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aufgerufen, sich an der Entwicklung zu beteiligen! \subsection{Zusammenhangskomponente}\label{graph:komponente} Ein maximaler, zusammenhängender Teilgraph $G^*$ eines Graphen $G$. + \subsection{Wurzelbaum und Suchtheorie} + \subsubsection{Wurzelbaum} + Ein \idx{Wurzelbaum} ist ein Paar $(T,v)$, wobei $T$ ein Baum ist und + $v$ eine ausgezeichnete Ecke, als so genannte \idx{Wurzel}.\\ + Die \idx{Länge einer Ecke} $l(e), e \in E$ bezeichnet den eindeutigen Weg + von $v$ nach $e$. + Die Länge des gesamten Baumes ist die maximale Länge einer Ecke. + + \subsubsection{(n, q)-Baum} + Besitzt ein Baum $n$ Blätter und hat die Wurzel genau $q$ direkte + Nachfolger, spricht man von einem \idx{(n,q)-Baum}. + Besitzt die Wurzel und jede innere Ecke genau $q$ direkte Nachfolger, + ist dies ein \idx{vollständiger (n, q)-Baum} + + \newtheorem{satz}{Satz}[section] + \begin{satz} + Sei $T$ ein (n, q)-Baum, wobei $n \ge 1, q \ge 2$. + Dann ist $l(T) = \log_q n$ + \end{satz} + + \subsubsection{Informationstheoretische Schranke} + Die Menge $\Tau(n,q)$ beschreibt alle (n, q)-Bäume. + Die Zahl $\log_q n = \min\{l(T)|T\in \Tau(n,q)\}$ heisst die + \idx{informationstheoretische Schranke} bzgl. (n, q). + \printindex \vspace*{\fill} % show license on bottom of page \doclicenseThis{}