The paper presents a robust algorithm for relationship inference in genome-wide association studies (GWAS) using high-throughput genotype data. The authors address the challenge of accurately specifying familial relationships, which is crucial for both family-based and population-based GWAS. Existing algorithms often assume homogeneous population structure, which can lead to biased results in the presence of population substructure. The proposed algorithm, named KING, is designed to handle unknown population substructure and provides robust estimation of kinship coefficients, independent of sample composition or population structure. Simulation experiments demonstrate the algorithm's power to accurately infer relationships among millions of unrelated pairs and thousands of relative pairs up to the 3rd degree. Application to HapMap and GWAS datasets shows that KING performs well even under extreme population stratification, while algorithms assuming a homogeneous population give systematically biased results. The algorithm is implemented in a freely available software package, KING, which is significantly faster than existing algorithms, making it suitable for large-scale GWAS datasets. The authors also discuss the implications of their findings for automated pedigree reconstruction and association mapping in the absence of pre-specified pedigree or population structure.The paper presents a robust algorithm for relationship inference in genome-wide association studies (GWAS) using high-throughput genotype data. The authors address the challenge of accurately specifying familial relationships, which is crucial for both family-based and population-based GWAS. Existing algorithms often assume homogeneous population structure, which can lead to biased results in the presence of population substructure. The proposed algorithm, named KING, is designed to handle unknown population substructure and provides robust estimation of kinship coefficients, independent of sample composition or population structure. Simulation experiments demonstrate the algorithm's power to accurately infer relationships among millions of unrelated pairs and thousands of relative pairs up to the 3rd degree. Application to HapMap and GWAS datasets shows that KING performs well even under extreme population stratification, while algorithms assuming a homogeneous population give systematically biased results. The algorithm is implemented in a freely available software package, KING, which is significantly faster than existing algorithms, making it suitable for large-scale GWAS datasets. The authors also discuss the implications of their findings for automated pedigree reconstruction and association mapping in the absence of pre-specified pedigree or population structure.