problem, where m is the number of loci (or markers) in a genotype and n is the number of individuals in the pedigree. Moreover, the algorithm also provides a general solution in O(mn 2) time, which is optimal because the descriptive size of a general solution could be as large as Θ(mn 2). The key ingredients of our construction are (i) a fast consistency checking procedure for the system of linear equations introduced in (Xiao et al. 2007) based on a careful investigation of the relationship between the equations (ii) a novel linear-time method for solving linear equations without invoking the Gaussian elimination method. Although such a fast method for solving equations is not known for general systems of linear equations, we take advantage of the underlying loop-free pedigree graph and some special properties of the linear equations.

Keywords: Haplotype inference; Pedigree analysis; Mating loop; Tree-pedigree; Linear-time algorithm; System of linear equation; General solution (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-008-9180-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:19:y:2010:i:2:d:10.1007_s10878-008-9180-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-008-9180-y

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().