Algorithm	Methodology	Parameters	Worst-case Complexity N: the number of samples; d: the dimension of the X and Y manifolds (default 2); k: the number of nearest neighbors L: the number of conditioning genes I: the dimension of the features data
CCM	Determining the causality from X to Y based on how well one can reconstruct the cross-mapped estimate of X from the nearest neighbors determined on Y space	E: The number of lags embedded in the shadow manifold Tau: The time lag between each consecutive pair of time samples (default: 1)	O (2EN log N) *+ O (2(E + 1) N) ** *Complexity of kd-tree algorithm for kNN search ** Complexity of regression and weight estimation
Granger Causality	Determining the causality from X to Y based on how much the past samples of X contribute in linearly estimating the current state of Y, compared to when the Y is estimated based merely upon its own past	Maxlag: The number of lags of the past sample included in estimating the current state of Y	O (IN + 2I2 N + I3) * * The complexity of linear regression
RDI and cRDI	Determining the causality from X to Y based on the amount of mutual information between the past of X and the current state of Y conditioned over the past of (potentially) all other variables than X	k: The number of neighbors for kNN estimation of mutual information d: The lags for which the mutual information from the lagged source to the current state of target is estimated. L: The number of the conditioning nodes other than X and Y. While small L’s can result in false positives since we won’t filter out confounding and/or intermediate factors, too large L’s will result in curse of dimensionality in smaller sample set regimes and increasing the computational complexity in larger sample set regimes.	O ((d + L + 1) N log N) * + O (kN) ** *Complexity of kd-tree algorithm **Complexity of inquiry of each neighbor
uRDI and ucRDI	Same as RDI method, but including the replacement of the empirical distribution of the past samples with a uniform distribution	All Parameters from RDI plus: BW: The bandwidth of the kernel estimator	O ((d + L + 1) N log N) * + O (kN) ** + O (N3) *** *Complexity of kd-tree algorithm **Complexity of inquiry of each neighbor ***Complexity of kernel density estimation