\begin{tikzpicture}[x=1cm,y=1cm,font=\small,>=Latex, pathvertex/.style={circle,draw=black,fill=white,inner sep=0pt,minimum size=3.8pt}] \node[anchor=west] at (-.2,.65) {(a) Landmark bits and counts}; \node[anchor=west] at (5.8,.65) {(b) Cell $\longrightarrow$ edge $\longrightarrow$ record}; \foreach \i in {0,...,5}{ \node[left] at (-.12,{-.45*\i-.225}) {$\i$}; \node[above] at ({.45*\i+.225},.12) {$\i$}; \foreach \j in {0,...,5}{ \pgfmathtruncatemacro{\bit}{\i+\j>=6} \ifnum\bit=1\fill[black!10] ({.45*\j},{-.45*\i}) rectangle ++(.45,-.45);\fi \draw[black!25] ({.45*\j},{-.45*\i}) rectangle ++(.45,-.45); \node at ({.45*\j+.225},{-.45*\i-.225}) {$\bit$}; } \pgfmathtruncatemacro{\diagbit}{2*\i>=6} \pgfmathtruncatemacro{\derived}{\i-2*\diagbit} \node at (3.3,{-.45*\i-.225}) {$\i$}; \node at (4.1,{-.45*\i-.225}) {$\diagbit$}; \node at (4.9,{-.45*\i-.225}) {$\derived$}; \draw[black!70] ({.45*\i},{-.45*\i}) rectangle ++(.45,-.45); } \foreach \x/\l in {3.3/{t_i},4.1/{\alpha_i},4.9/{r_i}}{ \node[above] at (\x,.12) {$\l$}; } \draw[blue!75!black,line width=1.3pt] (1.8,0) rectangle ++(.45,-.45); \draw[orange!85!black,line width=1.3pt] (.9,-.45) rectangle ++(.45,-.45); \node at (2.45,-3.18) {$M_{ij}=\mathbf1_{\{i+j\ge6\}}$}; \node[anchor=north west,text width=5.2cm,align=left] at (-.2,-3.65) {Diagonal entries give $\alpha_i$.\\[3pt] Off-diagonal entries give $\eta_{ij}$.\\[3pt] Outlined cells: $(0,4)$ and $(1,2)$.}; \draw[blue!75!black,line width=.8pt,rounded corners=2pt] (5.8,.1) rectangle (14.35,-2.35); \node[anchor=west] at (6.0,-.2) {Cell $(0,4)$: $M_{04}=\eta_{04}=0$}; \draw (6.4,-.87)--(8.65,-.87); \draw[blue!75!black,line width=1.8pt] (6.4,-.87)--(7.525,-.87); \foreach \x/\lab in {6.4/{v_0},7.525/{w_{04}},8.65/{v_4}}{ \node[pathvertex] at (\x,-.87) {}; \node[below=3pt] at (\x,-.87) {$\lab$}; } \node[above=3pt] at (6.9625,-.87) {$e_{04}$}; \node[anchor=west] at (9.35,-.88) {$e_{04}=v_0w_{04}$}; \node[anchor=west,align=left] at (6.0,-1.79) {$\Gamma(0,4)=(\alpha_0+\eta_{04},\,t_0+\alpha_4,\,r_4)$\\[4pt] $\phantom{\Gamma(0,4)}=(0+0,\,0+1,\,2)=(0,1,2)$}; \draw[orange!85!black,line width=.8pt,rounded corners=2pt] (5.8,-2.65) rectangle (14.35,-5.1); \node[anchor=west] at (6.0,-2.95) {Cell $(1,2)$: $M_{12}=\eta_{12}=0$}; \draw (6.4,-3.62)--(8.65,-3.62); \draw[orange!85!black,line width=1.8pt] (6.4,-3.62)--(7.525,-3.62); \foreach \x/\lab in {6.4/{v_1},7.525/{w_{12}},8.65/{v_2}}{ \node[pathvertex] at (\x,-3.62) {}; \node[below=3pt] at (\x,-3.62) {$\lab$}; } \node[above=3pt] at (6.9625,-3.62) {$e_{12}$}; \node[anchor=west] at (9.35,-3.63) {$e_{12}=v_1w_{12}$}; \node[anchor=west,align=left] at (6.0,-4.54) {$\Gamma(1,2)=(\alpha_1+\eta_{12},\,t_1+\alpha_2,\,r_2)$\\[4pt] $\phantom{\Gamma(1,2)}=(0+0,\,1+0,\,2)=(0,1,2)$}; \node[draw,inner sep=5pt] at (10.075,-5.64) {$\Gamma(0,4)=\Gamma(1,2)=(0,1,2)$}; \end{tikzpicture}