Set covering approach for reconstruction of sibling relationships

A new combinatorial approach for modelling and reconstructing sibling relationships in a single gener-ation 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 sib-ling 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 con-struction 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