PhD

The LaTeX sources of my Ph.D. thesis
git clone https://esimon.eu/repos/PhD.git
Log | Files | Refs | README | LICENSE

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}