An almost linear-time algorithm for graph realization
Mathematics of Operations Research
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Haplotyping as perfect phylogeny: conceptual framework and efficient solutions
Proceedings of the sixth annual international conference on Computational biology
Resolution of haplotypes and haplotype frequencies from SNP genotypes of pooled samples
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
A linear-time algorithm for the perfect phylogeny haplotyping (PPH) problem
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Pure Parsimony Xor Haplotyping
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
Algorithm for haplotype resolution and block partitioning for partial XOR-genotype data
Journal of Biomedical Informatics
Xor perfect phylogeny haplotyping in pedigrees
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Pure Parsimony Xor Haplotyping
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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A haplotype is an m-long binary vector. The xor-genotype of two haplotypes is the m-vector of their coordinate-wise xor. We study the following problem: Given a set of xor-genotypes, reconstruct their haplotypes so that the set of resulting haplotypes can be mapped onto a perfect phylogeny tree. The question is motivated by studying population evolution in human genetics, and is a variant of the perfect phylogeny haplotyping problem that has received intensive attention recently. Unlike the latter problem, in which the input is "full" genotypes, here we assume less informative input, and so may be more economical to obtain experimentally.Building on ideas of Gusfield, we show how to solve the problem in polynomial time, by a reduction to the graph realization problem. The actual haplotypes are not uniquely determined by that tree they map onto, and the tree itself may or may not be unique. We show that tree uniqueness implies uniquely determined haplotypes, up to inherent degrees of freedom, and give a sufficient condition for the uniqueness. To actually determine the haplotypes given the tree, additional information is necessary. We show that two or three full genotypes suffice to reconstruct all the haplotypes, and present a linear algorithm for identifying those genotypes.