This paper presents a robust algorithm for inferring relationships between individuals in genome-wide association studies (GWASs), called KING. The algorithm is designed to handle population substructure and provides accurate kinship coefficient estimates, which are crucial for identifying related individuals in GWAS data. The algorithm is efficient, allowing for the analysis of millions of pairwise comparisons in minutes, significantly faster than existing methods. KING is implemented in a freely available software package and has been tested on HapMap and GWAS datasets, demonstrating its effectiveness even under extreme population stratification. The algorithm is robust to population structure and can accurately infer relationships between individuals, including up to third-degree relatives. It also provides a tool for population structure analysis in GWAS data. The paper also discusses the computational efficiency of the algorithm, showing that it is significantly faster than existing methods, making it suitable for large-scale GWAS data analysis. The algorithm is applicable to a wide range of genetic studies, including forensic DNA analysis and paternity testing. The paper concludes that the robust relationship inference approach presented in KING is a valuable tool for GWAS data analysis, particularly in the presence of population structure.This paper presents a robust algorithm for inferring relationships between individuals in genome-wide association studies (GWASs), called KING. The algorithm is designed to handle population substructure and provides accurate kinship coefficient estimates, which are crucial for identifying related individuals in GWAS data. The algorithm is efficient, allowing for the analysis of millions of pairwise comparisons in minutes, significantly faster than existing methods. KING is implemented in a freely available software package and has been tested on HapMap and GWAS datasets, demonstrating its effectiveness even under extreme population stratification. The algorithm is robust to population structure and can accurately infer relationships between individuals, including up to third-degree relatives. It also provides a tool for population structure analysis in GWAS data. The paper also discusses the computational efficiency of the algorithm, showing that it is significantly faster than existing methods, making it suitable for large-scale GWAS data analysis. The algorithm is applicable to a wide range of genetic studies, including forensic DNA analysis and paternity testing. The paper concludes that the robust relationship inference approach presented in KING is a valuable tool for GWAS data analysis, particularly in the presence of population structure.