\begin{tikzpicture}[x=1cm,y=1cm,every node/.style={font=\small}] \path[use as bounding box] (0,-.65) rectangle (14.7,7.25); \node[anchor=west] at (.1,7) {(a)}; \node at (2.1,7) {\(M\), with \(n=5\)}; \foreach \j in {0,...,4} \node[font=\footnotesize] at ({.9+.5*\j},6.55) {\(\j\)}; \foreach \i in {0,...,4} \node[font=\footnotesize] at (.38,{6.12-.5*\i}) {\(\i\)}; \foreach \i/\bits in {0/{0,0,0,0,0},1/{0,0,0,0,1},2/{0,1,1,0,0},3/{1,1,0,0,1},4/{1,1,0,1,1}} { \foreach \b [count=\j from 0] in \bits { \ifnum\b=1 \fill[black!12] ({.65+.5*\j},{5.87-.5*\i}) rectangle ++(.5,.5); \fi \draw[black!35] ({.65+.5*\j},{5.87-.5*\i}) rectangle ++(.5,.5); \node at ({.9+.5*\j},{6.12-.5*\i}) {\(\b\)}; } } \node[font=\footnotesize] at (3.45,6.55) {$R_i$}; \foreach \i in {0,...,4}{\node[font=\footnotesize] at (3.45,{6.12-.5*\i}) {$\i$};} \node[font=\footnotesize] at (.38,3.55) {$Q_j$}; \foreach \j/\q in {0/2,1/3,2/1,3/1,4/3}{\node[font=\footnotesize] at ({.9+.5*\j},3.55) {$\q$};} \node[font=\footnotesize] at (1.9,3.0) {\(\sum_{i,j}M_{ij}=10\)}; \draw[-{Latex},thick] (3.8,5.6)--(4.65,5.6) node[midway,above,font=\footnotesize] {decode}; \node[anchor=west] at (4.55,7) {(b)}; \node at (9.15,7) {A representative path}; \draw[very thick,blue!70!black] (5.2,5.6)--(7.7,5.6); \draw[very thick,orange!85!black] (7.7,5.6)--(10.2,5.6); \draw[thick] (10.2,5.6)--(12.7,5.6); \node[circle,draw,fill=white,inner sep=2.8pt] at (5.2,5.6) {}; \foreach \x in {7.7,10.2,12.7} \node[circle,draw,fill=black,inner sep=2.8pt] at (\x,5.6) {}; \foreach \x/\v/\b in {5.2/{v_1}/{M_{11}=0},7.7/{x_{14}}/{M_{14}=1},10.2/{x_{41}}/{M_{41}=1},12.7/{v_4}/{M_{44}=1}}{ \node at (\x,6.05) {\(\v\)}; \node[font=\footnotesize] at (\x,5.08) {\(\b\)}; } \node[font=\footnotesize,text=black] at (6.45,5.86) {\(T_{14}\)}; \node[font=\footnotesize,text=black] at (8.95,5.86) {\(E_{14}\)}; \node[align=center,text width=9cm,font=\footnotesize] at (9.1,4.12) {Filled vertices are landmarks. The matrix selects \(v_2,v_4\)\\ and eight internal vertices. Both histograms use all ten.}; \node[anchor=west] at (.1,2.40) {(c)}; \node[text=black] at (3.55,2.40) {\(T_{14}=v_1x_{14}\)}; \node[anchor=west] at (7.05,2.40) {(d)}; \node[text=black] at (10.5,2.40) {\(E_{14}=x_{14}x_{41}\)}; \foreach \ox/\col/\vals in {1.2/{blue!70!black}/{1,1,3,3,2,0},8.15/{orange!85!black}/{2,1,2,3,1,1}}{ \begin{scope}[shift={(\ox,.20)}] \draw[-{Latex}] (-.42,0)--(4.1,0); \draw[-{Latex}] (-.42,0)--(-.42,1.75); \node[font=\footnotesize,rotate=90] at (-1.0,.85) {count}; \node[font=\footnotesize,anchor=west] at (3.75,-.3) {distance}; \foreach \h in {1,2,3}{ \draw (-.48,{.45*\h})--(-.36,{.45*\h}); \node[left,font=\footnotesize] at (-.5,{.45*\h}) {\(\h\)}; } \foreach \v [count=\j from 0] in \vals { \fill[\col!75] ({.7*\j-.2},0) rectangle ({.7*\j+.2},{.45*\v}); \node[above,font=\footnotesize] at ({.7*\j},{.45*\v+.03}) {\(\v\)}; \node[below,font=\footnotesize] at ({.7*\j},-.03) {\(\j\)}; } \end{scope} } \node[font=\footnotesize] at (3.3,-.45) {No landmark is at distance five.}; \node[font=\footnotesize] at (10.25,-.45) {One landmark is at distance five.}; \end{tikzpicture}