From: Florian Forster <octo@leeloo.octo.it>
Date: Sun, 20 Feb 2011 06:50:26 +0000 (+0100)
Subject: Fehlende Dateien (Bilder) eingecheckt.
X-Git-Url: https://git.octo.it/?p=diplomarbeit.git;a=commitdiff_plain;h=461b195a7aec442b519e401b07c0faa8ff99f6a9

Fehlende Dateien (Bilder) eingecheckt.
---

diff --git a/.gitignore b/.gitignore
new file mode 100644
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
--- 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.
 
-%\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}
@@ -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
-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.
 
@@ -1683,6 +1674,13 @@ für n Iterationen
 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}
diff --git a/images/16-e1-bitonic-1296542566.tex b/images/16-e1-bitonic-1296542566.tex
new file mode 100644
index 0000000..0d1ebc5
--- /dev/null
+++ b/images/16-e1-bitonic-1296542566.tex
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diff --git a/images/16-e1-oddeven-1296543330.tex b/images/16-e1-oddeven-1296543330.tex
new file mode 100644
index 0000000..4e02a88
--- /dev/null
+++ b/images/16-e1-oddeven-1296543330.tex
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diff --git a/images/16-ec-from-oes32-cut.tex b/images/16-ec-from-oes32-cut.tex
new file mode 100644
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diff --git a/images/16-ec-from-oes32.tex b/images/16-ec-from-oes32.tex
new file mode 100644
index 0000000..7d16782
--- /dev/null
+++ b/images/16-ec-from-oes32.tex
@@ -0,0 +1,270 @@
+\begin{tikzpicture}[auto]
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+\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);
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diff --git a/images/batcher-8.tex b/images/batcher-8.tex
new file mode 100644
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
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+\node[vertex] (v1) at (1.50,1) {};
+\path[comp] (v0) -- (v1);
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+% stage 1
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+\path[comp] (v14) -- (v15);
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+% 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
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
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
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
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}