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
Natural Computing: an international journal
Fixed-parameter algorithm for haplotype inferences on general pedigrees with small number of sites
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
An Efficient Algorithm for Haplotype Inference on Pedigrees with Recombinations and Mutations
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Fixed-parameter algorithm for general pedigrees with a single pair of sites
ISBRA'10 Proceedings of the 6th international conference on Bioinformatics Research and Applications
Efficient and accurate haplotype inference by combining parsimony and pedigree information
ANB'10 Proceedings of the 4th international conference on Algebraic and Numeric Biology
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
| Hi-index | 5.23 |
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 the 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 the MRHC on two-locus pedigrees or binary-tree pedigrees with missing data cannot be approximated unless P=NP. Next we show that the 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 the ratio O(log(n)). Our L-reduction for the approximation hardness gives a simple alternative proof that the MRHC on two-locus pedigrees is NP-hard, which is much easier to understand than the original proof. We also show that the 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 the MRHC on pedigrees where each member has a bounded number of children and mates mirroring real pedigrees.