Pseudocode C6 Power computation of Mgc against a given distribution. By repeatedly sampling from the joint distribution ${\displaystyle F_{XY}}$, sample data of size $n$ under the null and the alternative are generated for $r$ Monte-Carlo replicates. The power of Mgc follows by computing the test statistic under the null and the alternative using Algorithm C2. In the simulations we use $r=10$,$000$ MC replicates. Note that power computation for other benchmarks follows from the same algorithm by plugging in the respective test statistic.
Input: A joint distribution ${\displaystyle F_{XY}}$, the sample size $n$, the number of MC replicates $r$, and the type $1$ error level $a$.
Output: The power $ß$ of Mgc.
1:	function MGCPower(${\displaystyle F_{XY}}$, $n$, $r$, $a$)
2:	for $t:=1,\mathrm{\dots },r$ do
3:	for $i:=[n]$ do
4:	${\displaystyle x_i^0\stackrel{iid}{\sim }{F}_X,y_i^0\stackrel{iid}{\sim }{F}_Y}$	sample from null
5:	${\displaystyle (x_i^1,y_i^1)\stackrel{iid}{\sim }{F}_{XY},}$	sample from alternative
6:	end for
7:	for $i,j:=1,\mathrm{\dots },n$ do
8:	${\displaystyle a_{ij}^0={\delta }_x(x_i^0,x_j^0)}$, ${\displaystyle b_{ij}^0={\delta }_y(y_i^0,y_j^0)}$	pairwise distances under the null
9:	${\displaystyle a_{ij}^1={\delta }_x(x_i^1,x_j^1)}$, ${\displaystyle b_{ij}^1={\delta }_y(y_i^1,y_j^1)}$	pairwise distances under the alternative
10:	end for
11:	${\displaystyle c_0^{\ast }[t]=\mathrm{M}\mathrm{G}\mathrm{C}\mathrm{S}\mathrm{A}\mathrm{M}\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{S}\mathrm{T}\mathrm{A}\mathrm{T}(A^0,B^0)}$	Mgc statistic under the null
12:	${\displaystyle c_1^{\ast }[t]=\mathrm{M}\mathrm{G}\mathrm{C}\mathrm{S}\mathrm{A}\mathrm{M}\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{S}\mathrm{T}\mathrm{A}\mathrm{T}(A^1,B^1)}$	Mgc statistic under the alternative
13:	end for
14:	${\displaystyle {\omega }_{\alpha }\leftarrow {\mathrm{C}\mathrm{D}\mathrm{F}}_{1-\alpha }(c_0^{\ast }[t],t\in [r])}$	the critical value of Mgc under the null
15:	${\displaystyle \beta \leftarrow \sum _{t=1}^r(c_1^{\ast }[t]>{\omega }_{\alpha })/r}$	compute power by the alternative distribution
16:	end function