On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Large scale reconstruction of haplotypes from genotype data
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Efficient rule-based haplotyping algorithms for pedigree data
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Haplotype reconstruction from SNP alignment
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
The complexity of checking consistency of pedigree information and related problems
Journal of Computer Science and Technology - Special issue on bioinformatics
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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We study the complexity and approximation of the problem of reconstructing haplotypes from genotypes on pedigrees under the Mendelian Law of Inheritance and the minimum recombinant principle (MRHC). First, we show that MRHC for simple pedigrees where each member has at most one mate and at most one child (i.e. binary-tree pedigrees) is NP-hard. Second, we present some approximation results for the MRHC problem, which are the first approximation results in the literature to the best of our knowledge. We prove that MRHC on two-locus pedigrees or binary-tree pedigrees with missing data cannot be approximated (the formal definition is given in section 1.2) unless P=NP. Next we show that MRHC on two-locus pedigrees without missing data cannot be approximated within any constant ratio under the Unique Games Conjecture and can be approximated within ratio O$(\sqrt{{\rm log}(n)})$. Our L-reduction for the approximation hardness gives a simple alternative proof that MRHC on two-locus pedigrees is NP-hard, which is much easier to understand than the original proof. We also show that MRHC for tree pedigrees without missing data cannot be approximated within any constant ratio under the Unique Games Conjecture, too. Finally, we explore the hardness and approximation of MRHC on pedigrees where each member has a bounded number of children and mates mirroring real pedigrees.