The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The Haplotyping problem: an overview of computational models and solutions
Journal of Computer Science and Technology
Complexity and approximation of the minimum recombinant haplotype configuration problem
Theoretical Computer Science
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Deterministic Approximation Algorithms for the Nearest Codeword Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Haplotype-based prediction of gene alleles using pedigrees and SNP genotypes
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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Haplotype Inference (HI) is a computational challenge of crucial importance in a range of genetic studies. Pedigrees allow to infer haplotypes from genotypes more accurately than population data, since Mendelian inheritance restricts the set of possible solutions. In this work, we define a new HI problem on pedigrees, called Minimum-Change Haplotype Configuration (MCHC) problem, that allows two types of genetic variation events: recombinations and mutations. Our new formulation extends the Minimum-Recombinant Haplotype Configuration (MRHC) problem, that has been proposed in the literature to overcome the limitations of classic statistical haplotyping methods. Our contribution is twofold. First, we prove that the MCHC problem is APX-hard under several restrictions. Second, we propose an efficient and accurate heuristic algorithm for MCHC based on an L-reduction to a well-known coding problem. Our heuristic can also be used to solve the original MRHC problem and can take advantage of additional knowledge about the input genotypes. Moreover, the L-reduction proves for the first time that MCHC and MRHC are O({nm\over \log nm} -approximable on general pedigrees, where n is the pedigree size and m is the genotype length. Finally, we present an extensive experimental evaluation and comparison of our heuristic algorithm with several other state-of-the-art methods for HI on pedigrees.