Algorithm 6  Automatic FHE parameterisation by source and cost discovery over multi-directed graphs.

functionautoHE(g, n, $\mathit{concern}$)

for $i\mathrm{in}n$do                        ▹ Label graph sources and costs

$\mathrm{autoHE\_discover}(g,i,i,\mathit{concern},0)$

$r\leftarrow \mathrm{tuple}(\mathrm{dictionary}\left(\right),\mathrm{list}\left(\right))$                  ▹ Group representation

for $i\mathrm{in}n$do                      ▹ Assign + merge groups from labels

if $r\left[0\right].\mathrm{get}\left(i\right)\mathrm{is}\mathit{None}$ then

$r\left[0\right]\left[i\right]\leftarrow \mathrm{len}\left(r\right[1\left]\right)$

$r\left[1\right].\mathrm{append}\left(0\right)$

for $j\mathrm{in}g.\mathrm{nodes}\left(\right)$ do

$\mathit{src}\leftarrow j\left[1\right]\left[″\mathrm{sources}″\right]$

if $i\mathrm{in}\mathit{src}$ then

for $k\mathrm{in}\mathit{src}$ do

$r\left[0\right]\left[k\right]\leftarrow r\left[0\right]\left[i\right]$

if $\mathit{src}\left[k\right]>r\left[1\right]\left[r\right[0\left]\right[i\left]\right]$ then

$r\left[1\right]\left[r\right[0\left]\right[i\left]\right]=\mathit{src}\left[k\right]$

return r