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This is demonstrated by reduction of the phasing problem for genotypes to the phased version of the same problem for three common pedigree problems.
Algorithms for pedigree problems are of great interest to the computer science community, in part because of connections to machine learning algorithms, optimization methods, and combinatorics [ 4- 8].
□ Although this reduction establishes the hardness of these haplotype pedigree problems, it does so by constructing children whose haplotypes require many recombinations and would be extremely unlikely to occur naturally.
Given a pedigree with genotype data, for any of the three pedigree problems, we define a polynomial mapping to a corresponding haplotype problem with exactly 5| G| individuals haplotyped.
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The pedigree analysis problems we will consider are the likelihood, maximum probability haplotype, and minimum recombination haplotype problems.
Current haplotyping methods for pedigrees are incapable of solving the genome ancestry problem in animal resources for the following reasons: (i) Pedigrees of model animal resources often contain large number of generations to ensure diversity and reproducibility.
The result in Figure 5 shows that the knowledge of pedigree structure is indispensable in solving the genome ancestry problem.
The genome ancestry problem is closely related to haplotype inference with pedigree data.
We have presented a new algorithm for the multi-generation pedigree reconstruction problem.
In Almudevar (2003), some remaining challenges in the pedigree reconstruction problem were listed.
Yet even in his silence, Mr. Rafsanjani's pedigree presents a problem for Ayatollah Khamenei.
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