Table 1:

Computing time complexity of BLINK compared with PLINK and FarmCPU

Method	Model selection	Association test	Total	Complexity over M and N
PLINK	NA	c2MN	c2MN	O(MN)
FarmCPU	bsp(c+t)2N	(c+t)2MN	(M+bsp)(c+t)2N	O(MN)
BLINK	t(c+t)2N+(c+t)2N	(c+t)2MN	(M+t)(c+t)2N + (c+t)2N	O(MN)

The computing time is based on testing M markers on a sample with N individuals. All three methods contain common c covariates. FarmCPU and BLINK add t pseudo QTNs as additional covariates. FarmCPU examines t QTNs over b different levels of bin size and s different levels of bin numbers. Using the EMMA algorithm, each examination optimizes the ratio of genetic-to-residual variance with p iterations. BLINK selects t pseudo QTNs with a computing time of (c+t)²N. BLINK also eliminates optimization on bin size and on the genetic-to-residual variance ratio. The numbers of common covariates (c), pseudo QTNs (t), levels of bin size (b), and iterations (p) are much smaller than M and N. Therefore, the computing time complexity is MN in respect of big O for all three methods.