Aufgabe 1 korrektur und Overfull \hbox in 2 beheben
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@ -11,23 +11,33 @@
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\end{figure}
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\end{figure}
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\item
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\item
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Das Problem kann als Maximalflussproblem modelliert werden. Dafür haben wir
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Das Problem kann als Maximalflussproblem modelliert werden. Dafür haben wir
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eine Quelle $s$, eine Senke $t$ und Knoten $v_i$ mit $i \in \NN_{\leq n}$.
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eine Quelle $s$, eine Senke $t$ und Knoten $v_{i_{e/a}}$ mit $i \in \NN_{\leq n}$.
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Die Eingangskapazität eines Knoten $v_i$ entspricht dem Eingangsgrad $e_i$.
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Die Ausgangskapazität entspricht dem Ausgangsgrad $a_i$. Siehe \autoref{fig:task1b}.
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Wenn es einen vollständigen Fluss gibt, gibt es eine Lösung für das Problem,
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Die Eingangskapazität eines Knoten $v_{i_a}$ entspricht dem Ausgangsgrad $a_i$.
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Die Ausgangskapazität eines Knoten $v_{i_e}$ entspricht dem Eingangsgrad $e_i$.
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Für die Kantenkapazität $c \in \NN$ einer Kante $\tup{v_{i_a}, v_{j_e}}$ mit $i, j \leq n$ gilt,
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wenn $i = j$, sind Selbstkanten erlaubt, wenn $c > 0$.
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Ausserdem sind Mehrfachkanten erlaubt, wenn $c > 1$.
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Siehe \autoref{fig:task1b}.
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Wenn es einen vollständigen Fluss gibt, also alle in $t$ eingehenden Kanten vollständig benutzt werden, gibt es eine Lösung für das Problem,
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sonst nicht.
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sonst nicht.
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\points{4}
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\points{4}
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\begin{figure}
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\begin{figure}
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\centering
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\centering
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\includegraphics[page=2, width=0.5\textwidth]{figures.pdf}
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\includegraphics[page=2, width=0.8\textwidth]{figures.pdf}
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\caption{Das Problem als Maximalflussproblem.}
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\caption{Das Problem als Maximalflussproblem.}
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\label{fig:task1b}
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\label{fig:task1b}
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\end{figure}
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\end{figure}
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\item
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\item
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Die Modellierung ist korrekt, da der Eingangs- und Ausgangsgrad jedes Knotens $v_i$
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Die Modellierung ist korrekt, da die Eingangs- und Ausgangsgrade der Knoten
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von oben beschränkt wird von der Eingangskapazität $e_i$ bzw. Ausgangskapazität $a_i$.
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$v_i$ im Graphen durch die Kantenkapazitäten $a_i$ und $e_i$ Fluss beschränkt werden.
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Zudem erfüllt die Flusserhaltung den Zweck, dass die Summe der Eingangsgrade gleich der Summe der Ausgangsgrade sind, was in einem Graphen erfüllt sein muss.
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Durch wählen der Kantenkapazitäten der Kanten $(v_{i_a}, v_{j_e})$ im Fluss
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können Selbst- und Mehrfachkanten ein- oder ausgeschlossen werden.
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Damit entsprechen diese Kanten im Fluss den Kanten im Graphen.
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\points{2}
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\points{2}
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\end{tasks}
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\end{tasks}
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@ -23,7 +23,11 @@ entspricht, da dann alle neuen von $s$ ausgehenden Kanten vollständig ausgelast
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Also ist $f'$ ein zulässiger $s$-$t$-Fluss mit Wert $|f'|=\sum_{v:b(v)>0}b(v)$
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Also ist $f'$ ein zulässiger $s$-$t$-Fluss mit Wert $|f'|=\sum_{v:b(v)>0}b(v)$
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\item Sei $f'$ ein $s$-$t$-Fluss in $G'$. Da sein Wert maximal ist, sind alle Kanten zu $s$ und $t$ voll ausgelastet.\\
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\item Sei $f'$ ein $s$-$t$-Fluss in $G'$. Da sein Wert maximal ist, sind alle Kanten zu $s$ und $t$ voll ausgelastet.\\
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Für die Einschränkung $f:=f'\vert_E$ betrachtet man die Flusserhaltung jedes Knotens $v\in V$ in $G'$:
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Für die Einschränkung $f:=f'\vert_E$ betrachtet man die Flusserhaltung jedes Knotens $v\in V$ in $G'$:
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$$\textnormal{Nettozufluss}_f(v)=\textnormal{Nettozufluss}_{f'}(v)-[\textnormal{Beitrag der neuen Kante]}=0-(-b(v))=b(v)$$
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\begin{align*}
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\textnormal{Nettozufluss}_f(v) &= \textnormal{Nettozufluss}_{f'}(v)-[\textnormal{Beitrag der neuen Kante]} \\
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&= 0-(-b(v)) \\
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&= b(v)
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\end{align*}
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Also ist $f$ ein zulässiger b-Fluss in $G$.
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Also ist $f$ ein zulässiger b-Fluss in $G$.
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\end{enumerate}
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\end{enumerate}
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\points{2}
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\points{2}
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|
<gridsize name="32 pts (~12 mm)" value="32"/>
|
||||||
|
<gridsize name="4 pts" value="4"/>
|
||||||
|
<gridsize name="56 pts (~20 mm)" value="56"/>
|
||||||
|
<gridsize name="8 pts (~3 mm)" value="8"/>
|
||||||
|
<opacity name="10%" value="0.1"/>
|
||||||
|
<opacity name="30%" value="0.3"/>
|
||||||
|
<opacity name="50%" value="0.5"/>
|
||||||
|
<opacity name="75%" value="0.75"/>
|
||||||
|
<pen name="fat" value="1.2"/>
|
||||||
|
<pen name="heavier" value="0.8"/>
|
||||||
|
<pen name="ultrafat" value="2"/>
|
||||||
|
<symbolsize name="large" value="5"/>
|
||||||
|
<symbolsize name="small" value="2"/>
|
||||||
|
<symbolsize name="tiny" value="1.1"/>
|
||||||
|
<textsize name="Huge" value="\Huge"/>
|
||||||
|
<textsize name="LARGE" value="\LARGE"/>
|
||||||
|
<textsize name="Large" value="\Large"/>
|
||||||
|
<textsize name="footnote" value="\footnotesize"/>
|
||||||
|
<textsize name="huge" value="\huge"/>
|
||||||
|
<textsize name="large" value="\large"/>
|
||||||
|
<textsize name="script" value="\scriptsize"/>
|
||||||
|
<textsize name="small" value="\small"/>
|
||||||
|
<textsize name="tiny" value="\tiny"/>
|
||||||
|
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
|
||||||
|
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
|
||||||
|
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
|
||||||
|
<tiling name="falling" angle="-60" step="4" width="1"/>
|
||||||
|
<tiling name="rising" angle="30" step="4" width="1"/>
|
||||||
|
</ipestyle>
|
||||||
|
<ipestyle name="ngslides">
|
||||||
|
<symbol name="arrow/ng-fnormal(spx)">
|
||||||
|
<path stroke="sym-stroke" fill="white" pen="sym-pen">
|
||||||
|
-0.7 0 m
|
||||||
|
-1.7 0.333 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="arrow/ng-normal(spx)">
|
||||||
|
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
|
||||||
|
-0.7 0 m
|
||||||
|
-1.7 0.333 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="arrow/ng-pointed(spx)">
|
||||||
|
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
|
||||||
|
-0.7 0 m
|
||||||
|
-1.7 0.333 l
|
||||||
|
-0.8 0 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="arrow/ng-fpointed(spx)">
|
||||||
|
<path stroke="sym-stroke" fill="white" pen="sym-pen">
|
||||||
|
-0.7 0 m
|
||||||
|
-1.7 0.333 l
|
||||||
|
-0.8 0 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="arrow/ng-linear(spx)">
|
||||||
|
<path stroke="sym-stroke" pen="sym-pen">
|
||||||
|
-1.7 0.333 m
|
||||||
|
-0.7 0 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="arrow/ng-fdouble(spx)">
|
||||||
|
<path stroke="sym-stroke" fill="white" pen="sym-pen">
|
||||||
|
-0.7 0 m
|
||||||
|
-1.7 0.333 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
h
|
||||||
|
-1.7 0 m
|
||||||
|
-2.7 0.333 l
|
||||||
|
-2.7 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="arrow/ng-double(spx)">
|
||||||
|
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
|
||||||
|
-0.7 0 m
|
||||||
|
-1.7 0.333 l
|
||||||
|
-1.7 -0.333 l
|
||||||
|
h
|
||||||
|
-1.7 0 m
|
||||||
|
-2.7 0.333 l
|
||||||
|
-2.7 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/remark">
|
||||||
|
<path stroke="dark gray" fill="light yellow">
|
||||||
|
100 204 m
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/theorem">
|
||||||
|
<path stroke="dark blue" fill="light blue">
|
||||||
|
100 204 m
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/problem">
|
||||||
|
<path stroke="dark green" fill="light green">
|
||||||
|
100 204 m
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/definition">
|
||||||
|
<path stroke="dark gray" fill="light yellow">
|
||||||
|
96 96 m
|
||||||
|
304 96 l
|
||||||
|
304 204 l
|
||||||
|
96 204 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/algorithm">
|
||||||
|
<path stroke="dark gray" fill="light green" dash="dashed">
|
||||||
|
96 96 m
|
||||||
|
304 96 l
|
||||||
|
304 204 l
|
||||||
|
96 204 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/graph">
|
||||||
|
<path stroke="dark gray">
|
||||||
|
92 92 m
|
||||||
|
308 92 l
|
||||||
|
308 208 l
|
||||||
|
92 208 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/comic-bl">
|
||||||
|
<path stroke="dark gray" fill="light yellow">
|
||||||
|
100 96 m
|
||||||
|
110 96 s
|
||||||
|
110 92
|
||||||
|
106 88 s
|
||||||
|
116 92
|
||||||
|
118 96 s
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
100 204 l
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/comic-bm">
|
||||||
|
<path stroke="dark gray" fill="light yellow">
|
||||||
|
100 96 m
|
||||||
|
186 96 s
|
||||||
|
186 92
|
||||||
|
182 88 s
|
||||||
|
192 92
|
||||||
|
194 96 s
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
100 204 l
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/comic-br">
|
||||||
|
<path matrix="-1 0 0 1 400 0" stroke="dark gray" fill="light yellow">
|
||||||
|
100 96 m
|
||||||
|
110 96 s
|
||||||
|
110 92
|
||||||
|
106 88 s
|
||||||
|
116 92
|
||||||
|
118 96 s
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
100 204 l
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/comic-tl">
|
||||||
|
<path matrix="1 0 0 -1 0 300" stroke="dark gray" fill="light yellow">
|
||||||
|
100 96 m
|
||||||
|
110 96 s
|
||||||
|
110 92
|
||||||
|
106 88 s
|
||||||
|
116 92
|
||||||
|
118 96 s
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
100 204 l
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/comic-tm">
|
||||||
|
<path matrix="1 0 0 -1 0 300" stroke="dark gray" fill="light yellow">
|
||||||
|
100 96 m
|
||||||
|
186 96 s
|
||||||
|
186 92
|
||||||
|
182 88 s
|
||||||
|
192 92
|
||||||
|
194 96 s
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
100 204 l
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<symbol name="decoration/comic-tr">
|
||||||
|
<path matrix="-1 0 0 -1 400 300" stroke="dark gray" fill="light yellow">
|
||||||
|
100 96 m
|
||||||
|
110 96 s
|
||||||
|
110 92
|
||||||
|
106 88 s
|
||||||
|
116 92
|
||||||
|
118 96 s
|
||||||
|
300 96 l
|
||||||
|
4 0 0 4 300 100 304 100 a
|
||||||
|
304 200 l
|
||||||
|
4 0 0 4 300 200 300 204 a
|
||||||
|
100 204 l
|
||||||
|
4 0 0 4 100 200 96 200 a
|
||||||
|
96 100 l
|
||||||
|
4 0 0 4 100 100 100 96 a
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
</symbol>
|
||||||
|
<color name="dark blue" value="0.121 0.47 0.705"/>
|
||||||
|
<color name="dark brown" value="0.651 0.337 0.157"/>
|
||||||
|
<color name="dark cyan" value="0.106 0.62 0.467"/>
|
||||||
|
<color name="dark gray" value="0.5"/>
|
||||||
|
<color name="dark green" value="0.2 0.627 0.172"/>
|
||||||
|
<color name="dark orange" value="1 0.498 0"/>
|
||||||
|
<color name="dark pink" value="0.969 0.506 0.749"/>
|
||||||
|
<color name="dark purple" value="0.415 0.239 0.603"/>
|
||||||
|
<color name="dark red" value="0.89 0.102 0.109"/>
|
||||||
|
<color name="dark yellow" value="1 1 0.2"/>
|
||||||
|
<color name="light blue" value="0.651 0.807 0.89"/>
|
||||||
|
<color name="light brown" value="0.898 0.847 0.741"/>
|
||||||
|
<color name="light cyan" value="0.553 0.827 0.78"/>
|
||||||
|
<color name="light gray" value="0.8"/>
|
||||||
|
<color name="light green" value="0.698 0.874 0.541"/>
|
||||||
|
<color name="light orange" value="0.992 0.749 0.435"/>
|
||||||
|
<color name="light pink" value="0.992 0.855 0.925"/>
|
||||||
|
<color name="light purple" value="0.792 0.698 0.839"/>
|
||||||
|
<color name="light red" value="0.984 0.603 0.6"/>
|
||||||
|
<color name="light yellow" value="1 1 0.8"/>
|
||||||
|
<color name="pagenumber" value="0.5"/>
|
||||||
|
<color name="title" value="0.247 0.282 0.392"/>
|
||||||
|
<pen name="fat" value="3.6"/>
|
||||||
|
<pen name="heavier" value="2.4"/>
|
||||||
|
<pen name="normal" value="1.2"/>
|
||||||
|
<pen name="ultrafat" value="6"/>
|
||||||
|
<symbolsize name="large" value="15"/>
|
||||||
|
<symbolsize name="normal" value="9"/>
|
||||||
|
<symbolsize name="small" value="6"/>
|
||||||
|
<symbolsize name="tiny" value="3.3"/>
|
||||||
|
<textstretch name="Huge" value="2.4"/>
|
||||||
|
<textstretch name="LARGE" value="2.4"/>
|
||||||
|
<textstretch name="Large" value="2.4"/>
|
||||||
|
<textstretch name="footnote" value="2.4"/>
|
||||||
|
<textstretch name="huge" value="2.4"/>
|
||||||
|
<textstretch name="large" value="2.4"/>
|
||||||
|
<textstretch name="normal" value="2.4"/>
|
||||||
|
<textstretch name="script" value="2.4"/>
|
||||||
|
<textstretch name="small" value="2.4"/>
|
||||||
|
<textstretch name="tiny" value="2.4"/>
|
||||||
|
<textstyle name="algorithmic" begin="\begin{algorithmic}" end="\end{algorithmic}"/>
|
||||||
|
<textstyle name="definition" begin="\begin{definition}" end="\end{definition}"/>
|
||||||
|
<textstyle name="enumerate" begin="\begin{enumerate}" end="\end{enumerate}"/>
|
||||||
|
<textstyle name="example" begin="\begin{example}" end="\end{example}"/>
|
||||||
|
<textstyle name="lemma" begin="\begin{lemma}" end="\end{lemma}"/>
|
||||||
|
<textstyle name="proof" begin="\begin{proof}" end="\end{proof}"/>
|
||||||
|
<textstyle name="theorem" begin="\begin{theorem}" end="\end{theorem}"/>
|
||||||
|
<preamble>
|
||||||
|
\usepackage[ngerman]{babel}
|
||||||
|
\usepackage[sansdefault]{fontsetup}
|
||||||
|
\usepackage{ngutils}
|
||||||
|
|
||||||
|
\renewcommand{\theoremfont}{\normalfont\bfseries\color{dark blue}}
|
||||||
|
\renewcommand{\definitionfont}{\normalfont\bfseries\color{dark gray}}
|
||||||
|
|
||||||
|
\newcommand{\labelfont}{\normalfont\bfseries\color{dark blue}}
|
||||||
|
|
||||||
|
%\setlength{\leftmargini}{1.33em}
|
||||||
|
%\setlength{\leftmarginii}{1.33em}
|
||||||
|
%\setlength{\leftmarginiii}{1.33em}
|
||||||
|
%\setlength{\leftmarginvi}{1.33em}
|
||||||
|
|
||||||
|
\renewcommand{\labelenumi}{\labelfont\arabic{enumi}.}
|
||||||
|
\renewcommand{\labelenumii}{\labelfont\alph{enumii})}
|
||||||
|
\renewcommand{\labelenumiii}{\labelfont\roman{enumiii}.}
|
||||||
|
\renewcommand{\labelenumiv}{\labelfont\Alph{enumiv}.}
|
||||||
|
|
||||||
|
\renewcommand{\labelitemi}{\labelfont $\blockfull$}
|
||||||
|
\renewcommand{\labelitemii}{\labelfont $\blackpointerright$}
|
||||||
|
\renewcommand{\labelitemiii}{\labelfont $\bullet$}
|
||||||
|
\renewcommand{\labelitemiv}{\labelfont $\bullet$}
|
||||||
|
|
||||||
|
\setlength{\fboxsep}{1pt}
|
||||||
|
|
||||||
|
\newcommand{\bk}{\color{black}}
|
||||||
|
\newcommand{\wt}{\color{white}}
|
||||||
|
\newcommand{\bu}{\color{dark blue}}
|
||||||
|
\newcommand{\bn}{\color{dark brown}}
|
||||||
|
\newcommand{\cn}{\color{dark cyan}}
|
||||||
|
\newcommand{\gy}{\color{dark gray}}
|
||||||
|
\newcommand{\gn}{\color{dark green}}
|
||||||
|
\newcommand{\og}{\color{dark orange}}
|
||||||
|
\newcommand{\pk}{\color{dark pink}}
|
||||||
|
\newcommand{\pl}{\color{dark purple}}
|
||||||
|
\newcommand{\rd}{\color{dark red}}
|
||||||
|
\newcommand{\yo}{\color{dark yellow}}
|
||||||
|
\newcommand{\tl}{\color{title}}
|
||||||
|
</preamble>
|
||||||
|
<layout paper="1024 576" origin="16 16" frame="992 496" skip="16" crop="no"/>
|
||||||
|
<pagenumberstyle pos="1000 552" color="pagenumber" size="tiny" halign="right" valign="top"></pagenumberstyle>
|
||||||
|
<titlestyle pos="0 544" size="Large" color="title" valign="top"/>
|
||||||
|
</ipestyle>
|
||||||
|
<page>
|
||||||
|
<layer name="alpha"/>
|
||||||
|
<view layers="alpha" active="alpha"/>
|
||||||
|
<use layer="alpha" matrix="1 0 0 1 160 128" name="mark/disk(sx)" pos="256 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 32 96" name="mark/disk(sx)" pos="288 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 96 -256" name="mark/disk(sx)" pos="320 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 -96 32" name="mark/disk(sx)" pos="352 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 176 -208" name="mark/disk(sx)" pos="384 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 -192 -64" name="mark/disk(sx)" pos="416 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 160 -64" name="mark/disk(sx)" pos="448 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 -208 -208" name="mark/disk(sx)" pos="480 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 0 96" name="mark/disk(sx)" pos="512 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 32 32" name="mark/disk(sx)" pos="544 320" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 16 -128" name="mark/disk(sx)" pos="400 384" size="normal" stroke="black"/>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
416 448 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
320 416 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
416 64 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
256 352 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
560 112 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
224 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
608 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
272 112 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
512 416 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
576 352 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
256 352 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
560 112 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
224 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
608 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
272 112 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
512 416 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
416 64 m
|
||||||
|
576 352 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
560 112 m
|
||||||
|
224 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
560 112 m
|
||||||
|
608 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
560 112 m
|
||||||
|
272 112 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
560 112 m
|
||||||
|
512 416 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
560 112 m
|
||||||
|
576 352 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
608 256 m
|
||||||
|
272 112 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
608 256 m
|
||||||
|
512 416 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
608 256 m
|
||||||
|
576 352 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
512 416 m
|
||||||
|
576 352 l
|
||||||
|
</path>
|
||||||
|
<text matrix="1 0 0 1 -32 -24" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="11.3472" depth="0" halign="center" valign="bottom" size="script" style="math">1</text>
|
||||||
|
<text matrix="1 0 0 1 64 8" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="11.3472" depth="0" halign="center" valign="bottom" size="script" style="math">1</text>
|
||||||
|
<text matrix="1 0 0 1 -96 -88" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="11.3472" depth="0" halign="center" valign="bottom" size="script" style="math">2</text>
|
||||||
|
<text matrix="1 0 0 1 -128 -184" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="11.3568" depth="0.36" halign="center" valign="bottom" size="script" style="math">3</text>
|
||||||
|
<text matrix="1 0 0 1 -80 -344" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="10.98" depth="0" halign="center" valign="top" size="script" style="math">4</text>
|
||||||
|
<text matrix="1 0 0 1 160 -24" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="10.9872" depth="0.36" halign="center" valign="bottom" size="script" style="math">5</text>
|
||||||
|
<text matrix="1 0 0 1 224 -88" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="10.9872" depth="0.36" halign="center" valign="bottom" size="script" style="math">5</text>
|
||||||
|
<text matrix="1 0 0 1 64 -392" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="11.3568" depth="0.36" halign="center" valign="top" size="script" style="math">8</text>
|
||||||
|
<text matrix="1 0 0 1 264 -192" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="11.3568" depth="0.36" valign="center" size="script" style="math">6</text>
|
||||||
|
<text matrix="1 0 0 1 208 -344" transformations="translations" pos="352 448" stroke="black" type="label" width="8.8704" height="10.9968" depth="0.168" halign="center" valign="top" size="script" style="math">7</text>
|
||||||
|
<text matrix="1 0 0 1 32 -208" transformations="translations" pos="352 448" stroke="black" type="label" width="17.7408" height="11.3568" depth="0.36" halign="center" valign="bottom" size="script" style="math">10</text>
|
||||||
|
<path stroke="black">
|
||||||
|
416 256 m
|
||||||
|
416 64 l
|
||||||
|
</path>
|
||||||
|
</page>
|
||||||
|
<page>
|
||||||
|
<layer name="alpha"/>
|
||||||
|
<view layers="alpha" active="alpha"/>
|
||||||
|
<path layer="alpha" stroke="dark gray" arrow="ng-normal/normal">
|
||||||
|
320 192 m
|
||||||
|
448 192 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark purple" arrow="ng-normal/normal">
|
||||||
|
320 320 m
|
||||||
|
448 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark purple" arrow="ng-normal/normal">
|
||||||
|
320 320 m
|
||||||
|
448 192 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark purple" arrow="ng-normal/normal">
|
||||||
|
320 192 m
|
||||||
|
448 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark purple" arrow="ng-normal/normal">
|
||||||
|
320 192 m
|
||||||
|
448 320 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark purple" arrow="ng-normal/normal">
|
||||||
|
320 256 m
|
||||||
|
448 320 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark purple" arrow="ng-normal/normal">
|
||||||
|
320 256 m
|
||||||
|
448 192 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark gray" arrow="ng-normal/normal">
|
||||||
|
320 256 m
|
||||||
|
448 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="dark gray" arrow="ng-normal/normal">
|
||||||
|
320 320 m
|
||||||
|
448 320 l
|
||||||
|
</path>
|
||||||
|
<path matrix="1 0 0 1 128 0" stroke="black" arrow="ng-normal/normal">
|
||||||
|
320 320 m
|
||||||
|
448 256 l
|
||||||
|
</path>
|
||||||
|
<path matrix="1 0 0 1 128 0" stroke="black" arrow="ng-normal/normal">
|
||||||
|
320 256 m
|
||||||
|
448 256 l
|
||||||
|
</path>
|
||||||
|
<path matrix="1 0 0 1 128 0" stroke="black" arrow="ng-normal/normal">
|
||||||
|
320 192 m
|
||||||
|
448 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black" arrow="ng-normal/normal">
|
||||||
|
192 256 m
|
||||||
|
320 320 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black" arrow="ng-normal/normal">
|
||||||
|
192 256 m
|
||||||
|
320 256 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black" arrow="ng-normal/normal">
|
||||||
|
192 256 m
|
||||||
|
320 192 l
|
||||||
|
</path>
|
||||||
|
<use name="mark/disk(sx)" pos="192 256" size="normal" stroke="black"/>
|
||||||
|
<use matrix="1 0 0 1 128 0" name="mark/disk(sx)" pos="320 320" size="normal" stroke="dark blue"/>
|
||||||
|
<use matrix="1 0 0 1 128 0" name="mark/disk(sx)" pos="320 256" size="normal" stroke="dark blue"/>
|
||||||
|
<use matrix="1 0 0 1 128 0" name="mark/disk(sx)" pos="320 192" size="normal" stroke="dark blue"/>
|
||||||
|
<use name="mark/disk(sx)" pos="576 256" size="normal" stroke="black"/>
|
||||||
|
<text matrix="1 0 0 1 128 8" transformations="translations" pos="320 320" stroke="black" type="label" width="25.7016" height="8.5872" depth="8.4" halign="center" valign="bottom" size="footnote" style="math">v_{1_{e}}</text>
|
||||||
|
<text matrix="1 0 0 1 128 -56" transformations="translations" pos="320 320" stroke="black" type="label" width="25.7016" height="8.5872" depth="8.4" halign="center" valign="bottom" size="footnote" style="math">v_{2_{e}}</text>
|
||||||
|
<text matrix="1 0 0 1 128 -136" transformations="translations" pos="320 320" stroke="black" type="label" width="26.748" height="8.5872" depth="8.4" halign="center" valign="top" size="footnote" style="math">v_{n_{e}}</text>
|
||||||
|
<text matrix="1 0 0 1 -128 -56" transformations="translations" pos="320 320" stroke="black" type="label" width="7.7664" height="8.8368" depth="0.192" halign="center" valign="bottom" size="footnote" style="math">s</text>
|
||||||
|
<text matrix="1 0 0 1 256 -56" transformations="translations" pos="320 320" stroke="black" type="label" width="8.34" height="10.9416" depth="0.192" halign="center" valign="bottom" size="footnote" style="math">t</text>
|
||||||
|
<text matrix="0.894704 0.446659 -0.446659 0.894704 112.622 -137.236" pos="320 320" stroke="black" type="label" width="14.6328" height="5.448" depth="3.984" halign="center" valign="bottom" size="tiny" style="math">a_1</text>
|
||||||
|
<text matrix="0.894427 -0.447214 0.447214 0.894427 -73.1492 134.135" pos="256 224" stroke="black" type="label" width="15.5304" height="5.4408" depth="3.048" halign="center" valign="top" size="tiny" style="math">a_n</text>
|
||||||
|
<text transformations="translations" pos="256 260" stroke="black" type="label" width="14.6328" height="5.448" depth="3.984" halign="center" valign="bottom" size="tiny" style="math">a_2</text>
|
||||||
|
<text matrix="0.894427 -0.447214 0.447214 0.894427 182.851 206.135" pos="256 224" stroke="black" type="label" width="13.5696" height="5.52" depth="3.984" halign="center" valign="bottom" size="tiny" style="math">e_1</text>
|
||||||
|
<text matrix="0.894704 0.446659 -0.446659 0.894704 368.622 -209.236" pos="320 320" stroke="black" type="label" width="14.4648" height="5.5128" depth="3.048" halign="center" valign="top" size="tiny" style="math">e_n</text>
|
||||||
|
<text matrix="1 0 0 1 256 0" transformations="translations" pos="256 260" stroke="black" type="label" width="13.5696" height="5.52" depth="3.984" halign="center" valign="bottom" size="tiny" style="math">e_2</text>
|
||||||
|
<text matrix="1 0 0 1 128 0" transformations="translations" pos="320 224" stroke="black" type="label" width="5.3184" height="10.98" depth="1.32" halign="center" valign="center" size="footnote" style="math">\vdots</text>
|
||||||
|
<use name="mark/disk(sx)" pos="320 320" size="normal" stroke="dark orange"/>
|
||||||
|
<use name="mark/disk(sx)" pos="320 256" size="normal" stroke="dark orange"/>
|
||||||
|
<use name="mark/disk(sx)" pos="320 192" size="normal" stroke="dark orange"/>
|
||||||
|
<text matrix="1 0 0 1 0 8" transformations="translations" pos="320 320" stroke="black" type="label" width="26.7648" height="8.5872" depth="8.4" halign="center" valign="bottom" size="footnote" style="math">v_{1_{a}}</text>
|
||||||
|
<text matrix="1 0 0 1 0 -56" transformations="translations" pos="320 320" stroke="black" type="label" width="26.7648" height="8.5872" depth="8.4" halign="center" valign="bottom" size="footnote" style="math">v_{2_{a}}</text>
|
||||||
|
<text matrix="1 0 0 1 0 -136" transformations="translations" pos="320 320" stroke="black" type="label" width="27.8136" height="8.5872" depth="8.4" halign="center" valign="top" size="footnote" style="math">v_{n_{a}}</text>
|
||||||
|
<text transformations="translations" pos="192 160" stroke="black" type="minipage" width="384" height="50.1936" depth="38.304" valign="top" size="script">\begin{description}
|
||||||
|
\item[\color{dark purple}{Lila Kanten}] Kantenkapazität $1$ wenn keine Mehrfachkanten erlaubt sind.
|
||||||
|
|
||||||
|
\item[\color{dark gray}{Graue Kanten}] Kantenkapazität $0$ wenn keine Selbstkanten erlaubt sind.
|
||||||
|
\end{description}</text>
|
||||||
|
</page>
|
||||||
|
</ipe>
|
||||||
Loading…
Add table
Add a link
Reference in a new issue