Add figures
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@ -2,3 +2,6 @@ SRC=report.tex
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all:
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latexmk -pdf $(SRC)
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upload:
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scp report.pdf www.tobast:~/tobast.fr/public_html/m1/internship.pdf
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@ -332,7 +332,7 @@ subgraph isomorphism~\cite{ullmann1976algorithm}, a well-known algorithm for
|
|||
this problem, that uses the specificities of the graph to be a little faster.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Signatures}
|
||||
\section{Signatures}\label{sec:signatures}
|
||||
|
||||
The signature is computed as a simple hash of the element, and is defined for
|
||||
every type of expression and circuit. It could probably be enhanced with a bit
|
||||
|
|
@ -573,12 +573,14 @@ The refining function is detailed in Figure~\ref{alg:ullmann_refine}.
|
|||
\While{changes during last run}
|
||||
\For{each needle vertex $i$}
|
||||
\For{each haystack vertex $j$}
|
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\If{\lstc{perm[i][j]} $=$ 1}
|
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\For{each neighbour $k$ of $i$ in needle}
|
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\If{\lstc{perm[k] & haystack\_adjacency[j]}
|
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$= 0$}
|
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\State{} \lstc{perm[i][j]} $\gets 0$
|
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\EndIf{}
|
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\EndFor{}
|
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\EndIf{}
|
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\EndFor{}
|
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\EndFor{}
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\EndWhile{}
|
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|
|
@ -738,7 +740,24 @@ certain configurations, and a few other such cases that could be fixed.
|
|||
|
||||
\todo{More corner cases}
|
||||
|
||||
\todo{Corner case: io pins, io adjacency}
|
||||
\paragraph{I/O pins.} In Section~\ref{sec:signatures}, we introduce a term
|
||||
named \emph{IO adjacency} in the signatures of order higher than $0$. This is
|
||||
because some sub-circuits can be told apart from their signatures only through
|
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this information, and the absence of this term slowed down considerably the
|
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program before its introduction. This is the case for instance in circuits like
|
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the one in Figure~\ref{fig:io_adj_term}.
|
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|
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\begin{figure}
|
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\centering
|
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\includegraphics[width=0.8\textwidth]{img/io_adj_term.png}
|
||||
\caption{A case where the I/O adjacency term is necessary}\label{fig:io_adj_term}
|
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\end{figure}
|
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|
||||
Here, if the adjacent input and output pins of Group are not taken into account
|
||||
in the signatures of the gates (A, B, C, D, E), there is apparently no way to
|
||||
differentiate A from B and C from D. The example can of course be pushed
|
||||
further to way more dramatic cases, for instance with a (binary) tree of
|
||||
circuits in the same shape as above.
|
||||
|
||||
\paragraph{Split/merge trees.} A common pattern that tends to slow down the
|
||||
algorithm is split/merge trees. Those patterns occur when one wants to merge
|
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|
|
@ -763,7 +782,15 @@ interchangeable: indeed, when checking for an equality between two such trees,
|
|||
it does not matter which node is the left one; but once this is fixed, the
|
||||
nodes on the layer below cannot be freely exchanged.
|
||||
|
||||
\todo{Figure describing the problem}
|
||||
For instance, in Figure~\ref{fig:split_tree}, the orange borders are the
|
||||
boundaries of what can be taken into account for the signatures of order $1$ of
|
||||
the gates marked with a red dot. Thus, those signatures are exactly the same.
|
||||
|
||||
\begin{figure}
|
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\centering
|
||||
\includegraphics[width=0.8\textwidth]{img/tree_local.png}
|
||||
\caption{Case of a split (or merge) tree}\label{fig:split_tree}
|
||||
\end{figure}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
|
|
|||
Loading…
Reference in New Issue