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fig_movekernel.tex
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\begin{figure}[h!t]
\begin{center}
\begin{tikzpicture}[thick]
\begin{scope}[scale=0.8]
\node at (-1,2) {a)};
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node [draw, circle, dashed, black!50] at (\x, \y) {};
}
}
\foreach \x in {0,...,4}{
\foreach \y in {0,...,4}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x+1,\y);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,3}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x,\y + 1);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node(\x\y) [draw = black!50, dashed, circle,fill=white] at (\x, \y) {};
}
}
\node at (3,2){$v_0$};
\node at (2,2){$v_1$};
\node at (1,2){$v_2$};
\node at (1,3){$v_3$};
\node[draw = black, circle] at (3,2){};
\node[draw = red, circle] at (2,2){};
\node[draw = green!50!black, circle] at (4,2){};
\node[draw = blue, circle] at (3,3){};
\node[draw = purple, circle] at (3,1){};
\end{scope}
\begin{scope}[xshift=5cm, scale=0.8]
\node at (-1,2) {b)};
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node [draw, circle, dashed, black!50] at (\x, \y) {};
}
}
\foreach \x in {0,...,4}{
\foreach \y in {0,...,4}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x+1,\y);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,3}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x,\y + 1);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node(\x\y) [draw = black!50, dashed, circle,fill=white] at (\x, \y) {};
}
}
\node at (3,2){$v_0$};
\node at (2,2){$v_1$};
\node at (1,2){$v_2$};
\node at (1,3){$v_3$};
\draw
(0.5,2) -- (3,4.5) -- (5.5,2) -- (3,-0.5) -- (0.5,2);
\path[->,>=stealth']
(31) edge (21)
(32) edge (22)
(33) edge (23)
(42) edge (32)
(22) edge (12);
\node[draw = black, circle] at (2,2){};
\node[draw = red, circle] at (1,2){};
\node[draw = green!50!black, circle] at (3,2){};
\node[draw = blue, circle] at (2,3){};
\node[draw = purple, circle] at (2,1){};
\end{scope}
\begin{scope}[scale=0.8, yshift=-6cm]
\node at (-1,2) {c)};
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node [draw, circle, dashed, black!50] at (\x, \y) {};
}
}
\foreach \x in {0,...,4}{
\foreach \y in {0,...,4}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x+1,\y);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,3}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x,\y + 1);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node(\x\y) [draw = black!50, dashed, circle,fill=white] at (\x, \y) {};
}
}
\node at (3,2){$v_0$};
\node at (2,2){$v_1$};
\node at (1,2){$v_2$};
\node at (1,3){$v_3$};
\draw
(-0.5,2) -- (2,4.5) -- (4.5,2) -- (2,-0.5) -- (-0.5,2);
\path[->,>=stealth']
(21) edge (11)
(22) edge (12)
(23) edge (13)
(32) edge (22)
(12) edge (02);
\node[draw = black, circle] at (1,2){};
\node[draw = red, circle] at (0,2){};
\node[draw = green!50!black, circle] at (2,2){};
\node[draw = blue, circle] at (1,3){};
\node[draw = purple, circle] at (1,1){};
\end{scope}
\begin{scope}[xshift=5cm, scale=0.8,yshift=-6cm]
\node at (-1,2) {d)};
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node [draw, circle, dashed, black!50] at (\x, \y) {};
}
}
\foreach \x in {0,...,4}{
\foreach \y in {0,...,4}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x+1,\y);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,3}{
\path[-]
(\x,\y) edge[dashed, black!50] (\x,\y + 1);
}
}
\foreach \x in {0,...,5}{
\foreach \y in {0,...,4}{
\node(\x\y) [draw = black!50, dashed, circle,fill=white] at (\x, \y) {};
}
}
\node at (3,2){$v_0$};
\node at (2,2){$v_1$};
\node at (1,2){$v_2$};
\node at (1,3){$v_3$};
\draw
(-1.5,2) -- (1,4.5) -- (3.5,2) -- (1,-0.5) -- (-1.5,2);
\path[->,>=stealth']
(11) edge (12)
(12) edge (13)
(13) edge (14)
(22) edge (23)
(02) edge (03);
\node[draw = black, circle] at (1,3){};
\node[draw = red, circle] at (0,3){};
\node[draw = green!50!black, circle] at (2,3){};
\node[draw = blue, circle] at (1,4){};
\node[draw = purple, circle] at (1,2){};
\end{scope}
\end{tikzpicture}
\end{center}
\caption{Illustration of the translation of a small indexing kernel using translations in each induced subgraph. Kernel is initialized around $v_0$ (a), then moved left around $v_1$ (b) using the induced subgraph around $v_0$, then moved left again around $v_2$ (c) using the induced subgraph around $v_1$ then moved up around $v_3$ (d) using the induced subgraph around $v_2$. At the end of the process, the kernel has been localized around each vertex in the graph.}
\label{fig:movekernel}
\end{figure}