A recursive method for solving haplotype frequencies with application to genetics

Kwok Po NG*, Erics S. Fung, Yiu Fai Lee, Wai Ki Ching

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


Multiple loci analysis has become popular with the advanced developments in biological experiments. A lot of studies have been focused on the biological and the statistical properties of such multiple loci analysis. In this paper, we study one of the important computational problems: solving the probabilities of haplotype classes from a large linear system Ax = b derived from the recombination events in multiple loci analysis. Since the size of the recombination matrix A increases exponentially with respect to the number of loci, fast solvers are required to deal with a large number of loci in the analysis. By exploiting the nice structure of the matrix A, we develop an efficient recursive algorithm for solving such structured linear systems. In particular, the complexity of the proposed algorithm for the n loci problem is of O(n2n) operations and the memory requirement is of O(2n) locations for the 2n-by-2n matrix A. Numerical examples are given to demonstrate the effectiveness of our efficient solver. Finally, we apply our proposed method to analyze the haplotype classes for a set of single nucleotides polymorphisms (SNPs) from Hapmap data.

Original languageEnglish
Pages (from-to)1269-1285
Number of pages17
JournalJournal of Bioinformatics and Computational Biology
Issue number6
Publication statusPublished - Dec 2006

Scopus Subject Areas

  • Biochemistry
  • Molecular Biology
  • Computer Science Applications

User-Defined Keywords

  • Haplotypes
  • Loci
  • Recursive methods
  • SNPs


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