\subsection[Odd-Even-Mergesort-Netzwerk]{Versuche mit dem Odd-Even-Mergesort-Netzwerk}
\label{sect:sn-evolution-cut:oes}
+Wird \textsc{SN-Evolution-Cut} mit dem \emph{Odd-Even-Mergesort}-Netzwerk
+\oes{n} gestartet, gibt der Algorithmus meist Sortiernetzwerke zurück, die
+genauso effizient und schnell wie das entsprechende
+\emph{Odd-Even-Mergesort}-Netzwerk \oes{m} sind. Die Effizienz der
+Sortiernetzwerke, die mit Schnittmustern von \textsc{SN-Evolution-Cut} aus
+\oes{n} entstehen können, zeigt Tabelle~\ref{tbl:ec-oes-efficiency}
+tabellarisch.
+
+\begin{table}
+ \begin{center}
+ \rowcolors{2}{black!5}{}
+\begin{tabular}{|r|rrrrrrrrrrrrrrrr|}
+\hline
+ & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 \\
+\hline
+ 9 & 19 & & & & & & & & & & & & & & & \\
+ 10 & 19 & 26 & & & & & & & & & & & & & & \\
+ 11 & 19 & 26 & 31 & & & & & & & & & & & & & \\
+ 12 & 19 & 26 & 31 & 37 & & & & & & & & & & & & \\
+ 13 & 19 & 26 & 31 & 37 & 41 & & & & & & & & & & & \\
+ 14 & 19 & 26 & 31 & 37 & 41 & 48 & & & & & & & & & & \\
+ 15 & 19 & 26 & 31 & 37 & 41 & 48 & 53 & & & & & & & & & \\
+ 16 & 19 & 26 & 31 & 37 & 41 & 48 & 53 & 59 & & & & & & & & \\
+ 17 & 19 & 26 & 31 & 38 & 41 & 48 & 53 & 59 & 63 & & & & & & & \\
+ 18 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & & & & & & \\
+ 19 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & 82 & & & & & \\
+ 20 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & 82 & 91 & & & & \\
+ 21 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & 82 & 91 & 97 & & & \\
+ 22 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & 82 & 91 & 97 & 107 & & \\
+ 23 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & 82 & 91 & 97 & 107 & 114 & \\
+ 24 & 19 & 26 & 31 & 38 & 43 & 48 & 53 & 59 & 63 & 74 & 82 & 91 & 97 & 107 & 114 & 122 \\
+\hline
+\end{tabular}
+ \end{center}
+ \caption{Anzahl der Komparatoren der Ergebnisse von
+ \textsc{SN-Evolution-Cut} mit verschiedenen Größen des
+ \emph{Odd-Even-Mergesort}-Netzwerks und unterschiedlichen Werten für~$k$.
+ Jede Zeile gibt die Ergebnisse für ein Eingabenetzwerk \oes{n} an, jede
+ Spalte enthält die Ergebnisse für $m=n-k$, die Anzahl der Leitungen des
+ Ausgabenetzwerks.}
+ \label{tbl:ec-oes-efficiency}
+\end{table}
+
+\begin{figure}
+ \centering
+ \subfigure[11-Sortiernetzwerk aus 38~Komparatoren in 9~Schichten. Das
+ Netzwerk wurde von \textsc{SN-Evolution-Cut} aus \oes{17} erzeugt.]{\input{images/11-ec-from-oes17-fast.tex}\label{fig:11-ec-from-oes17-fast}}
+ \subfigure[12-Sortiernetzwerk aus 43~Komparatoren in 9~Schichten. Das
+ Netzwerk wurde von \textsc{SN-Evolution-Cut} aus \oes{18} erzeugt.]{\input{images/12-ec-from-oes18-fast.tex}\label{fig:12-ec-from-oes18-fast}}
+ \caption{Für einige Ziel-Leitungszahlen, unter anderem $m = 10$ und $m =
+ 11$, kann der \textsc{SN-Evolution-Cut}-Algorithmus Sortiernetzwerke
+ erzeugen, die \emph{schneller} aber weniger \emph{effizient} als \oes{m}
+ sind.}
+ \label{fig:ec-oes-fast_networks}
+\end{figure}
+
+Die Bewertungsfunktion, die \textsc{SN-Evolution-Cut} verwendet, bevorzugt
+schnelle Sortiernetzwerke. Dadurch kann es vorkommen, dass ein
+$m$-Sortiernetzwerk, das durch ein von \textsc{SN-Evolution-Cut} ausgegebenes
+Schnittmuster entsteht, schneller als \oes{m} ist. Diese Geschwindigkeit
+war allerdings in allen beobachteten Fällen nur dann möglich, wenn
+zusätzliche Komparatoren in Kauf genommen wurden. In den
+Tabellen~\ref{tbl:ec-oes-efficiency} und~\ref{tbl:ec-oes-speed} ist dieser
+Fall für $m = 11$ und $k \geqq 6$, beziehungsweise $m = 12$ und $k \geqq 6$ zu
+beobachten. Die entsprechenden schnellen Sortiernetzwerke sind in
+Abbildung~\ref{fig:ec-oes-fast_networks} dargestellt.
+
+\begin{table}
+ \begin{center}
+ \rowcolors{2}{black!5}{}
+\begin{tabular}{|r|rrrrrrrrrrrrrrrr|}
+\hline
+ & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 \\
+\hline
+ 9 & 6 & & & & & & & & & & & & & & & \\
+ 10 & 6 & 8 & & & & & & & & & & & & & & \\
+ 11 & 6 & 8 & 9 & & & & & & & & & & & & & \\
+ 12 & 6 & 8 & 9 & 10 & & & & & & & & & & & & \\
+ 13 & 6 & 8 & 9 & 10 & 10 & & & & & & & & & & & \\
+ 14 & 6 & 8 & 9 & 10 & 10 & 10 & & & & & & & & & & \\
+ 15 & 6 & 8 & 9 & 10 & 10 & 10 & 10 & & & & & & & & & \\
+ 16 & 6 & 8 & 9 & 10 & 10 & 10 & 10 & 10 & & & & & & & & \\
+ 17 & 6 & 8 & 9 & 9 & 10 & 10 & 10 & 10 & 10 & & & & & & & \\
+ 18 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & & & & & & \\
+ 19 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & 13 & & & & & \\
+ 20 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & 13 & 14 & & & & \\
+ 21 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & 13 & 14 & 14 & & & \\
+ 22 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & 13 & 14 & 14 & 15 & & \\
+ 23 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & 13 & 14 & 14 & 15 & 15 & \\
+ 24 & 6 & 8 & 9 & 9 & 9 & 10 & 10 & 10 & 10 & 12 & 13 & 14 & 14 & 15 & 15 & 15 \\
+\hline
+\oes{m}& 6 & 8 & 9 & 10 & 10 & 10 & 10 & 10 & 10 & 12 & 13 & 14 & 14 & 15 & 15 & 15 \\
+\hline
+\end{tabular}
+ \end{center}
+ \caption{Anzahl der Schichten der Ergebnisse von
+ \textsc{SN-Evolution-Cut} mit verschiedenen Größen des
+ \emph{Odd-Even-Mergesort}-Netzwerks und unterschiedlichen Werten für~$k$.
+ Jede Zeile gibt die Ergebnisse für ein Eingabenetzwerk \oes{n} an, jede
+ Spalte enthält die Ergebnisse für $m=n-k$, die Anzahl der Leitungen des
+ Ausgabenetzwerks.}
+ \label{tbl:ec-oes-speed}
+\end{table}
+
In Abschnitt~\ref{sect:anzahl_schnittmuster} wurde bereits untersucht, wie
viele \emph{unterschiedliche} Schnittmuster die konstruktiven Sortiernetzwerke
$\operatorname{OES}(32)$, $\operatorname{BS}(32)$ und $\operatorname{PS}(32)$
Jede Zeile gibt die Ergebnisse für ein Eingabenetzwerk \ps{n} an, jede
Spalte enthält die Ergebnisse für $m=n-k$, die Anzahl der Leitungen des
Ausgabenetzwerks.}
- \label{tbl:ec-ps-fast}
+ \label{tbl:ec-ps-speed}
\end{table}
Das \emph{Pairwise-Sorting-Netzwerk} $\operatorname{PS}(n)$, das \textit{Ian
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+\path[edge] (0,2.88) -- (7.00,2.88);
+\path[edge] (0,3.29) -- (7.00,3.29);
+\path[edge] (0,3.71) -- (7.00,3.71);
+\path[edge] (0,4.12) -- (7.00,4.12);
+\path[edge] (0,4.53) -- (7.00,4.53);
+\end{tikzpicture}
projects / diplomarbeit.git / commitdiff