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Summary: Optimization Methods and Software
Vol. 22, No. 1, February 2007, 1124
Set covering approach for reconstruction of sibling
relationships
W. A. CHAOVALITWONGSE*, T. Y. BERGER-WOLF§, B. DASGUPTA§ and
M. V. ASHLEY¶
Department of Industrial and Systems Engineering, Rutgers University, NJ, USA
DIMACS, Rutgers University, Piscataway, NJ, USA
§Department of Computer Science, University of Illinois, Chicago, IL, USA
¶Department of Biological Sciences, University of Illinois, Chicago, IL, USA
(Received 18 May 2005; in final form 20 April 2006)
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
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