Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
On the set covering polytope: I. all the facets with coefficients in {0, 1, 2}
Mathematical Programming: Series A and B
On the set covering polytope: II. lifting the facets with coefficients in {0, 1, 2}
Mathematical Programming: Series A and B
Optimal solution of set covering/partitioning problems using dual heuristics
Management Science
Algorithms for railway crew management
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Combinatorial optimization
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Simplification of the Covering Problem with Application to Boolean Expressions
Journal of the ACM (JACM)
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Solving hard set covering problems
Operations Research Letters
On approximating four covering and packing problems
Journal of Computer and System Sciences
On Approximating an Implicit Cover Problem in Biology
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
New Optimization Model and Algorithm for Sibling Reconstruction from Genetic Markers
INFORMS Journal on Computing
Computers and Operations Research
Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine
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A new combinatorial approach for modelling and reconstructing sibling relationships in a single generation of individuals without parental information is proposed in this paper. Simple genetic constraints on the full-sibling groups, imposed by the Mendelian inheritance rules, are employed to investigate data from codominant DNA markers. To extract the minimum number of biologically consistent sibling groups, the proposed combinatorial approach is employed to formulate this minimization problem as a set covering problem, which is a well-known NP-hard combinatorial optimization problem. We conducted a simulation study of a relaxed version of the proposed algorithm to demonstrate that our combinatorial approach is reasonably accurate and the exact version of the sibling relationship construction algorithm should be pursued. In addition, the results of this study suggest that the proposed algorithm will pave our way to a new approach in computational population genetics as it does not require any a priori knowledge about allele frequency, population size, mating system or family size distributions to reconstruct sibling relationships.