wl.tex (1101B)
1 \begin{frame}{Weisfeiler--Leman Isomorphism Test}% 2 \begin{columns}% 3 \begin{column}{55mm}% 4 \centering% 5 \input{mainmatter/graph/isomorphism.tex} 6 \end{column}% 7 \begin{column}{75mm}% 8 \begin{algorithmic} 9 \Function{Weisfeiler--Leman}{} 10 \FunctionInputs{} \(G=(V, E)\) graph 11 \FunctionInputs*{} \(k\) dimensionality 12 \FunctionOutput{} \(\chi_\infty\) coloring of \(k\)-tuples 13 \State 14 \State \(\chi_0(\vctr{x}) \gets \operatorname{iso}(\vctr{x}) \quad \forall \vctr{x}\in V^k\) 15 \For{\(\ell=1,2,\dotsc\)} 16 \State \(\symfrak{I}_\ell\gets \text{new color index}\) 17 \ForAll{\(\vctr{x}\in V^k\)} 18 \State \(c_\ell(\vctr{x}) \gets \lMultiBrace\,\chi_{\ell-1}(\vctr{y}) \middlerel{|} \vctr{y}\in\gfneighbors^k(\vctr{x})\,\rMultiBrace\) 19 \State \(\chi_\ell(\vctr{x}) \gets (\chi_{\ell-1}(\vctr{x}), c_\ell(\vctr{x})) \text{ in } \symfrak{I}_\ell\) 20 \EndFor 21 \EndFor 22 \State \textbf{until} \(\chi_\ell = \chi_{\ell-1}\) 23 \State \Output \(\chi_\ell\) 24 \EndFunction 25 \end{algorithmic} 26 \end{column}% 27 \end{columns}% 28 \end{frame}