tends to amplify distant relationships in the PLINK analysis (inflating Z1 somewhat, but inflating Z2 and Pi-Hat much more), especially for members of minority groups. The matrix of Z1 statistics was used to select the largest possible subgroup of unrelated individuals. This is known as the maximum clique problem in computer science and mathematics. To find the guaranteed maximum is extremely computationally demanding (it is an NP complete problem), so we used a greedy algorithm to achieve a reasonable answer in only a few seconds. This solution provides a subset of subjects such that no pairs have Z1 greater than .10. It is conceivable that a larger subset could be produced with much more computational effort, but the gain is likely to be minimal.
