Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time~\cite{Bo90},\cite{YBFT}. give restricted space algorithms for these problems proving  the following results:#R##N##R##N#\begin{itemize}#R##N#\item Isomorphism for bounded tree distance width graphs is in  \Log\ and thus complete for the class.  also show that for this kind of graphs a canon can be computed within logspace.#R##N#\item For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e.\  considering only isomorphisms mapping bags in one decomposition blockwise onto bags in the other decomposition)#R##N#is in \Log.#R##N#\item For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in \LogCFL.#R##N#\item As a corollary the isomorphism problem for bounded treewidth graphs is in \LogCFL. This improves the known \TCone\  upper bound for the problem given by Grohe and Verbitsky~\cite{GV06}.  #R##N#\end{itemize}
['Bireswar Das', 'Jacobo Torán', 'Fabian Wagner']
I am writing a research paper on a idea Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs.
[{"from": "human", "value": "I am writing a research paper on a idea Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time~\\cite{Bo90},\\cite{YBFT}. give restricted space algorithms for these problems proving  the following results:#R##N##R##N#\\begin{itemize}#R##N#\\item Isomorphism for bounded tree distance width graphs is in  \\Log\\ and thus complete for the class.  also show that for this kind of graphs a canon can be computed within logspace.#R##N#\\item For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e.\\  considering only isomorphisms mapping bags in one decomposition blockwise onto bags in the other decomposition)#R##N#is in \\Log.#R##N#\\item For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in \\LogCFL.#R##N#\\item As a corollary the isomorphism problem for bounded treewidth graphs is in \\LogCFL. This improves the known \\TCone\\  upper bound for the problem given by Grohe and Verbitsky~\\cite{GV06}.  #R##N#\\end{itemize}"}]