An almost linear-time algorithm for graph realization
Mathematics of Operations Research
A Survey of Combinatorial Gray Codes
SIAM Review
Efficient generation of the binary reflected gray code and its applications
Communications of the ACM
Communications of the ACM
Haplotyping as perfect phylogeny: conceptual framework and efficient solutions
Proceedings of the sixth annual international conference on Computational biology
Integer Programming Approaches to Haplotype Inference by Pure Parsimony
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Islands of Tractability for Parsimony Haplotyping
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms
INFORMS Journal on Computing
Computational Problems in Perfect Phylogeny Haplotyping: Typing without Calling the Allele
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Haplotype inference by pure Parsimony
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
A polynomial case of the parsimony haplotyping problem
Operations Research Letters
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The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies [1]. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper, we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given single nucleotide polymorphisms (SNP). Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project.