Fehlende Dateien (Bilder) eingecheckt.

diff --git a/.gitignore b/.gitignore
new file mode 100644 (file)
index 0000000..52d1d46
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,9 @@
+*.pdf
+*.ps
+.*.swp
+diplomarbeit.aux
+diplomarbeit.bbl
+diplomarbeit.blg
+diplomarbeit.log
+diplomarbeit.toc
+quellen/

diff --git a/diplomarbeit.tex b/diplomarbeit.tex
index c3bc372..c5d64e5 100644 (file)
--- a/diplomarbeit.tex
+++ b/diplomarbeit.tex
@@ -567,15 +567,6 @@ $\frac{1}{4} n \log(n) \log(n+1) = \mathcal{O}\left(n (log (n))^2\right)$
 Komparatoren, die in $\frac{1}{2} \log(n) \log(n+1) = \mathcal{O}(\log(n))$
 Schichten angeordnet sind.
 
 Komparatoren, die in $\frac{1}{2} \log(n) \log(n+1) = \mathcal{O}(\log(n))$
 Schichten angeordnet sind.
 

-%\begin{figure}
-%\begin{center}
-%\includegraphics[viewport=115 491 372 782,width=7.5cm]{images/sn-rekursiver-aufbau.pdf}
-%\end{center}
-%\caption{Rekursiver Aufbau von $S(n)$: Es besteht aus zwei Instanzen von
-%$S(n/2)$ und dem Mischer $M(n)$.}
-%\label{fig:bms_rekursiver_aufbau}
-%\end{figure}
-

 \subsection{Das Odd-Even-Mergesort-Netzwerk}
 
 Obwohl der Name ähnlich klingt, haben das \emph{Odd-Even-Mergesort-Netzwerk}
 \subsection{Das Odd-Even-Mergesort-Netzwerk}
 
 Obwohl der Name ähnlich klingt, haben das \emph{Odd-Even-Mergesort-Netzwerk}


@@ -1660,7 +1651,7 @@ selbst erzeugen kann.
 Wie in Abschnitt~\ref{sect:anzahl_schnittmuster} beschrieben, ist die Anzahl
 der \emph{unterschiedlichen} Schnittmuster und damit die Anzahl der Nachfolger
 sehr groß. Bei den untersuchten 16-Sortiernetzwerken lag die Anzahl der
 Wie in Abschnitt~\ref{sect:anzahl_schnittmuster} beschrieben, ist die Anzahl
 der \emph{unterschiedlichen} Schnittmuster und damit die Anzahl der Nachfolger
 sehr groß. Bei den untersuchten 16-Sortiernetzwerken lag die Anzahl der

-Nachfolger zwar noch unter 20000, bei den untersuchten 32-Sortiernetzwerken
+Nachfolger zwar noch unter 20.000, bei den untersuchten 32-Sortiernetzwerken

 wurden jedoch bereits bis zu $2,6 \cdot 10^8$ unterschiedliche Schnittmuster
 geschätzt.
 
 wurden jedoch bereits bis zu $2,6 \cdot 10^8$ unterschiedliche Schnittmuster
 geschätzt.
 


@@ -1683,6 +1674,13 @@ für n Iterationen
 gib Netzwerk zurück
 \end{verbatim}
 
 gib Netzwerk zurück
 \end{verbatim}
 

+Die Abbildungen~\ref{fig:markov-comparators-12},
+\ref{fig:markov-comparators-14}, \ref{fig:markov-comparators-12},
+\ref{fig:markov-comparators-16} und~\ref{fig:markov-comparators-18} zeigen die
+Anzahl der Komparatoren der Sortiernetzwerke, die \textsc{SN-Markov} auf
+seinem zufälligen Pfad durchläuft. Ausserdem eingezeichnet ist eine
+\emph{Gamma-Verteilung}.
+

 \begin{figure}
   \begin{center}
   \includegraphics[viewport=0 0 425 262,width=15cm]{images/markov-cycles-16.pdf}
 \begin{figure}
   \begin{center}
   \includegraphics[viewport=0 0 425 262,width=15cm]{images/markov-cycles-16.pdf}

diff --git a/images/16-e1-bitonic-1296542566.tex b/images/16-e1-bitonic-1296542566.tex
new file mode 100644 (file)
index 0000000..0d1ebc5
--- /dev/null
+++ b/images/16-e1-bitonic-1296542566.tex
@@ -0,0 +1,286 @@
+\begin{tikzpicture}[auto]
+\node[vertex] (v0) at (0.85,0.00) {};
+\node[vertex] (v1) at (0.85,8.86) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.11,0.68) {};
+\node[vertex] (v3) at (1.11,7.50) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v4) at (1.36,1.36) {};
+\node[vertex] (v5) at (1.36,10.23) {};
+\path[comp] (v4) -- (v5);
+
+\node[vertex] (v6) at (1.62,2.05) {};
+\node[vertex] (v7) at (1.62,3.41) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v8) at (1.88,2.73) {};
+\node[vertex] (v9) at (1.88,4.09) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v10) at (1.62,4.77) {};
+\node[vertex] (v11) at (1.62,5.45) {};
+\path[comp] (v10) -- (v11);
+
+\node[vertex] (v12) at (1.62,6.14) {};
+\node[vertex] (v13) at (1.62,6.82) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (1.11,8.18) {};
+\node[vertex] (v15) at (1.11,9.55) {};
+\path[comp] (v14) -- (v15);
+
+\node[vertex] (v16) at (2.73,0.00) {};
+\node[vertex] (v17) at (2.73,1.36) {};
+\path[comp] (v16) -- (v17);
+
+\node[vertex] (v18) at (2.98,0.68) {};
+\node[vertex] (v19) at (2.98,8.18) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (2.73,2.05) {};
+\node[vertex] (v21) at (2.73,2.73) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v22) at (2.73,3.41) {};
+\node[vertex] (v23) at (2.73,4.09) {};
+\path[comp] (v22) -- (v23);
+
+\node[vertex] (v24) at (2.73,4.77) {};
+\node[vertex] (v25) at (2.73,6.14) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (3.24,5.45) {};
+\node[vertex] (v27) at (3.24,6.82) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v28) at (2.73,7.50) {};
+\node[vertex] (v29) at (2.73,9.55) {};
+\path[comp] (v28) -- (v29);
+
+\node[vertex] (v30) at (2.98,8.86) {};
+\node[vertex] (v31) at (2.98,10.23) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (4.09,0.00) {};
+\node[vertex] (v33) at (4.09,0.68) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (4.09,1.36) {};
+\node[vertex] (v35) at (4.09,8.86) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (4.35,2.73) {};
+\node[vertex] (v37) at (4.35,3.41) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (4.35,5.45) {};
+\node[vertex] (v39) at (4.35,6.14) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (4.35,7.50) {};
+\node[vertex] (v41) at (4.35,8.18) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v42) at (5.20,1.36) {};
+\node[vertex] (v43) at (5.20,9.55) {};
+\path[comp] (v42) -- (v43);
+
+\node[vertex] (v44) at (5.45,2.05) {};
+\node[vertex] (v45) at (5.45,5.45) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (5.71,2.73) {};
+\node[vertex] (v47) at (5.71,4.77) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (5.97,3.41) {};
+\node[vertex] (v49) at (5.97,6.82) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (6.22,4.09) {};
+\node[vertex] (v51) at (6.22,6.14) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (5.45,7.50) {};
+\node[vertex] (v53) at (5.45,10.23) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (5.71,8.18) {};
+\node[vertex] (v55) at (5.71,8.86) {};
+\path[comp] (v54) -- (v55);
+
+\node[vertex] (v56) at (7.07,0.68) {};
+\node[vertex] (v57) at (7.07,8.18) {};
+\path[comp] (v56) -- (v57);
+
+\node[vertex] (v58) at (7.33,1.36) {};
+\node[vertex] (v59) at (7.33,7.50) {};
+\path[comp] (v58) -- (v59);
+
+\node[vertex] (v60) at (7.59,2.05) {};
+\node[vertex] (v61) at (7.59,2.73) {};
+\path[comp] (v60) -- (v61);
+
+\node[vertex] (v62) at (7.59,3.41) {};
+\node[vertex] (v63) at (7.59,5.45) {};
+\path[comp] (v62) -- (v63);
+
+\node[vertex] (v64) at (7.84,4.09) {};
+\node[vertex] (v65) at (7.84,4.77) {};
+\path[comp] (v64) -- (v65);
+
+\node[vertex] (v66) at (7.59,6.14) {};
+\node[vertex] (v67) at (7.59,6.82) {};
+\path[comp] (v66) -- (v67);
+
+\node[vertex] (v68) at (7.07,9.55) {};
+\node[vertex] (v69) at (7.07,10.23) {};
+\path[comp] (v68) -- (v69);
+
+\node[vertex] (v70) at (8.69,0.68) {};
+\node[vertex] (v71) at (8.69,1.36) {};
+\path[comp] (v70) -- (v71);
+
+\node[vertex] (v72) at (8.69,3.41) {};
+\node[vertex] (v73) at (8.69,4.09) {};
+\path[comp] (v72) -- (v73);
+
+\node[vertex] (v74) at (8.69,4.77) {};
+\node[vertex] (v75) at (8.69,5.45) {};
+\path[comp] (v74) -- (v75);
+
+\node[vertex] (v76) at (8.69,7.50) {};
+\node[vertex] (v77) at (8.69,8.18) {};
+\path[comp] (v76) -- (v77);
+
+\node[vertex] (v78) at (8.69,8.86) {};
+\node[vertex] (v79) at (8.69,9.55) {};
+\path[comp] (v78) -- (v79);
+
+\node[vertex] (v80) at (9.55,0.00) {};
+\node[vertex] (v81) at (9.55,3.41) {};
+\path[comp] (v80) -- (v81);
+
+\node[vertex] (v82) at (9.80,0.68) {};
+\node[vertex] (v83) at (9.80,2.73) {};
+\path[comp] (v82) -- (v83);
+
+\node[vertex] (v84) at (10.06,1.36) {};
+\node[vertex] (v85) at (10.06,2.05) {};
+\path[comp] (v84) -- (v85);
+
+\node[vertex] (v86) at (9.55,4.09) {};
+\node[vertex] (v87) at (9.55,10.23) {};
+\path[comp] (v86) -- (v87);
+
+\node[vertex] (v88) at (9.80,4.77) {};
+\node[vertex] (v89) at (9.80,9.55) {};
+\path[comp] (v88) -- (v89);
+
+\node[vertex] (v90) at (10.06,5.45) {};
+\node[vertex] (v91) at (10.06,8.86) {};
+\path[comp] (v90) -- (v91);
+
+\node[vertex] (v92) at (10.31,6.14) {};
+\node[vertex] (v93) at (10.31,8.18) {};
+\path[comp] (v92) -- (v93);
+
+\node[vertex] (v94) at (10.57,6.82) {};
+\node[vertex] (v95) at (10.57,7.50) {};
+\path[comp] (v94) -- (v95);
+
+\node[vertex] (v96) at (11.42,0.00) {};
+\node[vertex] (v97) at (11.42,1.36) {};
+\path[comp] (v96) -- (v97);
+
+\node[vertex] (v98) at (11.42,2.05) {};
+\node[vertex] (v99) at (11.42,4.77) {};
+\path[comp] (v98) -- (v99);
+
+\node[vertex] (v100) at (11.68,2.73) {};
+\node[vertex] (v101) at (11.68,5.45) {};
+\path[comp] (v100) -- (v101);
+
+\node[vertex] (v102) at (11.93,3.41) {};
+\node[vertex] (v103) at (11.93,6.14) {};
+\path[comp] (v102) -- (v103);
+
+\node[vertex] (v104) at (12.19,4.09) {};
+\node[vertex] (v105) at (12.19,6.82) {};
+\path[comp] (v104) -- (v105);
+
+\node[vertex] (v106) at (11.42,7.50) {};
+\node[vertex] (v107) at (11.42,10.23) {};
+\path[comp] (v106) -- (v107);
+
+\node[vertex] (v108) at (11.68,8.18) {};
+\node[vertex] (v109) at (11.68,9.55) {};
+\path[comp] (v108) -- (v109);
+
+\node[vertex] (v110) at (13.04,0.68) {};
+\node[vertex] (v111) at (13.04,1.36) {};
+\path[comp] (v110) -- (v111);
+
+\node[vertex] (v112) at (13.04,2.05) {};
+\node[vertex] (v113) at (13.04,3.41) {};
+\path[comp] (v112) -- (v113);
+
+\node[vertex] (v114) at (13.30,2.73) {};
+\node[vertex] (v115) at (13.30,4.09) {};
+\path[comp] (v114) -- (v115);
+
+\node[vertex] (v116) at (13.04,4.77) {};
+\node[vertex] (v117) at (13.04,6.14) {};
+\path[comp] (v116) -- (v117);
+
+\node[vertex] (v118) at (13.30,5.45) {};
+\node[vertex] (v119) at (13.30,6.82) {};
+\path[comp] (v118) -- (v119);
+
+\node[vertex] (v120) at (13.04,7.50) {};
+\node[vertex] (v121) at (13.04,8.86) {};
+\path[comp] (v120) -- (v121);
+
+\node[vertex] (v122) at (14.15,2.05) {};
+\node[vertex] (v123) at (14.15,2.73) {};
+\path[comp] (v122) -- (v123);
+
+\node[vertex] (v124) at (14.15,3.41) {};
+\node[vertex] (v125) at (14.15,4.09) {};
+\path[comp] (v124) -- (v125);
+
+\node[vertex] (v126) at (14.15,4.77) {};
+\node[vertex] (v127) at (14.15,5.45) {};
+\path[comp] (v126) -- (v127);
+
+\node[vertex] (v128) at (14.15,6.14) {};
+\node[vertex] (v129) at (14.15,6.82) {};
+\path[comp] (v128) -- (v129);
+
+\node[vertex] (v130) at (14.15,7.50) {};
+\node[vertex] (v131) at (14.15,8.18) {};
+\path[comp] (v130) -- (v131);
+
+\node[vertex] (v132) at (14.15,8.86) {};
+\node[vertex] (v133) at (14.15,9.55) {};
+\path[comp] (v132) -- (v133);
+
+\path[edge] (0,0.00) -- (15.00,0.00);
+\path[edge] (0,0.68) -- (15.00,0.68);
+\path[edge] (0,1.36) -- (15.00,1.36);
+\path[edge] (0,2.05) -- (15.00,2.05);
+\path[edge] (0,2.73) -- (15.00,2.73);
+\path[edge] (0,3.41) -- (15.00,3.41);
+\path[edge] (0,4.09) -- (15.00,4.09);
+\path[edge] (0,4.77) -- (15.00,4.77);
+\path[edge] (0,5.45) -- (15.00,5.45);
+\path[edge] (0,6.14) -- (15.00,6.14);
+\path[edge] (0,6.82) -- (15.00,6.82);
+\path[edge] (0,7.50) -- (15.00,7.50);
+\path[edge] (0,8.18) -- (15.00,8.18);
+\path[edge] (0,8.86) -- (15.00,8.86);
+\path[edge] (0,9.55) -- (15.00,9.55);
+\path[edge] (0,10.23) -- (15.00,10.23);
+\end{tikzpicture}

diff --git a/images/16-e1-oddeven-1296543330.tex b/images/16-e1-oddeven-1296543330.tex
new file mode 100644 (file)
index 0000000..4e02a88
--- /dev/null
+++ b/images/16-e1-oddeven-1296543330.tex
@@ -0,0 +1,270 @@
+\begin{tikzpicture}[auto]
+\node[vertex] (v0) at (0.87,0.00) {};
+\node[vertex] (v1) at (0.87,6.94) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.13,0.69) {};
+\node[vertex] (v3) at (1.13,1.39) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v4) at (1.13,2.08) {};
+\node[vertex] (v5) at (1.13,6.24) {};
+\path[comp] (v4) -- (v5);
+
+\node[vertex] (v6) at (1.39,2.77) {};
+\node[vertex] (v7) at (1.39,9.02) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v8) at (1.65,3.47) {};
+\node[vertex] (v9) at (1.65,8.32) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v10) at (1.91,4.16) {};
+\node[vertex] (v11) at (1.91,10.40) {};
+\path[comp] (v10) -- (v11);
+
+\node[vertex] (v12) at (2.17,4.86) {};
+\node[vertex] (v13) at (2.17,9.71) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (2.43,5.55) {};
+\node[vertex] (v15) at (2.43,7.63) {};
+\path[comp] (v14) -- (v15);
+
+\node[vertex] (v16) at (3.29,0.00) {};
+\node[vertex] (v17) at (3.29,0.69) {};
+\path[comp] (v16) -- (v17);
+
+\node[vertex] (v18) at (3.29,1.39) {};
+\node[vertex] (v19) at (3.29,6.94) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (3.55,2.08) {};
+\node[vertex] (v21) at (3.55,5.55) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v22) at (3.82,2.77) {};
+\node[vertex] (v23) at (3.82,3.47) {};
+\path[comp] (v22) -- (v23);
+
+\node[vertex] (v24) at (3.82,4.16) {};
+\node[vertex] (v25) at (3.82,4.86) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (3.55,6.24) {};
+\node[vertex] (v27) at (3.55,7.63) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v28) at (3.29,8.32) {};
+\node[vertex] (v29) at (3.29,9.02) {};
+\path[comp] (v28) -- (v29);
+
+\node[vertex] (v30) at (3.29,9.71) {};
+\node[vertex] (v31) at (3.29,10.40) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (4.68,0.00) {};
+\node[vertex] (v33) at (4.68,2.08) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (4.94,0.69) {};
+\node[vertex] (v35) at (4.94,1.39) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (4.68,2.77) {};
+\node[vertex] (v37) at (4.68,4.16) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (4.94,3.47) {};
+\node[vertex] (v39) at (4.94,8.32) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (4.68,4.86) {};
+\node[vertex] (v41) at (4.68,9.71) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v42) at (5.20,5.55) {};
+\node[vertex] (v43) at (5.20,6.24) {};
+\path[comp] (v42) -- (v43);
+
+\node[vertex] (v44) at (5.20,6.94) {};
+\node[vertex] (v45) at (5.20,7.63) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (4.94,9.02) {};
+\node[vertex] (v47) at (4.94,10.40) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (6.07,0.00) {};
+\node[vertex] (v49) at (6.07,2.77) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (6.33,0.69) {};
+\node[vertex] (v51) at (6.33,5.55) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (6.59,1.39) {};
+\node[vertex] (v53) at (6.59,6.24) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (6.07,3.47) {};
+\node[vertex] (v55) at (6.07,4.86) {};
+\path[comp] (v54) -- (v55);
+
+\node[vertex] (v56) at (6.07,7.63) {};
+\node[vertex] (v57) at (6.07,10.40) {};
+\path[comp] (v56) -- (v57);
+
+\node[vertex] (v58) at (6.33,8.32) {};
+\node[vertex] (v59) at (6.33,9.71) {};
+\path[comp] (v58) -- (v59);
+
+\node[vertex] (v60) at (7.46,1.39) {};
+\node[vertex] (v61) at (7.46,2.08) {};
+\path[comp] (v60) -- (v61);
+
+\node[vertex] (v62) at (7.46,4.16) {};
+\node[vertex] (v63) at (7.46,8.32) {};
+\path[comp] (v62) -- (v63);
+
+\node[vertex] (v64) at (7.72,4.86) {};
+\node[vertex] (v65) at (7.72,9.02) {};
+\path[comp] (v64) -- (v65);
+
+\node[vertex] (v66) at (7.98,5.55) {};
+\node[vertex] (v67) at (7.98,6.94) {};
+\path[comp] (v66) -- (v67);
+
+\node[vertex] (v68) at (8.84,0.69) {};
+\node[vertex] (v69) at (8.84,1.39) {};
+\path[comp] (v68) -- (v69);
+
+\node[vertex] (v70) at (8.84,2.08) {};
+\node[vertex] (v71) at (8.84,5.55) {};
+\path[comp] (v70) -- (v71);
+
+\node[vertex] (v72) at (9.10,3.47) {};
+\node[vertex] (v73) at (9.10,4.16) {};
+\path[comp] (v72) -- (v73);
+
+\node[vertex] (v74) at (9.10,4.86) {};
+\node[vertex] (v75) at (9.10,8.32) {};
+\path[comp] (v74) -- (v75);
+
+\node[vertex] (v76) at (8.84,6.24) {};
+\node[vertex] (v77) at (8.84,6.94) {};
+\path[comp] (v76) -- (v77);
+
+\node[vertex] (v78) at (8.84,9.02) {};
+\node[vertex] (v79) at (8.84,9.71) {};
+\path[comp] (v78) -- (v79);
+
+\node[vertex] (v80) at (9.97,0.69) {};
+\node[vertex] (v81) at (9.97,3.47) {};
+\path[comp] (v80) -- (v81);
+
+\node[vertex] (v82) at (10.23,1.39) {};
+\node[vertex] (v83) at (10.23,4.16) {};
+\path[comp] (v82) -- (v83);
+
+\node[vertex] (v84) at (10.49,2.08) {};
+\node[vertex] (v85) at (10.49,4.86) {};
+\path[comp] (v84) -- (v85);
+
+\node[vertex] (v86) at (9.97,5.55) {};
+\node[vertex] (v87) at (9.97,8.32) {};
+\path[comp] (v86) -- (v87);
+
+\node[vertex] (v88) at (10.23,6.24) {};
+\node[vertex] (v89) at (10.23,9.02) {};
+\path[comp] (v88) -- (v89);
+
+\node[vertex] (v90) at (10.49,6.94) {};
+\node[vertex] (v91) at (10.49,9.71) {};
+\path[comp] (v90) -- (v91);
+
+\node[vertex] (v92) at (11.36,2.77) {};
+\node[vertex] (v93) at (11.36,5.55) {};
+\path[comp] (v92) -- (v93);
+
+\node[vertex] (v94) at (11.62,3.47) {};
+\node[vertex] (v95) at (11.62,6.24) {};
+\path[comp] (v94) -- (v95);
+
+\node[vertex] (v96) at (11.88,4.16) {};
+\node[vertex] (v97) at (11.88,6.94) {};
+\path[comp] (v96) -- (v97);
+
+\node[vertex] (v98) at (12.14,4.86) {};
+\node[vertex] (v99) at (12.14,7.63) {};
+\path[comp] (v98) -- (v99);
+
+\node[vertex] (v100) at (13.01,1.39) {};
+\node[vertex] (v101) at (13.01,2.77) {};
+\path[comp] (v100) -- (v101);
+
+\node[vertex] (v102) at (13.27,2.08) {};
+\node[vertex] (v103) at (13.27,3.47) {};
+\path[comp] (v102) -- (v103);
+
+\node[vertex] (v104) at (13.01,4.16) {};
+\node[vertex] (v105) at (13.01,5.55) {};
+\path[comp] (v104) -- (v105);
+
+\node[vertex] (v106) at (13.27,4.86) {};
+\node[vertex] (v107) at (13.27,6.24) {};
+\path[comp] (v106) -- (v107);
+
+\node[vertex] (v108) at (13.01,6.94) {};
+\node[vertex] (v109) at (13.01,8.32) {};
+\path[comp] (v108) -- (v109);
+
+\node[vertex] (v110) at (13.27,7.63) {};
+\node[vertex] (v111) at (13.27,9.02) {};
+\path[comp] (v110) -- (v111);
+
+\node[vertex] (v112) at (14.13,0.69) {};
+\node[vertex] (v113) at (14.13,1.39) {};
+\path[comp] (v112) -- (v113);
+
+\node[vertex] (v114) at (14.13,2.08) {};
+\node[vertex] (v115) at (14.13,2.77) {};
+\path[comp] (v114) -- (v115);
+
+\node[vertex] (v116) at (14.13,3.47) {};
+\node[vertex] (v117) at (14.13,4.16) {};
+\path[comp] (v116) -- (v117);
+
+\node[vertex] (v118) at (14.13,4.86) {};
+\node[vertex] (v119) at (14.13,5.55) {};
+\path[comp] (v118) -- (v119);
+
+\node[vertex] (v120) at (14.13,6.24) {};
+\node[vertex] (v121) at (14.13,6.94) {};
+\path[comp] (v120) -- (v121);
+
+\node[vertex] (v122) at (14.13,7.63) {};
+\node[vertex] (v123) at (14.13,8.32) {};
+\path[comp] (v122) -- (v123);
+
+\node[vertex] (v124) at (14.13,9.02) {};
+\node[vertex] (v125) at (14.13,9.71) {};
+\path[comp] (v124) -- (v125);
+
+\path[edge] (0,0.00) -- (15.00,0.00);
+\path[edge] (0,0.69) -- (15.00,0.69);
+\path[edge] (0,1.39) -- (15.00,1.39);
+\path[edge] (0,2.08) -- (15.00,2.08);
+\path[edge] (0,2.77) -- (15.00,2.77);
+\path[edge] (0,3.47) -- (15.00,3.47);
+\path[edge] (0,4.16) -- (15.00,4.16);
+\path[edge] (0,4.86) -- (15.00,4.86);
+\path[edge] (0,5.55) -- (15.00,5.55);
+\path[edge] (0,6.24) -- (15.00,6.24);
+\path[edge] (0,6.94) -- (15.00,6.94);
+\path[edge] (0,7.63) -- (15.00,7.63);
+\path[edge] (0,8.32) -- (15.00,8.32);
+\path[edge] (0,9.02) -- (15.00,9.02);
+\path[edge] (0,9.71) -- (15.00,9.71);
+\path[edge] (0,10.40) -- (15.00,10.40);
+\end{tikzpicture}

diff --git a/images/16-ec-from-oes32-cut.tex b/images/16-ec-from-oes32-cut.tex
new file mode 100644 (file)
index 0000000..107b3bb
--- /dev/null
+++ b/images/16-ec-from-oes32-cut.tex
@@ -0,0 +1,926 @@
+\begin{tikzpicture}[auto]
+\path[edge] (0.00,0.00) -- (0.52,0.00);
+\path[edge minimum] (0.00,0.42) -- (0.52,0.42);
+\path[edge maximum] (0.00,0.84) -- (0.52,0.84);
+\path[edge] (0.00,1.26) -- (0.52,1.26);
+\path[edge maximum] (0.00,3.36) -- (0.52,3.36);
+\path[edge] (0.00,3.78) -- (0.52,3.78);
+\path[edge] (0.00,4.20) -- (0.52,4.20);
+\path[edge minimum] (0.00,4.62) -- (0.52,4.62);
+\path[edge] (0.00,6.71) -- (0.52,6.71);
+\path[edge minimum] (0.00,7.13) -- (0.52,7.13);
+\path[edge maximum] (0.00,7.55) -- (0.52,7.55);
+\path[edge] (0.00,7.97) -- (0.52,7.97);
+\path[edge] (0.00,9.23) -- (0.52,9.23);
+\path[edge minimum] (0.00,9.65) -- (0.52,9.65);
+\path[edge] (0.00,11.75) -- (0.52,11.75);
+\path[edge minimum] (0.00,12.17) -- (0.52,12.17);
+\path[edge] (0.00,1.68) -- (1.05,1.68);
+\path[edge minimum] (0.00,2.52) -- (1.05,2.52);
+\path[edge] (0.52,3.36) -- (1.05,3.36);
+\path[edge minimum] (0.52,4.20) -- (1.05,4.20);
+\path[edge maximum] (0.52,3.78) -- (1.21,3.78);
+\path[edge] (0.52,4.62) -- (1.21,4.62);
+\path[edge] (0.00,5.03) -- (1.05,5.03);
+\path[edge minimum] (0.00,5.87) -- (1.05,5.87);
+\path[edge maximum] (0.00,5.45) -- (1.21,5.45);
+\path[edge] (0.00,6.29) -- (1.21,6.29);
+\path[edge] (0.00,8.39) -- (1.05,8.39);
+\path[edge minimum] (0.52,9.23) -- (1.05,9.23);
+\path[edge maximum] (0.00,8.81) -- (1.21,8.81);
+\path[edge] (0.52,9.65) -- (1.21,9.65);
+\path[edge] (0.00,10.07) -- (1.05,10.07);
+\path[edge minimum] (0.00,10.91) -- (1.05,10.91);
+\path[edge] (0.52,0.84) -- (3.25,0.84);
+\path[edge minimum] (1.05,1.68) -- (3.25,1.68);
+\path[edge maximum] (0.52,1.26) -- (3.41,1.26);
+\path[edge] (0.00,2.10) -- (3.41,2.10);
+\path[edge] (1.05,4.20) -- (3.25,4.20);
+\path[edge minimum] (1.05,5.03) -- (3.25,5.03);
+\path[edge maximum] (1.21,4.62) -- (3.41,4.62);
+\path[edge] (1.21,5.45) -- (3.41,5.45);
+\path[edge] (0.52,7.55) -- (3.25,7.55);
+\path[edge minimum] (1.05,8.39) -- (3.25,8.39);
+\path[edge maximum] (0.52,7.97) -- (3.41,7.97);
+\path[edge] (1.21,8.81) -- (3.41,8.81);
+\path[edge] (1.05,10.91) -- (3.25,10.91);
+\path[edge minimum] (0.52,11.75) -- (3.25,11.75);
+\path[edge maximum] (0.00,11.33) -- (3.41,11.33);
+\path[edge] (0.52,12.17) -- (3.41,12.17);
+\path[edge] (0.52,0.42) -- (3.93,0.42);
+\path[edge minimum] (3.25,0.84) -- (3.93,0.84);
+\path[edge maximum] (3.41,2.10) -- (3.93,2.10);
+\path[edge] (1.05,2.52) -- (3.93,2.52);
+\path[edge] (1.21,3.78) -- (3.93,3.78);
+\path[edge minimum] (3.25,4.20) -- (3.93,4.20);
+\path[edge maximum] (3.41,5.45) -- (3.93,5.45);
+\path[edge] (1.05,5.87) -- (3.93,5.87);
+\path[edge] (0.52,7.13) -- (3.93,7.13);
+\path[edge minimum] (3.25,7.55) -- (3.93,7.55);
+\path[edge maximum] (3.41,8.81) -- (3.93,8.81);
+\path[edge] (1.05,9.23) -- (3.93,9.23);
+\path[edge] (0.00,10.49) -- (3.93,10.49);
+\path[edge minimum] (3.25,10.91) -- (3.93,10.91);
+\path[edge maximum] (3.41,12.17) -- (3.93,12.17);
+\path[edge] (0.00,12.59) -- (3.93,12.59);
+\path[edge] (3.25,1.68) -- (6.08,1.68);
+\path[edge minimum] (1.05,3.36) -- (6.08,3.36);
+\path[edge] (3.93,2.10) -- (6.24,2.10);
+\path[edge minimum] (3.93,3.78) -- (6.24,3.78);
+\path[edge maximum] (3.93,2.52) -- (6.40,2.52);
+\path[edge] (3.93,4.20) -- (6.40,4.20);
+\path[edge maximum] (0.00,2.94) -- (6.56,2.94);
+\path[edge] (3.41,4.62) -- (6.56,4.62);
+\path[edge] (3.25,8.39) -- (6.08,8.39);
+\path[edge minimum] (1.05,10.07) -- (6.08,10.07);
+\path[edge] (3.93,8.81) -- (6.24,8.81);
+\path[edge minimum] (3.93,10.49) -- (6.24,10.49);
+\path[edge maximum] (3.93,9.23) -- (6.40,9.23);
+\path[edge] (3.93,10.91) -- (6.40,10.91);
+\path[edge maximum] (1.21,9.65) -- (6.56,9.65);
+\path[edge] (3.41,11.33) -- (6.56,11.33);
+\path[edge] (3.93,0.84) -- (7.08,0.84);
+\path[edge minimum] (6.08,1.68) -- (7.08,1.68);
+\path[edge] (3.41,1.26) -- (7.24,1.26);
+\path[edge minimum] (6.24,2.10) -- (7.24,2.10);
+\path[edge maximum] (6.40,4.20) -- (7.08,4.20);
+\path[edge] (3.25,5.03) -- (7.08,5.03);
+\path[edge maximum] (6.56,4.62) -- (7.24,4.62);
+\path[edge] (3.93,5.45) -- (7.24,5.45);
+\path[edge] (3.93,7.55) -- (7.08,7.55);
+\path[edge minimum] (6.08,8.39) -- (7.08,8.39);
+\path[edge] (3.41,7.97) -- (7.24,7.97);
+\path[edge minimum] (6.24,8.81) -- (7.24,8.81);
+\path[edge maximum] (6.40,10.91) -- (7.08,10.91);
+\path[edge] (3.25,11.75) -- (7.08,11.75);
+\path[edge maximum] (6.56,11.33) -- (7.24,11.33);
+\path[edge] (3.93,12.17) -- (7.24,12.17);
+\path[edge] (6.08,3.36) -- (11.17,3.36);
+\path[edge minimum] (0.52,6.71) -- (11.17,6.71);
+\path[edge] (6.24,3.78) -- (11.33,3.78);
+\path[edge minimum] (3.93,7.13) -- (11.33,7.13);
+\path[edge] (7.08,4.20) -- (11.49,4.20);
+\path[edge minimum] (7.08,7.55) -- (11.49,7.55);
+\path[edge] (7.24,4.62) -- (11.64,4.62);
+\path[edge minimum] (7.24,7.97) -- (11.64,7.97);
+\path[edge maximum] (7.08,5.03) -- (11.80,5.03);
+\path[edge] (7.08,8.39) -- (11.80,8.39);
+\path[edge maximum] (7.24,5.45) -- (11.96,5.45);
+\path[edge] (7.24,8.81) -- (11.96,8.81);
+\path[edge maximum] (3.93,5.87) -- (12.12,5.87);
+\path[edge] (6.40,9.23) -- (12.12,9.23);
+\path[edge maximum] (1.21,6.29) -- (12.27,6.29);
+\path[edge] (6.56,9.65) -- (12.27,9.65);
+\path[edge] (7.08,1.68) -- (12.80,1.68);
+\path[edge minimum] (11.17,3.36) -- (12.80,3.36);
+\path[edge] (7.24,2.10) -- (12.95,2.10);
+\path[edge minimum] (11.33,3.78) -- (12.95,3.78);
+\path[edge] (6.40,2.52) -- (13.11,2.52);
+\path[edge minimum] (11.49,4.20) -- (13.11,4.20);
+\path[edge] (6.56,2.94) -- (13.27,2.94);
+\path[edge minimum] (11.64,4.62) -- (13.27,4.62);
+\path[edge maximum] (11.80,8.39) -- (12.80,8.39);
+\path[edge] (6.08,10.07) -- (12.80,10.07);
+\path[edge maximum] (11.96,8.81) -- (12.95,8.81);
+\path[edge] (6.24,10.49) -- (12.95,10.49);
+\path[edge maximum] (12.12,9.23) -- (13.11,9.23);
+\path[edge] (7.08,10.91) -- (13.11,10.91);
+\path[edge maximum] (12.27,9.65) -- (13.27,9.65);
+\path[edge] (7.24,11.33) -- (13.27,11.33);
+\path[edge minimum] (0.52,0.00) -- (15.00,0.00);
+\path[edge minimum] (3.93,0.42) -- (15.00,0.42);
+\path[edge minimum] (7.08,0.84) -- (15.00,0.84);
+\path[edge minimum] (7.24,1.26) -- (15.00,1.26);
+\path[edge minimum] (12.80,1.68) -- (15.00,1.68);
+\path[edge minimum] (12.95,2.10) -- (15.00,2.10);
+\path[edge minimum] (13.11,2.52) -- (15.00,2.52);
+\path[edge minimum] (13.27,2.94) -- (15.00,2.94);
+\path[edge] (12.80,3.36) -- (15.00,3.36);
+\path[edge] (12.95,3.78) -- (15.00,3.78);
+\path[edge] (13.11,4.20) -- (15.00,4.20);
+\path[edge] (13.27,4.62) -- (15.00,4.62);
+\path[edge] (11.80,5.03) -- (15.00,5.03);
+\path[edge] (11.96,5.45) -- (15.00,5.45);
+\path[edge] (12.12,5.87) -- (15.00,5.87);
+\path[edge] (12.27,6.29) -- (15.00,6.29);
+\path[edge] (11.17,6.71) -- (15.00,6.71);
+\path[edge] (11.33,7.13) -- (15.00,7.13);
+\path[edge] (11.49,7.55) -- (15.00,7.55);
+\path[edge] (11.64,7.97) -- (15.00,7.97);
+\path[edge] (12.80,8.39) -- (15.00,8.39);
+\path[edge] (12.95,8.81) -- (15.00,8.81);
+\path[edge] (13.11,9.23) -- (15.00,9.23);
+\path[edge] (13.27,9.65) -- (15.00,9.65);
+\path[edge maximum] (12.80,10.07) -- (15.00,10.07);
+\path[edge maximum] (12.95,10.49) -- (15.00,10.49);
+\path[edge maximum] (13.11,10.91) -- (15.00,10.91);
+\path[edge maximum] (13.27,11.33) -- (15.00,11.33);
+\path[edge maximum] (7.08,11.75) -- (15.00,11.75);
+\path[edge maximum] (7.24,12.17) -- (15.00,12.17);
+\path[edge maximum] (3.93,12.59) -- (15.00,12.59);
+\path[edge maximum] (0.00,13.01) -- (15.00,13.01);
+\node[vertex active minimum] (v0) at (0.52,0.00) {};
+\node[vertex active minimum] (v1) at (0.52,0.42) {};
+\path[comp active minimum] (v0) -- (v1);
+
+\node[vertex active maximum] (v2) at (0.52,0.84) {};
+\node[vertex active maximum] (v3) at (0.52,1.26) {};
+\path[comp active maximum] (v2) -- (v3);
+
+\node[vertex] (v4) at (0.52,1.68) {};
+\node[vertex] (v5) at (0.52,2.10) {};
+\path[comp] (v4) -- (v5);
+
+\node[vertex inactive minimum maximum] (v6) at (0.52,2.52) {};
+\node[vertex inactive minimum maximum] (v7) at (0.52,2.94) {};
+\path[comp inactive minimum maximum] (v6) -- (v7);
+
+\node[vertex active maximum] (v8) at (0.52,3.36) {};
+\node[vertex active maximum] (v9) at (0.52,3.78) {};
+\path[comp active maximum] (v8) -- (v9);
+
+\node[vertex active minimum] (v10) at (0.52,4.20) {};
+\node[vertex active minimum] (v11) at (0.52,4.62) {};
+\path[comp active minimum] (v10) -- (v11);
+
+\node[vertex inactive maximum] (v12) at (0.52,5.03) {};
+\node[vertex inactive maximum] (v13) at (0.52,5.45) {};
+\path[comp inactive maximum] (v12) -- (v13);
+
+\node[vertex inactive minimum] (v14) at (0.52,5.87) {};
+\node[vertex inactive minimum] (v15) at (0.52,6.29) {};
+\path[comp inactive minimum] (v14) -- (v15);
+
+\node[vertex active minimum] (v16) at (0.52,6.71) {};
+\node[vertex active minimum] (v17) at (0.52,7.13) {};
+\path[comp active minimum] (v16) -- (v17);
+
+\node[vertex active maximum] (v18) at (0.52,7.55) {};
+\node[vertex active maximum] (v19) at (0.52,7.97) {};
+\path[comp active maximum] (v18) -- (v19);
+
+\node[vertex inactive maximum] (v20) at (0.52,8.39) {};
+\node[vertex inactive maximum] (v21) at (0.52,8.81) {};
+\path[comp inactive maximum] (v20) -- (v21);
+
+\node[vertex active minimum] (v22) at (0.52,9.23) {};
+\node[vertex active minimum] (v23) at (0.52,9.65) {};
+\path[comp active minimum] (v22) -- (v23);
+
+\node[vertex] (v24) at (0.52,10.07) {};
+\node[vertex] (v25) at (0.52,10.49) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex inactive minimum maximum] (v26) at (0.52,10.91) {};
+\node[vertex inactive minimum maximum] (v27) at (0.52,11.33) {};
+\path[comp inactive minimum maximum] (v26) -- (v27);
+
+\node[vertex active minimum] (v28) at (0.52,11.75) {};
+\node[vertex active minimum] (v29) at (0.52,12.17) {};
+\path[comp active minimum] (v28) -- (v29);
+
+\node[vertex inactive maximum] (v30) at (0.52,12.59) {};
+\node[vertex inactive maximum] (v31) at (0.52,13.01) {};
+\path[comp inactive maximum] (v30) -- (v31);
+
+\node[vertex inactive minimum] (v32) at (1.05,0.00) {};
+\node[vertex inactive minimum] (v33) at (1.05,0.84) {};
+\path[comp inactive minimum] (v32) -- (v33);
+
+\node[vertex inactive maximum] (v34) at (1.21,0.42) {};
+\node[vertex inactive maximum] (v35) at (1.21,1.26) {};
+\path[comp inactive maximum] (v34) -- (v35);
+
+\node[vertex active minimum] (v36) at (1.05,1.68) {};
+\node[vertex active minimum] (v37) at (1.05,2.52) {};
+\path[comp active minimum] (v36) -- (v37);
+
+\node[vertex inactive maximum] (v38) at (1.21,2.10) {};
+\node[vertex inactive maximum] (v39) at (1.21,2.94) {};
+\path[comp inactive maximum] (v38) -- (v39);
+
+\node[vertex active minimum] (v40) at (1.05,3.36) {};
+\node[vertex active minimum] (v41) at (1.05,4.20) {};
+\path[comp active minimum] (v40) -- (v41);
+
+\node[vertex active maximum] (v42) at (1.21,3.78) {};
+\node[vertex active maximum] (v43) at (1.21,4.62) {};
+\path[comp active maximum] (v42) -- (v43);
+
+\node[vertex active minimum] (v44) at (1.05,5.03) {};
+\node[vertex active minimum] (v45) at (1.05,5.87) {};
+\path[comp active minimum] (v44) -- (v45);
+
+\node[vertex active maximum] (v46) at (1.21,5.45) {};
+\node[vertex active maximum] (v47) at (1.21,6.29) {};
+\path[comp active maximum] (v46) -- (v47);
+
+\node[vertex inactive minimum] (v48) at (1.05,6.71) {};
+\node[vertex inactive minimum] (v49) at (1.05,7.55) {};
+\path[comp inactive minimum] (v48) -- (v49);
+
+\node[vertex inactive maximum] (v50) at (1.21,7.13) {};
+\node[vertex inactive maximum] (v51) at (1.21,7.97) {};
+\path[comp inactive maximum] (v50) -- (v51);
+
+\node[vertex active minimum] (v52) at (1.05,8.39) {};
+\node[vertex active minimum] (v53) at (1.05,9.23) {};
+\path[comp active minimum] (v52) -- (v53);
+
+\node[vertex active maximum] (v54) at (1.21,8.81) {};
+\node[vertex active maximum] (v55) at (1.21,9.65) {};
+\path[comp active maximum] (v54) -- (v55);
+
+\node[vertex active minimum] (v56) at (1.05,10.07) {};
+\node[vertex active minimum] (v57) at (1.05,10.91) {};
+\path[comp active minimum] (v56) -- (v57);
+
+\node[vertex inactive maximum] (v58) at (1.21,10.49) {};
+\node[vertex inactive maximum] (v59) at (1.21,11.33) {};
+\path[comp inactive maximum] (v58) -- (v59);
+
+\node[vertex inactive minimum] (v60) at (1.05,11.75) {};
+\node[vertex inactive minimum] (v61) at (1.05,12.59) {};
+\path[comp inactive minimum] (v60) -- (v61);
+
+\node[vertex inactive maximum] (v62) at (1.21,12.17) {};
+\node[vertex inactive maximum] (v63) at (1.21,13.01) {};
+\path[comp inactive maximum] (v62) -- (v63);
+
+\node[vertex] (v64) at (1.73,0.42) {};
+\node[vertex] (v65) at (1.73,0.84) {};
+\path[comp] (v64) -- (v65);
+
+\node[vertex] (v66) at (1.73,2.10) {};
+\node[vertex] (v67) at (1.73,2.52) {};
+\path[comp] (v66) -- (v67);
+
+\node[vertex] (v68) at (1.73,3.78) {};
+\node[vertex] (v69) at (1.73,4.20) {};
+\path[comp] (v68) -- (v69);
+
+\node[vertex] (v70) at (1.73,5.45) {};
+\node[vertex] (v71) at (1.73,5.87) {};
+\path[comp] (v70) -- (v71);
+
+\node[vertex] (v72) at (1.73,7.13) {};
+\node[vertex] (v73) at (1.73,7.55) {};
+\path[comp] (v72) -- (v73);
+
+\node[vertex] (v74) at (1.73,8.81) {};
+\node[vertex] (v75) at (1.73,9.23) {};
+\path[comp] (v74) -- (v75);
+
+\node[vertex] (v76) at (1.73,10.49) {};
+\node[vertex] (v77) at (1.73,10.91) {};
+\path[comp] (v76) -- (v77);
+
+\node[vertex] (v78) at (1.73,12.17) {};
+\node[vertex] (v79) at (1.73,12.59) {};
+\path[comp] (v78) -- (v79);
+
+\node[vertex inactive minimum] (v80) at (2.26,0.00) {};
+\node[vertex inactive minimum] (v81) at (2.26,1.68) {};
+\path[comp inactive minimum] (v80) -- (v81);
+
+\node[vertex] (v82) at (2.41,0.42) {};
+\node[vertex] (v83) at (2.41,2.10) {};
+\path[comp] (v82) -- (v83);
+
+\node[vertex] (v84) at (2.57,0.84) {};
+\node[vertex] (v85) at (2.57,2.52) {};
+\path[comp] (v84) -- (v85);
+
+\node[vertex inactive maximum] (v86) at (2.73,1.26) {};
+\node[vertex inactive maximum] (v87) at (2.73,2.94) {};
+\path[comp inactive maximum] (v86) -- (v87);
+
+\node[vertex inactive minimum] (v88) at (2.26,3.36) {};
+\node[vertex inactive minimum] (v89) at (2.26,5.03) {};
+\path[comp inactive minimum] (v88) -- (v89);
+
+\node[vertex] (v90) at (2.41,3.78) {};
+\node[vertex] (v91) at (2.41,5.45) {};
+\path[comp] (v90) -- (v91);
+
+\node[vertex] (v92) at (2.57,4.20) {};
+\node[vertex] (v93) at (2.57,5.87) {};
+\path[comp] (v92) -- (v93);
+
+\node[vertex inactive maximum] (v94) at (2.73,4.62) {};
+\node[vertex inactive maximum] (v95) at (2.73,6.29) {};
+\path[comp inactive maximum] (v94) -- (v95);
+
+\node[vertex inactive minimum] (v96) at (2.26,6.71) {};
+\node[vertex inactive minimum] (v97) at (2.26,8.39) {};
+\path[comp inactive minimum] (v96) -- (v97);
+
+\node[vertex] (v98) at (2.41,7.13) {};
+\node[vertex] (v99) at (2.41,8.81) {};
+\path[comp] (v98) -- (v99);
+
+\node[vertex] (v100) at (2.57,7.55) {};
+\node[vertex] (v101) at (2.57,9.23) {};
+\path[comp] (v100) -- (v101);
+
+\node[vertex inactive maximum] (v102) at (2.73,7.97) {};
+\node[vertex inactive maximum] (v103) at (2.73,9.65) {};
+\path[comp inactive maximum] (v102) -- (v103);
+
+\node[vertex inactive minimum] (v104) at (2.26,10.07) {};
+\node[vertex inactive minimum] (v105) at (2.26,11.75) {};
+\path[comp inactive minimum] (v104) -- (v105);
+
+\node[vertex] (v106) at (2.41,10.49) {};
+\node[vertex] (v107) at (2.41,12.17) {};
+\path[comp] (v106) -- (v107);
+
+\node[vertex] (v108) at (2.57,10.91) {};
+\node[vertex] (v109) at (2.57,12.59) {};
+\path[comp] (v108) -- (v109);
+
+\node[vertex inactive maximum] (v110) at (2.73,11.33) {};
+\node[vertex inactive maximum] (v111) at (2.73,13.01) {};
+\path[comp inactive maximum] (v110) -- (v111);
+
+\node[vertex active minimum] (v112) at (3.25,0.84) {};
+\node[vertex active minimum] (v113) at (3.25,1.68) {};
+\path[comp active minimum] (v112) -- (v113);
+
+\node[vertex active maximum] (v114) at (3.41,1.26) {};
+\node[vertex active maximum] (v115) at (3.41,2.10) {};
+\path[comp active maximum] (v114) -- (v115);
+
+\node[vertex active minimum] (v116) at (3.25,4.20) {};
+\node[vertex active minimum] (v117) at (3.25,5.03) {};
+\path[comp active minimum] (v116) -- (v117);
+
+\node[vertex active maximum] (v118) at (3.41,4.62) {};
+\node[vertex active maximum] (v119) at (3.41,5.45) {};
+\path[comp active maximum] (v118) -- (v119);
+
+\node[vertex active minimum] (v120) at (3.25,7.55) {};
+\node[vertex active minimum] (v121) at (3.25,8.39) {};
+\path[comp active minimum] (v120) -- (v121);
+
+\node[vertex active maximum] (v122) at (3.41,7.97) {};
+\node[vertex active maximum] (v123) at (3.41,8.81) {};
+\path[comp active maximum] (v122) -- (v123);
+
+\node[vertex active minimum] (v124) at (3.25,10.91) {};
+\node[vertex active minimum] (v125) at (3.25,11.75) {};
+\path[comp active minimum] (v124) -- (v125);
+
+\node[vertex active maximum] (v126) at (3.41,11.33) {};
+\node[vertex active maximum] (v127) at (3.41,12.17) {};
+\path[comp active maximum] (v126) -- (v127);
+
+\node[vertex active minimum] (v128) at (3.93,0.42) {};
+\node[vertex active minimum] (v129) at (3.93,0.84) {};
+\path[comp active minimum] (v128) -- (v129);
+
+\node[vertex] (v130) at (3.93,1.26) {};
+\node[vertex] (v131) at (3.93,1.68) {};
+\path[comp] (v130) -- (v131);
+
+\node[vertex active maximum] (v132) at (3.93,2.10) {};
+\node[vertex active maximum] (v133) at (3.93,2.52) {};
+\path[comp active maximum] (v132) -- (v133);
+
+\node[vertex active minimum] (v134) at (3.93,3.78) {};
+\node[vertex active minimum] (v135) at (3.93,4.20) {};
+\path[comp active minimum] (v134) -- (v135);
+
+\node[vertex] (v136) at (3.93,4.62) {};
+\node[vertex] (v137) at (3.93,5.03) {};
+\path[comp] (v136) -- (v137);
+
+\node[vertex active maximum] (v138) at (3.93,5.45) {};
+\node[vertex active maximum] (v139) at (3.93,5.87) {};
+\path[comp active maximum] (v138) -- (v139);
+
+\node[vertex active minimum] (v140) at (3.93,7.13) {};
+\node[vertex active minimum] (v141) at (3.93,7.55) {};
+\path[comp active minimum] (v140) -- (v141);
+
+\node[vertex] (v142) at (3.93,7.97) {};
+\node[vertex] (v143) at (3.93,8.39) {};
+\path[comp] (v142) -- (v143);
+
+\node[vertex active maximum] (v144) at (3.93,8.81) {};
+\node[vertex active maximum] (v145) at (3.93,9.23) {};
+\path[comp active maximum] (v144) -- (v145);
+
+\node[vertex active minimum] (v146) at (3.93,10.49) {};
+\node[vertex active minimum] (v147) at (3.93,10.91) {};
+\path[comp active minimum] (v146) -- (v147);
+
+\node[vertex] (v148) at (3.93,11.33) {};
+\node[vertex] (v149) at (3.93,11.75) {};
+\path[comp] (v148) -- (v149);
+
+\node[vertex active maximum] (v150) at (3.93,12.17) {};
+\node[vertex active maximum] (v151) at (3.93,12.59) {};
+\path[comp active maximum] (v150) -- (v151);
+
+\node[vertex inactive minimum] (v152) at (4.46,0.00) {};
+\node[vertex inactive minimum] (v153) at (4.46,3.36) {};
+\path[comp inactive minimum] (v152) -- (v153);
+
+\node[vertex inactive minimum] (v154) at (4.62,0.42) {};
+\node[vertex inactive minimum] (v155) at (4.62,3.78) {};
+\path[comp inactive minimum] (v154) -- (v155);
+
+\node[vertex] (v156) at (4.77,0.84) {};
+\node[vertex] (v157) at (4.77,4.20) {};
+\path[comp] (v156) -- (v157);
+
+\node[vertex] (v158) at (4.93,1.26) {};
+\node[vertex] (v159) at (4.93,4.62) {};
+\path[comp] (v158) -- (v159);
+
+\node[vertex] (v160) at (5.09,1.68) {};
+\node[vertex] (v161) at (5.09,5.03) {};
+\path[comp] (v160) -- (v161);
+
+\node[vertex] (v162) at (5.24,2.10) {};
+\node[vertex] (v163) at (5.24,5.45) {};
+\path[comp] (v162) -- (v163);
+
+\node[vertex inactive maximum] (v164) at (5.40,2.52) {};
+\node[vertex inactive maximum] (v165) at (5.40,5.87) {};
+\path[comp inactive maximum] (v164) -- (v165);
+
+\node[vertex inactive maximum] (v166) at (5.56,2.94) {};
+\node[vertex inactive maximum] (v167) at (5.56,6.29) {};
+\path[comp inactive maximum] (v166) -- (v167);
+
+\node[vertex inactive minimum] (v168) at (4.46,6.71) {};
+\node[vertex inactive minimum] (v169) at (4.46,10.07) {};
+\path[comp inactive minimum] (v168) -- (v169);
+
+\node[vertex inactive minimum] (v170) at (4.62,7.13) {};
+\node[vertex inactive minimum] (v171) at (4.62,10.49) {};
+\path[comp inactive minimum] (v170) -- (v171);
+
+\node[vertex] (v172) at (4.77,7.55) {};
+\node[vertex] (v173) at (4.77,10.91) {};
+\path[comp] (v172) -- (v173);
+
+\node[vertex] (v174) at (4.93,7.97) {};
+\node[vertex] (v175) at (4.93,11.33) {};
+\path[comp] (v174) -- (v175);
+
+\node[vertex] (v176) at (5.09,8.39) {};
+\node[vertex] (v177) at (5.09,11.75) {};
+\path[comp] (v176) -- (v177);
+
+\node[vertex] (v178) at (5.24,8.81) {};
+\node[vertex] (v179) at (5.24,12.17) {};
+\path[comp] (v178) -- (v179);
+
+\node[vertex inactive maximum] (v180) at (5.40,9.23) {};
+\node[vertex inactive maximum] (v181) at (5.40,12.59) {};
+\path[comp inactive maximum] (v180) -- (v181);
+
+\node[vertex inactive maximum] (v182) at (5.56,9.65) {};
+\node[vertex inactive maximum] (v183) at (5.56,13.01) {};
+\path[comp inactive maximum] (v182) -- (v183);
+
+\node[vertex active minimum] (v184) at (6.08,1.68) {};
+\node[vertex active minimum] (v185) at (6.08,3.36) {};
+\path[comp active minimum] (v184) -- (v185);
+
+\node[vertex active minimum] (v186) at (6.24,2.10) {};
+\node[vertex active minimum] (v187) at (6.24,3.78) {};
+\path[comp active minimum] (v186) -- (v187);
+
+\node[vertex active maximum] (v188) at (6.40,2.52) {};
+\node[vertex active maximum] (v189) at (6.40,4.20) {};
+\path[comp active maximum] (v188) -- (v189);
+
+\node[vertex active maximum] (v190) at (6.56,2.94) {};
+\node[vertex active maximum] (v191) at (6.56,4.62) {};
+\path[comp active maximum] (v190) -- (v191);
+
+\node[vertex active minimum] (v192) at (6.08,8.39) {};
+\node[vertex active minimum] (v193) at (6.08,10.07) {};
+\path[comp active minimum] (v192) -- (v193);
+
+\node[vertex active minimum] (v194) at (6.24,8.81) {};
+\node[vertex active minimum] (v195) at (6.24,10.49) {};
+\path[comp active minimum] (v194) -- (v195);
+
+\node[vertex active maximum] (v196) at (6.40,9.23) {};
+\node[vertex active maximum] (v197) at (6.40,10.91) {};
+\path[comp active maximum] (v196) -- (v197);
+
+\node[vertex active maximum] (v198) at (6.56,9.65) {};
+\node[vertex active maximum] (v199) at (6.56,11.33) {};
+\path[comp active maximum] (v198) -- (v199);
+
+\node[vertex active minimum] (v200) at (7.08,0.84) {};
+\node[vertex active minimum] (v201) at (7.08,1.68) {};
+\path[comp active minimum] (v200) -- (v201);
+
+\node[vertex active minimum] (v202) at (7.24,1.26) {};
+\node[vertex active minimum] (v203) at (7.24,2.10) {};
+\path[comp active minimum] (v202) -- (v203);
+
+\node[vertex] (v204) at (7.08,2.52) {};
+\node[vertex] (v205) at (7.08,3.36) {};
+\path[comp] (v204) -- (v205);
+
+\node[vertex] (v206) at (7.24,2.94) {};
+\node[vertex] (v207) at (7.24,3.78) {};
+\path[comp] (v206) -- (v207);
+
+\node[vertex active maximum] (v208) at (7.08,4.20) {};
+\node[vertex active maximum] (v209) at (7.08,5.03) {};
+\path[comp active maximum] (v208) -- (v209);
+
+\node[vertex active maximum] (v210) at (7.24,4.62) {};
+\node[vertex active maximum] (v211) at (7.24,5.45) {};
+\path[comp active maximum] (v210) -- (v211);
+
+\node[vertex active minimum] (v212) at (7.08,7.55) {};
+\node[vertex active minimum] (v213) at (7.08,8.39) {};
+\path[comp active minimum] (v212) -- (v213);
+
+\node[vertex active minimum] (v214) at (7.24,7.97) {};
+\node[vertex active minimum] (v215) at (7.24,8.81) {};
+\path[comp active minimum] (v214) -- (v215);
+
+\node[vertex] (v216) at (7.08,9.23) {};
+\node[vertex] (v217) at (7.08,10.07) {};
+\path[comp] (v216) -- (v217);
+
+\node[vertex] (v218) at (7.24,9.65) {};
+\node[vertex] (v219) at (7.24,10.49) {};
+\path[comp] (v218) -- (v219);
+
+\node[vertex active maximum] (v220) at (7.08,10.91) {};
+\node[vertex active maximum] (v221) at (7.08,11.75) {};
+\path[comp active maximum] (v220) -- (v221);
+
+\node[vertex active maximum] (v222) at (7.24,11.33) {};
+\node[vertex active maximum] (v223) at (7.24,12.17) {};
+\path[comp active maximum] (v222) -- (v223);
+
+\node[vertex inactive minimum] (v224) at (7.76,0.42) {};
+\node[vertex inactive minimum] (v225) at (7.76,0.84) {};
+\path[comp inactive minimum] (v224) -- (v225);
+
+\node[vertex inactive minimum] (v226) at (7.76,1.26) {};
+\node[vertex inactive minimum] (v227) at (7.76,1.68) {};
+\path[comp inactive minimum] (v226) -- (v227);
+
+\node[vertex] (v228) at (7.76,2.10) {};
+\node[vertex] (v229) at (7.76,2.52) {};
+\path[comp] (v228) -- (v229);
+
+\node[vertex] (v230) at (7.76,2.94) {};
+\node[vertex] (v231) at (7.76,3.36) {};
+\path[comp] (v230) -- (v231);
+
+\node[vertex] (v232) at (7.76,3.78) {};
+\node[vertex] (v233) at (7.76,4.20) {};
+\path[comp] (v232) -- (v233);
+
+\node[vertex inactive maximum] (v234) at (7.76,4.62) {};
+\node[vertex inactive maximum] (v235) at (7.76,5.03) {};
+\path[comp inactive maximum] (v234) -- (v235);
+
+\node[vertex inactive maximum] (v236) at (7.76,5.45) {};
+\node[vertex inactive maximum] (v237) at (7.76,5.87) {};
+\path[comp inactive maximum] (v236) -- (v237);
+
+\node[vertex inactive minimum] (v238) at (7.76,7.13) {};
+\node[vertex inactive minimum] (v239) at (7.76,7.55) {};
+\path[comp inactive minimum] (v238) -- (v239);
+
+\node[vertex inactive minimum] (v240) at (7.76,7.97) {};
+\node[vertex inactive minimum] (v241) at (7.76,8.39) {};
+\path[comp inactive minimum] (v240) -- (v241);
+
+\node[vertex] (v242) at (7.76,8.81) {};
+\node[vertex] (v243) at (7.76,9.23) {};
+\path[comp] (v242) -- (v243);
+
+\node[vertex] (v244) at (7.76,9.65) {};
+\node[vertex] (v245) at (7.76,10.07) {};
+\path[comp] (v244) -- (v245);
+
+\node[vertex] (v246) at (7.76,10.49) {};
+\node[vertex] (v247) at (7.76,10.91) {};
+\path[comp] (v246) -- (v247);
+
+\node[vertex inactive maximum] (v248) at (7.76,11.33) {};
+\node[vertex inactive maximum] (v249) at (7.76,11.75) {};
+\path[comp inactive maximum] (v248) -- (v249);
+
+\node[vertex inactive maximum] (v250) at (7.76,12.17) {};
+\node[vertex inactive maximum] (v251) at (7.76,12.59) {};
+\path[comp inactive maximum] (v250) -- (v251);
+
+\node[vertex inactive minimum] (v252) at (8.29,0.00) {};
+\node[vertex inactive minimum] (v253) at (8.29,6.71) {};
+\path[comp inactive minimum] (v252) -- (v253);
+
+\node[vertex inactive minimum] (v254) at (8.44,0.42) {};
+\node[vertex inactive minimum] (v255) at (8.44,7.13) {};
+\path[comp inactive minimum] (v254) -- (v255);
+
+\node[vertex inactive minimum] (v256) at (8.60,0.84) {};
+\node[vertex inactive minimum] (v257) at (8.60,7.55) {};
+\path[comp inactive minimum] (v256) -- (v257);
+
+\node[vertex inactive minimum] (v258) at (8.76,1.26) {};
+\node[vertex inactive minimum] (v259) at (8.76,7.97) {};
+\path[comp inactive minimum] (v258) -- (v259);
+
+\node[vertex] (v260) at (8.92,1.68) {};
+\node[vertex] (v261) at (8.92,8.39) {};
+\path[comp] (v260) -- (v261);
+
+\node[vertex] (v262) at (9.07,2.10) {};
+\node[vertex] (v263) at (9.07,8.81) {};
+\path[comp] (v262) -- (v263);
+
+\node[vertex] (v264) at (9.23,2.52) {};
+\node[vertex] (v265) at (9.23,9.23) {};
+\path[comp] (v264) -- (v265);
+
+\node[vertex] (v266) at (9.39,2.94) {};
+\node[vertex] (v267) at (9.39,9.65) {};
+\path[comp] (v266) -- (v267);
+
+\node[vertex] (v268) at (9.55,3.36) {};
+\node[vertex] (v269) at (9.55,10.07) {};
+\path[comp] (v268) -- (v269);
+
+\node[vertex] (v270) at (9.70,3.78) {};
+\node[vertex] (v271) at (9.70,10.49) {};
+\path[comp] (v270) -- (v271);
+
+\node[vertex] (v272) at (9.86,4.20) {};
+\node[vertex] (v273) at (9.86,10.91) {};
+\path[comp] (v272) -- (v273);
+
+\node[vertex] (v274) at (10.02,4.62) {};
+\node[vertex] (v275) at (10.02,11.33) {};
+\path[comp] (v274) -- (v275);
+
+\node[vertex inactive maximum] (v276) at (10.17,5.03) {};
+\node[vertex inactive maximum] (v277) at (10.17,11.75) {};
+\path[comp inactive maximum] (v276) -- (v277);
+
+\node[vertex inactive maximum] (v278) at (10.33,5.45) {};
+\node[vertex inactive maximum] (v279) at (10.33,12.17) {};
+\path[comp inactive maximum] (v278) -- (v279);
+
+\node[vertex inactive maximum] (v280) at (10.49,5.87) {};
+\node[vertex inactive maximum] (v281) at (10.49,12.59) {};
+\path[comp inactive maximum] (v280) -- (v281);
+
+\node[vertex inactive maximum] (v282) at (10.65,6.29) {};
+\node[vertex inactive maximum] (v283) at (10.65,13.01) {};
+\path[comp inactive maximum] (v282) -- (v283);
+
+\node[vertex active minimum] (v284) at (11.17,3.36) {};
+\node[vertex active minimum] (v285) at (11.17,6.71) {};
+\path[comp active minimum] (v284) -- (v285);
+
+\node[vertex active minimum] (v286) at (11.33,3.78) {};
+\node[vertex active minimum] (v287) at (11.33,7.13) {};
+\path[comp active minimum] (v286) -- (v287);
+
+\node[vertex active minimum] (v288) at (11.49,4.20) {};
+\node[vertex active minimum] (v289) at (11.49,7.55) {};
+\path[comp active minimum] (v288) -- (v289);
+
+\node[vertex active minimum] (v290) at (11.64,4.62) {};
+\node[vertex active minimum] (v291) at (11.64,7.97) {};
+\path[comp active minimum] (v290) -- (v291);
+
+\node[vertex active maximum] (v292) at (11.80,5.03) {};
+\node[vertex active maximum] (v293) at (11.80,8.39) {};
+\path[comp active maximum] (v292) -- (v293);
+
+\node[vertex active maximum] (v294) at (11.96,5.45) {};
+\node[vertex active maximum] (v295) at (11.96,8.81) {};
+\path[comp active maximum] (v294) -- (v295);
+
+\node[vertex active maximum] (v296) at (12.12,5.87) {};
+\node[vertex active maximum] (v297) at (12.12,9.23) {};
+\path[comp active maximum] (v296) -- (v297);
+
+\node[vertex active maximum] (v298) at (12.27,6.29) {};
+\node[vertex active maximum] (v299) at (12.27,9.65) {};
+\path[comp active maximum] (v298) -- (v299);
+
+\node[vertex active minimum] (v300) at (12.80,1.68) {};
+\node[vertex active minimum] (v301) at (12.80,3.36) {};
+\path[comp active minimum] (v300) -- (v301);
+
+\node[vertex active minimum] (v302) at (12.95,2.10) {};
+\node[vertex active minimum] (v303) at (12.95,3.78) {};
+\path[comp active minimum] (v302) -- (v303);
+
+\node[vertex active minimum] (v304) at (13.11,2.52) {};
+\node[vertex active minimum] (v305) at (13.11,4.20) {};
+\path[comp active minimum] (v304) -- (v305);
+
+\node[vertex active minimum] (v306) at (13.27,2.94) {};
+\node[vertex active minimum] (v307) at (13.27,4.62) {};
+\path[comp active minimum] (v306) -- (v307);
+
+\node[vertex] (v308) at (12.80,5.03) {};
+\node[vertex] (v309) at (12.80,6.71) {};
+\path[comp] (v308) -- (v309);
+
+\node[vertex] (v310) at (12.95,5.45) {};
+\node[vertex] (v311) at (12.95,7.13) {};
+\path[comp] (v310) -- (v311);
+
+\node[vertex] (v312) at (13.11,5.87) {};
+\node[vertex] (v313) at (13.11,7.55) {};
+\path[comp] (v312) -- (v313);
+
+\node[vertex] (v314) at (13.27,6.29) {};
+\node[vertex] (v315) at (13.27,7.97) {};
+\path[comp] (v314) -- (v315);
+
+\node[vertex active maximum] (v316) at (12.80,8.39) {};
+\node[vertex active maximum] (v317) at (12.80,10.07) {};
+\path[comp active maximum] (v316) -- (v317);
+
+\node[vertex active maximum] (v318) at (12.95,8.81) {};
+\node[vertex active maximum] (v319) at (12.95,10.49) {};
+\path[comp active maximum] (v318) -- (v319);
+
+\node[vertex active maximum] (v320) at (13.11,9.23) {};
+\node[vertex active maximum] (v321) at (13.11,10.91) {};
+\path[comp active maximum] (v320) -- (v321);
+
+\node[vertex active maximum] (v322) at (13.27,9.65) {};
+\node[vertex active maximum] (v323) at (13.27,11.33) {};
+\path[comp active maximum] (v322) -- (v323);
+
+\node[vertex inactive minimum] (v324) at (13.79,0.84) {};
+\node[vertex inactive minimum] (v325) at (13.79,1.68) {};
+\path[comp inactive minimum] (v324) -- (v325);
+
+\node[vertex inactive minimum] (v326) at (13.95,1.26) {};
+\node[vertex inactive minimum] (v327) at (13.95,2.10) {};
+\path[comp inactive minimum] (v326) -- (v327);
+
+\node[vertex inactive minimum] (v328) at (13.79,2.52) {};
+\node[vertex inactive minimum] (v329) at (13.79,3.36) {};
+\path[comp inactive minimum] (v328) -- (v329);
+
+\node[vertex inactive minimum] (v330) at (13.95,2.94) {};
+\node[vertex inactive minimum] (v331) at (13.95,3.78) {};
+\path[comp inactive minimum] (v330) -- (v331);
+
+\node[vertex] (v332) at (13.79,4.20) {};
+\node[vertex] (v333) at (13.79,5.03) {};
+\path[comp] (v332) -- (v333);
+
+\node[vertex] (v334) at (13.95,4.62) {};
+\node[vertex] (v335) at (13.95,5.45) {};
+\path[comp] (v334) -- (v335);
+
+\node[vertex] (v336) at (13.79,5.87) {};
+\node[vertex] (v337) at (13.79,6.71) {};
+\path[comp] (v336) -- (v337);
+
+\node[vertex] (v338) at (13.95,6.29) {};
+\node[vertex] (v339) at (13.95,7.13) {};
+\path[comp] (v338) -- (v339);
+
+\node[vertex] (v340) at (13.79,7.55) {};
+\node[vertex] (v341) at (13.79,8.39) {};
+\path[comp] (v340) -- (v341);
+
+\node[vertex] (v342) at (13.95,7.97) {};
+\node[vertex] (v343) at (13.95,8.81) {};
+\path[comp] (v342) -- (v343);
+
+\node[vertex inactive maximum] (v344) at (13.79,9.23) {};
+\node[vertex inactive maximum] (v345) at (13.79,10.07) {};
+\path[comp inactive maximum] (v344) -- (v345);
+
+\node[vertex inactive maximum] (v346) at (13.95,9.65) {};
+\node[vertex inactive maximum] (v347) at (13.95,10.49) {};
+\path[comp inactive maximum] (v346) -- (v347);
+
+\node[vertex inactive maximum] (v348) at (13.79,10.91) {};
+\node[vertex inactive maximum] (v349) at (13.79,11.75) {};
+\path[comp inactive maximum] (v348) -- (v349);
+
+\node[vertex inactive maximum] (v350) at (13.95,11.33) {};
+\node[vertex inactive maximum] (v351) at (13.95,12.17) {};
+\path[comp inactive maximum] (v350) -- (v351);
+
+\node[vertex inactive minimum] (v352) at (14.48,0.42) {};
+\node[vertex inactive minimum] (v353) at (14.48,0.84) {};
+\path[comp inactive minimum] (v352) -- (v353);
+
+\node[vertex inactive minimum] (v354) at (14.48,1.26) {};
+\node[vertex inactive minimum] (v355) at (14.48,1.68) {};
+\path[comp inactive minimum] (v354) -- (v355);
+
+\node[vertex inactive minimum] (v356) at (14.48,2.10) {};
+\node[vertex inactive minimum] (v357) at (14.48,2.52) {};
+\path[comp inactive minimum] (v356) -- (v357);
+
+\node[vertex inactive minimum] (v358) at (14.48,2.94) {};
+\node[vertex inactive minimum] (v359) at (14.48,3.36) {};
+\path[comp inactive minimum] (v358) -- (v359);
+
+\node[vertex] (v360) at (14.48,3.78) {};
+\node[vertex] (v361) at (14.48,4.20) {};
+\path[comp] (v360) -- (v361);
+
+\node[vertex] (v362) at (14.48,4.62) {};
+\node[vertex] (v363) at (14.48,5.03) {};
+\path[comp] (v362) -- (v363);
+
+\node[vertex] (v364) at (14.48,5.45) {};
+\node[vertex] (v365) at (14.48,5.87) {};
+\path[comp] (v364) -- (v365);
+
+\node[vertex] (v366) at (14.48,6.29) {};
+\node[vertex] (v367) at (14.48,6.71) {};
+\path[comp] (v366) -- (v367);
+
+\node[vertex] (v368) at (14.48,7.13) {};
+\node[vertex] (v369) at (14.48,7.55) {};
+\path[comp] (v368) -- (v369);
+
+\node[vertex] (v370) at (14.48,7.97) {};
+\node[vertex] (v371) at (14.48,8.39) {};
+\path[comp] (v370) -- (v371);
+
+\node[vertex] (v372) at (14.48,8.81) {};
+\node[vertex] (v373) at (14.48,9.23) {};
+\path[comp] (v372) -- (v373);
+
+\node[vertex inactive maximum] (v374) at (14.48,9.65) {};
+\node[vertex inactive maximum] (v375) at (14.48,10.07) {};
+\path[comp inactive maximum] (v374) -- (v375);
+
+\node[vertex inactive maximum] (v376) at (14.48,10.49) {};
+\node[vertex inactive maximum] (v377) at (14.48,10.91) {};
+\path[comp inactive maximum] (v376) -- (v377);
+
+\node[vertex inactive maximum] (v378) at (14.48,11.33) {};
+\node[vertex inactive maximum] (v379) at (14.48,11.75) {};
+\path[comp inactive maximum] (v378) -- (v379);
+
+\node[vertex inactive maximum] (v380) at (14.48,12.17) {};
+\node[vertex inactive maximum] (v381) at (14.48,12.59) {};
+\path[comp inactive maximum] (v380) -- (v381);
+
+\end{tikzpicture}

diff --git a/images/16-ec-from-oes32.tex b/images/16-ec-from-oes32.tex
new file mode 100644 (file)
index 0000000..7d16782
--- /dev/null
+++ b/images/16-ec-from-oes32.tex
@@ -0,0 +1,270 @@
+\begin{tikzpicture}[auto]
+\node[vertex] (v0) at (0.87,0.00) {};
+\node[vertex] (v1) at (0.87,5.55) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.13,0.69) {};
+\node[vertex] (v3) at (1.13,6.24) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v4) at (1.39,1.39) {};
+\node[vertex] (v5) at (1.39,6.94) {};
+\path[comp] (v4) -- (v5);
+
+\node[vertex] (v6) at (1.65,2.08) {};
+\node[vertex] (v7) at (1.65,7.63) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v8) at (1.91,2.77) {};
+\node[vertex] (v9) at (1.91,8.32) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v10) at (2.17,3.47) {};
+\node[vertex] (v11) at (2.17,9.02) {};
+\path[comp] (v10) -- (v11);
+
+\node[vertex] (v12) at (2.43,4.16) {};
+\node[vertex] (v13) at (2.43,9.71) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (2.69,4.86) {};
+\node[vertex] (v15) at (2.69,10.40) {};
+\path[comp] (v14) -- (v15);
+
+\node[vertex] (v16) at (3.55,0.00) {};
+\node[vertex] (v17) at (3.55,0.69) {};
+\path[comp] (v16) -- (v17);
+
+\node[vertex] (v18) at (3.55,1.39) {};
+\node[vertex] (v19) at (3.55,2.08) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (3.55,2.77) {};
+\node[vertex] (v21) at (3.55,3.47) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v22) at (3.55,4.16) {};
+\node[vertex] (v23) at (3.55,4.86) {};
+\path[comp] (v22) -- (v23);
+
+\node[vertex] (v24) at (3.55,5.55) {};
+\node[vertex] (v25) at (3.55,6.24) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (3.55,6.94) {};
+\node[vertex] (v27) at (3.55,7.63) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v28) at (3.55,8.32) {};
+\node[vertex] (v29) at (3.55,9.02) {};
+\path[comp] (v28) -- (v29);
+
+\node[vertex] (v30) at (3.55,9.71) {};
+\node[vertex] (v31) at (3.55,10.40) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (4.42,0.00) {};
+\node[vertex] (v33) at (4.42,1.39) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (4.68,0.69) {};
+\node[vertex] (v35) at (4.68,5.55) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (4.42,2.08) {};
+\node[vertex] (v37) at (4.42,6.94) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (4.94,2.77) {};
+\node[vertex] (v39) at (4.94,4.16) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (5.20,3.47) {};
+\node[vertex] (v41) at (5.20,8.32) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v42) at (4.94,4.86) {};
+\node[vertex] (v43) at (4.94,9.71) {};
+\path[comp] (v42) -- (v43);
+
+\node[vertex] (v44) at (4.68,6.24) {};
+\node[vertex] (v45) at (4.68,7.63) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (4.42,9.02) {};
+\node[vertex] (v47) at (4.42,10.40) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (6.07,0.00) {};
+\node[vertex] (v49) at (6.07,2.77) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (6.33,0.69) {};
+\node[vertex] (v51) at (6.33,2.08) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (6.07,3.47) {};
+\node[vertex] (v53) at (6.07,4.86) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (6.07,5.55) {};
+\node[vertex] (v55) at (6.07,6.94) {};
+\path[comp] (v54) -- (v55);
+
+\node[vertex] (v56) at (6.07,7.63) {};
+\node[vertex] (v57) at (6.07,10.40) {};
+\path[comp] (v56) -- (v57);
+
+\node[vertex] (v58) at (6.33,8.32) {};
+\node[vertex] (v59) at (6.33,9.71) {};
+\path[comp] (v58) -- (v59);
+
+\node[vertex] (v60) at (7.20,1.39) {};
+\node[vertex] (v61) at (7.20,5.55) {};
+\path[comp] (v60) -- (v61);
+
+\node[vertex] (v62) at (7.46,2.08) {};
+\node[vertex] (v63) at (7.46,6.24) {};
+\path[comp] (v62) -- (v63);
+
+\node[vertex] (v64) at (7.72,4.16) {};
+\node[vertex] (v65) at (7.72,8.32) {};
+\path[comp] (v64) -- (v65);
+
+\node[vertex] (v66) at (7.98,4.86) {};
+\node[vertex] (v67) at (7.98,9.02) {};
+\path[comp] (v66) -- (v67);
+
+\node[vertex] (v68) at (8.84,0.69) {};
+\node[vertex] (v69) at (8.84,1.39) {};
+\path[comp] (v68) -- (v69);
+
+\node[vertex] (v70) at (8.84,2.08) {};
+\node[vertex] (v71) at (8.84,5.55) {};
+\path[comp] (v70) -- (v71);
+
+\node[vertex] (v72) at (9.10,3.47) {};
+\node[vertex] (v73) at (9.10,4.16) {};
+\path[comp] (v72) -- (v73);
+
+\node[vertex] (v74) at (9.10,4.86) {};
+\node[vertex] (v75) at (9.10,8.32) {};
+\path[comp] (v74) -- (v75);
+
+\node[vertex] (v76) at (8.84,6.24) {};
+\node[vertex] (v77) at (8.84,6.94) {};
+\path[comp] (v76) -- (v77);
+
+\node[vertex] (v78) at (8.84,9.02) {};
+\node[vertex] (v79) at (8.84,9.71) {};
+\path[comp] (v78) -- (v79);
+
+\node[vertex] (v80) at (9.97,0.69) {};
+\node[vertex] (v81) at (9.97,3.47) {};
+\path[comp] (v80) -- (v81);
+
+\node[vertex] (v82) at (10.23,1.39) {};
+\node[vertex] (v83) at (10.23,4.16) {};
+\path[comp] (v82) -- (v83);
+
+\node[vertex] (v84) at (10.49,2.08) {};
+\node[vertex] (v85) at (10.49,4.86) {};
+\path[comp] (v84) -- (v85);
+
+\node[vertex] (v86) at (9.97,5.55) {};
+\node[vertex] (v87) at (9.97,8.32) {};
+\path[comp] (v86) -- (v87);
+
+\node[vertex] (v88) at (10.23,6.24) {};
+\node[vertex] (v89) at (10.23,9.02) {};
+\path[comp] (v88) -- (v89);
+
+\node[vertex] (v90) at (10.49,6.94) {};
+\node[vertex] (v91) at (10.49,9.71) {};
+\path[comp] (v90) -- (v91);
+
+\node[vertex] (v92) at (11.36,2.77) {};
+\node[vertex] (v93) at (11.36,5.55) {};
+\path[comp] (v92) -- (v93);
+
+\node[vertex] (v94) at (11.62,3.47) {};
+\node[vertex] (v95) at (11.62,6.24) {};
+\path[comp] (v94) -- (v95);
+
+\node[vertex] (v96) at (11.88,4.16) {};
+\node[vertex] (v97) at (11.88,6.94) {};
+\path[comp] (v96) -- (v97);
+
+\node[vertex] (v98) at (12.14,4.86) {};
+\node[vertex] (v99) at (12.14,7.63) {};
+\path[comp] (v98) -- (v99);
+
+\node[vertex] (v100) at (13.01,1.39) {};
+\node[vertex] (v101) at (13.01,2.77) {};
+\path[comp] (v100) -- (v101);
+
+\node[vertex] (v102) at (13.27,2.08) {};
+\node[vertex] (v103) at (13.27,3.47) {};
+\path[comp] (v102) -- (v103);
+
+\node[vertex] (v104) at (13.01,4.16) {};
+\node[vertex] (v105) at (13.01,5.55) {};
+\path[comp] (v104) -- (v105);
+
+\node[vertex] (v106) at (13.27,4.86) {};
+\node[vertex] (v107) at (13.27,6.24) {};
+\path[comp] (v106) -- (v107);
+
+\node[vertex] (v108) at (13.01,6.94) {};
+\node[vertex] (v109) at (13.01,8.32) {};
+\path[comp] (v108) -- (v109);
+
+\node[vertex] (v110) at (13.27,7.63) {};
+\node[vertex] (v111) at (13.27,9.02) {};
+\path[comp] (v110) -- (v111);
+
+\node[vertex] (v112) at (14.13,0.69) {};
+\node[vertex] (v113) at (14.13,1.39) {};
+\path[comp] (v112) -- (v113);
+
+\node[vertex] (v114) at (14.13,2.08) {};
+\node[vertex] (v115) at (14.13,2.77) {};
+\path[comp] (v114) -- (v115);
+
+\node[vertex] (v116) at (14.13,3.47) {};
+\node[vertex] (v117) at (14.13,4.16) {};
+\path[comp] (v116) -- (v117);
+
+\node[vertex] (v118) at (14.13,4.86) {};
+\node[vertex] (v119) at (14.13,5.55) {};
+\path[comp] (v118) -- (v119);
+
+\node[vertex] (v120) at (14.13,6.24) {};
+\node[vertex] (v121) at (14.13,6.94) {};
+\path[comp] (v120) -- (v121);
+
+\node[vertex] (v122) at (14.13,7.63) {};
+\node[vertex] (v123) at (14.13,8.32) {};
+\path[comp] (v122) -- (v123);
+
+\node[vertex] (v124) at (14.13,9.02) {};
+\node[vertex] (v125) at (14.13,9.71) {};
+\path[comp] (v124) -- (v125);
+
+\path[edge] (0,0.00) -- (15.00,0.00);
+\path[edge] (0,0.69) -- (15.00,0.69);
+\path[edge] (0,1.39) -- (15.00,1.39);
+\path[edge] (0,2.08) -- (15.00,2.08);
+\path[edge] (0,2.77) -- (15.00,2.77);
+\path[edge] (0,3.47) -- (15.00,3.47);
+\path[edge] (0,4.16) -- (15.00,4.16);
+\path[edge] (0,4.86) -- (15.00,4.86);
+\path[edge] (0,5.55) -- (15.00,5.55);
+\path[edge] (0,6.24) -- (15.00,6.24);
+\path[edge] (0,6.94) -- (15.00,6.94);
+\path[edge] (0,7.63) -- (15.00,7.63);
+\path[edge] (0,8.32) -- (15.00,8.32);
+\path[edge] (0,9.02) -- (15.00,9.02);
+\path[edge] (0,9.71) -- (15.00,9.71);
+\path[edge] (0,10.40) -- (15.00,10.40);
+\end{tikzpicture}

diff --git a/images/batcher-8.tex b/images/batcher-8.tex
new file mode 100644 (file)
index 0000000..0aecaed
--- /dev/null
+++ b/images/batcher-8.tex
@@ -0,0 +1,125 @@
+\begin{tikzpicture}[scale=0.70,auto]
+
+% lower S(4)
+\draw[red box] (1,-.333) rectangle (5.35,3.333);
+% upper S(4)
+\draw[red box] (1,3.667) rectangle (5.35,7.333);
+
+% Recursive comparators
+\draw[green box] (5.85,-.333) rectangle (7.90,7.333);
+
+% lower merge block
+\draw[blue box] (8.40,-.333) rectangle (11.25,3.333);
+% upper merge block
+\draw[blue box] (8.40,3.667) rectangle (11.25,7.333);
+
+% stage 0
+\node[vertex] (v0) at (1.50,0) {};
+\node[vertex] (v1) at (1.50,1) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.50,2) {};
+\node[vertex] (v3) at (1.50,3) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v4) at (1.50,4) {};
+\node[vertex] (v5) at (1.50,5) {};
+\path[comp] (v4) -- (v5);
+
+\node[vertex] (v6) at (1.50,6) {};
+\node[vertex] (v7) at (1.50,7) {};
+\path[comp] (v6) -- (v7);
+
+% stage 1
+\node[vertex] (v8) at (3.00,0) {};
+\node[vertex] (v9) at (3.00,3) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v10) at (3.35,1) {};
+\node[vertex] (v11) at (3.35,2) {};
+\path[comp] (v10) -- (v11);
+
+\node[vertex] (v12) at (3.00,4) {};
+\node[vertex] (v13) at (3.00,7) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (3.35,5) {};
+\node[vertex] (v15) at (3.35,6) {};
+\path[comp] (v14) -- (v15);
+
+% stage 2
+\node[vertex] (v16) at (4.85,0) {};
+\node[vertex] (v17) at (4.85,1) {};
+\path[comp] (v16) -- (v17);
+
+\node[vertex] (v18) at (4.85,2) {};
+\node[vertex] (v19) at (4.85,3) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (4.85,4) {};
+\node[vertex] (v21) at (4.85,5) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v22) at (4.85,6) {};
+\node[vertex] (v23) at (4.85,7) {};
+\path[comp] (v22) -- (v23);
+
+% stage 3
+\node[vertex] (v24) at (6.35,0) {};
+\node[vertex] (v25) at (6.35,7) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (6.70,1) {};
+\node[vertex] (v27) at (6.70,6) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v28) at (7.05,2) {};
+\node[vertex] (v29) at (7.05,5) {};
+\path[comp] (v28) -- (v29);
+
+\node[vertex] (v30) at (7.40,3) {};
+\node[vertex] (v31) at (7.40,4) {};
+\path[comp] (v30) -- (v31);
+
+% stage 4
+\node[vertex] (v32) at (8.90,0) {};
+\node[vertex] (v33) at (8.90,2) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (9.25,1) {};
+\node[vertex] (v35) at (9.25,3) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (8.90,4) {};
+\node[vertex] (v37) at (8.90,6) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (9.25,5) {};
+\node[vertex] (v39) at (9.25,7) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (10.75,0) {};
+\node[vertex] (v41) at (10.75,1) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v42) at (10.75,2) {};
+\node[vertex] (v43) at (10.75,3) {};
+\path[comp] (v42) -- (v43);
+
+\node[vertex] (v44) at (10.75,4) {};
+\node[vertex] (v45) at (10.75,5) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (10.75,6) {};
+\node[vertex] (v47) at (10.75,7) {};
+\path[comp] (v46) -- (v47);
+
+\path[edge] (0,0) -- (12.25,0);
+\path[edge] (0,1) -- (12.25,1);
+\path[edge] (0,2) -- (12.25,2);
+\path[edge] (0,3) -- (12.25,3);
+\path[edge] (0,4) -- (12.25,4);
+\path[edge] (0,5) -- (12.25,5);
+\path[edge] (0,6) -- (12.25,6);
+\path[edge] (0,7) -- (12.25,7);
+\end{tikzpicture}

diff --git a/images/oe-transposition-cut0.tex b/images/oe-transposition-cut0.tex
new file mode 100644 (file)
index 0000000..35806f3
--- /dev/null
+++ b/images/oe-transposition-cut0.tex
@@ -0,0 +1,130 @@
+\begin{tikzpicture}[scale=0.50,auto]
+
+% Lines (some with red parts)
+\path[edge] (0,7) -- (13.50,7);
+\path[edge] (0,6) -- (13.50,6);
+\path[edge] (0,5) -- (13.50,5);
+
+\path[edge,color=red,very thick] (0,4) -- (3,4);
+\path[edge] (3,4) -- (13.50,4);
+
+\path[edge] (0,3) -- (3,3);
+\path[edge,color=red,very thick] (3,3) -- (4.5,3);
+\path[edge] (4.5,3) -- (13.50,3);
+
+\path[edge] (0,2) -- (4.50,2);
+\path[edge,color=red,very thick] (4.50,2) -- (6,2);
+\path[edge] (6,2) -- (13.50,2);
+
+\path[edge] (0,1) -- (6,1);
+\path[edge,color=red,very thick] (6,1) -- (7.5,1);
+\path[edge] (7.5,1) -- (13.50,1);
+
+\path[edge] (0,0) -- (7.50,0);
+\path[edge,color=red,very thick] (7.50,0) -- (13.50,0);
+
+% Red comparators
+\foreach \pos in {(3.00,3), (4.50,2), (6.00,1), (7.50,0)}
+{
+  \path[draw,color=red,very thick] \pos -- +(0,1);
+  \draw \pos circle(5pt)[color=red,fill=red] {};
+  \draw \pos+(0,1) circle(5pt)[color=red,fill=red] {};
+}
+
+% Blue comparators
+\foreach \pos in {(1.50,4), (10.50,0)}
+{
+  \path[draw,color=teal,thick] \pos -- +(0,1);
+  \draw \pos circle(5pt)[color=teal,fill=teal] {};
+  \draw \pos+(0,1) circle(5pt)[color=teal,fill=teal] {};
+}
+
+\node[vertex] (v0) at (1.50,0) {};
+\node[vertex] (v1) at (1.50,1) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.50,2) {};
+\node[vertex] (v3) at (1.50,3) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v6) at (1.50,6) {};
+\node[vertex] (v7) at (1.50,7) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v8) at (3.00,1) {};
+\node[vertex] (v9) at (3.00,2) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v12) at (3.00,5) {};
+\node[vertex] (v13) at (3.00,6) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (4.50,0) {};
+\node[vertex] (v15) at (4.50,1) {};
+\path[comp] (v14) -- (v15);
+
+\node[vertex] (v18) at (4.50,4) {};
+\node[vertex] (v19) at (4.50,5) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (4.50,6) {};
+\node[vertex] (v21) at (4.50,7) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v24) at (6.00,3) {};
+\node[vertex] (v25) at (6.00,4) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (6.00,5) {};
+\node[vertex] (v27) at (6.00,6) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v30) at (7.50,2) {};
+\node[vertex] (v31) at (7.50,3) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (7.50,4) {};
+\node[vertex] (v33) at (7.50,5) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (7.50,6) {};
+\node[vertex] (v35) at (7.50,7) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (9.00,1) {};
+\node[vertex] (v37) at (9.00,2) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (9.00,3) {};
+\node[vertex] (v39) at (9.00,4) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (9.00,5) {};
+\node[vertex] (v41) at (9.00,6) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v44) at (10.50,2) {};
+\node[vertex] (v45) at (10.50,3) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (10.50,4) {};
+\node[vertex] (v47) at (10.50,5) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (10.50,6) {};
+\node[vertex] (v49) at (10.50,7) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (12.00,1) {};
+\node[vertex] (v51) at (12.00,2) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (12.00,3) {};
+\node[vertex] (v53) at (12.00,4) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (12.00,5) {};
+\node[vertex] (v55) at (12.00,6) {};
+\path[comp] (v54) -- (v55);
+
+\end{tikzpicture}

diff --git a/images/oe-transposition-cut1.tex b/images/oe-transposition-cut1.tex
new file mode 100644 (file)
index 0000000..9960b49
--- /dev/null
+++ b/images/oe-transposition-cut1.tex
@@ -0,0 +1,108 @@
+\begin{tikzpicture}[scale=0.50,auto]
+
+% Lines (some with red parts)
+\path[edge] (0,7) -- (13.50,7);
+\path[edge] (0,6) -- (13.50,6);
+\path[edge] (0,5) -- (13.50,5);
+
+\path[edge,rounded corners] (0,3) -- (2.9,3) -- (3.1,4) -- (13.50,4);
+\path[edge,rounded corners] (0,2) -- (4.4,2) -- (4.6,3) -- (13.50,3);
+\path[edge,rounded corners] (0,1) -- (5.9,1) -- (6.1,2) -- (13.50,2);
+\path[edge,rounded corners] (0,0) -- (7.4,0) -- (7.6,1) -- (13.50,1);
+
+\path[draw,very thick,color=red,rounded corners]
+                       (0,4) -- (2.9,4)
+                  -- (3.1,3) -- (4.4,3)
+                  -- (4.6,2) -- (5.9,2)
+                  -- (6.1,1) -- (7.4,1)
+                  -- (7.6,0) -- (13.5,0);
+
+\node[vertex] (v0) at (1.50,0) {};
+\node[vertex] (v1) at (1.50,1) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.50,2) {};
+\node[vertex] (v3) at (1.50,3) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v6) at (1.50,6) {};
+\node[vertex] (v7) at (1.50,7) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v8) at (3.00,1) {};
+\node[vertex] (v9) at (3.00,2) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v12) at (3.00,5) {};
+\node[vertex] (v13) at (3.00,6) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (4.50,0) {};
+\node[vertex] (v15) at (4.50,1) {};
+\path[comp] (v14) -- (v15);
+
+\node[vertex] (v18) at (4.50,4) {};
+\node[vertex] (v19) at (4.50,5) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (4.50,6) {};
+\node[vertex] (v21) at (4.50,7) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v24) at (6.00,3) {};
+\node[vertex] (v25) at (6.00,4) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (6.00,5) {};
+\node[vertex] (v27) at (6.00,6) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v30) at (7.50,2) {};
+\node[vertex] (v31) at (7.50,3) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (7.50,4) {};
+\node[vertex] (v33) at (7.50,5) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (7.50,6) {};
+\node[vertex] (v35) at (7.50,7) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (9.00,1) {};
+\node[vertex] (v37) at (9.00,2) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (9.00,3) {};
+\node[vertex] (v39) at (9.00,4) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (9.00,5) {};
+\node[vertex] (v41) at (9.00,6) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v44) at (10.50,2) {};
+\node[vertex] (v45) at (10.50,3) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (10.50,4) {};
+\node[vertex] (v47) at (10.50,5) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (10.50,6) {};
+\node[vertex] (v49) at (10.50,7) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (12.00,1) {};
+\node[vertex] (v51) at (12.00,2) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (12.00,3) {};
+\node[vertex] (v53) at (12.00,4) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (12.00,5) {};
+\node[vertex] (v55) at (12.00,6) {};
+\path[comp] (v54) -- (v55);
+
+\end{tikzpicture}

diff --git a/images/oe-transposition-cut2.tex b/images/oe-transposition-cut2.tex
new file mode 100644 (file)
index 0000000..3aafbfd
--- /dev/null
+++ b/images/oe-transposition-cut2.tex
@@ -0,0 +1,94 @@
+\begin{tikzpicture}[scale=0.50,auto]
+
+\path[use as bounding box] (0,0) -- (13.50,7.5);
+
+\path[edge] (0,7) -- (13.50,7);
+\path[edge] (0,6) -- (13.50,6);
+\path[edge] (0,5) -- (13.50,5);
+
+\path[edge,rounded corners] (0,3) -- (2.9,3) -- (3.1,4) -- (13.50,4);
+\path[edge,rounded corners] (0,2) -- (4.4,2) -- (4.6,3) -- (13.50,3);
+\path[edge,rounded corners] (0,1) -- (5.9,1) -- (6.1,2) -- (13.50,2);
+\path[edge,rounded corners] (0,0) -- (7.4,0) -- (7.6,1) -- (13.50,1);
+
+% Moved (purple) comparators
+\foreach \pos in {(1.5,0), (1.5,2), (3,1), (4.5,0)}
+{
+  \path[comp,color=purple] \pos -- +(0,1);
+  \draw \pos circle(5pt)[color=purple,fill=purple] {};
+  \draw \pos+(0,1) circle(5pt)[color=purple,fill=purple] {};
+}
+
+\node[vertex] (v6) at (1.50,6) {};
+\node[vertex] (v7) at (1.50,7) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v12) at (3.00,5) {};
+\node[vertex] (v13) at (3.00,6) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v18) at (4.50,4) {};
+\node[vertex] (v19) at (4.50,5) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (4.50,6) {};
+\node[vertex] (v21) at (4.50,7) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v24) at (6.00,3) {};
+\node[vertex] (v25) at (6.00,4) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (6.00,5) {};
+\node[vertex] (v27) at (6.00,6) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v30) at (7.50,2) {};
+\node[vertex] (v31) at (7.50,3) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (7.50,4) {};
+\node[vertex] (v33) at (7.50,5) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (7.50,6) {};
+\node[vertex] (v35) at (7.50,7) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (9.00,1) {};
+\node[vertex] (v37) at (9.00,2) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (9.00,3) {};
+\node[vertex] (v39) at (9.00,4) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (9.00,5) {};
+\node[vertex] (v41) at (9.00,6) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v44) at (10.50,2) {};
+\node[vertex] (v45) at (10.50,3) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (10.50,4) {};
+\node[vertex] (v47) at (10.50,5) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (10.50,6) {};
+\node[vertex] (v49) at (10.50,7) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (12.00,1) {};
+\node[vertex] (v51) at (12.00,2) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (12.00,3) {};
+\node[vertex] (v53) at (12.00,4) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (12.00,5) {};
+\node[vertex] (v55) at (12.00,6) {};
+\path[comp] (v54) -- (v55);
+
+\end{tikzpicture}

diff --git a/images/oe-transposition-cut3.tex b/images/oe-transposition-cut3.tex
new file mode 100644 (file)
index 0000000..1343222
--- /dev/null
+++ b/images/oe-transposition-cut3.tex
@@ -0,0 +1,95 @@
+\begin{tikzpicture}[scale=0.50,auto]
+
+\path[use as bounding box] (0,0) -- (13.50,7.5);
+
+\draw[blue box] (2.5,.5) rectangle (12.5,7.5);
+
+\path[edge] (0,7) -- (13.50,7);
+\path[edge] (0,6) -- (13.50,6);
+\path[edge] (0,5) -- (13.50,5);
+\path[edge] (0,4) -- (13.50,4);
+\path[edge] (0,3) -- (13.50,3);
+\path[edge] (0,2) -- (13.50,2);
+\path[edge] (0,1) -- (13.50,1);
+
+% Moved (purple) comparators
+\foreach \pos in {(3,1), (3,3), (4.5,2), (6,1)}
+{
+  \path[comp,color=purple] \pos -- +(0,1);
+  \draw \pos circle(5pt)[color=purple,fill=purple] {};
+  \draw \pos+(0,1) circle(5pt)[color=purple,fill=purple] {};
+}
+
+\node[vertex] (v6) at (1.50,6) {};
+\node[vertex] (v7) at (1.50,7) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v12) at (3.00,5) {};
+\node[vertex] (v13) at (3.00,6) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v18) at (4.50,4) {};
+\node[vertex] (v19) at (4.50,5) {};
+\path[comp] (v18) -- (v19);
+
+\node[vertex] (v20) at (4.50,6) {};
+\node[vertex] (v21) at (4.50,7) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v24) at (6.00,3) {};
+\node[vertex] (v25) at (6.00,4) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v26) at (6.00,5) {};
+\node[vertex] (v27) at (6.00,6) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v30) at (7.50,2) {};
+\node[vertex] (v31) at (7.50,3) {};
+\path[comp] (v30) -- (v31);
+
+\node[vertex] (v32) at (7.50,4) {};
+\node[vertex] (v33) at (7.50,5) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (7.50,6) {};
+\node[vertex] (v35) at (7.50,7) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (9.00,1) {};
+\node[vertex] (v37) at (9.00,2) {};
+\path[comp] (v36) -- (v37);
+
+\node[vertex] (v38) at (9.00,3) {};
+\node[vertex] (v39) at (9.00,4) {};
+\path[comp] (v38) -- (v39);
+
+\node[vertex] (v40) at (9.00,5) {};
+\node[vertex] (v41) at (9.00,6) {};
+\path[comp] (v40) -- (v41);
+
+\node[vertex] (v44) at (10.50,2) {};
+\node[vertex] (v45) at (10.50,3) {};
+\path[comp] (v44) -- (v45);
+
+\node[vertex] (v46) at (10.50,4) {};
+\node[vertex] (v47) at (10.50,5) {};
+\path[comp] (v46) -- (v47);
+
+\node[vertex] (v48) at (10.50,6) {};
+\node[vertex] (v49) at (10.50,7) {};
+\path[comp] (v48) -- (v49);
+
+\node[vertex] (v50) at (12.00,1) {};
+\node[vertex] (v51) at (12.00,2) {};
+\path[comp] (v50) -- (v51);
+
+\node[vertex] (v52) at (12.00,3) {};
+\node[vertex] (v53) at (12.00,4) {};
+\path[comp] (v52) -- (v53);
+
+\node[vertex] (v54) at (12.00,5) {};
+\node[vertex] (v55) at (12.00,6) {};
+\path[comp] (v54) -- (v55);
+
+\end{tikzpicture}